LECTURE 9

ELECTRICAL MEASUREMENTS

INTRODUCTION: Measurements of most quantities are easiest to perform using electrical means. This is because electrical information can be processed with greater ease than information signals appearing in other energy forms. It would be a lot tedious, for example, to create a mechanical amplifier or device that works mechanically to compensate for errors. For non-electrical measurands such as Pressure, Force, Temperature or fluid flow, we can employ transducers (where it is possible) and re-express these quantities through electrical signals, which carry information about the measurands. In this lecture we look at a few ELECTRO-MECHANICAL INSTRUMENTS, ELECTRONIC INSTRUMENTS and BRIDGE CIRCUITS. ELECTROMECHANICAL INSTRUMENTS We will examine the following types of instruments:

1) Moving Coil Meters (1) based on the D’ Arsonal meter movement (popularly known as the Permanent Magnet Moving Coil Meter and normally abbreviated as PMMCM) and (2) based on the electrodynamic principle.

2) Moving Iron Meters. 3) Electrostatic Meters. 4) Induction Type meters.

MOVING COIL INSTRUMENTS. (1) THE D’ ARSONAL METER MOVEMENT: This is an application of the basic meter movement in which the force on the drum is applied by electrical means. The forces on the drum are created when a current flows in the surroundings of a field created by a permanent magnet. The construction details of a D’ Arsonal type of meter are shown in Fig.1.

SHUNT

N S

COIL CARRYINGCURRENT

SCALE

POINTER

DRUM OF ALUMINIUM

Fig.1 When a current flows in the coil, then each conductor of the coil experiences a force F given by: F= BIL, where B is the flux density due to the permanent magnet, I is the current in the coil and L is the length of a coil side. The direction of the force can be found by applying Fleming’s left hand rule. Now opposite sides of the coil experience the force. This results in a turning moment M, given by: M= 2x(F)x(W/2), where W is the width of the coil. Hence each turn of the coil develops a moment of M=FW = BILW. Now LxW is the area A of the coil. So the turning moment of a coil can be re-expressed as M=BIA. For a coil of N turns, the total moment is MT: MT=N M=NBIA. In accordance with the dynamics of a basic meter movement, as the drum starts rotating an opposing moment due to the spring and damping starts acting. Finally the pointer rests at point governed by: Cθ = NBIA, where θ is the deflection and C is the restoring spring constant. Therefore the deflection θ is given by:

θ =[NBA/C] I The expression in square brackets, NBA/C, is the sensitivity of the meter. DAMPING: In the D’Arsonal meter damping is achieved through the use of a solid aluminium drum. As the drum rotates in the magnetic field eddy currents, which oppose the motion are induced.

AGING: To partly compensate for aging of the permanent magnet a magnetic circuit shunt is sometimes placed near the poles of the magnet. As the flux between the poles starts weakening the magnetic circuit is moved further from the poles. This restores the sensitivity of the meter that would have been lost due to aging. TEMPERATURE COMPENSATION: First we recall the general expression for the deflection θ = [NBA/C] I. The current I can be redefined as I=Vm/rc , where Vm is the voltage across the PMMCM and rc is the resistance of the moving coil. Therefore θ = [NBA/C] [1/rc] Vm,

where N, B, A, C, and rc are supposed to be constants. As temperature of the surroundings increases the flux density in a PMMCM reduces, the recoiling springs weaken and the resistance of the coil in the magnetic field increases. All these effects give rise to instrumental errors (of a type called Temperature Errors). If we recall from error analysis, the relative error in the deflection is initially defined as:

c

c

r

dr

C

dC

B

dB

A

dA

N

dNd−−++=

θ

θ

On the right hand side of the last equation, the first two terms can be considered insensitive to changes therefore they are equal to ZERO. This results in the equation, which follows below.

c

c

r

dr

C

dC

B

dBd−−=

θ

θ

Now a known correlation exists between B and C such that a temperature increase of 10 degrees results in a flux decrease of 4% and weakening of the spring by 4%. Hence the temperature errors due to flux and restoring spring constant tend to auto-compensate. This leaves the dominant temperature error in the moving coil instrument as being caused by the resistance of the moving coil as indicated in the following equation.

Hence c

c

t r

drd≈

θ

θ

The meter temperature errors can be partly compensated for by connecting the meter, which has internal resistance of rc in series with a stable resistance, Rm, (made of Manganin) of higher value than rc. (Fig.2)

Rm50

rc2

Fig.2

The relative errors of Manganin due to temperature are negligible. If the deflection of the

compensated meter is called 2θ , then the relative error is now ]1[2

2

c

m

c

c

r

R

r

dr

d

+

��

���

�

=θ

θ

It is evident, from the last expression, that the relative errors of the meter due to temperature have been reduced by a factor of (1+ Rm/rc). However the sensitivity of the meter is also reduced by the introduction of the multiplier such that for the same applied voltage at the input, the deflection of the compensated meter is less than that of the uncompensated meter. MERITS OF THE D’ARSONAL METER:

1) High accuracy (typically to 0.01%). 2) Very good linearity. 3) High sensitivity (steep slope of the static characteristic) 4) Low power consumption. 5) Low hysteresis losses.

DEMERITS OF THE D’ARSONAL METER:

1) Inability to measure A.C. currents without modifications. 2) The delicate hairspring cannot withstand high overload currents. 3) The coil resistance is sensitive to temperature variations and requires

compensation. 4) Rather expensive.

Notwithstanding the said shortcomings, the D’Arsonal type meter is the most popular among moving coil instruments, as it happens to give the best accuracy and linearity.

The D’Arsonal Meter movement can be adapted to measure Voltages or Currents to realize voltmeters and ammeters respectively. However for many applications the range of the meter needs to be extended to enable it to measure large currents or voltages. The D’Arsonal Meter can also be modified to measure AC quantities. USING THE PMMCM TO MEASURE AC CURRENTS: As mentioned above, the PMMMC mechanism does not measure alternating currents. This is because the moving coil mechanism is inertial and therefore the pointer does not change as quickly as the AC current at 50 HZ. The indication will therefore be that of the average value of the current in the moving coil. The fig.3 (below) shows the typical indications of the meter under the action of different input currents.

V

R

Ammeter

Reading will beconstant I

I

t

I

Current

R

Ammeter

Reading will beconstant O when sinefrequency, f, is greaterthan 20 HZ.

I

t

I

Current

R

Ammeter

I

t

I

Current

HZ

Sine Wave Generator

HZ

Sine Wave Generator

V

f>20 HZf>20 HZ

Reading will beconstant I when sinefrequency, f, is greaterthan 20 HZ.

Fig. 3

The readings above can be derived from expressions of the average value of a wave (at the appendix of this lecture). It requires one to employ rectifiers to enable the meter to measure AC quantities. One may use Half-wave or Full-wave rectifiers fig.4 (Below).

A

Average VoltageV(t)

t

V(t)

Rload

Fig.4 In most cases of AC measurements we are interested in the Root Mean Square (RMS) value of an AC quantity. The RMS value of a Voltage or current informs about the heating effect of that Voltage or Current. Mathematically the heating effect is related to the RMS current by the equation: Heat = IRMS

2 RT, where IRMS is the RMS current, R is the resistance through which the current flows and T is the time over which the current has been flowing.

MAKING AMMETERS AND VOLTMETERS USING THE PMMCM: The Permanent Magnet Moving Coil meter movement can easily be adapted to measurements of voltages and currents to result in instruments called Voltmeters and Ammeters. They give a good accuracy and linearity. However there is a slight compromise on accuracy and linearity, which depends on the resistors (MULTIPLIERS and SHUNTS) introduced in the instruments. VOLTMETER BASED ON THE PMMCM: The internal resistance of a PMMCM is usually small and the coils in the meter are delicate to the extent that heavy currents can easily burn out the circuit elements of the meter. For the purpose of measuring voltages a large resistor, called MULTIPLIER is connected in series with the meter as shown in the Fig5. Below. This way we realize a voltmeter to measure within a given range.

Fig 5. The following example shows how to calculate the value of a multiplier resistor so that the meter can measure voltage within a desired range.

Example Given a meter with the following specifications:

1) Full scale deflection current = 2 mA. 2) Full scale deflection voltage is 1 mV.

Find the value of a multiplier resistor , Rm, to extend its range to measure voltages in the range VR= 0-100 Volts. Solution. The internal meter resistance, rc ,equals the ratio of its full scale deflection voltage to its full scale deflection current.

OhmsmA

mVrc 2/1

2

1==

Now VR=(Rm+rc) x (2mA) Or 100=(Rm+1/2). 2.10-3

Therefore Rm=49, 999.5 Ohms. AMMETER BASED ON THE PMMCM: In a similar argument the currents to be measured can be greater than the permissible limit currents for the coil and springs of a PMMCM. In such situations use is made of special resistors called SHUNTS to divert the excess current. In so doing we realize an ammeter to measure current within a given range (Fig 6). The following example illustrates how one calculates the value of a shunt resistor. Example Given a meter with the following specifications:

3) Full scale deflection current = 2 mA. 4) Full scale deflection voltage is 1 mV.

Find the value of a shunt resistor, Rsh, to enable the meter to indicate currents within the range 0 to 50 Amperes.

Fig.6

Solution Since the shunt and the meter are connected in parallel, then the full scale deflection voltage of the meter is the same as the voltage across the shunt. At full scale, the current in the shunt is Ish= (50)-(2.10-3 )A. The full scale voltage across the shunt is 1 mV. Therefore the required shunt resistor Rsh= (1mV)/(50-2. 10-3) = 2.00008x10-5 Ohms. In practice it is a big challenge to create a physical shunt with such a small resistance to pass a heavy current. This is because the resistance at the connecting points is of the same order as the shunt resistance itself. Secondly heavy currents result in appreciable heating effects. Thirdly small voltages at the connecting terminals caused by thermoelectric effect can cause appreciable errors. Therefore practical shunts are made with four terminals and the connections of the shunt to the meter are normally made at the factory using special low resistance materials and facilities.

USE OF PMMCM AS OHMMETER: There are two basic types of Ohmmeter realization: -Series Ohmmeter. -Parallel Ohmmeter. The series ohmmeter is best for measurements of high resistances while the parallel one is good for small resistances. Both series and parallel ohmmeters suffer from aging problems of the dry cells used in the instrument. This problem can be overcome by introducing electronic components to partly compensate for this or through the use of a Cross-Coil Ohmmeter. SERIES OHMMETER:

Fig 7

From previous discussion the deflection of a moving coil meter is governed by

IC

NBA���

���

=θ .

Since the current, I, is controlled by the relation cx rR

EI

+= , then for a linearly varying

resistance Rx, the pointer deflection has a non-linear sensitivity to Rx. The static

characteristic is dictated by the relationship ��

���

�+��

����

=cx rR

E

C

NBAθ .

PARALLEL OHMMETER: A typical scheme for the Parallel Ohmmeter is shown in the figure 8, below.

Fig.8 The deflection of the meter is given by

��

���

�++��

����

=)]([ RxrcRRr

ER

C

NBA

Mxc

xθ

where, xc Rr || is the effective resistance of the parallel connection of rc and Rx, and

MR is the resistance a scaling multiplier (usually placed inside the instrument). This deflection is also non-linear.

MOVING COIL RATIO-METERS (ALSO CALLED CROSS-COIL METER):

Fig. 9

The moving coil ratio-meter, shown in the figure above, is a modification of the moving coil device. Here, two coils are placed on the drum. The currents in the coils are such that there are two opposing moments acting on the drum. The pointer of the meter comes to rest at an equilibrium point where the opposing moments are at balance.

MOVING COIL OHMMETER: An Ohmmeter built on the moving coil ratio-meter principle is shown in the figure below.

Fig. 10

At equilibrium the deflection of the pointer is ��

���

�+

++���

���

=][ 2

1

L

xM

Rr

RRr

V

VKθ where K is a

constant r1 and r2 are the internal resistances coils 1 and 2 respectively, RL is a fixed resistor (normally placed in the instrument) and RM is a multiplier resistor (also placed in the instrument). The deflection requires a supply voltage just like in the case of the other ohmmeters considered earlier. However, fluctuations in the supply do not affect the position of the pointer as the term V in the last expression cancels out to result in an equation for

deflection given by ��

���

�+

++=

][ 2

1

L

xM

Rr

RRrKθ . This makes this type of meter particularly

useful in measurements on new electrical installations, where there is no electricity. In such situations the insulation of new installations is of primary importance. New installations require a high voltage insulation test (typically a high voltage of several thousands of Volts is required as supply V for the ohmmeter instrument). The supply ,V, is created by a hand-cranked alternator, which is connected to a voltage stepping up

transformer. This realizes a meter type popularly known as Megger-Ohm Tester for testing insulation resistance. The deflection of the meter is fairly linear over its working range. LINEAR OHMMETER AS mentioned above to get a linear Ohmmeter one needs to introuduce some electronic componenets. A linear Ohmmeter can be realilsed if we connect a current source in series with a resistance. Since the current in a current source is constant, then the voltage drop across the resistor will be proportional to the value of the resistor itself. If we connect a voltmeter across the unknown resistor then the result will be a linear static charexcteristic.(se Fig.11, below).

"A"Reference point

ELECTRONIC CURRENT SOURCE

2.FIXED CURRENT BETWEEN T1 and T2 is programmed by Current in R1, and itequals Ics =V2/R1 =1 mA

3. Therefore the Voltage across the Resistor Rx is Vx= 300x1 mA = 0.3 Volts.

4.NOTE:For the device to work properly, V1 is greater than V2. We chose V2= 10 Volts

OBSERVE: That Vx =(Icc)x(Rx)

CONCLUSION: The static sensitivity of the Vx to Rx characteristic is a constant. Hence the readings for Voltage are proportionalto the resistance Rx.

1.Current in R1 is (V2-0.7)/R1 or (5.7-0.7)/5000= 1mA

Rx 300

+ V25.7V

V1

R1

5000

+ V110V Q1

NPN

T2

T1

Fig. 11

In the current source described above, we should note, that the voltage drop across a diode that is conducting current is roughly 0.7 Volts. If we apply Kirrchoff’s second law for the circuit starting at point “A” going to V2 then through the Transistor, Q, and out to resistor R1 and back to “A”, then the voltage drop across R1 is 5.7-0.7 Volts or 5Volts. Hence the current in R1 is 1 mA. The current between points T1 and T2 is then going to be held constant, equal to that in R1, due to special properties possessed by transistors (not in the scope of this course). This current will remain constant whether we Short the terminals T1 and T2 together or even increase the value of Rx [provided, that Vx, the voltage drop across Rx is less than V1-(V2-0.7) ]. In this example, the Vx range is 10-5.7+0.7= 5 Volts. This range of voltages Vx, where the current source behaves like almost ideal (with constant current) is called the CURRENT SOURCE COMPLIANCE RANGE. Therefore, all that is connected around the resistor Rx can be seen as a single 1 mA current source with the equivalent circuit that is shown below (Fig. 12).

Unkown Resistor

Current Source I

I

Voltmeter

Fig.12

It is now clear, that when a moving coil voltmeter is connected across the unknown resistor, then the readings of the voltmeter will be directly proportional to the resistance. This way we realize a low cost linearly reading electronic Ohmmeter. Lastly the supplies V1 and V2 are created by special electronic circuitry (beyond the scope of this course) that even stabilizes their values to maintain them constant.

MULTIRANGE AMMETERS: Multi-range ammeters can be constructed using several configurations. One method is to use the circuit shown in Fig.13 and the other is to use the circuit shown in Fig. 14. The second circuit, Fig.14, is preferred to the first as the shunts have better immunity to stray resistances at the contacts of the switches, and this is critical because shunt resistances are usually very small valued resistors.

Fig. 13

Fig 14

Elements of the divider circuit (Fig. 14) are calculated using the following procedure. Let Rc+rc=Ri. Then

�

�

�

+−−==

−++−==

++−==

]32Im[]1Im)[1(Im)

]3Im[]21Im)[2(Im)

]321Im)[3(Im)

RRRIVmRiiii

RRRIVmRiii

RRRIVmRii

The first equation above corresponds to the range switch at position 3 while the second equation is associated with the range switch at position 2 and the last one for the range switch at position 1. The system of equations from above is then solved for unknown R1, R2 and R3.

���

�

�

���

�

�

�

�

�

���

�

�

���

�

�

−−−

−−−

−−−

=

���

�

�

���

�

�

3

2

1

ImImIm)1(

ImIm)2(Im)2(

Im)3(Im)3(Im)3(

R

R

R

I

II

III

Vm

Vm

Vm

Example Given:

1) Meter with full-scale deflection of 1 mA. 2) Internal resistance is 10 Ohms.

Required: Create a multi-range ammeter to measure on the ranges 2 mA, 20 mA and 200 mA. Solution After solving using a style similar to the equations above, the solutions should give R1= 0.1 Ohms, R2= 0.9 Ohms and R3=9.0 Ohms. And R1+R2+R3= 10 Ohms. MULTI-RANGE VOLTMETERS: There are several schemes for creating a multi-range voltmeter. These are shown in Fig.15 and Fig.16 .

Fig. 15

Fig. 16

The second scheme is preferred because some of the resistors along the divider can be of smaller values (Note that it is also difficult to make high valued, precise and stable resistors just as it is difficult to make very small resistors). The design for the values of the resistors using the circuit Fig.16 follows the given steps (below). Given Vm, Rm (Rm= resistance of meter and multiplier) and V1, V2 & V3 taken with reference to the point “Reference” then under the conditions of full scale deflection R1, R2 and R3 are determined by the relations,

RmVm

VmVR

VmV

Vm

R

Rm −=�

−=

11

11

Similarly,

RmVm

VVR

RmVm

VVR

233

122

−=

−=

And in general the resistance of the nth resistance, Rn, is found from the relationship

Vm

VVRn nn 1−−

= where Vn and Vn-1 are the scale ranges of the nth and n-1th ranges.

Example: A voltmeter has a sensitivity of 400 Ohm per Volt on a 15 Volt range. Find the appropriate multiplier resistors to be connected in series to extend the ranges so that we result in a 15 Volt, 40 Volt, 65 Volt and 150 volt ranges. Repeat the same problem if the multipliers were to be connected in parallel. MULTI-RANGE OHMMETER In a multi-range Ohmmeter a stabilized voltage source is used. Range resistors are selected by switching on to positions 1, 2 3 etc (see Fig.17)

Fig.17

TUTORIAL QUESTIONS

(i) Find an expression for the sensitivity function of the ohmmeter Fig. 17 in each range (neglecting resistance rc of the coil) assuming the deflection of the

meter to be governed by iC

BNA=θ , where i is the meter current.

(ii) It is stated that the meter behaves like a series Ohmmeter when the switch is at position ONE. Is this TRUE or FALSE. On which switch positions would you prefer to use the meter for measuring (a)-small resistances (b)-large resistances.

MULTIMETER The multimeter is an instrument, which integrates a multi-range voltmeter, multi-range ammeter and multi-range ohmmeter all in one package. In the typical construction of a multimeter there is a function switch , which selects either Voltmeter, Ammeter or Ohmmeter and Range select switches. Modern multimeters are digital and they incorporate many other functions such as transistor and IC testers, test oscillators, thermometers etc. The picture of a simple digital multimeter for measuring voltage, current and resistance and transistor parameters is shown in the given figure (fig. 18)

Fig. 18 (1) THE ELECTRODYNAMIC METER: In the electrodynamic meter, the moving coil of the meter is essentially the same as that of a PMMC except that the magnetic field around the moving coil is now created by a CURRENT IN A FIXED COIL INSTEAD OF A PERMANENT MAGNET (Fig.19).

Fig. 19 Electro-dynamic meter

When the fixed coil is wound on a soft iron magnetic material then the resulting instrument is called FERRODYNAMIC METER (Fig.20).

Fig.20, Ferro-dynamic Meter The deflection of the meter (fig. 19) can be derived through the following procedure: Let the energy store in all the coils (Fixed and Movable) be Wem. Then Wem= ½[ L1I1

2+L2I22]+M12I1I2

Where L1, L2 are the self inductances of the fixed and movable coils respectively and M12 is the mutual inductance between the fixed and movable coils.

The instantaneous torque, Mt, generated by the forces on the moving coil is given by

θd

dWemMt =

Considering that the self-inductances of the fixed and movable coils are constant then the expression for Mt reduces to

θθ d

iiMd

d

dWemMt

)( 2112==

Where, i1 and i2 are the instantaneous torques in the respective fixed and coils. For sinusoidal voltages let i1=IM1Cos wt and i2=IM2 Cos (wt+ψ ). The average value of the driving torque, Md, is derived according to the formula:

Md= +=

T

MM

T

dtWtCosWtCosd

dMIIdtMt

T 0

1221

0

)(][1

ψθ

Or with further derivations we arrive at the expression

Md= ][22

1221

θψ

d

dMCos

II MM

Now the spring will rest when the restoring torque, Cθ , balances Md. That is the condition Md = Cθ .

θ = ψθ CosIICd

dM

RMSRMS 21

12 ][

If θd

dM 12 is made almost constant by appropriate shaping of the electromagnet, then the

deflection is proportional to the power average power given by P= ψCosII RMSRMS 21

where ψCos is called “power factor”. The Electro-dynamic Meter Movement can also be used to realize Ammeters, Voltmeters, Wattmeters and even Frequency and Phase Meters. If any of the coils is supplied through a constant current source, then the meter will indicate linear reading with constant sensitivity.

MERITS OF ELECTRODYNAMIC METER: 1) The scale is linear on power measurements 2) It measures over a wide range of frequencies (typically from DC to 20 KHZ). 3) It is the most accurate among moving coil power measuring devices.

DEMERITS OF THE ELECTRODYNAMIC METER: 1) The magnetic field of fixed coils (which are air-cored) is very weak. Therefore

stray magnetic fields can affect the indication of the instrument (this is the reason why sometimes ferrodynamic meter is used but it must be also be noted that a ferrodynamic meter will degrade the accuracy because the magnetic circuit will introduce non-linearity and hysteresis errors).

2) The resistance of the moving coil suffers from temperature errors. TUTORIAL PROBLEM:

(i) A “Heavy Current Ammeter”, capable of indicating hundreds of amperes, can be realized using an electro-dynamic meter if the fixed coil is used as the path for the heavy current, while the moving coil carries a small constant current (supplied internally by a current source, see Fig. below).

Given that the fixed coil carries a current of 20 Amps at full-scale meter deflection and the resistance of the fixed coils is 0.5 micro-Ohms, design a multi-range ammeter to indicate in the ranges 0-100A and 0-300A.

(ii) Show the places on the meter circuits where the shunts and appropriate switches

are to be connected.

Scale

Constant CurrentSource

pointer

FirxedCoils

Heavy Current

Movablecoil

OSCILLOSCOPE It is used for visual observation of, measurement and recording of electrical signals. Since it possible to watch time varying signals the CRO is a convenient in determining various amplitude and time-dependent parameters of signals. Oscilloscopes have very high input impedance (like that of an almost perfect voltmeter) and can measure signals with frequency ranging up to e few gigahertz range. Some oscilloscopes are of analog type while others are a digital. Most recently there oscilloscopes that are designed to use a computer monitor as the display. Modern oscilloscopes can show multiple traces on the screen and allow one to store waveforms for repeat observations. OLD GENERATION OSCILLOSCOPES The older generation oscilloscopes, some of which may still be in use today are based on the cathode ray tube shown below in Fig.21

Fig. 21

The arrangement in Fig. 21 operates as follows. The objective is to produce a trace of electrode beams appearing as a bright spot on a screen that is coated with a

phosphorent powder. Phosphorous is a material that glows when electrons strike it. This way a human being observer in front of the screen can visually observe the position of the electron beam. This beam is emitted by a heated cathode. However the electrons emitted travel in all directions unless we restrict them in some way. Secondly we may desire a bright beam or a faint beam. Thirdly are main object is to measure electrical quantities. To achieve the desired beam brightness an electrode is placed very near the cathode. Its potential is varied by you (the user) so that we restrict or allow the number of electrons leaving the cathode. This forms the basis of the brightness control. The electrodes A1 and A2, which are essentially concentric cylinders, serve as both anode as they are placed at a very high positive potential (typically 3000 to 5000 Volts) and also en electrostatic way to focus the beam (“electrostatic focus”). The measurand is usually applied across the plates “VDP”. This way the amplitude of the wave is seen as a vertically varying wave. If we do not apply any voltage at the electrodes marked “HDP” then you (the observer) will see only a vertical line in response to a periodically changing wave. In order to observe a wave as it changes in real time (as it truly appears in nature) the beam spot has to be made to travel along the X-axis at the same speed as the measurand wave. This is achieved by Synchronizing a voltage applied at the “HDP” with the real wave. The voltage applied at the HDP is called a Time-Base waveform and has the shape shown in Fig.22. In the example shown in Fig. 22 you can observe waveforms that have a period of T= 1 milliseconds or less. If you change the time base to a bigger T you may observe the waveforms on a different time base, but the screen gets more crowded with waves. The user normally selects the appropriate T from a typical range of values: [T=0.01 u sec, T=0.1 u sec, T=1.0 u sec, T=10 u sec, T=0.1 milli sec, T=1 milli sec, T=10 milli sec, T=0.1 sec, T=1Sec, etc..etc]

Fig. 22-Time base wave applied at the HDP.

TRIGGER FUNCTION: In order to view a periodic waveform appearing as a stable trace, the TRIGGER function is required. The TRIGGER button commands the time base generator to start a scan each time the measurand wave completes a period and is about to start a new wave. Without the trigger the display on the screen will appear like a bush of waves. LISSOJOUS FIGURES In order to observe a wave as a function of another wave the oscilloscope is used in a mode called X-Y mode. The resulting patterns seen on the screen are called Lissajous Figures. NEW GENERATION OSCILLOSCOPES The new generation type of oscilloscopes use a LCD type or TFT type of screen, have storage facilities and are equipped with data logging facilities. The example of a modern oscilloscope is shown in the figure below. It consists of a personal computer, a hardware interface block and oscilloscope probes. This arrangement achieves all the functions required to realize an oscilloscope, Fig. 23

Fig. 23