Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16

Lecture 16:

Small Signal Amplifiers

Prof. Niknejad

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Lecture Outline

Review: Small Signal Analysis

Two Port Circuits– Voltage Amplifiers

– Current Amplifiers

– Transconductance Amps

– Transresistance Amps

Example: MOS Amp Again!

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Small Signal Analysis

Step 1: Find DC operating point. Calculate

(estimate) the DC voltages and currents (ignore

small signals sources)

Substitute the small-signal model of the

MOSFET/BJT/Diode and the small-signal models

of the other circuit elements.

Solve for desired parameters (gain, input

impedance, …)

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

A Simple Circuit: An MOS Amplifier

DSI

GSV

sv

DR DDV

GS GS sv V v= +

ov

Input signal

Output signal

Supply “Rail”

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Small-Signal Analysis

Step 1. Find DC Bias – ignore small-signal source

VGS,BIAS was found inLecture 15

IGS,Q

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Small-Signal Modeling

What are the small-signal models of the DC supplies?

Shorts!

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Small-Signal Models of Ideal Supplies

Small-signal model:

supplysupply

supply

ig

v

∂= = ∞

∂

supply 0r =

supplysupply

supply

0i

gv

∂= =

∂

supplyr = ∞

short

open

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Small-Signal Circuit for Amplifier

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Low-Frequency Voltage Gain

Consider first ω 0 case … capacitors are open-circuits

Transconductance

,2( ) D SAT

m n ox GS TGS T

IWg C V V

L V Vµ= − =

−

( )||out m s D ov g v R r= −

( )||v m D oA g R r= −

Design Variable

Design Variables

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Voltage Gain (Cont.)

Substitute transconductance:

Output resistance: typical value λn= 0.05 V-1

,

1 1200k

0.05 0.1on D SAT

r kIλ

= = Ω = Ω ⋅

Voltage gain: ( )2 0.125 || 200 14.3

0.32vA⋅ = − = −

( ),2||D SAT

v D oGS T

IA R r

V V

= − −

m Dg R

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Input and Output Waveforms

Output small-signal voltage amplitude: 14 x 25 mV = 350

Input small-signal voltage amplitude: 25 mV

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

What Limits the Output Amplitude?

1. vOUT(t) reaches VSUP or 0 … or

2. MOSFET leaves constant-current region and enterstriode region

, 0.31VDS DS SAT GS TnV V V V≤ = − =

, , 0.32Vo MIN DS SATv V= =

2.5 0.32V = 2.18Vamp = −

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Maximum Output Amplitude

vout(t)= -2.18 V cos(ωt) vs(t) = 152 mV cos(ωt)

How accurate is the small-signal (linear) model?

0.1520.5

0.32s

GS Tn

v

V V= ≈

−

Significant error in neglecting third term in expansionof iD = iD (vGS)

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Generalized Amplifier

sv S BIAS sv V v= +

ov

BIASV

DDV

SSVBIASIsi

SR

DDIL DD Di I i= −

( )D ini f v=LR

inv

Active Device

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Amplifier Terminology

Sources: Signal, its source resistance, and bias voltage or current

Load: Use resistor in Chap. 8, but could be a general impedance

Port: A pair of terminals across which a voltage and an associated current are defined

Source, Load: “one port”

Amplifier: “two port”

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

One-Port Models (EECS 40)

A terminal pair across which a voltage and associated current are defined

CircuitBlockabv

+

−

abi

thevv

thevR

abv

+

−

abi

thevithevRabv

+

−

abi

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Small-Signal Two-Port Models

We assume that input port is linear and that the amplifier is unilateral: – Output depends on input but input is independent of

output.

Output port : depends linearly on the current and voltage at the input and output ports

Unilateral assumption is good as long as “overlap”capacitance is small (MOS)

inv

+

−outv

+

−

outiini

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Math 54 Perspective

Can write linear system of equations for either iout or vout

in terms of two of iin, vin, iout, or vout: possibilities are

1 2out in outi v vα α= +

3 4out in outi i vα α= +

5 6out in outv v iα α= +

7 8out in outv i iα α= +

What is physical meaning of α1? of α6?

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

EE Perspective

Four amplifier types: determined by the output signal and the input signal … both of which we select (usually obvious)– Voltage Amp (VV)

– Current Amp (II)

– Transconductance Amp (VI)

– Transresistance Amp (IV)

We need methods to find the 6 α parameters for the four models and equivalent circuits for unilateral two ports

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Two-Port Small-Signal Amplifiers

si sR inR outR LRi inAi

ini

sv

sR

inR

outR

LRv inA vinv

+

−

Current Amplifier

Voltage Amplifier

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Two-Port Small-Signal Amplifiers

sv

sR

inRoutR LRm inG v

inv

+

−

si sR inR

outR

LRm inR i

ini

Transresistance Amplifier

Transconductance Amplifier

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Input Resistance Rin

Looks like a Thevenin resistance measurement, but note that theoutput port has the load resistance attached

attachedRremovedRt

tin

LSi

vR

,=

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Output Resistance Rout

Looks like a Thevenin resistance measurement, but note that theinput port has the source resistance attached

attachedRremovedRt

tout

SLi

vR

,=

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Finding the Voltage Gain Av

Key idea: the output port is open-circuited and the source resistance is shorted

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Finding the Current Gain Ai

Key idea: the output port is shorted and the sourceresistance is removed

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Finding the Transresistance Rm

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Finding the Transconductance Gm

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Common-Source Amplifier (again)

How to isolate DC level?

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

DC Bias

Neglect all AC signals

5 V

2.5 V

Choose IBIAS, W/L

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Load-Line Analysis to find Q

Q

D

DD outR

D

V VI

R

−=

1

10kslope =

0V

10kDI =

5V

10kDI =

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Small-Signal Analysis

inR = ∞

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

sv

sR

inRoutR LRm inG v

inv

+

−

Two-Port Parameters:

Find Rin, Rout, Gm

inR = ∞

m mG g= ||out o DR r R=

Generic Transconductance Amp

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad

Two-Port CS Model

Reattach source and load one-ports: