# FET Small-Signal Analysis

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FET Small-Signal Analysis

FET Small-Signal Model
Transconductance The relationship of VGS (input) to ID (output) is called transconductance. The transconductance is denoted gm. Transfer Curve

Graphical Determination of gm

Mathematical Definition of gm
Using differential calculus Maximum gm at VGS =0V: Effect of ID on gm for

Very large to assume input terminal approximate an open circuit
FET Impedance Input Impedance Zi: Very large to assume input terminal approximate an open circuit Output Impedance Zo: yos: admittance equivalent circuit parameter listed on FET specification sheets.

FET Specification

FET AC Equivalent Circuit

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

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

AC Equivalent Circuit

AC Equivalent Circuit

Impedances Input Impedance: Output Impedance:

Voltage Gain

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

AV ignoring the effects of rd
Example Fixed-bias configuration has an operating point defined by VGSQ = -2V and IDQ = mA, with IDSS = 10mA and VP = -8V. The value of yos is provided as 40 µS. Determine: gm Zi Zo AV AV ignoring the effects of rd

Solution

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.

AC Equivalent Circuit

Impedances Input Impedance: Output Impedance:

Voltage Gain

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

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

AC Equivalent Circuit

Impedances Input Impedance: Output Impedance:
Saat Vi=0, maka dari sisi input  Vgs+gmVgsRs =0 atau Vgs+(Io+ID)Rs=0, sehingga Vgs=-(Io+ID)Rs

Impedances Menghitung Zo didapatkan dengan cara bantuan arus Io, sedangkan untuk penguatan tegangan bantuan arus Io dihilangkan kembali\

Voltage Gain

Voltage Gain

Example

Solution

Solution

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.

AC Equivalent Circuit

Impedances Input Impedance: Output Impedance:

Voltage Gain

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

AC Equivalent Circuit

Impedances Input Impedance: Output Impedance:

Voltage Gain

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

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

AC Equivalent Circuit

Impedances Applying Kirchhoff’s voltage law around the output perimeter and Kirchhoff’s current law at node a ::

Impedances Input Impedance: Output Impedance:

Voltage Gain Applying Kirchhoff’s current law at node b ::

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

Depletion-Type MOSFETs
D-MOSFETs have similar AC equivalent models. The only difference is that VSGQ can be positive for n-channel devices and negative for p-channel devices. This means that gm can be greater than gm0.

D-MOSFET AC Equivalent Model

Example Find VGSQ and IDQ Determine gm and compare to gm0 rd
Find Zi, Zo, Av

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

E-MOSFET AC Equivalent Model
Forward transfer admittance gm and rd can be found in the specification sheet for the FET.

E-MOSFET CS Drain-Feedback Configuration

AC Equivalent Circuit

Impedances Output Impedance: Input Impedance:

The calculation

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

Voltage Gain

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

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

E-MOSFET CS Voltage-Divider Configuration

AC Equivalent Circuit

Impedances Input Impedance: Output Impedance:

Voltage Gain

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

Solution

E-MOSFET CS Voltage-Divider Configuration

AC Equivalent Circuit

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

Voltage Gain [Formula 9.55] [Formula 9.56]

Summary Table

Summary Table

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

Solution

To be continued……

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