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Chapter 8 Feedback . Introduction 8.1 The general feedback structure 8.2 Some properties of negative feedback 8.3 The four basic feedback topologies 8.4 The series-shunt feedback amplifier 8.5 The series-series feedback amplifier 8.6 The shunt-shunt and shunt-series feedback amplifier

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Chapter 8 feedback l.jpg

Chapter 8 Feedback

Introduction

8.1 The general feedback structure

8.2 Some properties of negative feedback

8.3 The four basic feedback topologies

8.4 The series-shunt feedback amplifier

8.5 The series-series feedback amplifier

8.6 The shunt-shunt and shunt-series feedback amplifier

8.10 Stability study using bode plot

8.11 Frequency compensation


Introduction l.jpg

It’s impossible to think of electronic circuits without some forms of feedback.

Negative feedback

Desensitize the gain

Reduce nonlinear distortion

Reduce the effect of noise

Control the input and output impedance

Extend the bandwidth of the amplifier

The basic idea of negative feedback is to trade off between gain and other desirable properties.

Positive feedback will cause the amplifier oscillation.

Introduction


Three parts l.jpg

PartI: The basic concept and some Properties of negative feedback

PartII: The four basic feedback and analysis

PartIII: The loop gain, stability problem

and frequency compensation

Three Parts:


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PartI feedback

The basic concept

Judgment and Properties

of feedback

examples


Parti the basic concept and some properties of negative feedback l.jpg
PartI: The basic concept and some feedbackProperties of negative feedback

8.1 The General Feedback Structure

This is a signal-flow diagram, and the quantities x represent either voltage or current signals.

In electronic circuits, part of or all output signal is fed back to input, and affects the input signal value, which is called feedback.



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Negative feedback and positive feedback feedback:

According to the effecting of feedback

1) positive feedback increases the signal that appears

at the input of the basic amplifier

2) negative feedback reduces the signal that appears

at the input of the basic amplifier

  • DC feedback and AC feedback:

  • Feedback quantity only contains DC quantity,is called DC

  • feedback

  • 2) Feedback quantity only contains AC quantity,is called AC

  • feedback

  • Usually AC feedback and DC feedback are concomitant


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The feedback judgment feedback:

  • No feedback

  • Feedback exists

  • No feedback


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The judgment of feedback parity feedback

Instantaneous polarity method:

1) Regulate the polarity of input signal relative to

ground at sometime.

2) Decide all points’ parity step by step, at last get

the parity of output signal.

3) According to the parity of output signal decides the

parity of amount of feedback.

4) If amount of feedbackincreases the signal that

appears at the input of the basic amplifier, the circuit

inducts the positive feedback. Otherwise, it inducts

the negative feedback.


Slide10 l.jpg

To integrated operational amplifiers feedback,the input quantity can be UD or iN(iP)


Slide11 l.jpg

To discrete components amplifiers feedback,the input quantity can be Ube or ib


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The judgment of DC feedback and AC feedback feedback

DC feedback,no AC feedback

AC feedback,no DC feedback


Example feedback positive or negative dc or ac l.jpg
Example feedback:feedback?Positive or negative?DC or AC?

AC and DC negative feedback


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The General Feedback Equation feedback

  • Open loop gain A

  • Feedback factor β

  • Loop gain Aβ

  • Closed loop gain Af

  • Amount of feedback (1+ Aβ)


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The General Feedback Equation feedback

  • If Aβ >>1, The gain of the feedback amplifier is almost entirely determined by the feedback network.

  • If Aβ >>1, which implies that the signal Xi at the input of the basic amplifier is reduced to almost zero.


8 2 some properties of negative feedback l.jpg

Gain desensitivity feedback

8.2 Some Properties of Negative Feedback

the percentage change in Af (due to variations in some circuit parameter) is smaller than the percentage change in A by the amount of feedback. For this reason the amount of feedback,

1 + Aβ, is also known as the desensitivity factor.


Some properties of negative feedback l.jpg

2. Bandwidth extension feedback

Some Properties of Negative Feedback

Note that the amplifier bandwidth is increased by the same factor by which its midband gain is decreased, maintaining the gain-bandwidth product at a constant value.


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3. Noise reduction feedback

Some Properties of Negative Feedback


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Some Properties of Negative Feedback feedback

4. Reduction in nonlinear distortion


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Some Properties of Negative Feedback feedback

4. Reduction in nonlinear distortion


Homework l.jpg

May 11th, 2008 feedback

8.1; 8.7;

Homework:


Partii the four basic feedback and analysis l.jpg
PartII: feedbackThe four basic feedback and analysis


8 3 the four basic feedback topologies l.jpg

Voltage amplifier---series-shunt feedback feedback

voltage mixing and voltage sampling

8.3 The Four Basic Feedback Topologies


The four basic feedback topologies l.jpg

Current amplifier---shunt-series feedback feedback

Current mixing and current sampling

The Four Basic Feedback Topologies


Example l.jpg
Example: feedback

Figure 8.5 A transistor amplifier with shunt–series feedback. (Biasing not shown.)


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Transconductance amplifier---series-series feedback feedback

Voltage mixing and current sampling

The Four Basic Feedback Topologies


Example27 l.jpg
Example: feedback

Figure 8.6 An example of the series–series feedback topology. (Biasing not shown.)


The four basic feedback topologies28 l.jpg

Transresistance amplifier---shunt-shunt feedback feedback

Current mixing and voltage sampling

The Four Basic Feedback Topologies


Example29 l.jpg
Example: feedback

Figure 8.7 (a) The inverting op-amp configuration redrawn as (b) an example of shunt–shunt feedback.


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May 11nd, 2008 feedback

8.14; 8.15; 8.17; 8.19

Homework:


8 4 the series shunt feedback amplifier l.jpg

The ideal situation feedback

The practical situation

Summary

8.4 The Series-Shunt Feedback Amplifier


The ideal situation l.jpg
The Ideal Situation feedback

  • A unilateral open-loop amplifier (A circuit).

  • An ideal voltage mixing voltage sampling feedback network (β circuit).

  • Assumption that the source and load resistance have been included inside the A circuit.


The ideal situation33 l.jpg
The Ideal Situation feedback

Equivalent circuit.

Rif and Rof denote the input and output resistance with feedback.


Input and output resistance with feedback l.jpg

Input resistance feedback

In this case, the negative feedback increases the input resistance by a factor equal to the amount of feedback.

Output resistance

In this case, the negative feedback reduces the output resistance by a factor equal to the amount of feedback.

Input and Output Resistance with Feedback


The practical situation l.jpg
The Practical Situation feedback

  • Block diagram of a practical series–shunt feedback amplifier.

  • Feedback network is not ideal and load the basic amplifier thus affect the values of gain, input resistance and output resistance.


The practical situation36 l.jpg
The Practical Situation feedback

The circuit in (a) with the feedback network represented by its h parameters.

Omit the controlled source h21I1


The practical situation37 l.jpg
The Practical Situation feedback

The circuit in (b) with h21 neglected.


The practical situation38 l.jpg

The load effect of the feedback network on the basic amplifier is represented by the components h11 and h22.

The loading effect is found by looking into the appropriate port of the feedback network while the port is open-circuit or short-circuit so as to destroy the feedback.

If the connection is a shunt one, short-circuit the port.

If the connection is a series one, open-circuit the port.

Determine the β.

The Practical Situation


Summary l.jpg

R amplifier is represented by the components i and Ro are the input and output resistances, respectively, of the A circuit.

Rif and Rof are the input and output resistances, respectively, of the feedback amplifier, including Rs and RL.

The actual input and output resistances exclude Rs and RL.

Summary


Example of series shunt feedback amplifier l.jpg
Example of Series-Shunt Feedback Amplifier amplifier is represented by the components


Example of series shunt feedback amplifier42 l.jpg

Op amplifier connected in noninverting configuration with the open-loop gain μ, Rid and ro

Find expression for A, β, the closed-loop gain Vo/Vi , the input resistance Rinand the output resistance Rout

Find numerical values

Example of Series-Shunt Feedback Amplifier




8 5 the series series feedback amplifier l.jpg

The ideal situation the open-loop gain

The practical situation

Summary

8.5 The Series-Series Feedback Amplifier


The ideal situation46 l.jpg
The Ideal Situation the open-loop gain

Transconductance gain


The ideal situation47 l.jpg
The Ideal Situation the open-loop gain

Tranresistance feedback factor


Input and output resistance with feedback48 l.jpg

Input resistance the open-loop gain

In this case, the negative feedback increases the input resistance by a factor equal to the amount of feedback.

Output resistance

In this case, the negative feedback increases the output resistance by a factor equal to the amount of feedback.

Input and Output Resistance with Feedback


The practical situation49 l.jpg
The Practical Situation the open-loop gain

Block diagram of a practical series–series feedback amplifier.

Feedback network is not ideal and load the basic amplifier thus affect the values of gain, input resistance and output resistance.


The practical situation50 l.jpg
The Practical Situation the open-loop gain

The circuit of (a) with the feedback network represented by its z parameters.


The practical situation51 l.jpg
The Practical Situation the open-loop gain

A redrawing of the circuit in (b) with z21 neglected.


The practical situation52 l.jpg

The load effect of the feedback network on the basic amplifier is represented by the components Z11 and Z22.

Z11 is the impedance looking into port 1 of the feedback network with port 2 open-circuited.

Z22 is the impedance looking into port 2 of the feedback network with port 1 open-circuited.

Determine the β.

The Practical Situation


Summary54 l.jpg

R amplifier is represented by the components i and Ro are the input and output resistances, respectively, of the A circuit.

Rif and Rof are the input and output resistances, respectively, of the feedback amplifier, including Rs and RL.

The actual input and output resistances exclude Rs and RL.

Summary


Example of series series feedback amplifier l.jpg
Example of Series-Series Feedback Amplifier amplifier is represented by the components


Example of series series feedback amplifier56 l.jpg
Example of Series-Series Feedback Amplifier amplifier is represented by the components


Example of series series feedback amplifier57 l.jpg
Example of Series-Series Feedback Amplifier amplifier is represented by the components


Example of series series feedback amplifier58 l.jpg
Example of Series-Series Feedback Amplifier amplifier is represented by the components


8 6 the shunt shunt and shunt series feedback amplifiers l.jpg
8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifiers amplifier is represented by the components

Fig8.19. Ideal structure for the shunt-shunt feedback amplifier.


The practical shunt shunt feedback amplifier l.jpg
The practical Shunt-Shunt feedback amplifier amplifier is represented by the components


Example 8 3 l.jpg
Example 8.3 amplifier is represented by the components


The shunt series configuration l.jpg
The shunt-series configuration amplifier is represented by the components

Fig 8.22 Ideal structure for the shunt–series feedback amplifier.


A practical shunt series feedback amplifier l.jpg
A practical shunt-series feedback amplifier amplifier is represented by the components


Example 8 4 l.jpg
Example 8.4 amplifier is represented by the components


Summary69 l.jpg
summary amplifier is represented by the components


The method of finding a circuit l.jpg

h,z,r,g parameter method for two-port feedback network. amplifier is represented by the components

Equivalent circuit method:

Find the feedback network;

Find the feedback network equivalent load Resistance to amplifier input, for output voltage sampling feedback, output short-circuit (Vo=0);for current sampling feedback, output Io open-circuit (Io=0).

Find the feedback network equivalent load Resistance to amplifier output, for input voltage mixing feedback, it should be disconnected from input to feedback network (Ii=0); for input current mixing feedback, let input connect to ground to disconnect from input signal to feedback network.

The method of finding A circuit


Slide71 l.jpg
引入负反馈的一般原则 amplifier is represented by the components

  • 为稳定静态工作点,应引入直流负反馈;

  • 为改善电路动态性能,应引入交流负反馈;

  • 当信号源为恒压源或内阻较小的电压源时,应引入串联负反馈;

  • 当信号源为恒流源或内阻较大的电压源时,应引入并联负反馈;


Slide72 l.jpg

  • 当负载需要稳定的电压信号时,应引入 amplifier is represented by the components 电压负反馈;

  • 当负载需要稳定的电流信号时, 应引入电流负反馈;

  • 若将电流信号转换成电压信号,应引入电压并联负反馈(shunt-shunt);

  • 若将电压信号转换成电流信号, 应引入电流串联负反馈(series-series)。


Example73 l.jpg
Example: amplifier is represented by the components

1)减小放大电路从信号源索取的电流并增强带负载的能力

2)将输入电流转换成与之成稳定稳定线性关系的输出电流

3)将输入电流转换成稳定的输出电压

答:引入series-shunt (电压串联负反馈) :8连10,3连9,4连6

答:引入shunt-series(电流并联负反馈):7连10,2连9;4连6

答:shunt-shunt(电压并联负反馈):2连9,8连10,5连6


Homework74 l.jpg

May 13th, 2008 amplifier is represented by the components

8.20; 8.25; 8.30; D8.37

Homework:


The stability problem l.jpg
The Stability Problem amplifier is represented by the components


The stability problem76 l.jpg

The condition for negative feedback to oscillate amplifier is represented by the components

Any right-half-plane poles results in instability.

Amplifier with a single-pole is unconditionally stable.

Amplifier with two-pole is also unconditionally stable.

Amplifier with more than two poles has the possibility to be unstable.

Stability study using bode plot

The Stability Problem


Slide77 l.jpg

Balance condition: amplifier is represented by the components

Magnitude condition:

Phase Condition:

Start up oscillation condition:

Judgment method of amplifier stability:

1) If ω180 is not exist, then the Amplifier is stable;

2) If ω180 is exist and ω180< ω1, then the amplifier is not stable;

3) If ω180 is exist and ω180> ω1, then the amplifier is stable;


The definitions of the gain and phase margins l.jpg
The Definitions of the Gain and Phase margins amplifier is represented by the components

  • Gain margin represents the amount by which the loop gain can be increased while stability is maintained.

  • Unstable and oscillatory

  • Stable and non-oscillatory

  • Only when the phase margin exceed 45º or gain margin exceed 6dB, can the amplifier be stable.


Example79 l.jpg
Example: amplifier is represented by the components


Effect of phase margin on closed loop response l.jpg
Effect of phase margin on closed-loop response amplifier is represented by the components

  • To see the relationship between phase margin and Close-Loop gain, consider a feedback amplifier with a large low-frequency loop gain.


Slide81 l.jpg

Stability analysis using Bode plot of | amplifier is represented by the components A|.


Stability analysis using bode plot of a l.jpg

Gain margin and phase margin amplifier is represented by the components

The horizontal line of inverse of feedback factor in dB.

A rule of thumb:

The closed-loop amplifier will be stable if the 20log(1/β) line intersects the 20log|A| curve at a point on the –20dB/decade segment.

The general rule states:

At the intersection of 20log[1/ | β (jω)| ] and 20log |A(jω)| the difference of slopes should not exceed 20dB/decade.

Stability Analysis Using Bode Plot of |A|


Frequency compensation l.jpg

The purpose is to modifying the open-loop transfer function of an amplifier having three or more poles so that the closed-loop amplifier is stable for any desired value of closed-loop gain.

Theory of frequency compensation is the enlarge the –20dB/decade line.

Implementation

Capacitance Cc added

Miller compensation and pole splitting

Frequency Compensation


Frequency compensation84 l.jpg
Frequency Compensation of an amplifier having three or more poles so that the closed-loop amplifier is stable for any desired value of closed-loop gain.


Frequency compensation miller compensation l.jpg
Frequency Compensation of an amplifier having three or more poles so that the closed-loop amplifier is stable for any desired value of closed-loop gain.-Miller compensation

  • A gain stage in a multistage amplifier with a compensating capacitor connected in the feedback path

  • An equivalent circuit.

  • Miller compensation can reduce the value of C


Homework87 l.jpg

May 20 of an amplifier having three or more poles so that the closed-loop amplifier is stable for any desired value of closed-loop gain.th, 2008

8.51; 8.54; 8.63; 8.66

Homework:


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