ece145a / 218a power gain definitions - university of ... notes, m. rodwell, copyrighted 2009...
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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
class notes, M. Rodwell, copyrighted 2009
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
generator from availablepower
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
generator from deliveredpower
amplifier from availablepower
/ ,,
deliveredgenaavMA PPG
Vgen
Sij
Zs=Zo ZL=Zo
Insertion Gain
enviroment Ohm 50a in gain
generator from availablepower
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...
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
Insertion Power Gain
tenvironmen Ohm?) (50 a in gain generator from availablepower
load todeliveredpower
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
class notes, M. Rodwell, copyrighted 2009
Transducer Power Gain
gain case-general
generator from availablepower
load todeliveredpower
/ ,
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
class notes, M. Rodwell, copyrighted 2009
Operating Power Gain
).( tomatched *is* impedanceinput Amplifier gensource ZZ
. tomatched benot might or might impedanceoutput Amplifier loadZ
oZ benot might or might impedanceGenerator
oZ benot might or might impedance Load
. uponnot but upon depends sLP ZZG
generator from deliveredpower
power load
/ ,
deliveredgenloadP PPG
matchedinput withgain hence
iff //:Note ,
p
*
ingenTavgloaddeliveredgenload
G
ZZGPPPP
class notes, M. Rodwell, copyrighted 2009
Available Power Gain
).( tomatched benot might or might impedanceinput Amplifier gensource Z Z
. tomatched *is* impedanceoutput Amplifier loadZ
oZ benot might or might impedanceGenerator
oZ benot might or might impedance Load
. uponnot but upon depends LsA ZZG
generator from availablepower
amplifier from availablepower
/ ,,
genavaavA PPG
matchedoutput withgain hence
iff //:Note
a
*
outloadTavgloadavgava
G
ZZGPPPP
class notes, M. Rodwell, copyrighted 2009
Maximum Available Power Gain
).( tomatched *is* impedanceinput Amplifier gensource Z Z
. tomatched *is* impedanceoutput Amplifier loadZ
oZ benot might or might impedanceGenerator
oZ benot might or might impedance Load
.nor neither upon depends max Ls ZZG
.generator from deliveredpower
amplifier from availablepower
/ ,,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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
||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
class notes, M. Rodwell, copyrighted 2009
. 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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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