Feedback Section 8.1. Topics General Feedback Examples of Feedback Circuits – Bandwidth Extension...

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Transcript of Feedback Section 8.1. Topics General Feedback Examples of Feedback Circuits – Bandwidth Extension...

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Feedback Section 8.1 Slide 2 Topics General Feedback Examples of Feedback Circuits Bandwidth Extension Gain Sensitivity Input and Output Impedance Types of Amplifiers Slide 3 General Feedback System H(s)=Feedforward network, represents an amplifier, Open-loop transfer function, a.k.a. A G(s)=Feedback network, usually frequency independent, a.k.a, . Y(s)/X(s)=Closed-loop transfer function Slide 4 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! Slide 5 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. Slide 6 Common-Source Stage Poor definition of the gain (g m r o ): Both g m and r o depend vary with process and temperature. Slide 7 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.g m r o is sufficiently large 3.Bias of the gate is not shown! Results: 1.If C1 and C2 are made of the same material, then Process and temperature variations do not change C1/C2. Slide 8 Gain Desensitization The closed loop gain is approximately, 1/. If A is sufficiently large, Y/X is relatively insensitive to variations of A. A is called the loop gain. (Taylor series expansion) Slide 9 Calculation of Loop Gain The input is set to 0. The negative of the transfer function is the loop gain. V F =-AV t Slide 10 Calculation of Loop Gain Slide 11 Use Feedback to Desensitive Gain Slide 12 Loop Gain Calculation Example The loading of C2 is neglected! Slide 13 Common Gate Loop Gain Example Feed forward: M1 and RD Feedback: R1 and R2 R1+R2>>RD M1 operates as a subtractor. (Loop gain) Slide 14 Bandwidth Modification Gain is reduced by 1+A o. Bandwidth is increased by 1+A o Slide 15 Bandwidth Modification as a Result of Feedback Slide 16 Achieving High gain and High Bandwidth 1. Apply feedback to Improve speed of each amplifier 2. Cascade to improve gain! Slide 17 Input Impedance Modification Example Loop is opened! Slide 18 Calculation of Loop Gain (loop gain) Slide 19 Closed Loop Input Impedance Slide 20 Feedback Mechanism (Feed forward amplifier) Subtraction occurs in the current domain at the Input terminal. Slide 21 Output Impedance Modification Senses Vout Return a current Slide 22 Calculation of Output Resistance at Low Frequencies (Loop gain) Slide 23 Linearity Improvement Slide 24 Types of Amplifiers Slide 25 Ideal Amplifier Models Slide 26 Realistic Model (Voltage) Transimpedance Transconductance Current amplifier More than one model is possible. Slide 27 Examples of Four Types of Amplifiers (Suffers from large output impedacne) Slide 28 Amplifiers with Improved Performance Slide 29 Voltage Sensing How do you measure voltage across a port ? 1.Place a voltmeter in parallel 2.Use a voltmeter of high input impedance so It does not disturb the circuit. R1+R2 must be large enough so that A1 does feel the effect of the resistive divider. Slide 30 Example: Voltage Sensing Slide 31 Current Sensing (Current Meter resistance) Current is sensed by measuring voltage across r. (Implementation) RS is ideally small. Slide 32 Return Voltage to the Input (Differential pair implementation) (Single-ended Implementation) Slide 33 Example: Voltage Subtraction Slide 34 Return Current to the Input (KCL) (Use RF large enough to approximate current Source) Slide 35 Example Differential pair performs voltage subtraction. (Sensing Achieves via R1 and R2) Slide 36 Voltage Sensing/Current Feedback Slide 37 Input Impedance of Ideal Feedback Networks (Voltage Sensing) (Current Sensing) Slide 38 Output Impedance of Ideal Feedback Networks (Return Voltage) (Return Current) Slide 39 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. Slide 40 Example 1 Slide 41 Example 2