1 Small Signal Model MOS Field-Effect Transistors (MOSFETs)

Quiz No 3 DE 27 (CE) (a) Draw small signal model (4) (b) Find expression for R out (2) (c) Prove v o /v sig = ( β 1 α 2 R C )/(R sig +r π ) (4). R out

Figure 4.2 The enhancement-type NMOS transistor with a positive voltage applied to the gate. An n channel is induced at the top of the substrate beneath the gate.

Enhancement-type NMOS transistor:

MOSFET Analysis i D = i S, i G = 0

Large-signal equivalent-circuit model of an n-channel MOSFET : Operating in the saturation region.

Large-signal equivalent-circuit model of an p-channel MOSFET : Operating in the saturation region.

Large Signal Model : MOSFET

Transfer characteristic of an amplifier

Conceptual circuit utilized to study the operation of the MOSFET as a small-signal amplifier. The DC BIAS POINT To Ensure Saturation-region Operation

Signal Current in Drain Terminal

Figure 4.35 Small-signal operation of the enhancement MOSFET amplifier.

Total instantaneous voltages v GS and v D

Small-signal ‘π’ models for the MOSFET

Common Source amplifier circuit Example 4-10

Small Signal ‘T’ Model : NMOSFET

Small Signal Models ‘T’ Model

Single Stage MOS Amplifier

Amplifiers Configurations

Common Source Amplifier (CS) :Configuration

Common Source Amplifier (CS) Most widely used Signal ground or an ac earth is at the source through a bypass capacitor Not to disturb dc bias current & voltages coupling capacitors are used to pass the signal voltages to the input terminal of the amplifier or to the Load Resistance CS circuit is unilateral – –R in does not depend on R L and vice versa

Small Signal Hybrid “π” Model (CS)

Small Signal Hybrid “π” Model : (CS)

Small-signal analysis performed directly on the amplifier circuit with the MOSFET model implicitly utilized.

Input Resistance is infinite (R i =∞) Output Resistance = R D Voltage Gain is substantial Common Source Amplifier (CS) Summary

Common-source amplifier with a resistance R S in the source lead

The Common Source Amplifier with a Source Resistance The ‘T’ Model is preferred, whenever a resistance is connected to the source terminal. r o (output resistance due to Early Effect) is not included, as it would make the amplifier non unilateral & effect of using r o in model would be studied in Chapter ‘6’

Small-signal equivalent circuit with r o neglected.

Small-signal Analysis.

Voltage Gain : CS with R S

Source Resistance can be used to control the magnitude of the signal v gs & thus ensure that v gs does not become too large to cause non-linear distortion v gs << 2(V GS -V t ) << V OV

Common Source Configuration with R s R s causes a negative feedback thus improving the stability of drain current of the circuit but at the cost of voltage gain R s reduces i d by the factor –(1+g m R s ) = Amount of feedback R s is called Source degeneration resistance as it reduces the gain

Small-signal equivalent circuit directly on Circuit

A common-gate amplifier based on the circuit

Common Gate (CG) Amplifier The input signal is applied to the source Output is taken from the drain The gate is formed as a common input & output port. ‘T’ Model is more Convenient r o is neglected

A small-signal equivalent circuit

A small-signal Analusis : CG

Small signal analysis directly on circuit

The common-gate amplifier fed with a current-signal input.

Summary : CG 4. CG has much higher output Resistance 5.CG is unity current Gain amplifier or a Current Buffer 6.CG has superior High Frequency Response.

Common Gate R in in independent of R L & R in = 1/g m & g m in order of mA/V. Input resistance of the CG Amplifier is relatively low (in order of 1kv) than CS Amplifier Loss of signal CG is acts as Unity gain current amplifier current buffer – useful for a Cascade circuitry

A common-drain or source-follower amplifier.

Small-signal equivalent-circuit model

Small-signal Analysis : CD

(a) A common-drain or source-follower amplifier :output resistance R out of the source follower.

(a) A common-drain or source-follower amplifier. : Small- signal analysis performed directly on the circuit.

Common Source Circuit (CS)

Common Source Circuit (CS) With R S

Common Gate Circuit (CG) Current Follower

Common Drain Circuit (CD) Source Follower

Summary & Comparison

Quiz No 4 Draw/Write the Following: BJTMOSFET TypesnpnpnpnMOSpMOS Symbols ‘π’ Model T Model gmgm R e /r s r π /r g

Problem 5-44

SOLUTION : DC Analysis

IEIE Check for Active Mode IBIB

Solution Small Signal Analysis

Solution Small Signal Analysis : Input Resistance R in ibib + vbvb -

Solution Small Signal Analysis : Output Resistance I test IEIE I E /(1+ß) I RC R out

Solution Small Signal Analysis : Voltage Gain vivi + - v eb Vo

Solution Small Signal Analysis : Voltage gain + - vivi + - v eb

Solution Small Signal Analysis : Voltage Gain + - vivi

vivi Vo

Problem

Small Signal Model MOSFET : CD

Solution Small Signal Analysis 1/g m g m v sg D

1/g m g m v sg D Solution Small Signal Analysis : Input Resistance R in I g =0

1/g m g m v sg D Solution Small Signal Analysis : Output Resistance I test IDID I G =0 I RD R out V test

1/g m g m v sg D Solution Small Signal Analysis : Voltage Gain vivi + - v sg

1/g m g m v sg D Solution Small Signal Analysis : Voltage gain + - vivi + - v sg

Solution Small Signal Analysis : Voltage Gain + - vivi

vivi

Solution Small Signal Analysis

Problem 6-127(e)

Common Emitter –Common Base (CE-CB) Common Emitter –Common Collector (CE-CC) Common Collector - Common Emitter –(CC-CE) Common Collector - Common Base – (CC-CB) Transistor Pairings Amplifiers

DC Analysis 6-127(e)

Small Signal Model

R in R out

Problem6-127(f) Replacing BJT with MOSFET

Small Signal Model

R in R out

Problem 6-127(f)

Solution P6-127(f) v be2 v eb1

v be2 v eb1 + vivi - Solution P6-127(f)

Problem 6-127(f) with MOSFET

- - v gs2 v sg1 + + Solution P6-127(f)

- - v gs2 v sg1 + + Solution P6-127(f) + vivi - i g1 =0

Comparison BJT/MOSFET Cct

Small Signal Model

Figure P6.123 Problem V BE =0.7 V β =200 K’ n (W/L)=2mA/V 2 V t =1V

Figure P6.123 DC Analysis

V BE =0.7 V β =200 K’ n (W/L)=2mA/V 2 V t1 =1V V t2 =25mV 0.7V I=0.7/6.8=0.1mA I G =0 2V 1mA

Small Signal Model

Small Signal Model : Voltage Gain i g =0 + vivi - + v be2 -

Small Signal Model : Input Resistance i g =0 R in + vivi - i