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Ref:080130HKNEE3110 Feedback Amplifiers1 Lecture 2 Feedback Amplifier Introduction of Two-Port Network Negative Feedback (Uni-lateral Case) Feedback Topology Analysis of feedback applications –Close-Loop Gain –Input/Output resistances

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Ref:080130HKNEE3110 Feedback Amplifiers2 Two-Port Network (z-parameters) (Open-Circuit Impedance) Open-circuit input impedance At port 1 Open-circuit reverse transimpedance At port 2 Open-circuit forward transimpedance Open-circuit output impedance

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Ref:080130HKNEE3110 Feedback Amplifiers3 Two-Port Network (y-parameters) (Short-Circuit Admittance) Short-circuit input admittance At port 1 Short-circuit reverse transadmittance At port 2 Short-circuit forward transadmittance Short-circuit output admittance

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Ref:080130HKNEE3110 Feedback Amplifiers4 Two-Port Network (h-parameters) (hybrid) Short-circuit input impedance At port 1 Open-circuit reverse voltage gain At port 2 Short-circuit forward current gain Open-circuit output admittance

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Ref:080130HKNEE3110 Feedback Amplifiers5 Two-Port Network (g-parameters) (inverse-hybrid) Open-circuit input admittance At port 1 Short-circuit reverse current gain At port 2 Open-circuit forward current gain Short-circuit output impedance

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Ref:080130HKNEE3110 Feedback Amplifiers6 z-parameter example Note: (1) z-matrix in the last circuit = sum of two former z-matrices (2) z-parameters is normally used in analysis of series-series circuits (3) Z 12 = Z 21 (reciprocal circuit) (4) Z 12 = Z 21 and Z 11 = Z 22 (symmetrical and reciprocal circuit)

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Ref:080130HKNEE3110 Feedback Amplifiers7 y-parameter example

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Ref:080130HKNEE3110 Feedback Amplifiers8 y-parameter example (Cont ) Note: the y-matrix is equal to the sum of two former ones. Therefore, y-parameters is normally used in analysis of shunt-shunt circuits What connection should be for h- or g- parameters?

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Ref:080130HKNEE3110 Feedback Amplifiers9 General Feedback Structure A : Open Loop Gain A = V o / V : feedback factor = V f / V o

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Ref:080130HKNEE3110 Feedback Amplifiers10 Negative Feedback Properties Negative feedback takes a sample of the output signal and applies it to the input to get several desirable properties. In amplifiers, negative feedback can be applied to get the following properties –Desensitized gain : gain less sensitive to circuit component variations –Reduce nonlinear distortion : output proportional to input (constant gain independent of signal level) –Reduce effect of noise –Control input and output impedances by applying appropriate feedback topologies –Extend bandwidth of amplifier All of these properties can be achieved by trading off gain

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Ref:080130HKNEE3110 Feedback Amplifiers11 Gain De-sensitivity Feedback can be used to desensitize the closed-loop gain to variations in the basic amplifiler. Assume is constant. Take differentials of the closed loop gain equation gives, Divided by A v, the close loop gain sensitivity is equal to, This result shows the effects of variations in A on A CL is mitigated by the feedback amount. (1+A ) is also called the desensitivity amount. Differential respected with A

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Ref:080130HKNEE3110 Feedback Amplifiers12 Basic Feedback Topologies Depending on the input signal (voltage or current) to be amplified and form of the output (voltage or current), amplifiers can be classified into four categories. Depending on the amplifier category, one of four types of feedback structures should be used. (Type of Feedback)(Type of Sensing) (1) Series (Voltage) Shunt (Voltage) (2) Series (Voltage) Series (Current) (3) Shunt (Current) Shunt (Voltage) (4) Shunt (Current) Series (Current)

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Ref:080130HKNEE3110 Feedback Amplifiers13 Feedback Structure (Series-Shunt) Voltage amplifier voltage-controlled voltage source Requires high input impedance, low output impedance Voltage-voltage feedback Voltage Gain Calculation:

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Ref:080130HKNEE3110 Feedback Amplifiers14 Input/Output Resistance (Series-Shunt) Input Resistance: Output Resistance (Closed loop output resistance with zero input voltage)

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Ref:080130HKNEE3110 Feedback Amplifiers15 h-parameter Modeling Only uni-lateral case will be considered : (1)NO reverse dependent signal found in the amplifier network. |h 12a | = 0 (2)NO reverse dependent signal found in the feedback network. |h 21f | = 0

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Ref:080130HKNEE3110 Feedback Amplifiers16 Uni-lateral

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Ref:080130HKNEE3110 Feedback Amplifiers17 Series-Shunt Example Equivalent circuit It is observed that: (1)Series connection in input ports (2)Shunt connection in output ports Series-Shunt connection h-parameter should be used.

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Ref:080130HKNEE3110 Feedback Amplifiers18 h-parameter analysis 1

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Ref:080130HKNEE3110 Feedback Amplifiers19

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Ref:080130HKNEE3110 Feedback Amplifiers20 Feedback Structure (Series-Series)

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Ref:080130HKNEE3110 Feedback Amplifiers21 Input/Output Resistance (Series-Series) Input Resistance: Output Resistance (Closed loop output resistance with zero input voltage)

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Ref:080130HKNEE3110 Feedback Amplifiers22 Series-Series Example CE amplifier with an un-bypassed emitter ac small signal equivalent circuit

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Ref:080130HKNEE3110 Feedback Amplifiers23 Feedback Network with z-parameter Reduce equivalent circuit

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Ref:080130HKNEE3110 Feedback Amplifiers24 Close loop analysis

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Ref:080130HKNEE3110 Feedback Amplifiers25 Final R in and R out

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Ref:080130HKNEE3110 Feedback Amplifiers26 Feedback Structure (Shunt-Shunt)

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Ref:080130HKNEE3110 Feedback Amplifiers27 Input/Output Resistance (Shunt-Shunt) Input Resistance: Output Resistance (Closed loop output resistance with zero input voltage)

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Ref:080130HKNEE3110 Feedback Amplifiers28 Shunt-Shunt Example CE amplifierac small signal equivalent circuit Shunt-Shunt connection found! y-parameter

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Ref:080130HKNEE3110 Feedback Amplifiers29 Feedback Network y-parameter modeling

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Ref:080130HKNEE3110 Feedback Amplifiers30

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Ref:080130HKNEE3110 Feedback Amplifiers31 Feedback Structure (Shunt-Series)

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Ref:080130HKNEE3110 Feedback Amplifiers32 Input/Output Resistance (Shunt-Series) Input Resistance: Output Resistance (Closed loop output resistance with zero input voltage)

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Ref:080130HKNEE3110 Feedback Amplifiers33 Summary Feedback Structure Close loop gain Input impedance Output impedance Parameter used Series- Shunt h-parameter Series- Series z-parameter Shunt- Shun y-parameter Shunt- Series g-parameter

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Ref:080130HKNEE3110 Feedback Amplifiers34 Supplementary Find the input and output resistance from - Two port network, and - Circuit theory

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Ref:080130HKNEE3110 Feedback Amplifiers35 Circuit Theory

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Ref:080130HKNEE3110 Feedback Amplifiers36 Two Port Network

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Ref:080130HKNEE3110 Feedback Amplifiers37

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