Feedback

Section 8.1

Topics

• General Feedback• Examples of Feedback Circuits– Bandwidth Extension– Gain Sensitivity– Input and Output Impedance

• Types of Amplifiers

General Feedback System

H(s)=Feedforward network, represents an amplifier, “Open-loop” transfer function, a.k.a. AG(s)=Feedback network, usually frequency independent, a.k.a, β.Y(s)/X(s)=“Closed-loop” transfer function

Behavior of a well-designed Negative Feedback System

The error term is minimized!

An accurate copy of the input.

The input of H(s) is a virtual ground because the error term is minimized!

Elements of Feedback System

• Feed forward amplifier• Means of Sensing the Output• Feedback network• Means of Generating Feedback Error

C2 senses the output voltage, converts it to a current feedback signal, which is added tot eh current produced by Vin through C1.

Common-Source Stage

Poor definition of the gain (gmro): Both gm and ro depend vary with process and temperature.

Gain Desensitization Example

Assumption:1. The frequency is low enough that C2 does not load the output node and CGS behaves as an open circuit.2. gmro is sufficiently large3. Bias of the gate is not shown!

Results:4. If C1 and C2 are made of the same material, then Process and temperature variations do not change C1/C2.

Gain Desensitization

The closed loop gain is approximately, 1/β.If Aβ is sufficiently large, Y/X is relatively insensitive to variationsof A. Aβ is called the loop gain.

(Taylor series expansion)

Calculation of Loop GainThe input is set to 0.

The negative of the transfer function is the loop gain.

VF=-βAVt

Calculation of Loop Gain

Use Feedback to Desensitive Gain

Loop Gain Calculation Example

The loading of C2 is neglected!

Common Gate Loop Gain Example

Feed forward: M1 and RDFeedback: R1 and R2R1+R2>>RD

M1 operates as a subtractor.

(Loop gain)

Bandwidth Modification

Gain is reduced by 1+βAo.Bandwidth is increased by 1+βAo

Bandwidth Modification as a Result of Feedback

Achieving High gain and High Bandwidth

1. Apply feedback to Improve speed of each amplifier2. Cascade to improve gain!

Input Impedance Modification Example

Loop is opened!

Calculation of Loop Gain

(loop gain)

Closed Loop Input Impedance

Feedback Mechanism

(Feed forward amplifier)

Subtraction occurs in the current domain at the Input terminal.

Output Impedance Modification

Senses VoutReturn a current

Calculation of Output Resistance at Low Frequencies

(Loop gain)

Linearity Improvement

Types of Amplifiers

Ideal Amplifier Models

Realistic Model

(Voltage) Transimpedance

Transimpedance

TransconductanceCurrent amplifier

More than one model is possible.

Examples of Four Types of Amplifiers

(Suffers from large output impedacne)

Amplifiers with Improved Performance

Voltage Sensing

How do you measure voltage across a port?1. Place a voltmeter in parallel2. Use a voltmeter of high input impedance soIt does not disturb the circuit.

R1+R2 must be largeenough so that A1does feel the effectof the resistive divider.

Example: Voltage Sensing

Current Sensing

(Current Meter resistance)Current is sensed by measuring voltageacross r.

(Implementation)RS is ideally small.

Return Voltage to the Input

(Differential pair implementation) (Single-ended Implementation)

Example: Voltage Subtraction

Return Current to the Input(KCL)

(KCL)

(Use RF large enoughto approximate currentSource)

Example

Differential pairperforms voltage subtraction.

(SensingAchieves via R1 and R2)

Voltage Sensing/Current Feedback

Input Impedance of Ideal Feedback Networks

(Voltage Sensing)

(Current Sensing)

Output Impedance of Ideal Feedback Networks

(Return Voltage) (Return Current)

Polarity of Feedback

1. Assume the input signal goes up or down

2. Follow the change through the forward amplifier and the feedback network

3. Determine whether the returned quantity opposes or enhances the original effect produced by the input change.

Example 1

Example 2