Lecture 26: Single stage amps, CD, BJT - University of ...ee105/sp04/handouts/lectures/...single...

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Department of EECS University of California, Berkeley

EECS 105 Spring 2004, Lecture 26

Lecture 26: Single stage amps, CD, BJT

Prof J. S. Smith


EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith

Context

Today, we will continue to discuss biasing and small signal models for single transistor amplifiers, including the common base amplifier, and the similar bipolar transistor amplifiers, common emitter, common base, and common collector.

Next, we will be discussing the frequency response of these amplifiers

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Lecture Outline

Common Drain Amp

Bipolar:Common Emitter AmpCommon Base AmpCommon Collector Amp



Transistor terminalsGate (Base)

– Less current than other terminals– S→D current a sensitive function of G-S voltage

(E→C) (B-E)Source (emitter)

– Relatively large amount of current– S→D current a sensitive function of G-S voltage(E→C) (B-E)

Drain (collector)– Relatively large amount of current (=Source)– S→D current not a sensitive function of voltage at this

terminal

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Common-Source Amplifier

Isolate DC level

The input is at the gate, whichdoesn’t need any (much) current,and is a sensitive terminal (→S):large voltage and current gain



Common Gate Amplifier

DC bias:

SUP BIAS DSI I I= =

current gain=1Impedance buffer

Gain of transistortends to hold this node at ss ground:low input impedanceload for current input

Notice that IOUT must equal-Is

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CG as a Current Amplifier: Find Ai

out d ti i i= = −

1iA = −



CG Input Resistance

At input:

Output voltage:

t outt m gs mb t

o

v vi g v g vr

⎛ ⎞−= − + + ⎜ ⎟

⎝ ⎠( || ) ( || )out d oc L t oc Lv i r R i r R= − =

gs tv v= −

( )||t oc L tt m t mb t

o

v r R ii g v g v

r⎛ ⎞−

= + + ⎜ ⎟⎝ ⎠

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Approximations…

We have this messy result

But we don’t need that much precision. Let’s start approximating:

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||1

m mbt o

oc Lin t

o

g gi r

r RR vr

+ += =

+

1m mb

o

g gr

+ >> ||oc L Lr R R≈ 0L

o

Rr

≈

1in

m mb

Rg g

=+



CG Output Resistance

( ) 0s s tm gs mb s

S o

v v vg v g vR r

−− − − + =

1 1 ts m mb

S o o

vv g gR r r

⎛ ⎞+ + + =⎜ ⎟

⎝ ⎠

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CG Output Resistance

Substituting vs = itRS

1 1 tt S m mb

S o o

vi R g gR r r

⎛ ⎞+ + + =⎜ ⎟

⎝ ⎠

The output resistance is (vt / it)|| roc

|| 1oout oc S m o mb o

S

rR r R g r g rR

⎛ ⎞⎛ ⎞= + + +⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠



Approximating the CG Rout

The exact result is complicated, so let’s try tomake it simpler:

Sgm µ500≈ Sgmb µ50≈ Ω≈ kro 200

][|| SSombSomoocout RRrgRrgrrR +++=

][|| SSomoocout RRrgrrR ++≅

Assuming the source resistance is less than ro,

)]1([||][|| SmoocSomoocout RgrrRrgrrR +=+≈

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CG Two-Port Model

Function: a current buffer• Low Input Impedance• High Output Impedance



Common-Drain Amplifier

21 ( )2DS ox GS T

WI C V VL

µ= −

2 DSGS T

ox

IV V WCL

µ= +

Weak IDS dependence

In the common drain amp,the output is taken from aterminal of which the currentis a sensitivefunction

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CD Voltage Gain

Note vgs = vt – vout||

outm gs mb out

oc o

v g v g vr r

= −

( )||

outm t out mb out

oc o

v g v v g vr r

= − −



CD Voltage Gain (Cont.)

KCL at source node:

Voltage gain (for vSB not zero):

( )||

outm t out mb out

oc o

v g v v g vr r

= − −

1|| mb m out m t

oc o

g g v g vr r

⎛ ⎞+ + =⎜ ⎟

⎝ ⎠

1||

out m

inmb m

oc o

v gv g g

r r

=+ +

1out m

in mb m

v gv g g

≈ ≈+

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CD Output Resistance

Sum currents at output (source) node:

|| || tout o oc

t

vR r ri

= t m t mb ti g v g v= +

1out

m mb

Rg g

≈+



CD Output Resistance (Cont.)

ro || roc is much larger than the inverses of the transconductances ignore

1out

m mb

Rg g

≈+

Function: a voltage buffer• High Input Impedance• Low Output Impedance

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Voltage and current gain

Current tracks input

voltage tracks input



Bipolar single stage amps.

BJT AmpsBJT BiasingCommon Emitter AmpCommon Base AmpCommon Collector Amp

– AKA Emitter Follower

β Multiplier ConceptEmitter Degeneration

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Bipolar Amplifiers

Common-emitter amplifier:

Biasing: adjustVBIAS = VBE sothat IC = ISUP.



Small-Signal Two-Port Model

Parameters: (IC = 1 mA, β =100, VA = 3V)

oc3V|| || 3k||r 3k

1mAout o oc ocR r r r= = = ≈

25mV100 2.5k1mAin

m

R rgπβ

= = = = Ω

1mA 1 S 40mS25mV 25m mG g= = = =

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Common-Base Amplifier

To find IBIAS, note that IBIAS = IE = - (1/αF)IC

Common-base currentgain Ai = - αF



CB Input Resistance

Summing currents at the input node:

( ) 0t m o t ovi g v v v grπ

ππ

+ + + − =small 1

t m ti g vrπ

⎛ ⎞= +⎜ ⎟⎝ ⎠

1 11 1t m

in m mt m

v gR g gi r gπ β

− −⎛ ⎞ ⎛ ⎞= = + = + ≈⎜ ⎟ ⎜ ⎟

⎝ ⎠⎝ ⎠

25mV 251mA

= = Ω

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CB Output Resistance

notepolarity

put roc back inafter finding vt / it

Same topology as CG amplifier, but with rπ || RS rather than RS

( )|| 1 ( ||out oc o m SR r r g r Rπ⎡ ⎤= +⎣ ⎦

( )|| 1out oc o mR r r g rπ⎡ ⎤= +⎣ ⎦SR rπ>>

( )|| 1out oc oR r r β= +



Output Impedance Details

First draw small signal equivalent circuit with transistor and simplify as much as possibleThen (if needed) add the small signal equivalent circuitIf frequency is low, get rid of caps!

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Output Impedance Calculation

tv+

−

ti

rπ vπ

+

−

SR

mg vπ or

( )tt m

o

v vi g vr

ππ

− −= +

( || )t Sv i R rπ π= −

||( || ) t St m t S t

o o

v R ri g i R r ir r

ππ

−= − + +

||1 ( || ) S tt m S

o o

R r vi g R rr r

ππ

⎛ ⎞+ + =⎜ ⎟

⎝ ⎠



Common-Base Two-Port Model

Why did we consider it a current amp?

Current Amp :• Unity Current Gain (-1)• Small Input Impedance• Large (huge!) Output Impedance

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Common-Collector Amplifier

DC Bias:output is one“VBE drop” downfrom input

“Emitter Follower”



Common-Collector Input Resistance

( 1) ( || || )t t t L o ocv i r i R r rπ β= + +

( 1)( || || )in L o ocR r R r rπ β= + +

( 1)in LR r Rπ β≈ + +

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Common-Collector Output Resistance

Divider between vt and vπ :

1 1( || ) 0t m t o oci g v v r v r rπ π π− −+ + − =

tS

rv vr R

ππ

π

=+

( )1 1( || )t t m t o ocS

ri v g r v r rr R

ππ

π

− −⎛ ⎞= + +⎜ ⎟+⎝ ⎠



Common-Collector Output Res. (cont)

Looking into base of emitter follower: load impedance larger by factor β+1Looking into emitter of follower: “source”impedance smaller by factor β+1

( )1 1( || )t t m t o ocS

ri v g r v r rr R

ππ

π

− −⎛ ⎞= + +⎜ ⎟+⎝ ⎠

( ) 11t t mS

i v g rr Rππ

⎛ ⎞= + ⎜ ⎟+⎝ ⎠

1t S

outt

v r RRi

π

β+

= =+

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Common-Collector Voltage Gain

KCL at the output node: note vπ = vt - vout

( ) 1 1||out oc o mv r r g v v rπ π π

− −= +

( ) ( )1 1|| ( )out oc o m t outv r r g r v vπ

− −= + −

( )( ) ( )1 1 1||out oc o m m tv r r g r g r vπ π

− − −+ + = + out tv v=



Common-Collector Two-Port Model

typo: RL

Voltage Amp :• Unity Voltage Gain (+1)• Large Input Impedance• Small Output Impedance

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Summary of Two-Port Parameters

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