Transcript

This product was funded by a grant awarded under the President’s High Growth Job Training Initiative as implemented by the U.S. Department of Labor’s Employment & Training Administration. The information contained in this product was created by a grantee organization and does not necessarily reflect the official position of the U.S. Department of Labor. All references to non-governmental companies or organizations, their services, products, or resources are offered for informational purposes and should not be construed as an endorsement by the Department of Labor. This product is copyrighted by the institution that created it and is intended for individual organizational, non-commercial use only.

Contents

June 2008

Introduction 2

Equipment & Component List 3

Digital Multimeters 4

Instek GOS-622G Oscilloscope 6

Elenco XK-700 Electronic Trainer 12

The Oscilloscope Project 1 Measuring Amplitude & Voltage 19

Project 2 Measuring Period & Frequency 21

Project 3 Instantaneous Voltage & RMS Values 23

Project 4 Additional Input Modes & Operations 26

Project 5 Advanced Measurement Techniques 29

Diodes & Rectifiers

Project 6 Forward & Reverse Bias Diode 31

Project 7 Half-Wave Rectifiers 33

Project 8 Full-Wave Bridge Rectifiers 35

Inductance

Project 9 Inductive Kick 37

Project 10 Inductors in Series & Parallel 39

Project 11 Relationship of XL to Inductance & Frequency 40

Project 12 Relationships in Series RL Circuits 41

Project 13 Relationships in Parallel RL Circuits 43

Capacitance

Project 14 RC Time Constants 45

Project 15 Capacitance in Series & Parallel 50

Project 16 Relationship of XC to Capacitance & Frequency 52

Project 17 Relationships in Series RC Circuits 54

Project 18 Relationships in Parallel RC Circuits 56

Series Resonance

Project 19 Relationships of XL & XC to Frequency 58

Project 20 Circuit Characteristics when XL is equal to XC 59

Project 21 Bandwidth Related to Q 61

Parallel Resonance

Project 22 Circuit Characteristics when XL is equal to XC 65

Project 23 Bandwidth Related to Q 68

Formulas 70

Instructor Sign Off Sheet 73

2

Introduction

This lab book is designed for students who have completed the first Concepts of Electronics course and have a good foundational understanding of Ohm’s Law principles as well as the rules of series, parallel and combination circuits in resistive loads. This course introduces alternating current and the relationships of resistive inductive and capacitive loads. Since alternating current waveforms are much more complex than direct current, an oscilloscope will be used to observe these waveforms. The oscilloscope used in this course is the Instek model GOS-622G. This lab book provides hands-on experiences to reinforce the electronic theory learned in this course. Most of the projects in this book promote understanding of the intended points made by performing calculations and making electrical measurements. The results are then compared and conclusions are drawn at optimum times during the projects. The projects in this lab manual are designed to help students develop and improve their abilities to:

• Follow instructions carefully, • Make accurate measurements and calculations, • Analyze technical data appropriately, • Draw logical conclusions from their observations and calculations.

When performing each lab experiment, make sure the meter and test instruments are set to the correct function and range to ensure accurate readings. There are also many calculations and measurements in these lab projects that will require rounding of decimal points. To ensure a correct answer, make sure each number is rounded to the nearest hundredth (two decimal places). For example, if an answer calculates to 3.457 mA, the correct answer would be 3.46 mA. If an answer calculates to 21.3523 kΩ, the correct answer would be 21.35 kΩ. If the answer is a whole number or if the hundredths place is a zero, the extra zeros do not need to be added. For example, an answer of 10 volts does not need to be written as 10.00 V. The answers must also be written in metric prefix form with the correct unit label. For example, an answer of 11270 Ω should be written as 11.27 kΩ. An answer of .482 A should be written as 482 mA, etc. For your convenience, the Ohm’s Law formulas along with many other formulas used in this course have been added toward the back of this lab manual. Also included is an instructor sign-off sheet. Have your instructor initial and date this sheet in the appropriate location when the corresponding project is correct and complete. This will help both you and your instructor track your progress throughout the experiments.

3

Equipment

• Elenco XK-700 electrical trainer

• Multi-range digital multi-meter (DMM)

• Instek GOS-622G dual trace oscilloscope

• Stopwatch

• Breadboard jumper wires Components

• Diode, 1N4002, 1 amp (4)

• Resistors

o 100 Ω, carbon film, 1 watt, 5% tolerance (2)

o 1 kΩ, carbon film, 1 watt, 5% tolerance

o 3.3 kΩ, carbon film, 1 watt, 5% tolerance

o 4.7 kΩ, carbon film, 1 watt, 5% tolerance

o 10 kΩ, carbon film, 1 watt, 5% tolerance

o 18 kΩ, carbon film, 1 watt, 5% tolerance

o 27 kΩ, carbon film, 1 watt, 5% tolerance

o 680 kΩ, carbon film, 1 watt, 5% tolerance

o 10 MΩ, carbon film, 1 watt, 5% tolerance

• Capacitors

o 0.1µF, ceramic disc, 50V (2)

o 1.0µF, electrolytic, non-polarized, 50V (2)

o 47µF, electrolytic, non-polarized, 50V

• Inductors

o 100 mH, D.C.R. 150 Ω (2)

o 1.5 H, iron core, filter choke

4

Multimeters are very useful test instruments. By operating a multi-position switch on the meter they can be quickly and easily set to be used as a voltmeter, an ammeter or an ohmmeter. Some meters have additional features used to measure capacitance and frequency as well. They have several settings called “ranges” for each type of meter and the choice of either alternating or direct current measurements. Voltmeter To test for voltage, first determine whether the application you're testing uses AC or DC voltage. Then set the dial to the appropriate function and plug the red test lead into the correct jack used to measure voltage. Like all test procedures, when testing voltage, set the meter to the range just higher than the expected voltage and decrement it down as needed to increase the accuracy of the reading. If you don't know the expected range, set the range to the highest one available. Take the black test lead and place it on the negative polarity point of the circuit you want to measure. The red test lead will go on the more positive polarity point. When measuring voltage, the test leads of the meter must always be connected in parallel or “across” the component or circuit to be measured as in Figure P-2 on the next page.

DC Voltage Function Ranges from 200mV to 1000V DC

AC Voltage Function Ranges from 200mV to 700V AC

Transistor Test Function

Resistance Function Ranges from 200Ω to 200MΩ

“V, Ω” jack Use this jack for the red test lead when measuring voltage or resistance.

“COM” jack Use this jack for the black test lead.

“mA” jack Use this jack for the red test lead when measuring current from 0 to 200mA.

“A” jack Use this jack for the red test lead when measuring current from 200mA to 20A

Capacitance Function Ranges from 2nF to 200µF

AC Current Function Ranges from 2mA to 20A.

DC Current Function Ranges from 2mA to 20A.

Continuity / Diode Test Function

ON / OFF power switch

Digital Multimeters

Figure P-1

5

6.00

A mA COM VΩ

VPower Supply 6V

Voltmeter leads connected in parallel with resistor being measured.

Figure P-2

12.00

A mA COM VΩ

mA Power Supply 12V

Ammeter leads connected in series with the circuit being measured.

Figure P-3

1000

A mA COM VΩ

Ω

Remove power from the circuit prior to taking resistance measurement.

Figure P-4

Ammeter To measure current, break the circuit where you want to take the reading. Set the meter to AC or DC current depending on the source being tested. Plug the test lead into the correct jack to measure the expected current. Note: Most meters have a separate jack that needs to be used to measure current from 0 to 200mA and from 200mA to 10A or sometimes 20A. Insert the meter in series or “in line” with the circuit to be measured by placing the red test lead on the positive polarity point and the black lead on the negative polarity point (see Figure P-3). Similar to the voltage, the correct current range needs to be selected. Start by selecting the next range higher than the expected reading. If the meter ever reads “0” when an actual reading should be present, check the fuse for the 200mA port.

Ohmmeter To test for resistance, first remove the power from the circuit component to be tested. This prevents the meter from becoming damaged by the source. After ensuring that all power is off, set the dial to the resistance function. Select the appropriate range on the dial. Remove the component to be measured from the circuit (This prevents false readings from any other components in the circuit). Make sure the test leads are plugged into the correct jack to measure resistance. Connect your test leads to the component and take the reading. It's important that you have good contact between the test leads and the component being tested. Dirt, oil and poor test lead connection can undesirably alter resistance readings.

6

Figure P-5

Instek GOS-622G Oscilloscope Front Panel Controls Cathode Ray Tube (CRT) Controls:

Vertical Axis Controls:

(1) INTEN Controls the brightness of the trace.(2) FOCUS Allows for focusing of the trace to the sharpest image. (3) TRACE ROTATION Potentiometer for aligning the horizontal trace in parallel with the grid lines. (4) CRT SCREEN For viewing waveform.

(5) CH 1 Vertical input terminal for Channel 1. When in X-Y operation, X-axis input terminal.

(6) AC-DC-GND Selects connection mode between Channel 1 input signal and vertical amplifier. (7)

VOLTS/DIV

Selects the Channel 1 vertical axis sensitivity from 1mV/DIV to 5V/DIV in 12 ranges.

(8)

VARIABLE

Fine adjustment of Channel 1 vertical axis sensitivity. When in CAL position, sensitivity is calibrated to the indicated value.

(9) POSITION Vertical position control of Channel 1 trace. (10)

CH 2

Vertical input terminal for Channel 2. When in X-Y operation, Y-axis input terminal.

(11) AC-DC-GND Selects connection mode between Channel 2 input signal and vertical amplifier. (12)

VOLTS/DIV

Selects the Channel 2 vertical axis sensitivity from 1mV/DIV to 5V/DIV in 12 ranges

(13)

VARIABLE

Fine adjustment of Channel 2 vertical axis sensitivity. When in CAL position, sensitivity is calibrated to the indicated value.

(14) POSITION Vertical position control of Channel 2 trace. (15)

MODE

Selects operation of CH 1 and CH2 CH 1 CH 2 DUAL ADD

The oscilloscope operates as a single-channel instrument using CH 1. The oscilloscope operates as a single-channel instrument using CH 2. The oscilloscope operates as a dual-channel instrument using both CH 1 and CH 2. CHOP/ALT are automatically changed by the TIME/DIV setting. The oscilloscope displays the algebraic sum of the two signals.

(16) CHOP Allows for the two traces to be displayed in the CHOP mode at all ranges. (17) CH 2 INV The oscilloscope displays the algebraic difference of the two signals when in

ADD mode.

1 32

4

7 6 5 8 11 1310

9 1412

18 19 20

21 22 23 1516 17

24

25

26

27

28

29

31

3032

33 35 36 34

7

Horizontal Axis Controls:

Trigger Controls:

(18) TIME/DIV Selects the rate at which the waveform is displayed across the CRT screen (sweep speed).

(19) SWP. UNCAL When pushed in, the sweep time can be made slower using the SWP.VAR control (20) by a factor of ≥2.5 of the indicated value. When not pushed in, the indicated values are calibrated.

(20) SWP. VAR Vernier control of sweep time. Allows horizontal time scale to be set in between the discrete TIME/DIV settings. The indicated values are calibrated when the SWP. UNCAL (19) button is not pushed in.

(21) POSITION Horizontal positioning control of the trace. (22) X 10 MAG When button is pushed in, a magnification of 10 occurs on the horizontal scale. (23) X-Y X-Y operation is enabled when pressed.

When in X-Y mode, time is no longer measured on the X axis. The X axis represents the CH 1 input and the Y axis represents the CH 2 input.

(24) EXT TRIG Input terminal is used in common for external triggering a signal. To use this terminal, set SOURCE switch (25) to the EXT position. On this setting, a better-conditioned signal can be used to trigger the scope while observing a relatively weak signal.

(25) SOURCE Selects the internal triggering source signal. CH1

(X-Y) When the VERT MODE switch (15) is set to DUAL or ADD, selects CH 1 for the internal triggering source signal. When in X-Y mode, select CH 1 for the X-axis signal.

CH 2 When the VERT MODE switch (15) is set to DUAL or ADD, selects CH 2 for the internal triggering source signal.

LINE Selects the AC power line frequency signal as the triggering signal. EXT The external signal applied through EXT TRIG input terminal (24) is

used for the external triggering source signal. When in the X-Y mode, the X-axis operates with the external sweep signal.

(26) TRIG. ALT When the VERT MODE switch (15) is set to DUAL or ADD, and the SOURCE switch (25) is selected at CH 1 or CH 2, with the engagement of the TRIG. ALT switch (26), CH1 and CH 2 will be alternately selected for the internal triggering source signal.

(27) COUPLING Selects the coupling of the triggering signal to the trigger circuit in accordance with the characteristics of the measured signal.

AC This coupling is for AC triggering which is used most commonly. As the triggering signal is applied to the trigger circuit through an AC coupling circuit, stable triggering can be attained without being affected by the DC component of the input signal. The low-range cutoff is 10-Hz.

HF REJ (High frequency rejection) The triggering signal is fed to the trigger circuit through an AC coupling circuit and a low pass filter (approx. 50-kHz). The higher frequencies are rejected and only the lower frequencies are applied to the trigger circuit. (Useful for noise reduction)

TV Useful for observation of TV video signals. The triggering signal is AC coupled and fed through the triggering circuit to the TV sync separator circuit. The separator circuit picks off the sync signal, which is used to trigger the sweep. Thus the video signal can be displayed stably. Being linked to the TIME/DIV switch, the sweep speed is switched for TV-V and TV-H as follows: TV-V: 0.5s – 0.1ms TV-H: 50µs – 0.1µs

DC The triggering signal is DC-coupled to the trigger circuit. This mode is used when triggering is desired with the DC component of the triggering signal or when a signal with very low frequency or a signal with a large duty cycle ratio is needed to be displayed.

(28) SLOPE Selects the polarity of the triggering signal. + Triggering occurs as the triggering signal crosses the triggering level in

a positive-going direction. – Triggering occurs as the triggering signal crosses the triggering level in

a negative-going direction.

8

Others:

(29) LEVEL Displays a stationary waveform and sets a start point for the waveform. The trigger level changes in the positive direction when the control knob is turned clockwise, and it changes in the negative direction as the knob is turned counter-clockwise.

(30) LOCK When the LEVEL LOCK switch is engaged, the triggering level is automatically maintained within the amplitude of the triggering signal, and stable triggering is made without requiring level adjustment (although jitter may not be suppressed when in the ALT mode).

(31) HOLDOFF Used when the signal waveform is complex and stable triggering cannot be attained with the LEVEL knob alone.

(32) TRIGGER MODE Selects the desired trigger mode.

AUTO When no triggering signal is applied or when triggering signal is less than 50-Hz, sweep runs in the free run mode.

NORM When no triggering signal is applied, sweep is in a steady state and the trace is blanked out. Used primarily for observation of a signal ≤ 50-Hz.

(33) POWER Main power switch of the instrument. When this switch is turned on, the LED (34) is also turned on.

(34) POWER LED indicating oscilloscope power is turned on. (35) GND Ground terminal of oscilloscope main frame. (36) CAL This terminal delivers the calibration voltage of 2-VP-P, 1-kHz, positive square wave.

The output is 2kΩ.

9

Instek GOS-622G Oscilloscope Basic Operation Before applying power to the oscilloscope, ensure the instrument switch settings and controls are set to the default settings according to the table below.

After the switches and controls are set to the default settings, connect the power cord to the AC line outlet and continue as follows.

1. Engage the POWER switch (33) and make sure the power LED (34) is turned on. A trace should appear on the CRT screen (4) in about 20 seconds. If no trace appears after one minute, double check the switch and control settings.

2. Adjust the trace with the appropriate brightness and sharpness with the INTEN (1) and FOCUS (2) controls. NOTE: Set the intensity only bright enough to legibly see a trace. Setting the trace intensity too high for a long period of time could cause permanent damage to the CRT screen.

3. Align the trace with the horizontal center line of the grid by adjusting the CH 1 POSITION (9) control and TRACE ROTATION (3) control (adjustable by screwdriver).

4. Align the begining of the trace with the left-most vertical grid line on the CRT screen by adjusting the HORIZ. POSITION (21) control.

5. Connect a probe to the CH 1 INPUT terminal (5). Make sure the slide switch on the probe is set to the “X1” position.

6. Connect the probe tip to the CAL (36) terminal.

7. Set the CH 1 AC-DC-GND (6) switch to AC and release the GND. A square waveform similar to the one shown in Figure P-6 should now be displayed on the CRT screen (The vertical lines of a square wave may be invisible on your screen but you should still be able to view the peaks and valleys of the waveform).

Since the CH 1 VOLTS/DIV (7) is set to 0.5 V/DIV, we can determine the peak to peak voltage of the waveform. Each vertical grid square or division represents 0.5 V. Since the peak to peak waveform is approximately 4 divisions from top to bottom our peak to peak voltage is 2 volts (0.5-V x 4 divisions = 2-VP-P).

8. Now change the CH 1 VOLTS/DIV (7) setting to 0.1 V/DIV, and set the switch on the Channel 1 probe to X10. You should now be viewing a square wave that is approximately 2 vertical grid squares (divisions) high. By turning on the probe’s X10 switch, a multiplier of 10 is introduced into the waveform’s vertical calculation. The peak to peak voltage of the waveform can then be

Control No. Setting

COUPLING SLOPE TRIG ALT LEVEL LOCK HOLDOFF TRIGGER MODE TIME/DIV SWP. UNCAL HORIZ. POSITION X10 MAG X-Y

(27) (28) (26) (30) (31) (32) (18) (19) (21) (22) (23)

AC + Released Pushed in MIN (c-clockwise) AUTO 0.5 mS/DIV Released Mid-position Released Released

Control No. Setting

POWER INTEN FOCUS VERT MODE CHOP CH 2 INV VERT POSITION VOLTS/DIV VARIABLE AC-DC-GND SOURCE

(33) (1) (2) (15) (16) (17) (9), (14) (7), (12) (8), (13) (6), (11) (25)

OFF Mid-position Mid-position CH 1 Released Released Mid-position 0.5 V/DIV CAL (clockwise) GND Set to CH 1

Figure P-6

10

found by taking the CH 1 VOLTS/DIV setting times a multiplier of 10, times the number of divisions of the waveform (0.1 x 10 x 2 = 2-VP-P).

The X10 setting on the probe is mainly used for increasing the number of voltage ranges the oscilloscope is capable of measuring, therefore making it a more versatile instrument. It also allows for viewing waveforms with higher voltage and amplitude that may otherwise be very difficult to observe.

9. The next step will be to determine the frequency of the waveform. Frequency is equal to the reciprocal of the period, or the length of time needed to complete one waveform cycle. With the TIME/DIV (18) set to 0.5-mS/DIV, the waveform cycle is approximately 2 horizontal divisions in length. The period can then be found by taking the TIME/DIV setting times the number of divisions for one cycle (0.5-mS x 2 = 1-mS). The reciprocal of the 1-mS period will then be the frequency of the waveform (1/.001-S = 1000-Hz).

10. Now change the TIME/DIV (18) setting from 0.5-mS/DIV to 0.1-mS/DIV. By changing the time base to a shorter length of time for each division, the waveform, in a sense will appear “stretched out”. This allows for a more accurate frequency measurement.

Each division is separated by 5 smaller divisions indicated as graticule marks on the middle vertical and horizontal grid lines. Each of these marks represents 0.2 of a whole division. For example, if one complete cycle of the waveform being measured is just short of 10 divisions by an amount of one graticule mark, then you would use the value of 9.8 (9.8 divisions) x (0.1-ms/DIV) = 0.98-mS period. The reciprocal of the 0.98-mS period would then be 1020-Hz. A more accurate reading of the same input waveform from step 9.

NOTE: For precision and ease of measuring it is common practice to move and align the waveform with the vertical and horizontal graticule marks on the CRT screen. This is done by turning the VERT POSITION (9), (14) and the HORIZ POSITION (21) controls.

Just as the vertical scale has an X10 setting directly on the probes, the horizontal scale has the X10 MAG (22) switch that can be used the same way to magnify the amount of time per division by 10 times. Although usually not used as often as the vertical magnifier, the X10 MAG can be used to examine waveforms with extremely low frequencies.

11. Set the TIME/DIV (18) back to 0.5-mS/DIV.

12. Set the VERT MODE (15) switch to CH2 and align the trace with the horizontal center line of the grid by adjusting the CH2 POSITION (14) control.

13. Connect a second probe to the CH2 INPUT terminal (10).

14. Connect the probe tip to the CAL (36) terminal so both CH1 and CH2 probes are connected.

15. Set the CH2 VOLTS/DIV (12) control to 0.1 V/DIV and select X10 on the CH 2 probe.

16. Set the CH2 AC-DC-GND (11) switch to AC and release the GND. You should now see the same square wave signal as before, the only difference being the input is now on CH2 instead of CH1.

17. Set the VERT MODE (15) switch to DUAL. You should now be able to see the waveforms of both CH1 and CH2 as shown in Figure P-8. You are able to move the waveform of each channel by using the corresponding CH1 or CH2 VERT POSITION (9), (14) controls.

The DUAL channel mode is very useful for comparing two different waveforms and to observe such characteristics as phase, voltage, and frequency relationships between the two waveforms. Obviously in order for an accurate voltage or amplitude reading, both CH1 and CH2 must be set to the same VOLTS/DIV.

Figure P-7

One cycle

Figure P-8

11

18. Set the VERT MODE (15) switch to ADD. The ADD mode displays the sum of CH1 and CH2 input signals. As you can see the sum of the two 2-VP-P signals is now displayed as a 4-VP-P square wave. When using the ADD mode, it is important that both CH1 and CH2 be set to the same VOLTS/DIV.

The ADD mode is mostly used in conjunction with the CH2 INV (17) switch. The CH2 INV switch inverts the polarity of the CH2 input only. This allows subtractions to be used (CH1 minus CH2) and ungrounded voltage drops in a circuit to be determined. For example, in most cases the oscilloscope’s ground is connected to the signal generator’s ground through the wiring of the power cables and the building’s receptacle plugs. This restricts the oscilloscope to test only across grounded components.

If we look at Figure P-9, typically the oscilloscope ground would be connected to the circuit ground at point C so all of the voltage measurements will be taken with respect to that point. The measurements can then be taken across R2 by placing the probe at point B or for total circuit voltage at point A. The oscilloscope cannot, however measure from point A with respect to point B since the oscilloscope ground and the circuit ground are essentially the same point. Doing so could result in shorting R2 thereby giving inaccurate voltage readings. To then find the voltage drop at R1, the oscilloscope would essentially subtract the voltage drop (B to C) from the voltage (A to C).

VA R1

R2

A

B

C

Figure P-9

12

The Elenco XK-700 Electronic Trainer

This guide will explain the basic operations and features of the Elenco electronic trainer that you will be using for the majority of the lab experiments in this course. Please take a few minutes to read through this guide and study the illustrations so you will become familiar with the different functions of this trainer. In this user guide you will identify the five main sections of the trainer. You will also learn the purpose and the function of each section. The five sections of this trainer are listed below. See Figure P-10 for a pictorial diagram of the trainer.

1. Power supply section 2. Variable resistance section 3. Function generator 4. Digital section 5. Breadboard section

Figure P-10

Variable Resistance Section

Function / Signal Generator

Digital Section

Breadboard Section Power Supply Section

13

Power Supply

The Elenco trainer has several built in DC power supplies to satisfy most electronic design needs. The two variable DC power supplies produce up to +20 volts and -20 volts at 500 milliamps. Below 15v the available current is over 1 amp. Three fixed power supplies produce +12vdc, -12vdc, or +5vdc at 1 amp each. All of the power supplies are regulated to within 150 millivolts. In other words, if you increase the current draw from no load to 500 milliamps, the voltage will change less than 150 millivolts.

Figure 1

Figure 1

A variety of different voltages are available at the power output terminals. Because the Elenco trainer uses both the +20v and -20v adjustable voltage controls, a combined voltage of up to 40vdc is possible. (See Figure P-12)

Variable negative voltage control Varies negative voltage from 0 to -20v at indicated output terminal.

Variable positive voltage control Varies positive voltage from 0 to 20v at indicated output terminal.

Power output terminals This provides 30VAC center tapped at 15VAC. This also provides the output terminal for positive and negative variable voltages.

On – Off switch Allows power to be applied to all outputs. Switch will light when on.

Ground

-12VDC fixed voltage

+12VDC fixed voltage

+5VDC fixed voltage

Fuse holder 1.25A 250V

0 to +20vdcGround

0 to 40vdc

0 to -20vdc

DC Voltmeter

0 to +20vdc 0 to -20vdc

DC Voltmeter DC Voltmeter

Figure P-11

Figure P-12

14

The power supply section’s output terminal block also allows for the stepped down AC voltage to be used direct from the center tapped transformer. The transformer provides a voltage of 30VAC from line to line or 15VAC from either line to the center tapped ground (See Figure P-13).

WARNING: Do not short the 15 VAC output to ground!

Variable resistance section

The Elenco trainer has two built in variable resistors or “potentiometers” that are available to use for certain lab experiments. The values of the variable resistors are 1k ohm and 100k ohm max. Taking a resistance measurement from one side of the terminal block to the other will give the full value of the resistor (1k ohm or 100k ohm) regardless of the position of the knob. If you take a measurement from either end of the terminal block to the middle wiper connection, you will get a variable value that will change with respect to the position of the knob. (See Figure P-15)

Figure P-14

Figure P-15

100k ohm potentiometer 1k ohm potentiometer

1k terminal block 100k terminal block 1kΩ potentiometer

0 to 1k ohm

Full 1k ohm

Ohmmeter

Ohmmeter

30VAC

15VAC

Step Down Transformer

120VAC

AC Voltmeter

AC Voltmeter

Figure P-13

15

Function / Signal Generator

The included function generator is capable of producing sine, square and triangle waveforms. The frequency of this generator is variable from one hertz to over 100,000 hertz in the following five ranges: 10-Hz, 100-Hz, 1-kHz, 10-kHz and 100-kHz. A fine adjustment control makes for easy selection of any frequency between these ranges. The output voltage amplitude is variable between 0 and 15-VP-P. The output of the function generator may be taken from the terminal marked “FREQ” with respect to a ground terminal in the power supply section.

Internal Impedance

Every function generator has internal impedance that must be considered when measuring certain values in the AC circuit. This internal impedance can act as an immeasurable voltage divider and can slightly skew the measured values of the circuit.

You may notice as you progress through these lab exercises that some measurements to not exactly match up to their corresponding calculations. Although this can be caused by many different variables such as meter inaccuracy or tolerance of components, the internal impedance of the generator is one factor that is sometimes overlooked. To better understand how the internal impedance can affect a circuit, see Figure P-17.

In Figure P-17, RS represents the internal impedance of the generator. As you can see, the internal impedance acts as a resistor in series with the circuit and can therefore create an undesired voltage drop in the circuit. In order to eliminate as much error as possible it is very important that the load resistors (R1 & R2) are relatively large in resistive value as compared with RS. On the next page you will determine the internal impedance of your function generator. This should give you an idea of how this will affect your circuit values.

Waveform Selection Use to select square, triangle or sine waveforms.

Frequency Range Selector Selects 5 frequency ranges from 10 to 100,000 hertz.

Amplitude Control Controls the voltage amplitude of the waveform. 0 – 15VP-P

DC Offset Control Controls the DC level of the generator output. DC may be varied + 10V from zero level.

Fine Frequency Control Allows easy selection of desired function generator frequency.

Signal Output Terminal Terminal provides connection point for output signal (with respect to ground).

Figure P-16

R1

R2

RS

Function Generator

Figure P-17

16

Find the Internal Impedance of the Function Generator

1. Connect the red lead of the DMM to the generator output (FREQ terminal) and the black test lead to ground (GND).

2. Set the open circuit or “no-load” voltage to 6-VRMS. 3. Once the open circuit voltage is set, connect the circuit as shown in Figure P-18 using the 1-kΩ

variable resistor on the Elenco trainer. 4. Connect the voltmeter across the load

and adjust the variable resistor until the voltage equals half the open circuit voltage or 3-VRMS.

5. Disconnect the power from the circuit

and measure the resistance of the variable resistor with an ohmmeter. The resistance measured should be very close to the internal impedance of the generator.

What is the internal impedance of the function generator (ZSource) on your Elenco trainer?

ZSource = _____________________ Digital Section The digital section of the trainer consists of two “no bounce” logic switches, 8 LED indicator lamps, 8 data switches and a clock generator. The clock generator output is a 5V pulsating square wave. The frequency of the pulsations can be adjusted with the frequency range selector and fine frequency control in the function generator section.

Figure P-19

Clock Generator Output Terminal Provides connection point for pulsating clock signal (5VP-P).

Input Terminal for LED Indicators “A” input terminal corresponds with “A” LED etc.

Logic Switches No bounce switches

Data Switches Supplies output of 5V or 0V depending on position.

Data Switch Output Terminals Output terminals for corresponding switches

Logic Switch Output Terminals Output terminals for corresponding switches

Figure P-18

Voltmeter

8-VRMS

4.00 V

1-kΩ variable resistor terminal

17

Breadboard Section The Elenco trainer is equipped with two breadboards containing a total of 1660 tie points including 6 independent bus lines.

Figure P-20

The board is made of plastic with a matrix of holes. Wires and component leads can be pushed into the holes to make appropriate connections. Each “hole” on the board contains a metal spring contact. When a wire or component lead is pushed down into the hole an electrical connection is made with that hole’s spring contact. The breadboards provide an interconnection between certain holes on the board using metallic “bus” connections made underneath the surface. The holes are internally connected so that each 50 hole horizontal bus line is independent from the other and each small 5 hole vertical bus line is also connected independently. Figure P-21 shows the internal connections of the holes on the breadboard.

Figure P-21 Because of the built-in interconnections and the typical circuit board layout, some of the following techniques are commonly used when working with a breadboard.

• A jumper wire can be used to connect the positive source lead to one of the horizontal buss lines marked with a “plus” (+) sign.

• Another jumper wire can be used to connect the negative source lead or GND to one of the horizontal buss lines marked with a “minus” (-) symbol.

• A short jumper wire can then be used to connect each horizontal source connection row to the appropriate point(s) in the circuit on the vertical bus line portion of the board.

• When connecting component leads, plug one lead of a component into a vertical column hole and the other lead of the component into another vertical column hole in a separate bus line. Connect the component, spaced as necessary for the size of the component.

Vertical bus line

Horizontal bus line

18

Figures P-22 & P-23 are sample series and parallel circuit connections using a breadboard. These are just a small sample of the many different methods and combinations for connecting circuits using breadboards. These examples are shown using the positive variable voltage supply.

Sample parallel circuit layout (a) Pictorial Diagram (b) Schematic Diagram

(a)

GroundVariable

0 to +20vdc Variable

0 to -20vdc

470Ω 680Ω 560Ω VAR2

R3

+

(b)

R1

Sample series circuit layout (a) Pictorial Diagram (b) Schematic Diagram

(b)

470Ω

680Ω

560Ω

VA _

R1

R2

R3

+

Figure P-22

(a)

GroundVariable 0 to +20vdc

Variable0 to -20vdc

Power Figure P-23

19

The Oscilloscope

Measuring Amplitude & Voltage Project Objectives:

• To provide practice using an oscilloscope to measure peak to peak voltage and amplitude of a sine wave.

Items Needed: - Elenco electronics Trainer - Oscilloscope - Jumper Wires - Digital muti-meter NOTE: In order to complete the lab projects in this book it is very important that you understand the basics of how an oscilloscope operates. If you are using an Instek GOS-622G or similar model, be sure to complete the tutorial beginning on page 9 of this lab book prior to working on the lab projects. If you are using a different oscilloscope to complete these projects, make sure you read and completely understand the owner’s manual that came with your instrument.

It is also very important that you know the default switch and control settings that would allow you to accurately observe a waveform. Occasionally the projects in this lab book will refer to the default control settings found on page 9 of this book. If you are not using the Instek model GOS-622G, make sure you are familiar with the controls and the default settings of your oscilloscope.

Experiment

1. Insert a jumper wire into the FREQ output terminal found in the analog section of the Elenco trainer.

2. Insert a second jumper wire into the GND terminal in the power supply section of the trainer.

3. Connect a probe to the channel 1 input of the oscilloscope. Connect the probe tip to the output (FREQ) wire. Connect the ground clip lead of the channel 1 probe to the GND jumper wire.

4. Make sure the oscilloscope controls are set to the default setting as shown on page 9 of this

book. Also make sure the switch on the channel 1 probe is set to X10.

5. Turn on the power switch to the oscilloscope and use the vertical and horizontal position controls to align the trace with the center horizontal grid line.

6. Make sure the WAVEFORM control on the Elenco trainer is set to “sine wave”. Apply power to

the trainer and set the CH1 AC-DC-GND switch to AC (release ground switch).

7. Adjust the frequency from the Elenco trainer with the COURSE FREQ and FINE ADJUST controls found in the function generator section of the Elenco trainer. Adjust until a waveform with two complete cycles fills the oscilloscope CRT screen (see Figure 1-1). If a waveform does not exist or if the height of the waveform is very short, try increasing the AMPLITUDE control.

8. Set the CH1 VOLTS/DIV setting to 0.1V/DIV. Adjust the amplitude

from the Elenco trainer until you get a peak to peak waveform of 6 vertical divisions (grid lines) high.

The peak to peak voltage can now be calculated. Multiply the

CH1 VOLTS/DIV setting times the number of divisions from the positive peak to the negative

peak of the waveform. _________ VOLTS/DIV x _________ divisions = _________

Figure 1-1

20

The result then needs to be multiplied by 10 since the CH1 probe is set to X10.

What is the peak to peak voltage of the waveform? ________________ VP-P.

This means the peak voltage or amplitude must be ________________ Vpeak and the RMS

or effective voltage must equal ________________ VRMS. (VRMS = Vpeak x 0.707) Since voltmeters read AC voltage in RMS values, we can confirm this calculation.

9. Use a voltmeter set for AC volts to measure the voltage from the generator. Compare the result

with the calculated RMS value in the previous step.

Voltmeter reads ________________ V.

10. Keep the frequency set so two complete waveform cycles are showing on the oscilloscope CRT screen (as in Figure 1-1). Set the CH1 VOLTS/DIV setting for each example below and make sure the switch on the CH1 probe is set to X10. Set the peak to peak waveform to the specified number of vertical divisions using the AMPLITUDE control on the Elenco trainer. Draw each waveform and indicate the peak voltage or “amplitude” of the waveform. Be sure the voltage level is accurate on your drawing. Do not use a voltmeter for this portion of the exercise.

You can easily read the waveform by moving it using the CH1 vertical position control on the oscilloscope.

11. Set each waveform to read the given amplitude for each example. Draw the waveform and

indicate the VOLTS/DIV setting that was used. Make sure the X10 setting on the CH1 probe is used. Do not use a voltmeter.

VOLTS/DIV = 0.5V/DIV 3 divisions peak to peak

Voltage = ________ Vpeak

VOLTS/DIV = 50mV/DIV 7 divisions peak to peak

Voltage = ________ Vpeak

VOLTS/DIV = 0.1V/DIV 4.5 divisions peak to peak

Voltage = ________ Vpeak

Amplitude = 2.5 Vpeak

VOLTS/DIV = _________

Amplitude = 5 Vpeak Amplitude = 400 mVpeak

VOLTS/DIV = _________ VOLTS/DIV = _________

21

The Oscilloscope

Measuring Period & Frequency Project Objectives:

• To provide practice using an oscilloscope to measure the period and frequency of a waveform.

Items Needed: - Elenco electronics Trainer - Oscilloscope - Jumper Wires NOTE: Before beginning this lab project, make sure the oscilloscope is set according to the default switch and control settings found in the table on page 9 of this book.

Experiment

1. Connect the CH1 oscilloscope probe across the FREQ and GND terminals on the Elenco trainer and set the WAVEFORM for a sine wave.

2. Apply power to both the oscilloscope and the function generator. Align the trace in a manner

that it begins with the left-most vertical grid line and is in line with the horizontal center grid line. Set the time base (TIME/DIV) to 1mS/DIV and the CH1 VOLTS/DIV to 0.1V/DIV.

3. Set the CH1 AC-DC-GND switch to AC (release the ground switch). If a sine wave does not

appear, try increasing the AMPLITUDE on the function generator. If a waveform still does not appear, double check the default oscilloscope settings on page 9.

4. Using the COURSE FREQ and FINE ADJUST controls on the

function generator, adjust the signal to obtain a sine wave cycle that is 7 horizontal divisions in length. Your oscilloscope CRT screen should resemble Figure 2-1 (disregarding the vertical aspect of the waveform).

The period or the amount of time to complete one cycle of the waveform can now be determined. The TIME/DIV is set to 1mS/DIV and the cycle is 7 divisions in length, the period will be the product of the two or 7mS.

The times 10 magnifier is not put into consideration in the case with this example. This is because the horizontal X10 MAG switch is not actuated in accordance with the oscilloscope default control settings.

Since frequency is the reciprocal of the period, the frequency can now be determined.

What is the frequency of this waveform? __________________

What would the frequency be if one cycle was 10 divisions in length? __________________

What would the frequency be if one cycle was 5 divisions in length? ___________________

5. Just as the frequency can be determined from the reciprocal of the period, the period can also

be determined from the reciprocal of the frequency

For example, set the frequency to a 1-kHz signal. In order to accomplish this, we first need to

find the period. The reciprocal of 1000-Hz is 1mS. This means that it takes 1mS to complete

one full cycle of the waveform.

( f = ) 1 period

( period = ). 1 f

Figure 2-1

7 divisions

22

The easiest method to display this particular waveform would be to divide the 1mS period by 10 since there are 10 horizontal divisions on an oscilloscope. The TIME/DIV setting would then be 0.1 mS/division and one complete cycle would be showing on the oscilloscope screen stretching across all 10 divisions as shown in Figure 2-2.

Unfortunately this is not so simple with every frequency value. Take 60-Hz for example. The reciprocal of 60 equals a period of 16.67mS. Divide 16.67mS by ten since there are ten horizontal divisions on the oscilloscope screen. Since a TIME/DIV setting of 1.667mS does not exist, the next highest selection must be used. In this case it would be the 2mS/division setting.

Since each horizontal division represents 2mS, the frequency of the waveform would need to be adjusted so the length of one complete cycle would stretch 8.33 divisions on the screen. The waveform should look similar to Figure 3 (Disregarding the vertical aspect of the waveform at this time).

6. Adjust the amplitude and VOLTS/DIV setting for a peak to peak waveform of 6 vertical divisions. Use the COURSE FREQ and FINE ADJUST controls to configure the horizontal length of each waveform according to the period given in each example below. Draw each waveform, record the frequency and indicate the TIME/DIV setting used.

You can move the waveform for easier reading by using the horizontal position control on the oscilloscope.

7. Keep the peak to peak waveform set at 6 divisions. Adjust the waveform for the frequency given. Draw each waveform and record the period.

Figure 2-2

Figure 2-3

Period = 2 mS

Frequency = _________

Period = 0.5 mS Period = 8 mS

Frequency = _________ Frequency = _________TIME/DIV = _________ TIME/DIV = _________ TIME/DIV = _________

Frequency = 200 Hz

Period = ____________

Frequency = 1.6 kHz Frequency = 400 Hz

Period = ____________ Period = ____________TIME/DIV = __________ TIME/DIV = __________ TIME/DIV = __________

23

The Oscilloscope

Instantaneous Voltage & RMS Values Project Objectives:

• To use an oscilloscope to measure the instantaneous and RMS voltage values of a sine wave and verify through calculations.

• To compare the accuracy of voltage measurement with an oscilloscope and a DMM with various frequencies applied.

Items Needed: - Elenco Electronics Trainer - Oscilloscope - Jumper Wires - Digital multi-meter

NOTE: Before beginning this lab project, make sure the oscilloscope is set according to the default switch and control settings found in the table on page 9 of this book.

Experiment 1 – Instantaneous Sine Wave Values

1. Connect the CH1 oscilloscope probe across the FREQ and GND terminals on the Elenco trainer and set the WAVEFORM for a sine wave.

2. Set the CH1 VOLTS/DIV to 0.1V/DIV and make sure the switch on the CH1 probe is set to X10.

3. Set the TIME/DIV to 0.1mS/DIV and adjust the frequency to obtain a cycle length of 8 divisions.

What is the frequency of the waveform? ___________

4. Adjust the AMPLITUDE for a peak to peak waveform stretching 8 vertical divisions. Draw the waveform in Figure 3-1.

5. From the screen, measure the voltage at each 0.1 mS interval and record “Measured Voltage” column in the table below.

How many degrees does each 0.1mS division represent? ___________________

What is the peak voltage value of the waveform? _________________________

time (ms) degree of rotation Measured Voltage Computed Voltage 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

6. Use the formula (E(INST) = E(PEAK) x SIN∠θ) to calculate the instantaneous voltage at every 0.1 mS division. Enter the calculated results into the table and verify each measurement.

Figure 3-1

24

7. Using a voltmeter set for AC volts, measure the output of the generator and compare the result to the instantaneous voltage at 45 degrees.

Generator output = ____________________ VAC. Since voltmeters measure RMS values

and the SIN of 45 degrees is 0.707, measuring the waveform at 45 degrees on an oscilloscope should be relatively close to the RMS or effective value of generator output.

Using this method to find the instantaneous voltage of a sine wave in 45 degree increments is simple if the waveform cycle is exactly 8 horizontal divisions in length. Unfortunately not every frequency can be set to an 8 division cycle.

8. Set the TIME/DIV to 0.5mS/DIV and change the frequency from the generator to 200 Hz. Change the CH1 VOLTS/DIV to 0.2V/DIV and set the voltage to 12 VP-P. Sketch the waveform as Figure 3-2.

A frequency of 200 Hz on the 0.5mS/DIV setting will result in a waveform 10 divisions in length. In order to accurately determine the instantaneous voltage values of a waveform in increments of 45 degrees, the waveform will need to be 8 horizontal divisions in length. This can be done by using the SWP.VAR. control in the horizontal section of the oscilloscope.

9. Depress the SWP. UNCAL button to unlock the variable sweep (SWP.VAR.) control and adjust the variable sweep until the waveform is 8 divisions in length. If you are not sure of the location of these controls on your oscilloscope, refer to the front panel controls diagram and description on page 6.

Once you have a waveform measuring 6 VPEAK and stretching 8 divisions in length, use the oscilloscope to measure the instantaneous voltage readings at every 45 degree increment and record in the table below. Use the formula given in step 6 to calculate the instantaneous voltage values and compare the results with the measured values.

time (ms) degree of rotation Measured Voltage Computed Voltage 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

10. Release the SWP. UNCAL control!!!

Using the variable sweep control is very useful to measure instantaneous voltage values of a sine wave but will distort the frequency and period of the waveform. It is recommended to lock out the SWP.VAR control by releasing the SWP. UNCAL during normal measuring conditions. Leaving the variable sweep control in an “un-calibrated” state may cause frequency and period readings to be inaccurate.

The vertical sections also have a variable voltage control VAR. which is useful in dual-trace mode for setting the peak voltage of two waveforms equal to easily observe phase relationships between the two waveforms. Similar to the SWP.VAR, when used, the voltage aspect of the waveform will be inaccurate. Therefore the VAR. control should be set clockwise to the CAL. position when measuring voltage.

Figure 3-2

25

Experiment 2 – Voltmeter Response to Frequency

In the previous experiment an oscilloscope was used to determine the RMS value of a sine wave’s voltage. One reason you might want to do this is convenience. If a signal is already displayed on the screen, a reading can be taken without connecting a voltmeter.

A more fundamental reason for using an oscilloscope to measure RMS voltage has to do with the frequency of the signal being measured. The frequency ranges on most digital meters are very limited. For example, many DMMs can only measure to several kHz. Some of the higher quality DMMs however, can measure to much higher frequencies.

Oscilloscopes can usually measure a much broader range of frequencies. Even inexpensive oscilloscopes can usually measure waveforms in the tens of MHz while top of the line instruments can measure in the hundreds of MHz even to the GHz range.

With this experiment we will compare the ability of the oscilloscope and digital multi-meter to measure voltage at different frequencies.

1. Connect the CH1 probe across the FREQ output of the signal generator. Adjust the generator

to a 100-Hz sine wave with a 12-VP-P (6VPEAK) voltage.

2. Calculate the RMS voltage and record in the table below for each frequency.

3. Using the digital multi-meter, measure and record the RMS voltage of the waveform. Repeat for the other frequencies indicated in the table.

Frequency Peak Voltage Calculated RMS DMM reading

100 Hz 6 VPEAK

1000 Hz 6 VPEAK

10,000 Hz 6 VPEAK

15,000 Hz 6 VPEAK

20,000 Hz 6 VPEAK

50,000 Hz 6 VPEAK

100,000 Hz 6 VPEAK

What conclusions can you draw from this data?

________________________________________________________________

________________________________________________________________

________________________________________________________________

The Oscilloscope

Additional Input Modes & Operations

26

Project Objectives:

• To practice using an oscilloscope to measure and compare two different waveforms at the same time in dual trace mode.

• To practice using an oscilloscope to add two input signals and measure ungrounded components in a series circuit.

Items Needed: - Elenco Electronics Trainer - Oscilloscope - Resistors - Digital multi-meter - Jumper wires 4.7kΩ, 10kΩ, 18kΩ, 27kΩ - 1 µF Capacitor

Once again, before starting this lab project, be sure the oscilloscope is set according to the default switch and control settings found in the table on page 9 of this book.

Experiment 1 – Dual Trace Mode

1. Align both CH1 and CH2 traces with the horizontal center grid line on the CRT screen. You can switch to CH2 by selecting CH2 with the MODE switch.

2. Connect the circuit as shown in Figure 4-1. Use the left and center terminal on the 1kΩ variable

resistor located in the variable resistor section on the Elenco trainer. Turn the knob of the variable resistor to the full counter-clockwise position.

3. Connect the CH1 probe across the function generator output and set the generator for a 8-VP-P, 2-kHz sine wave using the 50 µS/DIV horizontal time base setting.

4. Connect the CH2 probe tip between R1 and R2 and set the oscilloscope MODE switch to DUAL.

Make sure the CH2 VOLTS/DIV is set the same as CH1. Both probe switches should also be set to X10.

The dual trace mode permits multiple waveforms to be viewed at the same time. In this case, only one trace is visible because R1 is currently set at minimum or zero ohms, therefore no voltage drop exists across R1 and the two probes are essentially measuring the same point.

5. Turn the knob for R1 to the full clockwise position and

sketch the waveforms as Figure 4-2. Label each waveform as CH1 and CH2. Since R1 and R2 are both resistive loads, their voltage drops will always be in phase with each other. In other words, the two waveforms will intersect the 0V centerline of the screen at the same point.

VA8-VP-P 2-kHz

Figure 4-1

R11kΩ

rheostat

R2

4.7kΩCH1 CH2 GND

Figure 4-2

Figure 4-3

27

6. Remove power from the power supply and replace R2 with a 1µF capacitor. Set the CH2 probe to X1 and connect it across the capacitor. Apply power to the circuit. Sketch the waveforms as Figure 4-3. Once again, label each waveform as CH1 and CH2.

As you will learn later in this course, resistive and capacitive loads “are out of phase”. This can be determined because both waveforms do not intersect each other at the (0V) horizontal centerline of the screen. The amount of phase angle shift between two waveforms can be determined by the divisions separating the two waveforms. For example, if the waveform cycle on the CH1 input stretches the full 10 divisions and there are 360 angular degrees per cycle, then each division would represent 36 angular degrees.

What is the phase shift (in degrees) between the two waveforms? ____________________

Experiment 2 – Differential Measurements

Considering Figure 4-4, suppose you want to measure the voltage across R1 using an oscilloscope. At first, you might try connecting the scope like a voltmeter by attaching the probe tip to point “a” and the ground clip to point “b”. In most cases however, this will not work. If the oscilloscope ground and the generator ground are not isolated from each other, then R2 will be shorted by the ground clip on the probe. If the leads are reversed so that the ground clip is at point “a” and the probe tip is at point “b” then the entire source output is shorted to ground. The best way to measure ungrounded components in a circuit is by using differential measurements. Refer to Figure 4-5. CH1 measures the total source voltage from point “a” to ground at point “c” while CH2 measures across R2 from point “b” to ground at point “c”. The oscilloscope has an “ADD/INVERT” mode which permits a display of CH1 minus CH2. The result on the screen would then be the signal voltage from point “a” to point “b” or VR1.

NOTE: The Elenco trainers used in this course have an internal ground which is isolated from the line ground. Because of this, the ground clip on the oscilloscope probes will not short the circuit as indicated above (as long as the oscilloscope is used in single channel mode). Most signal generators and oscilloscope grounds will not be isolated. Using differential measurements is therefore the preferred method for measuring ungrounded circuit components. 1. Connect the circuit shown in Figure 4-6.

2. Connect the CH1 probe tip to point “a” and connect the CH2 input

probe to point “b”. Clip the ground lead of both probes to the circuit ground at point “c”. Make sure both probes are set to X10.

3. Set the source (CH1) to 6-VP-P with a 1-kHz frequency.

R1

R2

Source

Figure 4-4

a

b

c

CH1 CH2 GND

Figure 4-5

R1

R2

Source a

b

c

R210kΩ

6-VP-P1 kHz

Figure 4-6

a

b

c

R118kΩ

28

What is the peak voltage of CH1? _______________

What is the peak voltage of CH2? _______________ Since CH1 is measuring the full source voltage and CH2 is measuring the voltage drop across R2, the voltage drop across R1 can be determined by subtracting the CH2 voltage value from the CH1 value.

What is the calculated voltage drop across R1? _______________

4. Leave the circuit connected and set the MODE switch to “ADD”.

As you can see the ADD mode adds both CH1 and CH2 input signals. With both channels added, the oscilloscope should be showing a sine wave with a peak voltage slightly over 4 volts. The ADD mode is most often used with the CH2 INV switch. The CH2 INV switch inverts the waveform on the CH2 input only. This allows for a differential measurement of CH1 minus CH2 and would be equivalent to the voltage drop across R1.

5. Press the CH2 INV switch and record the peak voltage of the waveform. Compare the result to

the calculated R1 voltage drop in step 3.

What is the measured voltage drop across R1? _______________ Differential measurements can also be used with larger circuits containing more than just two voltage drops.

6. Add a 27kΩ resistor R3 in series with the circuit so your circuit

resembles Figure 4-7.

7. Before applying power to the circuit, calculate and record the “peak” voltage drops across the three resistances.

Peak V1 calculated = _______________

Peak V2 calculated = _______________

Peak V3 calculated = _______________

8. Use the ADD mode with the CH2 INV switch to measure the “peak” voltage drop across each resistor. Keep the ground clip for both input probes attached to ground at point “d”.

Measure V1 by connecting the CH1 probe to point “a” and CH2 to point “b”.

Peak V1 measured = _______________ Measure V2 by connecting the CH1 probe to point “b” and CH2 to point “c”.

Peak V2 measured = _______________ Measure V3 by connecting the CH1 probe to point “c” and CH2 to point “d”.

Peak V3 measured = _______________

The Oscilloscope

Advanced Measurement Techniques Project Objectives:

R210kΩ

6-VP-P1 kHz

Figure 4-7

a

b

c

R118kΩ

R327kΩ

d

29

• To practice using an oscilloscope to measure superimposed ac and dc voltages. • To practice using an oscilloscope to indirectly measure current using a current sensing resistor.

Items Needed: - Elenco electronics Trainer - Oscilloscope - Resistors - Digital multi-meter - Jumper wires 100Ω, 1k, 3.3k, 4.7k, 10k, 18k

Make sure the oscilloscope is set according to the default switch and control settings.

Experiment 1 – Superimposed AC and DC

Thus far in this course the focus has been on using the “AC” position of the AC-DC-GND vertical coupling switch. The “AC” position is best for keeping the display centered and showing only the AC or time varying aspects of a signal. The AC setting however, blocks all DC information so there is no way of knowing if the AC signal is superimposed with a DC voltage. In other words, if the vertical coupling is set to AC rather than DC you will not know if there is a DC offset along with the AC signal. The AC setting is mainly used for observing the frequency of signal or when observation of only the AC portion of the circuit is required.

In order for the oscilloscope to “block out” the DC voltage, the AC setting places a capacitor in series with the oscilloscope input. This can lead to possible distortions of the displayed waveform.

For example, observe a 20Hz waveform in both the AC and DC switch positions. What differences

do you see?__________________________________________________________

__________________________________________________________________

We will now experiment with the effect of superimposed AC and DC signals using the DC OFFSET control found in the Function Generator section of the Elenco trainer.

1. Center the CH1 trace if necessary and establish a 2VP-P sine wave with a 1kHz frequency. Use

the 50mV/DIV setting and 0.1mS/DIV for the time base.

2. Set the vertical coupling (AC-DC-GND) to DC. Turn the DC OFFSET control on the generator until the waveform is centered 2 divisions above the horizontal center line on the screen.

3. Use a DMM on its DC volts setting to measure the input to the oscilloscope and record the

value, then change the DMM to its AC volts setting and repeat the measurement.

DC input voltage = ________________ AC input voltage = ________________ Sketch the waveform as Figure 5-1 then change the coupling to AC and sketch the waveform on the same grid. Label each waveform as DC or AC coupling. How did the vertical shift compare to the dc value

measured on the DMM? _____________________

______________________________________

______________________________________

______________________________________ Experiment 2 – Measuring Current with an Oscilloscope

Figure 5-1

RLoadET

ILoad

Figure 5-2

30

If we consider Figure 5-2, the load current (ILoad) is determined by Ohm’s Law (ELoad / RLoad) where “ELoad” is the RMS value of the source voltage and “ILoad” is the RMS value of the load current. An oscilloscope can indirectly measure this load current by adding a current sensing resistor (RS) in series with the circuit as shown in Figure 5-3. The voltage can then be measured across the sensing resistor using an oscilloscope, converted to RMS, and then computed as ILoad = VS / RS. This method will be fairly accurate as long as RS is very small compared to RLoad.

1. Using an ohmmeter, accurately measure and record the resistance of the 100-Ω sensing resistor and the 4.7-kΩ RLoad.

Measured RS =

_________________ Measured RLoad = _________________

2. Connect the circuit in Figure 5-3. Use the CH1 probe to set the generator to a 6-VP-P, 100-Hz sine wave.

3. Use the CH2 probe to measure the peak voltage across the sensing resistor. Convert the peak

voltage to RMS and record the value in the space below.

Measured VS = _________________ (RMS)

4. Use Ohm’s Law to determine the RMS value of the load current (ILoad = VS / RS)

Indirectly measured ILoad = _________________ (RMS)

5. Break the circuit and insert a DMM set for AC mA. Measure and record the circuit current. Compare the result to the indirect method of measuring in step 4.

Reminder – When measuring current, ammeters must be connected in series so all the circuit current flows through the meter.

Directly Measured ILoad = _________________ (RMS)

6. Replace the one resistor RLoad of Figure 5-3 with the entire network of resistors in Figure 5-4. Repeat steps 1-5 using the oscilloscope to indirectly measure ILoad and compare with the direct measurement using the DMM.

Indirectly measured ILoad = _________________ (RMS)

Directly Measured ILoad = _________________ (RMS)

How do the results compare? _____________________

_________________________________________

_________________________________________

Diodes & Rectifiers

Forward and Reverse Bias Diode

Figure 5-3

CH1 CH2 GND

RLoad 4.7kΩ

ET

ILoad

RS = 100Ω

Figure 5-4

1kΩ

4.7kΩ

10kΩ

18kΩ

3.3kΩ

Replaces only RLoad

31

Project Objectives:

• To demonstrate how a forward and reverse bias diode can control the current of a dc circuit.

Items Needed: - Electronics Trainer - Digital multi-meter -Diode 1amp - Jumper Wires - 1k Ω resistor

Experiment

1. Without applying power, measure the diode with a DMM set to the diode test position ( ). Connect the negative lead of the meter to the cathode and the positive lead to the anode. With the meter connected in this configuration you will be measuring the forward voltage of the diode.

Forward voltage of the diode: Vforward = ___________________ V.

2. Swap the meter leads connected to the diode so the negative lead is connected to the anode and the positive lead is connected to the cathode. With this configuration you will be measuring the reverse voltage of the diode.

Reverse voltage of the diode: Vreverse = ___________________ V.

When testing a good diode with the diode tester on a DMM, you should get a voltage reading of approximately 0.6 – 0.75 V when connected to read the forward voltage of the diode. When reading the reverse voltage, you should not get a reading on the meter.

3. Connect the circuit in Figure 6-2 use the positive dc

variable supply on your Elenco trainer to apply 5 volts to the circuit.

The resistor is in the circuit to monitor current. Since this is a 1kΩ resistor, the voltage drop across the resistor will be approximately the same value of current in the circuit measured in milliamperes. For example, if you measured 15 volts across the resistor, through the use of Ohm’s Law the current in the circuit will then be 15mA. Use this method to determine the circuit current by measuring VR with a DMM.

IT = ___________________ mA (approximately)

What is the voltage drop across the forward-biased diode? ___________________ V.

4. Remove power from the circuit and flip the diode around so the cathode will now be connected to the positive side of the voltage source and the anode will be connected to the 1kΩ resistor.

5. Apply 5 volts to the circuit. Determine the circuit current using the same method as in step 3.

IT = ___________________ mA

What is the voltage drop across the reverse-biased diode? ___________________ V.

For the reverse-biased condition, is the diode acting like an open or a short? _____________

6. Remove power from the circuit and turn the diode around once more so that it is forward-biased. Set VA in steps as indicated and record the current and diode voltage drop at each step.

VA = 0.25 V: IT = ___________________ mA VD = ___________________ V

Anode Cathode

Figure 6-1

+–

VA VR R1 kΩ

Figure 6-2

32

VA = 0.5 V: IT = ___________________ mA VD = ___________________ V

VA = 1 V: IT = ___________________ mA VD = ___________________ V

VA = 2 V: IT = ___________________ mA VD = ___________________ V

VA = 4 V: IT = ___________________ mA VD = ___________________ V

VA = 10 V: IT = ___________________ mA VD = ___________________ V Once the applied voltage reached a certain level of forward biasing, did the voltage drop across the diode increase, decrease or stay about the same as compared to the change in the applied voltage?

________________________________________________________________ This experiment verifies that a diode will conduct when current flows in one direction but not the other. Will a diode conduct when the anode is positive or negative with respect to the cathode?

________________________________________________________________ What would happen if an AC current were applied to a diode?

________________________________________________________________

________________________________________________________________

________________________________________________________________

________________________________________________________________

Diodes & Rectifiers

Half-Wave Rectifiers

33

Project Objectives:

• To demonstrate the characteristics of a half-wave rectifier and the effects of capacitor filtering.

Items Needed: - Electronics Trainer - DMM - Capacitors - Jumper Wires -10k Ω resistor 0.1 µF, 1 µF - Oscilloscope -Diode 1amp

Experiment

1. Connect the circuit in Figure 7-1.

2. Set the function generator to a 100 Hz sine wave with a peak voltage of 6 VAC.

What is the RMS input voltage? ________________ Sketch two complete cycles of the input waveform in the space provided as Figure 7-2.

Which VOLTS/DIV setting was used?

_____________________________________

Which TIME/DIV setting was used?

_____________________________________

3. Using a DMM, measure the output in both AC and DC volts.

ACoutput = _________________________

DCoutput = _________________________

4. Connect the oscilloscope across RL. Sketch two complete cycles of the new waveform as Figure 7-3 and record the peak voltage reading. Make sure the oscilloscope channel being used is set for “DC” coupling (AC-DC-GND switch).

Vpeak = ________________________________

Why is the peak voltage of the rectified waveform slightly less than the applied 6 V in step 2?

_____________________________________

_____________________________________

_____________________________________

_____________________________________

5. Make sure the function generator is set to a frequency of 100-Hz and an amplitude of 6 Vpeak. Connect the 0.1 µF capacitor in parallel to the 10 kΩ resistor.

Using a DMM, measure the new DC output voltage. DCoutput = _____________________

AC

D1

RL10kΩ DCoutput

Figure 7-1

Figure 7-2

Figure 7-3

34

Sketch two complete cycles of the new waveform as Figure 7-4 with the 0.1 µF capacitor added to the circuit. Capacitors can be used in a variety of electronic applications. In the case with this lab experiment a capacitor is being used as an electronic filter to smooth out the ripple from the DC output. When the current reaches the peak in the dc output the capacitor becomes fully charged. When the supply current drops below the capacitor charge level, the capacitor will begin to discharge. This helps smooth out the dc ripple. Obviously different sized capacitors will act as better filters than others.

What would happen if the capacitor currently in the circuit were replaced with a larger one?

________________________________________________________________

________________________________________________________________

6. Replace the 0.1 µF capacitor with a 1.0 µF capacitor.

Use a DMM to measure the new DC output voltage. DCoutput = _____________________

Sketch two complete cycles of the new waveform as Figure 7-5 with the 1.0 µF capacitor added to the circuit. Was your prediction in step 5 proven by adding a larger

capacitor across the load? ___________________ List two advantages of adding a filter to a rectifier circuit.

_____________________________________

_____________________________________

_____________________________________

Figure 7-4

Figure 7-5

35

Diodes & Rectifiers

Full-Wave Bridge Rectifiers Project Objectives:

• To demonstrate the characteristics of a full-wave bridge rectifier and the effects of capacitor filtering.

Items Needed: - Electronics Trainer - DMM - Capacitor, 1.0 µF (2) - Jumper Wires -10k Ω resistor - Oscilloscope -Diode 1amp (4)

Experiment

1. Connect the circuit in Figure 8-1.

2. Set the function generator to a 100 Hz sine wave with a peak

voltage of 6 VPEAK.

What is the RMS input voltage? ____________ Sketch two cycles of the input waveform as Figure 8-2.

Which VOLTS/DIV setting was used? ________________

Which TIME/DIV setting was used? _________________

3. Using a DMM, measure the DC output voltage. DCoutput = ________________________

If you notice, the load (R1) is not connected to ground. In most cases this prevents an oscilloscope to be used to measure directly across the load with a single input channel. This is because the oscilloscope ground and the generator ground are usually tied together. A direct measurement of the output would then essentially short out one of the diodes. This can be overcome, however by using both input channels on the oscilloscope and performing a differential measurement.

4. Connect the oscilloscope as shown in Figure 8-1. Set the

vertical MODE switch to ADD and perform a differential measurement between CH1 and CH2 by pressing the CH2 INV switch. Sketch two complete cycles of the waveform as Figure 8-3 and record the peak voltage reading.

Vpeak = ________________________________

Figure 8-1

D1 D2

D3D4

R1

10 kΩ DC out

AC

CH1 CH2 GND

Figure 8-2

Figure 8-3

36

Why is the peak of the rectified waveform approximately 1.4 volts less than the peak of the applied voltage instead of 0.7 volts as in half-wave rectifiers?

________________________________________________________________

________________________________________________________________

5. Connect two 1.0 µF capacitors in parallel to the 10 kΩ resistor. See Figure 8-4.

Using a DMM, measure the new DC output voltage. DCoutput = _____________________

In the space provided in Figure 8-5, sketch two complete cycles of the new waveform with the 1.0 µF capacitors added to the circuit.

As you can see, capacitor filtering will smooth the DC output signal reducing or eliminating the ripple. The smoothed output of the rectifier can then be used to power sensitive electronic equipment whereas the non-filtered output is unsuitable.

Figure 8-4

D1 D2

D3D4

R110 kΩ DC out

AC

C1 C2 1 µF 1 µF

Figure 8-5

37

Inductance

Inductive Kick Project Objective:

• To measure the inductive “kick” voltage of an RL circuit using an oscilloscope.

Items Needed: - Electronics Trainer - 1.5 H inductor (iron core) - DMM - Jumper Wires - Oscilloscope - 1kΩ Resistor

In this lab project we will attempt to measure the inductive “kick” that results from interrupting the current through an inductor.

Experiment

1. Measure the DC resistance of the 1.5-H inductor.

Rl measures ________________.

2. Construct Figure 9-1 and connect the oscilloscope probe across R1. Apply 15Vdc to the circuit.

The inductive kick that we want to measure will be a negative voltage spike that last for only 1 - 2 milliseconds. In order to best read the spike with the oscilloscope, it is recommended that the scope time base and sweep be set so that the trace slowly moves across the screen. 0.1 - 0.5 sec/division should be fine.

3. Set the “VOLTS/DIV” on the scope to 5. Make sure the switch on the test probe is set to X10.

4. In order to measure the voltage spike, current needs to be abruptly removed from the circuit. While watching the trace on the scope, disconnect the circuit at point “P” by removing a jumper wire from the power supply to the breadboard RL circuit. You may need to do this several times in order to get an accurate reading on the spike. The trace intensity can also be increased as needed but only to the amount of brightness that is needed for reading the voltage spike. Record the voltage of the spike below. Remember to multiply the scope reading by ten since the X10 probe is being used.

Voltage spike measured = ________________.

The spike occurs because the instant the power is disconnected, the magnetic field collapses which induces a voltage in the coil. This causes a great deal of energy to be released in a very short amount of time.

Using Figure 9-2A shows a similar circuit in a steady state before the power is disconnected. Notice the polarity of the inductor along with the current flow.

DC

L

Rl

R1

P

1kΩ

15V

Figure 9-1

1.5H

DC

Rl

R1

Figure 9-2A

+

―IT

IT

I1 IL

DC R1

Rl

+

―IT

IT

Figure 9-2B

38

When the current flow to the inductor is interrupted as in Figure 9-2B, the magnetic field collapses. This collapse causes a change in polarity of the inductor. The inductor will then attempt to maintain the same current as when the circuit was in a steady state. This current will pass through R1 for a very short length of time. The amplitude of the voltage spike will depend on the ratio of resistance of R1 to Rl.

5. Use circuit analysis to calculate the current through the inductor before the power supply was interrupted.

IL steady state current = ___________________.

6. Immediately after the current source is interrupted, the current must remain the same for a short length of time through the remainder of the circuit. Using Ohm’s Law and the current calculated in step 5, calculate the amplitude of the voltage spike at R1. Compare your result to the measured voltage in step 4.

R1 voltage spike calculated = ___________________.

It is easy to see how by abruptly breaking the current through a large inductor such as motor or coil, a voltage into the thousands of volts can be created. Even small inductances in electronic systems can create enough voltage to cause problems if circuit protection devices are not used.

In most cases these voltage spikes are undesirable but they can be controlled through proper circuit design. One example of a regular use of inductive kick is the ignition system on most automobiles. Here, the primary winding of the ignition coil is interrupted at the appropriate time by a control circuit to create the spark needed at each spark plug.

39

Inductance

Inductors in Series and Parallel Project Objectives:

• To demonstrate through circuit measurements that series and parallel connected inductances are analyzed in the same manner as series and parallel connected resistances.

Items Needed: - Electronics Trainer - DMM - 100 mH inductor (2) - Jumper Wires - Oscilloscope - 100 Ω resistor

Experiment In this exercise we will be recording the AC circuit current with a single inductor, then two inductors in series, and finally two inductors in parallel. The effects of total inductance will be illustrated by connecting two coils in series and in parallel.

1. Measure the resistance of the two 100-mH inductors that will be used in this project. Record the

results below.

Resistance of L1 = _________________. Resistance of L2 = _________________.

2. Connect the circuit shown in Figure 10-1. Set the source voltage to 8-VP-P and the frequency to 2-kHz.

What is the RMS value of the source voltage?

Source voltage = ___________________ RMS

3. If VA were DC, what would the current be through this

circuit? _________________.

4. Measure the RMS voltage drop across R1 (V1) and calculate the current.

V1 = _______________. IT = _______________.

Why is the current a lower value than if DC were applied?

________________________________________________________________

________________________________________________________________

5. Insert the second inductor (L2) in series with the circuit. Make sure the source is still set to 8-VP-

P, 2-kHz. Measure V1 and calculate the current.

V1 = _______________. IT = _______________.

Was the current higher or lower with two inductors in series? _______________.

We can conclude that inductors connected in series add similar to resistors connected in series.

6. Configure the circuit so L2 is in parallel with L1 and R1 is in series with the main current line. Measure V1 and calculate the current.

V1 = _______________. IT = _______________.

Was the current higher or lower with two inductors in parallel? _______________.

We can conclude that inductors connected in parallel add like resistors connected in parallel.

VA8-VP-P 2- kHz

R1100Ω

L1 = 100mH

Figure 10-1

40

Inductance

Relationship of XL to Inductance and Frequency Project Objectives:

• To verify the XL formula and the direct relationship of inductive reactance to both inductance and frequency by measuring circuit parameter changes associated with the changes in inductance and frequency.

Items Needed: - Electronics Trainer - Digital multi-meter - 100 mH inductor (2) - Jumper Wires - Oscilloscope - Resistor 1-kΩ

Experiment

1. Connect the circuit shown in Figure 11-1.

2. Set the function generator to a frequency of 1-kHz and set VA to 3-VRMS. Measure the voltage across the resistor (VR) and the voltage across the inductor (VL).

VR = _______________ VL = _______________

3. Using the known values for the resistor, calculate the circuit current and XL using Ohm’s Law. (XL = VL/I).

IT = _______________ XL = _______________

4. Now calculate XL using the XL formula. (XL = 2πfL). Compare the result to the Ohm’s Law method in step 3.

XL = _______________________________

5. Insert a second 100-mH inductor (L2) in series with L1 and R1. Make sure the VA and frequency remain the same. Measure VR, calculate IT, measure the voltage across the total inductance of L1 and L2, then calculate XL total using Ohm’s Law.

VR = __________________ IT = __________________

VL = __________________ XL = __________________

What happened to XL when the value of inductance in the circuit was doubled? __________

________________________________________________________________

Is XL directly or inversely proportional to the amount of inductance? __________________

6. Remove L2 and configure the circuit to once again resemble Figure 11-1. Make sure the source still measures 3-VRMS. Change the frequency to 2-kHz. Repeat the measurements and calculations used in the previous steps.

VR = __________________ IT = __________________

VL = __________________ XL = __________________

Compare the result of XL in this step to the result of XL in steps 3 and 4. What happened to XL

when the frequency of the circuit was doubled? ________________________________

________________________________________________________________

Is XL directly or inversely proportional to frequency? _____________________________

VA

3-VRMS 1-kHz

L1

R1

100mH

1kΩ

Figure 11-1

41

Inductance

Relationships in Series RL Circuits Project Objectives:

• To observe key electrical relationships in a series RL circuit. • To demonstrate that simple DC analysis techniques cannot be used to determine AC circuit

parameters containing inductive reactance due to out-of-phase elements. • To determine the value of inductance in a series RL circuit.

Items Needed: - Electronics Trainer - Digital multi-meter - 100 mH inductor - Jumper Wires - Oscilloscope - Resistor 1-kΩ

Experiment

1. Measure the resistance of the 1kΩ resistor.

R measured = ________________ Ω

2. Connect the circuit shown in Figure 12-1.

3. Set the function generator to a frequency of 2-kHz and set the source to 12-VP-P. Measure the RMS values of VA, VR, and VL.

VA = _____________________ RMS

VR = _____________________ RMS

VL = _____________________ RMS

Does VR plus VL equal the applied voltage? __________

Why? ___________________________________________________________

4. Use the following vector addition formula to find the sum of VR and VL.

VT calculated = _______________.

All things considered, is this relatively close to the measured value of VA? __________

5. Calculate the following: IT from (VR / R); XL from (VL / IT); and Z from (VT / IT).

IT = ________________ XL = ________________ Z = ________________

Does Z equal the arithmetic sum of R and XL? ________. We may conclude that since VA is

not equal to VR + VL and Z is not equal to R + XL, these values must be the result of two vectors out of phase.

6. Use the vector formula (Pythagorean Theorem) to calculate Z and compare the result to the calculated Z in step 4. Add the measured resistance of L to R before making the calculation.

Z calculated = _____________________

7. In the space provided to the right, draw a vector diagram using the voltage values measured in step 2.

8. Use the vector diagram along with trigonometry to determine the phase angle.

∠θ = ______________________________

12-VP-P 2-kHz

L

R

100mH

1kΩ

Figure 12-1

VT = VR2 + VL

2

42

9. Use a dual-trace oscilloscope to perform a phase comparison of VA and IT. Since the circuit current is in phase with the resistor voltage, the resistor voltage can be used to represent the circuit current. Connect CH2 of the oscilloscope across the resistor and CH1 across VA as shown in Figure 12-2.

Set the source to CH1 and mode to “Dual Trace”. Measure the phase difference between the two traces. Remember, a complete cycle is 360 degrees.

∠θ measured = _________________________

Does this oscilloscope phase measurement reasonably

agree with the calculated phase angle

performed in step 7? ______________________

10. Draw both of the waveforms you see in the dual-trace mode as Figure 12-3. Label each waveform (IT and VA).

According to your results, does the IL lead or lag VL?

____________________________________

When the value of inductive reactance and the frequency of the circuit are known, the value of inductance in the circuit can be determined by using the following formula:

11. Determine the circuit inductance using the calculated XL value in step 5. Compare the result to

the marked inductance rating on the component. L = ______________________. This method of determining inductance in a circuit can be extremely useful. If the frequency in a circuit is known, a simple current measurement and an inductor voltage drop measurement is all the information required to determine the value of inductance in the circuit.

Figure 12-2

L100mH

R 1kΩ

4-VRMS 2-kHz

VA

CH1 CH2 GND

Figure 12-3

L = XL

2π f

43

Inductance

Relationships in Parallel RL Circuits Project Objectives:

• To observe key electrical relationships in parallel RL circuits. • To demonstrate that simple DC analysis techniques cannot be used to determine AC circuit

parameters containing inductive reactance due to out-of-phase elements.

Items Needed: - Electronics Trainer - Digital multi-meter - 100 mH inductor - Jumper Wires - Oscilloscope (Dual Trace) - Resistors, 1kΩ

Experiment

1. Connect the circuit in Figure 13-1.

2. Set the function generator to a frequency of 2-kHz and the source voltage to 12-VP-P. Measure the following RMS voltages.

VA = ________________________ RMS

VR = ________________________ RMS

VL = ________________________ RMS

The voltage across each component should be the same and equal to VA. This verifies that the voltage across the resistor is in phase with the voltage across the inductor in a parallel RL circuit.

3. Measure the total current and each individual branch current. Record your results below.

NOTE: Remember to break the circuit and insert the ammeter in series with the component(s) to be measured. Also, check to make sure the meter lead is plugged into the mA port and the function is set for AAC.

IT = _________________ IR = _________________ IL = _________________

Does the total current equal the arithmetic sum of the branch currents? _______________

Why? ___________________________________________________________

_______________________________________________________________

Use vector addition to find the sum of IR and IL. ( )

IT calculated = ______________. Is this relatively

close to the measured IT? ______________

4. In the space provided, draw a vector diagram using the current values measured in step 3.

Use the vector diagram along with trigonometry to determine the phase angle.

∠θ = ___________________________________

5. Find Z by (VA / IT) and XL by (VL / IL).

Z = ________________ XL = _______________

IT = IR2 + IL

2

Figure 13-1

L100mH

R1kΩ

VA 4-VRMS 2kHz

44

If we were to calculate Z by the known values of R and XL, could we use the exact same

method(s) as calculating total parallel resistances in a DC circuit? ____________________

Explain your answer: _________________________________________________

________________________________________________________________

________________________________________________________________

6. Determine the value of inductance in the circuit by using the following formula:

Compare the calculated value to the 100mH rating of the component.

Calculated inductor value = ___________________

L = XL

2π f

45

Capacitance

RC Time Constants Project Objectives:

• To demonstrate the charging and discharging characteristics of a capacitor. • To observe that a capacitor takes five time constants to change from one set voltage to another.

Items Needed: - Electronics Trainer - Digital multi-meter - Resistors, 680kΩ, 1kΩ - Jumper Wires - Capacitor 47 µF (non-polarized) - Stopwatch

Experiment 1 – Charging Characteristics

1. Construct the circuit shown in Figure 14-1. Use the variable DC power supply as the source but make sure no power is applied to the circuit at this point.

2. Take a DC voltage reading across the capacitor to make

sure it is fully discharged. If a voltage reading is present, connect a 1kΩ resistor in parallel to the resistor until the meter reads 0 volts.

3. Making sure there is an open connection between points A

and B, set the applied voltage to 20 VDC.

4. Connect the voltmeter across the 680kΩ resistor and set the meter to the 20 VDC range.

5. Close the open connection between points A and B and immediately begin recording the voltage in 5 second increments for the first 20 seconds, 10 second increments until 1 minute and then 20 second increments until 3 minutes have passed. Record your results in the “Resistor Voltage” row of the table below.

In order to find the charge voltage of the capacitor, the resistor voltage needs to be subtracted from the applied 20 volts. Record these calculations in the row labeled “Capacitor Voltage”.

6. Use the measured capacitor voltage values and plot them on Graph G1 on the following page.

Use a straight edge to connect the measurement points.

Is this graph linear or exponential? _______________________________

The charging current eventually charged the capacitor to a voltage equal to (VA, VR) _______.

Was the current maximum at the beginning or end of the charge time? _________________

At the first instant of charge time, the voltage across the resistor was equal to (VA, VC) ______.

At the end of the charge time, the voltage across the resistor was ______ volts. The voltage across the capacitor is equal to VA.

Time 0.05 0.10 0.15 0.20 0.30 0.40 0.50 1.00 1.20 1.40 2.00 2.20 2.40 3.00

Resistor Voltage

Capacitor Voltage

Figure 14-1BA

680 kΩ

47 µF

46

47

7. The time that a capacitor needs to charge can be divided into 5 time constants. During each time constant the voltage increases by 63.2% of the maximum remaining voltage. For example, if the applied voltage were 100V, the voltage after the first time constant would be 63.2% of 100V or 63.2V. The second time constant would be 63.2% of the remaining voltage. To find the remaining voltage we need to subtract the voltage after the first time constant from the applied voltage. 100V – 63.2V = 36.8V. The remaining 36.8V then needs to be multiplied by 63.2%. 36.8V x .632 = 23.26V. We then add the 23.26V to the voltage after the first time constant. 63.2V + 23.26V = 86.46V. The voltage after the second time constant would be 86.46V. The remaining 3 time constants can then be calculated using the same method.

Using the previous example above as a reference, calculate the voltage after each time constant. Use 20 volts for your applied voltage.

VCALC after Time Constant 1 = ___________________

VCALC after Time Constant 2 = ___________________

VCALC after Time Constant 3 = ___________________

VCALC after Time Constant 4 = ___________________

VCALC after Time Constant 5 = ___________________

8. To calculate the length of time for one time constant we need to use the formula (t = R x C) t = time for one time constant in seconds R = resistance in ohms C = capacitance in farads

What is the length of each time constant in this circuit? __________________________

9. Using your calculation for the time constant length, mark the location of each time constant on the graph you created in step 6.

10. Record the approximate voltage after each time constant according to the graph.

VMEAS after Time Constant 1 = ___________________

VMEAS after Time Constant 2 = ___________________

VMEAS after Time Constant 3 = ___________________

VMEAS after Time Constant 4 = ___________________

VMEAS after Time Constant 5 = ___________________ Do these numbers coincide with the calculations in step 7. ________________________ List 3 reasons why the measured values may not perfectly match the calculated values.

1. ______________________________________________________________

2. ______________________________________________________________

3. ______________________________________________________________

48

Experiment 2 – Discharging Characteristics

1. Turn the power supply off and disconnect all wires from the power supply to the circuit components. Connect a voltmeter across the 680 kΩ resistor and set the range for 20 VDC.

2. Insert a jumper wire across the same connection points the

power supply was connected in Experiment 1 and immediately begin recording the voltage in 5 second increments for the first 20 seconds, 10 second increments until 1 minute and then 20 second increments until 3 minutes have passed. Record your results in the “Capacitor Discharge Voltage” row of the table below.

3. Use the measured capacitor discharge voltage values and plot them on Graph G2 on the next

page. Use a straight edge to connect the measurement points.

Is this graph linear or exponential? _______________________________ Did the capacitor take the same time to discharge through the resistor as it did to charge?

____________. At the end of the discharge time VC = __________; VR = __________.

Time 0.05 0.10 0.15 0.20 0.30 0.40 0.50 1.00 1.20 1.40 2.00 2.20 2.40 3.00

Capacitor Discharge

Voltage

Figure 14-2

680 kΩ

47 µF

jumper wire

49

50

Capacitance

Capacitance in Series and Parallel Project Objectives:

• To demonstrate that capacitors in series add similar to resistances in parallel and capacitors in parallel add similar to resistances in series.

Items Needed: - Electronics Trainer - Digital multi-meter - Resistors 10MΩ, 1kΩ - Jumper Wires - Capacitors 2 - 1.0 µF - Stopwatch

Experiment

1. Construct the circuit shown in Figure 15-1. Use the variable DC power supply as the source but make sure no power is applied to the circuit at this point.

2. Make sure an open connection exists between points a and b. Verify the capacitor is fully discharged by touching the capacitor leads across a 1kΩ resistor. Set the applied voltage to 20-VDC.

3. Set the voltmeter for the 20-VDC range and connect it across the resistor as shown in Figure 15-1.

4. At the same time, close the circuit between points A & B and use a stopwatch to begin timing

the length of capacitor charge time. Stop timing when the resistor voltage reaches 100mV.

Make three different attempts at timing the capacitor charge time. Make sure the power supply is disconnected and the capacitor is discharged through the 1kΩ resistor between each attempt. After recording the time for all three attempts, record the average charge time of the capacitor. NOTE: All three attempts should be within several seconds of each other. If one of the readings is too far off, omit it when calculating the average.

Charge time attempt #1 = ______________ seconds.

Charge time attempt #2 = ______________ seconds.

Charge time attempt #3 = ______________ seconds.

Average charge time = ________________ seconds

5. Disconnect the power supply from the circuit. Completely discharge the capacitor through the 1kΩ resistor. Insert a second 1.0 µF capacitor (C2) in series with C1 as shown in Figure 15-2. Repeat step 4.

Charge time attempt #1 = ______________ seconds.

Charge time attempt #2 = ______________ seconds.

Charge time attempt #3 = ______________ seconds.

Average charge time = ________________ seconds

Did the capacitor charge time increase or decrease from the result in step 4? _____________

When multiple capacitors are connected in series, an effect occurs that is similar to increasing

the distance between the plates of a single capacitor.

V

a b

C11 µF

R10MΩ

Figure 15-1

V

a b

C11 µF

R10MΩ

Figure 15-2

C21 µF

51

This causes the total circuit capacitance to (increase, decrease) _____________________

Since the new RC time is approximately (double, half) __________________ the length of

time as with a single capacitor and the resistance has not changed, it can be concluded that the

new total capacitance is ____________ µF. Our observations conclude that capacitors in

series add similar to resistors in ______________________.

6. Disconnect the power supply from the circuit. Completely discharge the capacitors through the 1kΩ resistor. Remove C2 and connect it in parallel with C1. Configure the circuit so the 10MΩ resistor is connected in series with the two parallel capacitors as shown in Figure 15-3. Once again, repeat step 4.

Charge time attempt #1 = ______________ seconds.

Charge time attempt #2 = ______________ seconds.

Charge time attempt #3 = ______________ seconds.

Average charge time = ________________ seconds

The charge time is now approximately (double, half) __________________ the time recorded in step 4. When capacitors are connected in parallel, an effect of increasing the plate area of a single capacitor occurs.

This causes the total circuit capacitance to (increase, decrease) _____________________

The total capacitance of C1 and C2 in parallel is (double, half) __________________ the

capacitance of C1 alone and the new value of capacitance in the circuit would be _______ µF.

In conclusion, capacitors in parallel add like resistors in __________________.

V

a b

C11 µF

R10MΩ

Figure 15-3

C21 µF

52

Capacitance

Relationship of XC to Capacitance and Frequency Project Objectives:

• To verify the XC formula and the inverse relationship of capacitive reactance to both capacitance and frequency by measuring the circuit parameter changes associated with the changes in capacitance and frequency.

Items Needed: - Electronics Trainer - Digital multi-meter - Resistor 18 kΩ - Jumper Wires - Oscilloscope - Capacitors 0.1µF, 1.0 µF

Experiment

1. Measure and record the resistance value of the 18kΩ resistor.

R measured = _______________________ 2. Connect the circuit shown in Figure 16-1

3. Set the function generator to a frequency of 100-Hz and

set VA to 12-VP-P. Measure the RMS source voltage, the voltage across the resistor (VR) and the voltage across the capacitor (VC).

VA = __________________________ RMS

VR = __________________________ RMS

VC = __________________________ RMS

4. Calculate the circuit current using the known values of R.

Calculate XC using Ohm’s Law (XC = VC / I).

IT = ___________________ XC = ___________________

5. Calculate XC by using the XC formula.

Compare to the value of XC in step 3.

XC = ______________________________

6. Change C to a 1.0 µF capacitor and find the values as in steps 2 and 3.

VR = __________________________ RMS

VC = __________________________ RMS

IT = ___________________ XC = ___________________

Calculate XC using the XC formula as in step 4. XC = __________________________

What happened to XC when the value of capacitance was increased? ________________

_______________________________________________________________

The value of capacitance increased by approximately ten times. The XC of the 1.0 µF capacitor

was approximately (ten times, one-tenth) ________________ the XC of the 0.1 µF

capacitor. Is XC directly or inversely proportional to capacitance? ___________________

C0.1µF

R18 kΩ

12-VP-P 100 Hz

Figure 16-1

VA

53

7. Keep the 1.0-µF capacitor in the circuit and the source set at 12-VP-P. Change the frequency to 200-Hz. Repeat the measurements and calculations used in the previous steps.

VR = __________________________ RMS

VC = __________________________ RMS

IT = ___________________ XC = ___________________

Calculate XC using the XC formula as in step 6. XC = __________________________ Is the XC with 200-Hz approximately double or half the value it was with the 100-Hz applied in

step 4? _________________________________________________________

8. Keep the frequency set at 200-Hz and change C back to a 0.1-µF capacitor. Repeat the measurements and calculations used in the previous steps.

VR = __________________________ RMS

VC = __________________________ RMS

IT = ___________________ XC = ___________________

Calculate XC using the XC formula as in step 6. XC = __________________________

Is the XC of the 0.1-µF capacitor at 200-Hz about one-half that at 100-Hz in step 4? _______

Is XC directly or inversely proportional to frequency? ____________________________ List two reasons why the XC calculated using Ohm’s Law and the XC calculated using the capacitive reactance formula may be slightly different.

1. _____________________________________________________________

_____________________________________________________________

2. _____________________________________________________________

_____________________________________________________________

54

Capacitance

Relationships in Series RC Circuits Project Objectives:

• To observe key electrical relationships in a series RC circuit. • To demonstrate that simple DC analysis techniques cannot be used to determine AC circuit

parameters containing capacitive reactance due to out-of-phase elements. • To determine the value of capacitance in a series RC circuit.

Items Needed: - Electronics Trainer - Digital multi-meter - Resistor 18 kΩ - Jumper Wires - Oscilloscope (Dual Trace) - Capacitor 0.1µF

Experiment

1. Measure the resistance of the 18kΩ resistor.

R measured = ________________ Ω

2. Connect the circuit shown in Figure 17-1.

3. Set the generator to voltage 12VP-P and the frequency to 100-Hz. Measure the RMS values of VA, VR and VC.

VA = _____________________ RMS

VR = _____________________ RMS

VC = _____________________ RMS

Does the sum of VR and VC equal VA? ______________.

This is because VR and VC are not in phase with each other. Arithmetic addition cannot be used. Vector addition must be used instead to add the two phases together.

4. Use the following vector addition formula to find the sum of VR and VC

VT calculated = _______________. Is this reasonably close to the value of VA in step 2 all

factors considered? ________

5. Calculate the following: IT from (VR / R); XC from (VC / IT); and Z from (VT / IT).

IT = ________________ XC = ________________ Z = ________________

Does Z equal the arithmetic sum of R and XC? ________. We may conclude that since VA is

not equal to VR + VC and Z is not equal to R + XC, these values must be the result of two vectors out of phase.

6. Use the vector formula (Pythagorean Theorem) to calculate Z. Compare the result to the calculated Z in step 4.

Z calculated = ________________________

7. In the space provided to the right, draw a vector diagram using the voltages from step 2.

8. Use the vector diagram along with trigonometry to determine the phase angle.

∠θ = _______________________________

Figure 17-1

C0.1 µF

R18 kΩ

12-VP-P 100 Hz

VT = VR2 + VC

2

55

9. Use a dual-trace oscilloscope to perform a phase comparison of VA and circuit current. Since the circuit current is in phase with the resistor voltage, the resistor voltage can be used to represent the circuit current. Connect CH2 of the oscilloscope across the resistor and CH1 across VA as shown in Figure 17-2.

Set the source to CH1 and mode to “Dual Trace”. Measure the phase difference between the two traces.

∠θ measured = _________________________

Does this oscilloscope phase measurement reasonably agree with the calculated phase angle

performed in step 7? _______________________

10. Draw both of the waveforms you see in the dual-trace mode as Figure 17-3. Label each waveform (IT and VA).

As you may recall, the circuit current is being

represented by the voltage across the resistor. According to your results, does the IC lead or lag

VC? ______________________________

When the value of capacitive reactance and the

frequency are known, the value of capacitance

in the circuit can be determined using the following formula:

11. Determine the circuit capacitance using the calculated XC in step 4. Compare the result to the

specified capacitance rating of the component. C = ____________________________

Just as the inductance in a circuit can be determined by performing a few simple measurements

and calculations, the capacitance in a circuit can be determined in a similar way. The circuit

frequency, current, and capacitor voltage drop are all the information required to determine the

circuit capacitance.

Figure 17-2

C0.1µF

R 18 kΩ

12-VP-P 100 Hz

VA

CH1 CH2 GND

Figure 17-3

C = 1

2π f XC

56

Capacitance

Relationships in Parallel RC Circuits Project Objectives:

• To observe key electrical relationships in a parallel RC circuit. • To demonstrate that simple DC analysis techniques cannot be used to determine AC circuit

parameters containing capacitive reactance due to out-of-phase elements.

Items Needed: - Electronics Trainer - Digital multi-meter - Resistor - 1kΩ - Jumper Wires - Oscilloscope (Dual Trace) - Capacitor 0.1µF

Experiment

1. Connect the circuit in Figure 18-1.

2. Set the function generator to a frequency of 1-kHz and the source voltage to 8-VP-P. Measure the following RMS voltages.

VA = ________________________ RMS

VR = ________________________ RMS

VC = ________________________ RMS

Does VR equal VC? ______________________

Is VR in phase or out of phase with VC?_____________________________________

3. Measure and record the total circuit current and the current through each parallel branch. Remember to break the circuit and insert the meter in series with the component(s) being measured.

IT = _________________ IR = _________________ IC = _________________

Does the total current equal the arithmetic sum of the branch currents? _______________

Why? ___________________________________________________________

_______________________________________________________________ Use vector addition to find the sum of IR and IC. ( )

IT calculated = ______________. Is this close to the

measured value in step 3? ___________________

4. In the space provided to the right, draw a vector diagram using the current values obtained in step 3.

Use the vector diagram along with trigonometry to determine the phase angle.

∠θ = ___________________________________

If the frequency was decreased, would ∠θ increase,

decrease, or stay the same? ___________________

Figure 18-1

8-VP-P 1-kHz

R21kΩ

C0.1µF

IT = IR2 + IC

57

5. Find Z by (VA / IT) and XC by (VC / IC).

Z = ________________________ XC = _______________________ If we were to calculate Z by the known values of R and XC, could we use the same

method(s) as calculating total parallel resistances in a DC circuit? ____________________

Explain your answer: _________________________________________________

________________________________________________________________

________________________________________________________________

6. In order to calculate Z in a resistive/reactive parallel circuit we need to use a formula that employs a combination of the Pythagorean Theorem and the reciprocal formula for calculating parallel resistances. The formula shown below can be used.

Using the formula above, calculate Z from R and XC. Compare to the value of Z in step 5.

Z calculated = _____________________.

7. Determine the value of capacitance in the circuit by using the following formula:

Compare the calculated value to the 0.1µF rating of the capacitor.

Calculated capacitor value = ___________________

+ 1 R

2

) ( 1XC

2

) ( Z =

1

C = 1

2π f XC

58

Series Resonance

Relationships of XL and XC to Frequency Project Objectives:

• To verify the direct and inverse relationships of XL and XC to frequency when the frequency of the applied signal is changed.

Items Needed: - Electronics Trainer - Digital multi-meter - 100 mH inductor - 0.1 µF Capacitor - Jumper Wires - Oscilloscope - 100 Ω Resistor

Experiment

1. Connect the circuit in Figure 19-1.

2. Set the source voltage to 8-VP-P and the frequency to 1-kHz. Measure the RMS values of VA, VR, VL and VC. Calculate IT using the measured values of R. Calculate XL and XC using Ohm’s Law.

VA = _______________ VR = _______________

VL = _______________ VC = _______________

IT = _______________ XL = _______________

XC = _______________

3. Change the frequency to 2-kHz. Reset the source to 8-VP-P. Once again, measure the RMS values of VA, VR, VL and VC and calculate IT, XL and XC.

VA = _______________ VR = _______________

VL = _______________ VC = _______________

IT = _______________ XL = _______________

XC = _______________

When the frequency was doubled, XL (doubled, halved, stayed the same) _______________

and XC (doubled, halved, stayed the same) ___________________________________

Is XL directly or inversely proportional to frequency? _____________________________

Is XC directly or inversely proportional to frequency? _____________________________ When an AC circuit contains both inductance and capacitance, a frequency must exist where XL and XC become resonant and completely cancel each other out. In this circuit would the

resonant frequency be higher or lower than the 2-kHz setting? ______________________

8-VP-P 1-kHz

L100mH

C0.1µF

R100Ω

Figure 19-1

59

Series Resonance

Circuit Characteristics When XL is equal to XC Project Objectives:

• To demonstrate the effects of a circuit set at a frequency where XL = XC. • To show the resistive effects of a series RLC circuit at resonance.

Items Needed: - Electronics Trainer - Digital multi-meter - 100 mH inductor - 0.1 µF Capacitor - Jumper Wires - Oscilloscope - 100 Ω Resistor NOTE: The function generator on the Elenco trainer has a large amount of internal impedance as compared to the resonant impedance of the circuit in this project. This internal impedance acts as an un-measurable voltage divider in the circuit and may slightly distort the waveform or cause the source voltage to appear to change as the frequency is adjusted closer to resonance. This change in source voltage will not affect the outcome of the lab project.

Experiment

1. Connect the circuit in Figure 20-1. Set VA at 8-VP-P, 1.2 kHz.

2. Connect the voltmeter to measure VR and slowly adjust the frequency from the signal generator until VR is at its highest value. Measure and record VR, VL and VC. Calculate IT from the measured values of R then calculate XL and XC.

VR = ________________ IT = ________________

VL = ________________ XL = ________________

VC = ________________ XC = ________________

What is the approximate frequency of the altered sine wave?

Approximate frequency = _______________________

Since the voltage across the inductor (leads, lags) _____________ the current by

approximately 90 degrees and the voltage across the capacitor (leads, lags) _____________

the current by about 90 degrees, then VL and VC are close to 180 degrees out of phase with

each other. Since the current is the same throughout a series circuit we can conclude that XL

and XC are vectorally opposite and are equal at a resonant frequency. This means that they

cancel out each other’s effects on total impedance.

Assuming XL and XC are perfectly equal and opposite, would the circuit current be in phase with

the applied voltage? ______________

3. Change the frequency to 2 kHz. Measure VL and VC and determine whether the circuit is acting more inductive or capacitive.

VL = ___________________ VC = ___________________

Is the circuit now acting like an RL or RC circuit? _____________

IT now (leads, lags) _____________ VA by an angle between 0 and 90 degrees; thus the

circuit is (inductive, capacitive) _________________________

8-VP-P 1.2 kHz

L100mH

C0.1µF

R100Ω

Figure 20-1

60

4. Now change the frequency to 1 kHz. Measure VL and VC and determine whether the circuit is acting more inductive or capacitive.

VL = ___________________ VC = ___________________

Is the circuit now acting like an RL or RC circuit? _____________

IT now (leads, lags) _____________ VA by an angle between 0 and 90 degrees; thus the

circuit is (inductive, capacitive) _________________________

We may conclude that at a resonant frequency where XL = XC, the series circuit essentially

acts as a pure ________________________ circuit.

At frequencies above resonance, a series RLC circuit will act as a(n) _____________ circuit.

At frequencies below resonance, a series RLC circuit will act as a(n) _____________ circuit.

At a resonant frequency, is Z higher or lower than it would be at any other frequency? Why?

________________________________________________________________

________________________________________________________________

61

Series Resonance

Bandwidth Related to Q Project Objectives:

• To determine the bandwidth of a series RLC circuit. • To verify that the bandwidth is narrower with higher quality circuit components and wider with

lower quality circuit components.

Items Needed: - Electronics Trainer - Digital multi-meter - Inductors, 1.5H, 100mH - 0.1 µF Capacitor - Jumper Wires - Oscilloscope - Resistors, 100Ω, 1kΩ

Experiment 1

1. Set the generator to an RMS voltage of 3-V and the frequency to 500-Hz. Make sure no load is connected when setting the source voltage.

2. Connect the circuit in Figure 21-1.

3. Measure across VR and set the frequency for resonance (maximum VR). Measure VL, and VC. Calculate IT at resonance using the measured values of R.

VR = _________________ IT = _________________

VL = _________________ VC = _________________

Measure the frequency at resonance. Remember, frequency is the reciprocal of the period.

Approximate frequency = _________________________

The total circuit Q can be determined by the following formula:

What is the approximate Q of this circuit? (Use the “no load” 3-VRMS for VA) ______________ Use the following formula to calculate bandwidth:

Bandwidth = ________________________

If the current decreased to 70.7% of IMAX what would be the approximate value of the current?

_______________________. What would VR equal? ________________________

Bandwidth in a series resonant circuit is defined as the difference between the two frequencies, one above and one below resonance at which the circuit current is 70.7% of the maximum current which occurs at resonance.

4. Adjust the frequency above resonance where VR equals 70.7% of maximum VR. Record this frequency then adjust the frequency below resonance until VR once again equals 70.7% of maximum VR. Record this frequency and then determine the measured bandwidth from the difference of the two frequencies recorded.

f above resonance where VR is at 70.7% = ___________________________________

f below resonance where VR is at 70.7% = ___________________________________

Measured Bandwidth = ________________________________________________

This measured bandwidth should resonably compare with the calculated bandwidth in step 3.

3-VRMS 500-Hz

L1.5 H

C0.1 µF

R100 Ω

Figure 21-1

Q = VL VA

Bandwidth = fR Q

62

5. Change the 100Ω resistor to a 1kΩ resistor and repeat the steps above.

VR = ____________________ IT = ____________________

VL = ____________________ VC = ____________________

Resonant frequency = _________________________________

Q = ______________ Calculated Bandwidth = ______________

f above resonance where VR is at 70.7% = ____________________

f below resonance where VR is at 70.7% = ____________________

Measured Bandwidth = ________________________________

What happens to the Q of a circuit when the resistance becomes larger?

________________________________________________________________

________________________________________________________________

What happens to the bandwidth of a circuit when the Q becomes larger?

________________________________________________________________

________________________________________________________________

63

Experiment 2

1. Connect the circuit shown in Figure 21-2. Set the “open circuit” source for an RMS value of 3-V and the frequency to 1-kHz. Make a “frequency run” to enable graphing the circuit current versus frequency. Measure and record VR in increments of 100-Hz starting at 1-kHz and ending at 2.5-kHz. Calculate the circuit current for each increment by (VR / R) and record in the table below.

2. Use the current values from the table to create a graph on the

following page. Label the following points on the graph: (1) The approximate resonant frequency, (2) the circuit’s bandwidth points which are 0.707 x current value at resonance.

Frequency VR IT

1.0 kHz

1.1 kHz

1.2 kHz

1.3 kHz

1.4 kHz

1.5 kHz

1.6 kHz

1.7 kHz

1.8 kHz

1.9 kHz

2.0 kHz

2.1 kHz

2.2 kHz

2.3 kHz

2.4 kHz

2.5 kHz

3-VRMS 1-kHz

L100 mH

C0.1 µF

R100 Ω

Figure 21-2

64

1.0

2.0

3.0

4.0

5.0

6.0

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Frequency in kHz

Cur

rent

in m

A

Bandwidth, IT versus Frequency

2.1 2.2 2.3 2.4 2.5

65

Parallel Resonance

Circuit Characteristics When XL is equal to XC Project Objectives:

• To demonstrate the effects of a parallel RLC circuit when set at a frequency where XL = XC. • To show the resistive effects of a parallel RLC circuit at resonance.

Items Needed: - Electronics Trainer - Digital multi-meter - 100 mH inductor - 0.1 µF Capacitor - Jumper Wires - Oscilloscope - Resistors 100 Ω (2), 1 kΩ

Experiment

1. Set the “no-load” generator source to 5-VRMS and the frequency to 1-kHz.

2. Connect the circuit in Figure 22-1

3. Connect a voltmeter across R1 and adjust the circuit frequency until the voltage across R1 is minimum. Record VR1 and measure the frequency.

VR1 = _______________________________

frequency = __________________________

4. Measure and record the voltage from point A to point B (VA-B). Calculate IT from VR1. Measure VR2 and calculate IC. Measure VR3 and Calculate IL.

VA-B = ________________________ IT = _________________________

VR2 = ________________________ IC = _________________________

VR3 = ________________________ IL = _________________________

With V1 set to the minimum voltage, are IC and IL close to being equal? ________________

In theory, due to the canceling effects of the capacitive and inductive currents in a parallel

resonant circuit, the total circuit current should be equal to zero and the total circuit impedance

should be infinitely high. In practical circuits, however, impedance (Z) is maximum at resonance

and circuit current (IT) is therefore minimum. This is due to the quality (Q) of the circuit.

5. Calculate the impedance of only the parallel portion of the circuit using the IT and VA-B values from step 4.

Z = _________________________

Use the XC formula to find the XC of the capacitor at the resonant frequency.

XC = _________________________

Use the XL formula to find the XL of the capacitor at the resonant frequency.

XL = _________________________

Notice that Z is greater than either branch’s opposition to current. This differs to a purely

resistive parallel circuit where Z would be less than the lowest value resistive branch.

R1 1 kΩ

R2100 Ω

R3100 Ω

C0.1 µF

L100 mH

A

BFigure 22-1

R Q = XL

1 2πfCXC =

XL = 2πfL

66

6. Use a dual-trace oscilloscope to perform a phase comparison. Since the voltage across R1 is in phase with the circuit current, VR1 can be used to represent the circuit current. Connect CH1 of the oscilloscope across the source and CH2 across R1 as shown in Figure 22-2.

Set the source to CH1 and mode to “Dual Trace”. Make sure the VOLTS/DIV settings are the same for both channels. Draw and label both waveforms at resonance (VA and IT). Are the two waveforms in phase or out of phase?

___________________________________

7. Keep the same circuit but change the frequency to 2 kHz. Measure V2 and V3. Calculate IC and IL.

V2 = ______________ IC = ______________

V3 = ______________ IL = ______________

The circuit at this frequency is acting equivalent to an (RL, RC) circuit? _________________ Therefore, when a frequency is above the resonant frequency, a parallel RLC circuit will act

(resistive, inductive, capacitive) _________________. This differs from a series RLC

circuit, which above resonance acts (resistive, inductive, capacitive) _________________. Using the same oscilloscope connections and settings in step 5, draw and label both the VA and the IT waveforms when the frequency is set above the resonant frequency. Are the two waveforms in phase or out of phase?

___________________________________

Is the circuit current leading or lagging the voltage?

___________________________________

8. Now change the frequency to 1 kHz which is well below the resonant frequency. Measure V2 and V3. Calculate IC and IL.

Waveforms at Resonance

Waveforms above Resonance

Figure 22-2

CH1 CH2

R1 1 kΩ

R2100 Ω

R3100 Ω

C0.1 µF

L100 mH

A

B

67

V2 = _________________________ IC = _________________________

V3 = _________________________ IL = _________________________

The circuit at this frequency is acting equivalent to an (RL, RC) circuit? _________________ Therefore, when a frequency is below the resonant frequency, a parallel RLC circuit will act

(resistive, inductive, capacitive) _________________. This differs from a series RLC

circuit, which above resonance acts (resistive, inductive, capacitive) _________________. Once again, use the same oscilloscope connections and settings in step 5. Draw and label the VA and the IT waveforms when the frequency is set below the resonant frequency. Are the two waveforms in phase or out of phase?

___________________________________

Is the circuit current leading or lagging the voltage?

___________________________________

Waveforms below Resonance

68

Parallel Resonance

Bandwidth Related to Q Project Objectives:

• To determine the bandwidth of a parallel RLC circuit. • To note how Q and Z are changed when a shunt resistance is added to a circuit.

Items Needed: - Electronics Trainer - Digital multi-meter - 100 mH inductor - 0.1 µF Capacitor - Jumper Wires - Oscilloscope - Resistors, 100Ω (2), 18kΩ

Experiment

1. Set the “no-load” source from the generator to 5-VRMS and the frequency to 1-kHz.

2. Connect the circuit in Figure 23-1

3. Measure the voltage across R1 and adjust the circuit frequency until VR1 is minimum and the circuit is at resonance. Record VR1 and measure the approximate resonant frequency.

VR1 = _______________________________

Resonant frequency = ___________________

4. Measure and record the voltage from point A to point B (VA-B). Calculate IT from VR1. Measure VR2 and calculate IC.

VA-B = ________________________ IT = _________________________

VR2 = ________________________ IC = _________________________

What is the Q of this circuit? (IC / IT) _______________

5. Calculate the impedance of the parallel portion of the circuit by dividing VA-B by IT.

Z = __________________________

If the impedance above decreased to 70.7% what would be its approximate value?

ZMAX x 0.707 = _______________________

What would IT equal if VA-B were divided by the decreased value of Z?

IT = _______________________

Similar to the bandwidth in a series resonant circuit, bandwidth in a parallel resonant circuit can be determined by computing the frequency on both sides of resonance where the impedance is 70.7% of its maximum value. The low frequency must then be subtracted from the high value.

6. Find the two frequencies at which Z = 70.7% of ZMAX by indirectly measuring IT with the

oscilloscope at R1. Increase or decrease the frequency as necessary until the voltage drop across R1 matches the IT value determined in step 5. One frequency will be above the resonant frequency and the other will be below.

Frequency above resonance where Z is at 70.7% = _____________________________

Frequency below resonance where Z is at 70.7% = _____________________________

R1 100Ω

R2100Ω

C0.1 µF

L100 mH

A

BFigure 23-1

69

Determine the bandwidth from fhigh - flow Bandwidth = __________________________

Use the bandwidth formula (Bandwidth = fR/Q) to determine the bandwidth. Use the resonant frequency along with the value of Q computed in step 4 to find the answer.

Bandwidth = __________________________

This calculated bandwidth should resonably compare with the measured value, however this could be slightly inaccurate due to circuit resistances and the internal impedance of the generator among other factors.

7. Connect an 18 kΩ resistor in parallel with the circuit (between points A and B). Repeat the

procedures in steps 3 through 6 to determine the bandwidth. Be sure to once again set V1 for minimum.

V1 = _______________ IT = ________________ VA-B = _______________ Calculate Z of the parallel portion of the circuit by dividing VA-B by IT.

Z = ___________________

What will the total circuit current be at the two frequencies when Z = 70.7% of ZMAX?

Current when Z is 70.7% of ZMAX = _________________________________________ Find the two frequencies, one above and one below resonance at which Z = 70.7% of ZMAX by measuring IT (VR1).

f above resonance where IT is at 70.7% = ____________________________________

f below resonance where IT is at 70.7% = ____________________________________

Determine the bandwidth from fhigh - flow Bandwidth = __________________________

Is the bandwidth with the 18-kΩ shunt wider or narrower than without it? _______________

Does this mean that the Q of the circuit increased or decreased? ____________________

70

Formulas

Capacitance & Capacitive Reactance

XC = 1

2 π f C C = 1

2 π f XC f = 1

2 π C XC

Inductance & Inductive Reactance

XL = 2 π f L L = XL

2π f f =

XL

2π L

EI R

PR

IE

E x I ER

P

R

I2 x R

P

EER

P x R

I x RP

I EP

P

I

E

I PI E

Ohm’s Law AC sine wave formulas

EINST = EPEAK sin ∠θ EPEAK = EINST / sin ∠θ sin ∠θ = EINST / EPEAK Peak to Peak = Peak x 2 Peak = Peak to Peak / 2 Peak = RMS x 1.414 RMS = Peak x 0.707 Average = Peak x 0.637 Average = RMS x 0.9 Frequency = Period =

1

Period1

Frequency

RL Series Circuits

Z = R2 + XL2

ET = ER2 + EL

2

VA = P2 + VARsL2

IT = IR2 + IL

2

RL Parallel Circuits

VA = P2 + VARsL2

Z =+ )1

R

2

(1

)1 XL

2

(RC Series Circuits

Z = R2 + XC2

ET = ER2 + EC

2

VA = P2 + VARsC2

IT = IR2 + IC

2

RC Parallel Circuits

VA = P2 + VARsC2

Z =+ )1

R

2

(1

)1 XC

2

(RLC Circuits

fR = 1

2 π LC Bandwidth = fR

Q

(fR = frequency at resonance)

71

Notes:

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_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

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_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

72

Notes:

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

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_____________________________________________________________________

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73

Instructor Sign-off sheet Student Name:

Project Lab Project Description Instructor Initial Date

Project 1 Measuring Amplitude & Voltage

Project 2 Measuring Period & Frequency

Project 3 Instantaneous Voltage & RMS Values

Project 4 Additional Input Modes & Operations

Project 5 Advanced Measurement Techniques

Project 6 Forward & Reverse Bias Diode

Project 7 Half-Wave Rectifiers

Project 8 Full-Wave Bridge Rectifiers

Project 9 Inductive Kick

Project 10 Inductors in Series & Parallel

Project 11 Relationship of XL to Inductance & Frequency

Project 12 Relationships in Series RL Circuits

Project 13 Relationships in Parallel RL Circuits

Project 14 RC Time Constants

Project 15 Capacitance in Series & Parallel

Project 16 Relationship of XC to Capacitance & Frequency

Project 17 Relationships in Series RC Circuits

Project 18 Relationships in Parallel RC Circuits

Project 19 Relationships of XL & XC to Frequency

Project 20 Series, Circuit Characteristics when XL is equal to XC

Project 21 Series, Bandwidth Related to Q

Project 22 Parallel, Circuit Characteristics when XL is equal to XC

Project 23 Parallel, Bandwidth Related to Q


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