ECE 453 Wireless Communication Systems Amplifiers

ECE 453 – Jose Schutt‐Aine 1

Jose E. Schutt-AineElectrical & Computer Engineering

University of [email protected]

ECE 453Wireless Communication Systems

Amplifiers


• Definitions– Used to increase the amplitude of an input signal to a

desired level– This is a fundamental signal processing function– Must be linear (free of distortion) – Shape of signal

preserved

Amplifiers

( ) ( ),o iv t Av t where A is the voltage gain

vi(t) vo(t)AMP

: ov

i

vVoltage Gain Av

( ) :( )

Lp

I

Load Power PPower Gain AInput Power P


Amplifiers

1 1 2 2DCP V I V I

100L

DC

P Power EfficiencyP

Since output associated with the signal is larger than the input signal, power must come from DC supply

DC I L dissipatedP P P P


• Bipolar Junction Transistor (BJT)– First Introduced in 1948 (Bell labs)– Consists of 2 pn junctions– Has three terminals: emitter, base, collector

Bipolar Junction Transistor

4


BJT – Modes of Operation

Mode EBJ CBJ

Cutoff Reverse Reverse

Forw. Active Forward Reverse

Rev. Active Reverse Forward

Saturation Forward Forward

5


B

C

E

Structure of BJT’s

Collector surrounds emitter region electrons will be collected

6


PNP

NPN

BJT Transistor Polarities


Ebers-Moll Model

NPN Transistor

// 1 1BC TBE T v Vv V SC S

R

Ii I e e

// 1 1BC TBE T v Vv VSE S

F

Ii e I e

// 1 1BC TBE T v Vv VS SB

F R

I Ii e e

1F

FF

1

RR

R

Describes BJT operation in all of its possible modes

8


Biasing Bipolar Transistors


Biasing of Amp

( ) ( )I QI IV t V v t

Bias will provide quiescent points for input and output about which variations will take place. Bias maintain amplifier in active region.

( ) ( )o QO oV t V v t

( ) ( )o v Iv t A v to

vI at Q

dvAdv

Amplifier characteristics are determined by bias point


Small-Signal Model

• What is a small-signal incremental model?

– Equivalent circuit that only accounts for signal level fluctuations about the DC bias operating points

– Fluctuations are assumed to be small enough so as not to drive the devices out of the proper range of operation

– Assumed to be linear

– Derives from superposition principle


2. Emitter Bias

BJT Bias

Provides good stability with respect to changes in with temperature

12

Thevenin Equivalent


BJT Emitter Bias

th th B BE E EE R I V R I

1E B C BI I I I

( 1)th BE

B BQth E

E VI IR R

2

1 2th CC

RE VR R

1 21 2

1 2th

R RR R RR R

13

Thevenin Equivalent

1th BE th B E BE V R I R I


Hybrid- Incremental Model for BJTs

r: input resistance looking into the baserx: parasitic series resistance looking into base – ohmic base resistancegm: BJT transconductancero=rce: output collector resistance related to the Early effect


Hybrid- Parameters

tanC

C Cm

BE TI cons t

i Igv V

:b

vr is defined as ri

mb

g vSince i

m

then rg

A Ace o

C B

V Vr r

I I

is associated with the Early effectce or r

1 er r

me

gr

mg r

Can show that

1 1m

e

gr r


Common Emitter (CE) Amplifier

Bias: Choose R1 & R2 to set VBVE is then set. Choose RE to set IE~IC. Quiescent point of Vout will be determined by RC. Emitter is an AC short.


Incremental Model for CE Amplifier

1 2BR R R

Hybrid- model (ignoring rx)

iin B

i

vR R ri

B inSometimes R r and R r

r

E

ro

+

-

gmv

vout

RCvin

C

RB

Rsig

+v

-

RL

B

+

vi

-

ii io


B o C Lo m sig

B sig

R r r R Rv g v

R r R

iv v o m o C Lv g v r R R

ov m o C L

i

vA g r R Rv

gain from base to collector

, sigB i

sig

v rand if R r v

r R

sig in sig B

iin sig B sig

v R v R rv

R R R r R

CE Amplifier


Open-circuit voltage gain:

vo m o CA g r R In most cases o C vo m Cr R A g R

B

v m o C LB sig

R rG g r R R

R r R

o C Lv

sig

r R RG

r R

and for the case where BR r

CE Amplifier


Output Impedance

out C oR R r

,o C out CIf r R R R

Lv vo

L o

Rfrom which A AR R

It can be seen that if Rsig >> r, the gain will be highly dependent on . This is not good because of variations

,sig v m C L oIf R r G g R R r

CE Amplifier


1o m E m E

vv g v R v g Rr r

Emitter Follower (Common Collector)

1in B b o E m B

vv v R i v v v R g Rr r

Incremental modelcircuit


Emitter follower has unity voltage gain

11

11 1

m Em Eo

in m E BBm E

g Rg r Rrv

v g r R r RRg Rr r

Emitter Follower

Using mg r

1

11

Eo

in E B

Rvv R r R

11 Bin E m

Rv v R gr r


1in B Er r R R

Emitter Follower – Input Impedance

1 / 1//

B E minin

b

v R r R g rvri v r


Emitter Follower – Output Impedance

oB

B

vir R

o o o m o oo m

E B E B B

v v v g r v vi g vR r R R r R r R

1 1 1( 1)m

o o o B EE B B E B

gi v v r R RR r R r R R r R


Using mg r

/ ( 1)( 1) / ( 1)

E B E Boout

o B E E B

R r R R r Rv Ri r R R R r R

/ ( 1)out E BR R r R

' '( 1)( 1) 1

EMB out E

E

rRA and R Rr R

Output Impedance (cont’)

If we neglect RB


Common Base Configuration


,i o m C m i Cv v v g v R g v R

o Cm C

i e

v RVoltage gain g Rv r

11o m m

i im

i g v g vCurrent gaini i

g vr

out CR R 1inrr

Common Base Configuration


m Cg R

CR

1r

/( 1)ER r

1Er R

1m Cg R

r

CR

CE CB EF

Avo

Rin

Rout

BJT Topologies - Summary


Feedback – Basic Concept


1. The closed-loop transfer function is a function of frequency

2. The manner in which the loop gain varies with frequency determines the stability or instability of the feedback amplifier

3. The frequency at which the phase of the transfer function is equal to 180o will be unstable if the magnitude is greater than unity

Feedback and Frequency Dependence


1 ( )f

A sA s

A s s

Feedback and Stability

When loop gain A(j)(j) has 180o phase, we have positive feedback

1 ( )f

A jA j

A j j


Nyquist Plot

- Radial distance is |A|- Angle is phase of - Intersects negative real axis at 180


Stability and Pole Location ( ) 2 coso ot tj t j t

nv t e e e e t


Oscillator

• Closed‐Loop Transfer function:

–

• Barkhausen’s criteria for oscillation:––

• = oscillation‐frequency.

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ECE 453 Wireless Communication Systems Amplifiers

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