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FET Small-Signal Analysis

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FET Small-Signal Model Transconductance The relationship of V GS (input) to I D (output) is called transconductance. The transconductance is denoted g m. Transfer Curve

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Graphical Determination of g m

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Mathematical Definition of g m Using differential calculus Maximum g m at V GS =0V: Effect of I D on g m for

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FET Impedance Input Impedance Z i : Very large to assume input terminal approximate an open circuit Output Impedance Z o : y os : admittance equivalent circuit parameter listed on FET specification sheets.

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FET Specification

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FET AC Equivalent Circuit

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JFET Fixed-Bias Configuration The input is on the gate and the output is on the drain.

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JFET Fixed-Bias Configuration Once again: same step as BJT to redraw the network to AC equivalent circuit. Capacitor – short circuit DC batteries V GG and V DD are set to zero volts by a short-circuit equivalent

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AC Equivalent Circuit

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Impedances Input Impedance:Output Impedance:

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Voltage Gain

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Phase Relationship A CS amplifier configuration has a 180-degree phase shift between input and output.

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Example Fixed-bias configuration has an operating point defined by V GSQ = -2V and I DQ = 5.625 mA, with I DSS = 10mA and V P = -8V. The value of y os is provided as 40 µS. Determine: a) g m b) Z i c) Z o d) A V e) A V ignoring the effects of r d

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Solution

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JFET CS Self-Bias Configuration This is a CS amplifier configuration therefore the input is on the gate and the output is on the drain.

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AC Equivalent Circuit

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Impedances Input Impedance: Output Impedance:

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Voltage Gain

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Phase Relationship A CS amplifier configuration has a 180-degree phase shift between input and output.

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JFET CS Self-Bias Configuration – Unbypassed Rs If Cs is removed, it affects the gain of the circuit.

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AC Equivalent Circuit

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Impedances Input Impedance: Output Impedance:

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Impedances

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Voltage Gain

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Example

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Solution

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JFET CS Voltage-Divider Configuration This is a CS amplifier configuration therefore the input is on the gate and the output is on the drain.

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AC Equivalent Circuit

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Impedances Input Impedance:Output Impedance:

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Voltage Gain

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JFET Source Follower (Common-Drain) Configuration In a CD amplifier configuration the input is on the gate, but the output is from the source.

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AC Equivalent Circuit

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Impedances Input Impedance:Output Impedance:

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Voltage Gain

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Phase Relationship A CD amplifier configuration has no phase shift between input and output.

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JFET Common-Gate Configuration The input is on source and the output is on the drain.

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AC Equivalent Circuit

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Impedances Applying Kirchhoffs voltage law around the output perimeter and Kirchhoffs current law at node a ::

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Impedances Input Impedance: Output Impedance:

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Voltage Gain Applying Kirchhoffs current law at node b ::

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Phase Relationship A CG amplifier configuration has no phase shift between input and output.

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Depletion-Type MOSFETs 1.D-MOSFETs have similar AC equivalent models. 2.The only difference is that V SGQ can be positive for n- channel devices and negative for p-channel devices. 3.This means that g m can be greater than g m0.

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D-MOSFET AC Equivalent Model

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Example Find –V GSQ and I DQ –Determine g m and compare to g m0 –r d –Find Z i, Z o, A v

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Enhancement-Type MOSFETs There are two types of E-MOSFETs: nMOS or n-channel MOSFETs pMOS or p-channel MOSFETs

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E-MOSFET AC Equivalent Model g m and r d can be found in the specification sheet for the FET. Forward transfer admittance

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E-MOSFET CS Drain-Feedback Configuration

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AC Equivalent Circuit

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Impedances Input Impedance: Output Impedance:

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The calculation

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The AC analysis of E-MOSFET Remember that, the biasing arrangement are limited for E-MOSFET

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Voltage Gain

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Phase Relationship This is a CS amplifier configuration therefore it has 180-degree phase shift between input and output.

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Do it Determine input and output and also A V impedance for k=0.3X10 -3

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E-MOSFET CS Voltage-Divider Configuration

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AC Equivalent Circuit

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Impedances Input Impedance: Output Impedance:

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Voltage Gain

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Phase Relationship This is a CS amplifier configuration therefore it has 180-degree phase shift between input and output.

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Solution

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E-MOSFET CS Voltage-Divider Configuration

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AC Equivalent Circuit

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Impedances Input Impedance: [Formula 9.52] Output Impedance:[Formula 9.53] [Formula 9.54]

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Voltage Gain [Formula 9.55] [Formula 9.56]

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Summary Table

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Try yourself Design a self-bias network that have gain of 10. The device should be biased at V GSQ =1/3V P

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Solution

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To be continued……

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