elex3_general amp concepts

8/9/2019 ELEX3_General Amp Concepts

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GENERAL AMPLIFIER

CONCEPTSEngr. Jomer V. Catipon

[email protected]

0928 6654227


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By the end of the discussion, the student must be able to:

1. Differentiate linear electronics from digital electronics.2. Define amplifier and ideal amplifier.

3. Define an ideal source and a dependent source.

4. Enumerate the different dependent sources.

5. Draw the block diagram of a complete amplifier model

utilizing the VCVS.6. Define gain, power gain, voltage gain and current gain.

7. Explain the relationships of dB power, voltage and current

gains.

8. Explain the relationship between decibel loss and decibel

gain.

9. Explain the effect of input and output loads to the voltage

gain of an amplifier.

10.Derive the gain formula for a cascaded amplifier.


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11. Solve worded problems regarding gain.

12. Derive equations for particular circuits.13. Design circuits given particular conditions.


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I will praise the name of

God with a song,

and will magnify him withthanksgiving.

- Psalm 69:30


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LINEAR VS DIGITAL ELECRONICS

1. DIGITAL ELECTRONICS is concerned with all phases of electronics in which

signals are represented in terms of finite number of

digits, the most common of which is the binary

system.

- Includes all arithmetic computations on such

numbers, as well as associated logic operations.

2. LINEAR ELECTRONICS

- is concerned with all phases of electronics in whichsignals are represented by continuous or analog

variables.

- includes all signal-processing functions (for

example, amplification) associated with such signals.


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Actually the term linear is a misnomer since many of the

circuits is classified as such are non linear in nature.

On a slightly humorous vein, a better term might be non-

digital electronics to indicate that a large percentage of

electronic applications other than digital are often classifiedunder the category of linear electronics.

However, the classification term linear electronics has

become so embedded within the electronics industry that its

usage will no doubt continue.

The nonlinear circuits are classified in this category.


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One of the most important application of linear

electronics is amplification.

This operation was one of the very earliest applications

of electronic devices, and still remains essential

operation in virtually all phases of the industry.


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AMPLIFIER

An amplifier uses a small input signal to create a large

output signal, while minimizing distortion of the waveform.

Amplifiers are used for both electrical and optical signals.


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1. Weak-signal amplifiers

- are used primarily in wireless receivers, also employed

in acoustic pickups, audio tape players, and compact discplayers.

- are designed to deal with exceedingly small input

signals, in some cases measuring only a few nanovolts

(units of 10-9 volt).

- must generate minimal internal noise while increasingthe signal voltage by a large factor.

- The most effective device for this application is the field-

effect transistor.

The specification that denotes the effectiveness of a

weak-signal amplifier is sensitivity, defined as the number

of microvolts (units of 10-6 volt) of signal input that

produce a certain ratio of signal output to noise output

(usually 10 to 1).


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2. Power amplifiers

- are used in wireless transmitters, broadcast

transmitters, and hi-fi audio equipment.

- The most frequently-used device for power amplification is the bipolar transistor. However, vacuum

tubes, once considered obsolete, are becoming

increasingly popular, especially among musicians. Many

professional musicians believe that the vacuum tube

provides superior fidelity.


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IDEAL AMPLIFIER

- will pass the input signal through to the output undistorted

but enlarged (gain set by user), with no delay. It will not be

affected by the output impedance of the source (sensor).

In addition the ideal amplifier will be able to drive any load:

supply any current.

No real amplifier is ideal, but an op amp can come close,

at least with regard to gain at low frequency.

The typical IC op amp has an open loop gain of 106 and a

low frequency input impedance of about 1012 ohms.


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Amplifiers in any system form are often represented by a

block diagram such as shown below.

The input voltage signal is denoted as Vi(t) and the

output voltage signal is denoted as Vo(t). The quantity t

refers to time. And the functions Vi(t) and Vo(t) represent

the fact that both voltages are functions of time.


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Input and output signal of an IDEAL AMPLIFIER


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VOLTAGE GAIN, A

GAIN - ratio of the output signal to the input signal. Thesignal may be in the form of current for current gain (Ai,

or ), power for power gain (Ap or G), or voltage for

voltage gain (A orAv).

A = Vo(t) / Vi(t)

And Vo(t) = A Vi(t)

If the amplifier is not perfectly linear, the equation will nolonger be correct. The equation assumes that the amplifier

is ideal.


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EXAMPLE 1

The voltage gain ofr an essentially linear amplifier isdetermined from oscilloscope. The waveforms are shown

below. Determine the voltage gain.


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ANSWER:

A = output voltage / input voltage

= (2 V/division)(3 divisions) / (0.05 V/division)(4 divisions)A = 30


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SOURCE MODELS

All sources of electrical energy can be represented interms of either voltage sources or current sources.

Ideal Voltage Source and Ideal Current Source


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IDEAL SOURCES their values are independent of any

external loads connected to the devices.

IDEAL VOLTAGE SOURCE

-Assumed to generate a voltage Vs, which is independent

of the current flowing through the source. The (+) and (-)

terminals show the respective positive and negativeterminals for the voltage.

-Have zero internal resistance

IDEAL CURRENT SOURCE

-Assumed to generate a current Is, which is independent of

the voltage across the source. The arrow indicates the

assumed positive reference direction for the current.

-Have infinite internal resistance


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Practical sources may be modeled b a combination of an

ideal source and one or more passive circuit components.

In a wide variety of situations, at relatively low frequencies,the passive component is resistance.

Thevenin and Norton Models for more practical sources


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Either of the models may be used to represent a practical

source provided that the only significant passive circuit

parameter is resistance.

Is = Vs/ Rs

And

Vs = Is Rs


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EXAMPLE 2

The open circuit voltage of a transducer output is 80 mV.The equivalent output resistance is 2 kohms. Determine

two circuit models for the source.


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Is = Vs/Rs

= 80 mV / 2 kohms

= 40 A

ANSWER:


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CONTROLLED-SOURCE MODELS

There are four possible combinations of input output

control, and all of these occur in actual systems:

1. Voltage- controlled voltage source

2. Voltage- controlled current source

3. Current controlled voltage source

4. Current- controlled current source


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1. VOLTAGE-CONTROLLED VOLTAGE SOURCE (VCVS)

- The most common combination

- A is the voltage gain


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2. VOLTAGE-CONTROLLED CURRENT SOURCE (VCIS)

-The value of the current at the output is io = gm Vi

- gm is the transconductance of the device, in Siemens S


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3. CURRENT- CONTROLLED VOLTAGE SOURCE (ICVS)

- The value of the voltage at the output is Vo = Rm Ii

- Rm is the transresistance of the device, in ohms.


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4. CURRENT- CONTROLLED CURRENT SOURCE (ICIS)

- The value of the output current is io = ii- is the current gain


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COMPLETE AMPLIFIER SIGNAL MODEL

Block diagram of a linear amplifier and a common form of a signal

model utilizing a VCVS


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INPUT IMPEDANCE

- Is the effective impedance across the two input terminals

as seen by a signal source

OUTPUT IMPEDANCE

- Is the impedance portion of the Thevenin or Norton

equivalent circuit as viewed at the output terminals.

VOLTAGE GAIN

- output signal voltage/ input signal voltage


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ANSWER:


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INPUT AND OUTPUT LOADING EFFECTS

Connection of an amplifier to a signal source and load


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NET VOLTAGE GAIN FROM THE OPEN-CIRCUIT

VOLTAGE TO THE OUTPUT LOAD VOLTAGE, Aso

From the input circuit,

From the output circuit,

Substituting equation 1 to equation 2,


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Rearranging the terms,


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CASCADE LOADING EFFECTS

Cascade connection of two amplifier stages to a signal source and load


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The voltage Vi1 at the input of stage 1 is:

The voltage Vi2 at the input of the second stage is:

Then the output voltage across the load is:


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Dividing both sides by Vs,

Rearranging the terms,


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ANSWER:

a. Aso = 12.99

b. Vi = 0.1818 V

Vo open circuit = 9.09 V

Vo loaded circuit = 2.958 V


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DECIBEL GAIN COMPUTATIONS

Decibel gain and loss relationships are widely used in

analyzing and specifying linear amplifier circuits.

The decibel power gain GdB in decibels is defined by:

GdB = 10 log10G = 10 log10 (Po/Pi)

POWER GAIN, G

is defined as:

G = Po/ Pi


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Assuming that Po is delivered to an RL and that input impedance

is Rin,

Then,

Note that:

Assuming that RL = Rin


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Power input and output comparison for a linear amplifier

Thus, a factor of 10 appears in decibel computationinvolving power gain and a factor of 20 appears when

voltage and current gains are used.


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DECIBEL VOLTAGE GAIN

When two or more stages are connected in cascade,

decibel measures are particularly convenient to use indealing with combination

Cascaded amplifier connection


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The net voltage gain is determined in absolute form as

the product of all the individual gains.

The decibel gain is:

The net decibel gain is the sum of the individual decibel

gains for the different stages.


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When the output voltage is less than the input voltage, the

decibel voltage gain is negative.

A negative voltage gain should not be confused withnegative linear gain. The former corresponds to the

reduction of the signal level through the circuit, while the

latter corresponds to an inversion of the polarity.


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Voltage gains and their equivalents


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DECIBEL VOLTAGE LOSSES

For voltage divider networks, it is usually moreconvenient to work with losses rather than gains.

Negative gain, therefore is a positive loss and Positive

gain is a negative loss.


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EXAMPLE 5

Determine the decibel gain of the complete amplifier circuitby combining the decibel gain of the amplifier with the

decibel losses of the input and output circuits.


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ANSWER:

i dB = 2.5 dB

o dB = 1.94 dB

Aso dB = 29.54 dB


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FREQUENCY RESPONSE CONSIDERATIONS

All linear circuits have frequency-limiting characteristics.

PHASORS


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The complex impedance Z is defined as:

Z = V/I

Since Z is complex,

Z = R + jX

R is the resistance and X is the reactance.

Y is admittance. Y = I/V = 1/ Z

Admittance Y,

Y = G + jB

G is the conductance and B is the susceptance.


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THE THREE BASIC CIRCUIT PARAMETERS IN

COMPLEX IMPEDANCES


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The radian frequency, in radians per second is related to

the cyclic frequency f by:

Resistance is represented by:

Zc = 1/jwC

And ZL = jwL


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TRANSFER FUNCTION

A complex function H (j) can be defined as:

The transfer function H(j ) is called the steady-state

transfer function for the circuit. The steady state transfer

function is a generalization of the gain to the case where

frequency-dependent elements are present, and it

provides a mathematical basis for the output/input ratio.

Since H(j ) is a complex function, it can be represented in

polar form as:


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M() = /H(j)/ is the magnitude or amplitude of the

complex function, and () is the phase shift for the

same function .

Development of steady-state transfer function concept


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1. Type of amplifier that is used primarily in wireless

receivers, also employed in acoustic pickups, audio

tape players, and compact disc players.

A. Weak signal

B. Power

C. Ideal

D. Signal

RECITATION


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2. A/n _____ uses a small input signal to create a large

output signal, while minimizing distortion of the

waveform.

A. Amplifier

B. Transformer

C. Attenuator

D. Buffer

RECITATION


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3. In a VCIS, gm is the ____ .

A. Transconductance

B. Current gainC. Transresistance

D. Voltage gain

RECITATION


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4. For two amplifiers in cascade, which of the following

relationships is false?

A.A

t =A

1 +A

2B. At dB= 20 log A1 + 20 log A2

C. Aso = ILF X A1 X IFBS X A2 X O LF

D. At dB = 20 log (A1A2)

RECITATION


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5. Which of the following is False about transfer functions?

A. It is a generalization of the gain to the case where

frequency-dependent elements are presentB. It provides a mathematical basis for the output/input

ratio.

C. H(j) = M() () where M() is the amplitude

response and () is the phase response.

D. None of the above

RECITATION


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6. Differentiate linear electronics from digital electronics.

7. Define amplifier and ideal amplifier.

8. Define an ideal source and a dependent source.9. Enumerate the different dependent sources.

10. Draw the block diagram of a complete amplifier model

utilizing the VCVS.

11. Define gain, power gain, voltage gain and current gain.12.Explain the relationships of dB power, voltage and current

gains.

13.Explain the relationship between decibel loss and decibel

gain.

14.Explain the effect of input and output loads to the voltagegain of an amplifier.

15.Derive the gain formula for a cascaded amplifier.


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SEATWORK 1

I. ANALYSIS PROBLEMS:

1. A signal source having an open-circuit voltage of 30 mV

and an internal output resistance of 2.5 kohms is

connected to the input of the amplifier circuit (with Ri = 5

kohms, Ro = 100 ohms, open circuit voltage gain is200) and a 300 ohms resistive load is connected across

the output.

a. Draw the complete equivalent circuit.

b. Calculate the net loaded voltage gain Aso between

the open circuit source voltage and the load.c. Calculate the amplifier input and output voltages from

the circuit model under loaded conditions.

d. Use the result of part (b) to predict the output voltage

directly and compare it with the result obtained in (c).


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2. Two linear amplifier circuits are connected in cascade,

and the source and load are connected as shown below:

a. Draw the complete equivalent circuit.

b. Calculate the net loaded voltage gain Aso between the

open-circuit source voltage and the load.

c. For Vs = 40 mV, determine Vi1, Vi2 and Vo from thecircuit model.

d. Use the result of part (b) to predict the output voltage

directly, and compare it with the value obtained in part

(c).


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II. DERIVATION PROBLEM:

3. Assume that an amplifier circuit is matched at both inputand output; that is, the source internal resistance is equal

to the input resistance, and the load resistance is equal to

the output resistance. Show that the loaded gain is:

Aso = A/4


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ASSIGNMENT 1

I. DESIGN PROBLEMS:

1. A certain amplifier is to be selected to amplify the signal

between a 1 kohms resistance source and a 5 kohms

load. If the signal loss due to loading effects at each

end is not to exceed 0.5 dB( that is 1 dB in total),

determine:a. the minimum value of input impedance

b. the maximum value of output impedance.

2. A certain amplifier with an adjustable gain A is to be

placed between a 500 ohm resistive source and a 2

kohms resistive load. The input and outputimpedances of the amplifier are 1.5 kohms and 500

ohms respectively. The open circuit source voltage is

50 mV, and it is desired to establish 4V across the

load. Determine the required value ofA

.


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II. RESEARCH:

3. Bode plot

4. One pole low pass model of amplifiers

RC Low-pass Circuit

Break-point approximations


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END

elex3_general amp concepts

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