App_II_CH1_Feedback.pdf

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CHAPTER 1 FEEDBACK AMPLIFIERS

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1.1 INTRODUCTION

In electronics I, we have seen small-signal voltage gain and other characteristics of transistors

are function of transistor parameters. In general, these parameters vary with temperature and they

have range of values for a given type of transistor. This means that the Q-point, voltage gain, and

other circuit properties can vary from one circuit to another, and can be function of temperature.

Such transistor circuit characteristics can be made essentially independent of the individual

transistor parameters by using feedback.

Feedback is the process where by a portion of the output is returned to the input to form part of

the system excitation. There are two basic types of feedback: negative feedback & positivefeedback.

Negative feedback: In this case the feedback signal is out of phase with the input signal. The

amplifier introduces a 1800

phase shift into the circuit, while the feedback network does not.

Positive feedback: In this case the feedback signal is in phase with the amplifier input signal.

Both the amplifier and the feedback signal introduce a 1800

phase shift. The result is a 3600

phase shift around the loop, causing the feedback signal to be in phase with the original signal.

The positive feedback is used in oscillator circuits. In this chapter, we will concentrate on

negative feedback.

Negative feedback circuits bring a number of improvements with some reduction of the gain,

among them being:

1 Better stabilized voltage gain: variations in the gain as a result of change in transistor

parameter are reduced by feedback. This reduction in sensitivity of gain is one of the most

attractive features of negative feedback.

2. Increase in bandwidth: the bandwidth of the circuit that incorporates negative feedback is

larger than the basic amplifier.

3. Reduction of non-linear distortion: negative feedback reduces the large signal distortion that

could arise due to the non-linear response of the transistor.

4. Minimize noise sensitivity: negative feedback may increase signal to noise ratio if noise is

generated with the feedback loop.


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5. Control of impedance level: the input and output impedances can be increased or decreased

using the appropriate type of negative feedback circuit.

On the other hand, negative feedback circuits have disadvantages like reduction in the overall

gain (the price required to improve circuit performance), and instability (oscillation) at high

frequencies.

1.2 Basic representation of feedback amplifiers

In feedback representation we may sample the output voltage or current by means of a suitable

sampling network and apply this signal to the input through the feedback two port networks as

shown below.

At the input the feedback signal is combined with the signal through the mixer network and is

feed into the amplifier. The signal source of the feedback amplifier is either a signal voltage or a

signal current.

The feedback network is usually a passive two port network which may contain resistors,

capacitors, and inductors. Most often it is simply a resistive configuration. The output voltage is

sampled by connecting the feedback network in shunt across the output for voltage sampling

and forcurrent sampling the feedback network is connected in series with the output.

Figure 1.1: Representation of any single-loop feedback amplifier


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1.3 Basic Topologies of feedback amplifiers:

There are four basic ways of connecting the feedback signal. Both voltage and current can be

feedback to the input either in series or parallel. Specifically, there can be:

1.

Voltage-series feedback (Fig. 1.2a).2. Current-series feedback (Fig. 1.2b).3. Current-shunt feedback (Fig. 1.2c).4. Voltage-shunt feedback (Fig. 1.2d).

Figure 1.2 feedback-amplifier topologies.

The source resistance Rs is considered to be part of the amplifier, and the transfer gain A (Av,

Gm, Ai, Rm) includes the effect of the loading of the network upon the amplifier.


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Voltage amplifiers:

If the amplifier input resistance Ri is large compared with the source resistance Rs then Vi Vs. If

the external load resistance RL is large compared with the output resistance Ro of the amplifier,

then VoAv Vi Av Vs. This amplifier provides a voltage output proportional to the voltage

input, and the proportionality factor is independent of the magnitude of the source and loadresistances. Such a circuit is called a voltage amplifier. An ideal voltage amplifier must have

infinite input resistance and zero output resistance.

Figure 1.3 voltage amplifier

Current amplifiers:

If the amplifier input resistanceRi is low/ zero compared with the source resistance Rs then Ii Is

and if Ro >> RL, I L Ai Ii Ai Is. A current amplifier is an amplifier which provides an output

current proportional to the signal current, and the proportionality factor is independent of Rs and

RL. Hence the output current is proportional to the signal current.An ideal current amplifier must

have zero input resistance and infinite output resistance.

Figure 1.4 current amplifier


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Transconductance amplifier

This amplifier supplies an output current which is proportional to the signal voltage,

independently of the magnitude of Rs and RL.It has an infinite input resistance Ri and infinite

output resistance Ro. Since it has large input resistance, it must be driven by a low resistance

source. It presents a high output resistance and hence drives a low resistance load.

Vi Vs for Ri >> Rs andIo GMVi GMVs , ifRo>>RL Note that GM=Io / Vi

Figure 1.5 Transconductance amplifier

Transresistance amplifier

This amplifier provides an output voltage Vo in proportion to the signal current Is independently

of Rs and RL. In this case Ri Ri , Ii Is, and ifRo


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1.4 EFFECTS OF NEGATIVE FEEDBACK

Generally, we can model all types of feedback amplifiers using the following block diagram. S s is any

input signal (voltage or current) that is supplied by a source. S f is a sample of the output feedback to the

input through the mixer. Si is the net input (error) signal given to the amplifier.

SoSs

Sf

A

_

+ SiSource Load

Figure 1.2: Negative feedback amplifier model

1. Gain reductionThe ration of the output and the input without feedback is given as,

The portion of the output feed to the input is,

Thus, the net signal given to the amplifier is therefore,

Hence, the gain of the feedback circuit is given by

Where ( is the feedback factor.

The effect of negative feedback is that for the price of gain reduction, many desirable

characteristics are obtained.

2. Change in Input and output impedanceConsider the voltage-series feedback circuit shown in the figure 1.3.


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Vs

Vf_

+

Vo_

+

_

+

Zif

Zi

Is Zo

Zof

Vi_

+

AVi

Figure 1.3: Voltage-Series feedback

The input impedance of the feedback circuit can be evaluated as,

The output impedance is determined by Appling a voltage V, resulting a current I, and shorting

the input terminal, Vs=0 in the fig. 1.3.

The voltage V is then,

For, Vs=0,

So that

Rearranging terms we have

Therefore, the output impedance with feedback:

Note: similar approach can be followed to determine the input and output impedance of the

remaining feedback circuits. However, it is very important to note that A and are different for

different types of feedback amplifiers.

Summary of effects of feedback on the input and output impedance is provided in the table

below and the derivation is left for the students as exercise.


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Voltage-series Voltage-shunt Current-series Current-shunt

increased decreased increased decreased

decreased decreased increased increased

From the table above, voltage (shunt) feedback tends to decrease impedance, and current (series)

feedback tends to increase impedance.

3. Gain StabilityIn addition to the factor setting a precise gain value, we are also interested in how stable the

feedback amplifier is compared to an amplifier without feedback.

Differentiating Eq. (1.1) leads to

This shows that magnitude of the relative change in gain is reduced by the factor of

compared to that without feedback.

4. Reduction in frequency distortionFor a negative-feedback amplifier having , the gain with feedback is . It follows

that if the feedback network is purely resistive, the gain with feedback is not dependent on

frequency even though the basic amplifier gain is frequency dependent. Practically, the

frequency distortion arising because of varying amplifier gain with frequency and it is

considerably reduced in a negative-voltage feedback amplifier circuit.

5. Bandwidth extensionIt is interesting to note that the product of gain and frequency remains the same so that the gain

bandwidth product of the basic amplifier is the same value for the feedback amplifier. Since the

feedback amplifier has lower gain, the net operation was to trade gain for bandwidth so that it

increases for any decrease in gain. See fig. 1.4.


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Mathematically, it can be expressed as

Figure 1.4 Effect of feedback on bandwidth.

SUMMARY OF EFFECT OF NEGATIVE FEEDBACK


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1.5 ANALYSIS OF FEEDBACK AMPLIFIER

To find Af, Rif, and Rofthe following steps are carried out:

1. Identify the topology as indicated below. Tests for the type of sampling are the following: Set VO = 0 (that is, set RL = 0). If Xf becomes zero, the original system

exhibited voltage sampling.

Set Io= 0 (that is set RL= ). If Xfbecomes zero, current sampling waspresent in the original amplifier.

2. Draw the basic amplifier circuit without feedback.To find the input circuit:

Set VO = 0 for voltage sampling. In other words, short circuit theoutput node. Set IO = 0 for current sampling. In other words open circuit the output

loop.

To find the output circuit:

Set Vi = 0 for shunt comparison. In other words, short circuit the inputnode (so that none of the feedback current enters the amplifier input).

Set Ii= 0 for series comparison. In other words, open circuit the inputloop. (So that none of the feedback voltage reaches the amplifier

input).

3. Use a Thevenins source if Xfis a voltage and a Nortons source if Xfis a current.4. Replace the active device by the proper model.5. Indicate Xfand Xo on the circuit obtained by carrying out steps 2, 3, and 4.

Evaluate

6. Evaluate A by applying KVL and KCL to the equivalent circuit obtained after step 4.7. From A and , Find D, Af, Rif, Rof

We will illustrate the approximate analysis procedure in the following examples.


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Example 1: For the following emitter-follower amplifier, determine the type of feedback, gain,

input and output impedance.

Vs

Vo

VCC

RBRC

REVf

Vs

VoRB

RC

REVf

Vs

Vi_

+

+

_

(b)(a)

Feedback type:

Looking at the second figure (fig. b), the output voltage is sampled and feedback to the circuit in

the form of voltage. Such type of feedback is called voltage-series feedback.

Equivalent cir cuit without feedback:

Input circuit: setting (shorting the output), E terminal appears at the ground.

Output circuit: setting (opening the input), , and the current source appears in series

with the output circuit.

Therefore, the equivalent circuit without feedback resembles the one shown here.

Vs

_

+

Zi

hie

IsZo

Vi Ii

hfeIiRB

RC

+

_

=Vf REVo

The gain of the amplifier without feedback; _


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The feedback parameter

Thus, the gain of the feedback amplifier is

Input impedance

Output impedance

Example 2: For the following amplifier, determine the type of feedback, voltage gain, input and

output impedance.

Vs

Vo

VCC

RBRC

REVf

Vs

RB

RC

REVf

Vs

+

_

(b)(a)

Vo

Io

Type of topology:

The output current is sampled and fed back to the input in the form of voltage. Therefore, it is

current-series feedback amplifier.


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Input circuit: setting (opening the output), appears in series with the input circuit.

Output circuit: setting (opening the input), appears in series with the output circuit

Therefore, the equivalent circuit without feedback resembles the one shown here.

Vs Vo_

+

_

+

Zi

hie

IsZo

Vi

RE RE

IoIi

hfeIiRBVf

+_

The gain of the amplifier without feedback is



The voltage gain then is calculated as

Input impedance

Output impedance looking back to the circuit just before is


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Hence, the output impedance looking back to the circuit after is

Example 3:For the following amplifier, determine the type of feedback and voltage gain.

Vs

VDD

rs

RD

(a)

RFVo

Is rs

(b)

RF

Source

transfromation IF

Ii

Vo

+

_

RS

RD

Type of feedback: the output voltage is sampled and fed back to the input in the form of current,

hence, voltage-shunt feedback.


Input circuit: is determined by setting Vo=0,

Output circuit: is determined by setting Vi=0 or shorting the input terminal

Is

rs Vo

+

_

RDvgs gmvgs

+

_

RF RF

The gain of the amplifier without feedback is

If , then the gain will be simplified as


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The voltage gain then is calculated as

References:

1 ROBERT BOYLESTAD AND LOUIS NASHELSKY, ELECTRONIC DEVICES AND CIRCUIT THEORY,7th

EDITION

2 JACOB MILLMAN ,MICROELECTRONICS, 2ND

EDITION

Date post:	03-Apr-2018
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