ece145a / 218a power gain definitions - university of ... notes, m. rodwell, copyrighted 2009...

class notes, M. Rodwell, copyrighted 2009

ECE145a / 218a Power Gain Definitions

Mark Rodwell

University of California, Santa Barbara

[email protected] 805-893-3244, 805-893-3262 fax


Vgen

Sij,raw

Zs=Zo ZL=Zomatch match

Sij,matched

Zs=Zin*

Vgen

Sij

ZL=Zout*

Power Gain Definitions: Summary

Transducer Gain

ZL

Zs

Vgen

Sij

gain case-general

generator from availablepower

power load

/ ,

genavloadT PPG

Available Gain

matchedoutput withgain


amplifier from availablepower

/ ,,

genavaavA PPG

Operating Gain

ZL

Zs=Zin*

Vgen

Sij

matchedinput withgain

generator from deliveredpower

power load

/ ,

deliveredgenloadP PPG

Zs

Vgen

Sij

ZL=Zout*

Maximum Available Gain

exist...not may ...M AG

matched portsboth gain with



/ ,,

deliveredgenaavMA PPG

Vgen

Sij

Zs=Zo ZL=Zo

Insertion Gain

enviroment Ohm 50a in gain


load todeliveredpower

/ ,,

2

21

o

o

genavaav

Z

Z

PPS

After impedance-matching:

0,22,11

rawmax,

2

,21

matchedmatched

matched

SS

GS

....but only if unconditionally stable...


Types of 2-Ports To Consider

0 nor r ....neithe

ora transist bemight port -2 The

2211 SS

zero toequalor close &

in-built matching withtransistor

a bemight port -2 The

2211 SS

ijSarbitrary withamplifier

generala bemight port -2 The

load. at the andgenerator at the

networks matching *additional* add tochoose could we these,of allFor


Insertion Power Gain

tenvironmen Ohm?) (50 a in gain generator from availablepower


hence

ifonly but 4//

/ if And

4/ ifBut

2

,propertiesparameter -S From

0

2

21

0

2

21

22

,

0

2

0

0

2

,0

21

0

ZZ

ZS

ZZZSVVPP

ZVPZZ

ZVPZZ

V

VS

o

o

Lgengenoutgenavload

outloadL

gengenavgen

ZZZgen

out

Lgen


Transducer Power Gain

gain case-general



/ ,

genavloadT PPG

).( tomatched benot might or might impedanceinput Amplifier gensource Z Z

. tomatched benot might or might impedanceoutput Amplifier loadZ

oZ benot might or might impedanceGenerator

oZ benot might or might impedance Load

. and both upon depends LsT ZZG


Operating Power Gain

).( tomatched *is* impedanceinput Amplifier gensource ZZ

. tomatched benot might or might impedanceoutput Amplifier loadZ



. uponnot but upon depends sLP ZZG


power load

/ ,

deliveredgenloadP PPG

matchedinput withgain hence

iff //:Note ,

p

*

ingenTavgloaddeliveredgenload

G

ZZGPPPP


Available Power Gain

).( tomatched benot might or might impedanceinput Amplifier gensource Z Z

. tomatched *is* impedanceoutput Amplifier loadZ



. uponnot but upon depends LsA ZZG



/ ,,

genavaavA PPG

matchedoutput withgain hence

iff //:Note

a

*

outloadTavgloadavgava

G

ZZGPPPP


Maximum Available Power Gain

).( tomatched *is* impedanceinput Amplifier gensource Z Z

. tomatched *is* impedanceoutput Amplifier loadZ



.nor neither upon depends max Ls ZZG

.generator from deliveredpower


/ ,,max

deliveredgenaav PPG

exist.not may MAGpossible benot may matchingut input/outp usSimultaneo

matchedoutput andinput both gain with hence

) and ( iff //:Note

max

,

G

ZZZZGPPPP *

outload

*

ingenTavgloaddeliveredgenava


MAG Does Not Always Exist

later. covered be Will

y.instabilitamplifier potential toscorrespond condition This

exists.longer no case, thisIn

possible.not is

output &input of matching ussimultaneo , largely sufficient With

e.interactivmutually become ingoutput tun &input then0, If

output. andinput between termsninteractiorepresent and

max

1221

1221

1221

G

SS

SS

SS


||S21||2 After Matching to Z0 = MAG Before Matching

rawmatched

rawavgload

avgload

ogen

oout

gen

outmatched

GS

GPP

PP

ZV

ZV

V

VS

max,

2

,21

max,

2

22

2

,21

:So

/but

/

4/

/2

r. transisto theof MAGdB theisamplifier theof gain insertion dB The

0,22,11 matchedmatched SS

matching.after obtain expect to should wegain theus llsnetwork te

matchinga design webefore r MAG transisto theexamining :nImplicatio


. and between difference thecarefully Note

4

Gain l Unilateras M ason'is gainpower Resulting

output andinput M atch2)

0

feedback lossless external ithfeedback w device Cancel 1)

overallFET

12212211

2

1221

overall

12

overall

12

ijij

FETFETFETFET

FETFET

YY

GGGG

YYU

SY

Mason's Unilateral Power Gain (1)

ionextrapolat for OK be should U

substrateby sheilded is CM OS,bulk For

ionextrapolat for use tohard U

ninteractio -- frompeak shows U FETs,V-III In

find toionextrapolatfor useful U

dB/decade 20-at off rolls Umodel, BJTsimpleFor

design IC torelevance historical ofmostly U

unilateral madeeasily not are amplifiers M onolithic

max

max

max

f

C

f

RRC

f

ds

dsds

0

5

10

15

20

25

30

10 100 1000

MS

G/M

AG

, dB

Frequency, GHz

Common base

Common Collector

Common emitter

U


Makes input-output coupling =0

No interaction of input, output tuning networks

mostly of historical relevance.

Mason's gain is invariant with respect to

embedding the device in a lossless reciproc

al network.

It is the only* function of the DUT 2-port parameters

which is invariant with respect to such embedding

*except, of course, any other function which has a 1:1

mapping with U

Mason's Unilateral Power Gain (2): Additional Points

0

5

10

15

20

25

30

10 100 1000

MS

G/M

AG

, dB

Frequency, GHz

Common base

Common Collector

Common emitter

U

S. Mason, "Power Gain in Feedback Amplifier," in Transactions of the IRE Professional Group on Circuit Theory, vol. CT-1, no. 2, pp. 20-25, June 1954. doi: 10.1109/TCT.1954.1083579http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1083579&isnumber=23422

M. S. Gupta, "Power gain in feedback amplifiers, a classic revisited," in IEEE Transactions on Microwave Theory and Techniques, vol. 40, no. 5, pp. 864-879, May 1992.doi: 10.1109/22.137392http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=137392&isnumber=3740

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1083579&isnumber=23422



Singhakowinta's gain

0

5

10

15

20

25

30

35

10 100 1000

Gain

s, dB

Frequency, GHz

MAG/MSG common emitter

U

MAG/MSG common base

Gmax,S

Gain Capability of Two-port AmplifiersA. Singhakowinta & A. R. BoothroydInternational Journal of ElectronicsVolume 21, Issue 6, 1966http://dx.doi.org/10.1080/00207216608937931A. Singhakowinta and A. Boothroyd, "On Linear Two-Port Amplifiers," in IEEE Transactions on Circuit Theory, vol. 11, no. 1, pp. 169-169, March 1964. doi: 10.1109/TCT.1964.1082263http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1082263&isnumber=23381

overall overall

12 12

max

1) Add external lossless feedback

to maximize the MAG/MSG

0 , 0

2) Stabilize if necessary

3) Match input and output

Resulting power gain is Singhakowinta's Gain

Y S

G

1/2 1/2

,

max,

(2 1) 2 ( 1)

This is the highest gain obtainable under conditions

of unconditional stability.

has a 1:1 relationship with U.

S

S

U U U

G

http://dx.doi.org/10.1080/00207216608937931



Why Ga and Gp Matter: Matching Network Design

Circuit simulators (ADS, etc)

provide contour plots of Ga vs

source impedance and Gp vs load

impedance.

These, the Ga & Gp circles, show

the variation in transistor gain as

generator and load impedance are

tuned.

The center of these circles are the

(generator, load) impedances

required for maximum gain

S,opt L,opt

available gain operating gain

We can then separately design

Input & Output Tuning Networks

to provide these impedances...

...added to device, the amplifier is realized

Caution: the above assumes that MAG exists; we must examine this critical point in the next lecture


Simple Matching Example: Unilateral Device Model

gsin

DSmFET

match

in

ds

gs

m

ings

dsm

in

out

ds

gs

inm

dsgsmloadout

gsingsininin

outLinloadinava

gd

CZRj

ZRgS

fff

fS

R

R

C

gf

f

f

RC

Rg

P

P

RC

IgRVgRIP

CIVRIP

RRPPPPG

SC

load

)(1

)||(2 ,inspection from while,

at thenmatch,-impedance weIf

42 where

4

4)2/(

/ and

because //

device. unilateral

0 0 model; FETSimple

0

0,21

2

2

max2

21

max2

2

max

22

2

22

22

22

2

max

12

ece145a / 218a power gain definitions - university of ... notes, m. rodwell, copyrighted 2009...

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