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 1

Introduction 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.

Three Parts: 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

Judgment and Properties PartI The basic concept Judgment and Properties of feedback examples

PartI: The basic concept and some Properties 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.

The feedback judgment for amplifier circuits

Negative feedback and positive 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 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 Usually AC feedback and DC feedback are concomitant

The feedback judgment ： No feedback Feedback exists

The judgment of feedback parity 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 feedback increases the signal that appears at the input of the basic amplifier, the circuit inducts the positive feedback. Otherwise, it inducts the negative feedback.

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

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

The judgment of DC feedback and AC feedback DC feedback，no AC feedback AC feedback，no DC feedback

Example ：feedback？Positive or negative？DC or AC？ AC and DC negative feedback

The General Feedback Equation Open loop gain A Feedback factor β Loop gain Aβ Closed loop gain Af Amount of feedback (1+ Aβ)

The General Feedback Equation 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 Gain desensitivity 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 2. Bandwidth extension 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.

Some Properties of Negative Feedback 3. Noise reduction

Some Properties of Negative Feedback 4. Reduction in nonlinear distortion

Some Properties of Negative Feedback 4. Reduction in nonlinear distortion

Homework: May 11th, 2008 8.1; 8.7;

PartII: The four basic feedback and analysis

8.3 The Four Basic Feedback Topologies Voltage amplifier---series-shunt feedback voltage mixing and voltage sampling

The Four Basic Feedback Topologies Current amplifier---shunt-series feedback Current mixing and current sampling

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

Transconductance amplifier---series-series feedback The Four Basic Feedback Topologies Transconductance amplifier---series-series feedback Voltage mixing and current sampling

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

Transresistance amplifier---shunt-shunt feedback The Four Basic Feedback Topologies Transresistance amplifier---shunt-shunt feedback Current mixing and voltage sampling

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

Homework: May 11nd, 2008 8.14; 8.15; 8.17; 8.19

8.4 The Series-Shunt Feedback Amplifier The ideal situation The practical situation Summary

The Ideal Situation 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.

Rif and Rof denote the input and output resistance with feedback. The Ideal Situation Equivalent circuit. Rif and Rof denote the input and output resistance with feedback.

Input and Output Resistance with Feedback Input resistance 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.

The Practical Situation 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 Situation The circuit in (a) with the feedback network represented by its h parameters. Omit the controlled source h21I1

The Practical Situation The circuit in (b) with h21 neglected.

The Practical Situation 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.

Summary Ri 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.

Example of Series-Shunt Feedback Amplifier 41

Example of Series-Shunt Feedback Amplifier 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 Rin and the output resistance Rout Find numerical values

Example of Series-Shunt Feedback Amplifier

Example of Series-Shunt Feedback Amplifier

The practical situation Summary 8.5 The Series-Series Feedback Amplifier The ideal situation The practical situation Summary

The Ideal Situation Transconductance gain

The Ideal Situation Tranresistance feedback factor

Input and Output Resistance with Feedback Input resistance 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.

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

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

The Practical Situation 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.

Summary Ri 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.

Example of Series-Series Feedback Amplifier

Example of Series-Series Feedback Amplifier

Example of Series-Series Feedback Amplifier

Example of Series-Series Feedback Amplifier

8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifiers Fig8.19. Ideal structure for the shunt-shunt feedback amplifier.

The practical Shunt-Shunt feedback amplifier

Example 8.3

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

A practical shunt-series feedback amplifier

Example 8.4

summary

The method of finding A circuit h,z,r,g parameter method for two-port feedback network. 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.

引入负反馈的一般原则 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；

当负载需要稳定的电压信号时，应引入 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)。

Example: 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

Homework: May 13th, 2008 8.20; 8.25; 8.30; D8.37

The Stability Problem

The Stability Problem The condition for negative feedback to oscillate 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

Start up oscillation condition: Balance condition: 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 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.

Example:

Effect of phase margin on closed-loop response To see the relationship between phase margin and Close-Loop gain, consider a feedback amplifier with a large low-frequency loop gain.

Stability analysis using Bode plot of |A|.

Stability Analysis Using Bode Plot of |A| Gain margin and phase margin 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.

Frequency Compensation 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 Compensation-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

Homework: May 20th, 2008 8.51; 8.54; 8.63; 8.66