Mixed Signal IC Design Notes set 4: Broadband Design ...€¦ · ECE194J /594J notes, M. Rodwell,...
Transcript of Mixed Signal IC Design Notes set 4: Broadband Design ...€¦ · ECE194J /594J notes, M. Rodwell,...
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Mixed Signal IC DesignNotes set 4:Broadband Design Techniques
Mark RodwellUniversity of California, Santa Barbara
[email protected] 805-893-3244, 805-893-3262 fax
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Getting more bandwidth
At this point we have learned basics (MOTC etc)
How can we get more bandwidth…. ?Resistive feedbacktransconductance-transimpedanceemitter-follower buffers, benefits and headachesemitter degeneration…basicsemitter degeneration and area scalingft-doubler stages..distributed amplifiersbroadbanding / peaking with LC networks….examples….
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration, I
./such that ncombinatio RCan want instead wefind will We.resistance
emitteran only using introduced on wasdegeneratiEmitter
mbeee gCCR =
Re Ce Re
ReCe
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration, 2
later....back themadd and removed, etc ,ithcan work w wesuch that is topology that thenoteNext
cbbb CR
ReCe ReCe
CbegmVbe
Vbe
+
-
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration, 3
( )
changedont y back...the added be nowcan etc and )1(
and )/1/( So,cancel) termsdependent frequency that the(note
*/1But
)( so :Vbe from Working
12
13
321
cbbb
Embeinin
mEbe
EmbeEEE
bebembembebe
CRRgCjCjZ
gRVI
RgVCjRIV
VCjgIVgIVCjI
−
−
+==
+=
=+=
+===
ωω
ω
ωω
ReCe
CbegmVbe
Vbe
+
-
Ve
Vb
I1
I2
I3
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration, Summary
ReCe
CbegmVbe
Vbe
+
-
+
-
Rbb Ccbi
Ccbx
Rbb Ccbi
Ccbx
1)1( −+= Embein RgCC1
, )1( −+= Emmextrinsicm Rggg
Other element values do not change...
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration, Unbypassed emitter resistance
1, )1( −+= Emmextrinsicm Rggg
can be shown by elementary nodal analysis, work through…Key observation: degeneration by this method results in a seriesinput resistance, which can increase Cbe charging time.
Rex
CbegmVbe
Vbe
+
-+
-
Rex
Cbe gmVbeVbe
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration, combination case
ReCe
Cin
gmextVin
Vin+
-
Rex
CcbiCcbx
Rex
RbbCcbi
Ccbx
Rbb
CbegmVbe
Vbe
+
-
1)1( −+= Embein RgCC1
, )1( −+= Emmextrinsicm Rggg
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration and Area Scaling 1
[ ]LLextmbbgencbbbgenbe
LextmV
RRgRRCRRCa
RgA
+++++=
−=
)1)(()( have then we
,gain a desire weIf stage. CS heConsider t
,1
,
emitter area =Aecurrent density =JeCurrent =Ae*Je=Ietransconductance=gminput capacitance=Cbecollector capacitance=Ccbbase resistance=Rbb
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration and Area Scaling 2
Ce Reemitter area =Aecurrent density =JeCurrent =Ae*Je=Ietransconductance=gminput capacitance=Cbecollector capacitance=Ccbbase resistance=Rbb
Bigger transistor, before degenerationemitter area =kAecurrent density =JeCurrent =kAe*Je=Iketransconductance=kgminput capacitance=kCbecollector capacitance=kCcbbase resistance=Rbb/know degenerate:Re picked such that (1+gmRe)=kintrinsic transconductance=kgmextrinsic transconductance=kgm/(1+gmRe)=gminput capacitance=kCbe/(1+gmRe)=Cbecollector capacitance=kCcbbase resistance=Rbb/k
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration and Area Scaling 3
Ce Re
[ ] [ ]
bandwidthhighest thegives and Ccb, vsRbb with associated sdelay term exchangesk of choice eappropriat So,
)1()1(
)1(
1:Kby Rbb decreased and 1:Kby Ccb increased havebut Cin, and gm original theleft with are We1.:Kby ddegenerate
then bigger, K timesr transisto themade have We
,,1
,1
LLextmgencbbbbe
Lextmbbcbbegen
LLextmbb
gencbbb
genbe
RRgRkCkRCRgRCCRa
RRgk
RRkCk
RRCa
++++++=
++
++
+=
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration and Area Scaling 4: Emitter Follower Case
? thisdo want tomight weWhy
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Emitter Degeneration and Area Scaling 5: Emitter Follower Case
( )
this.address tomethod one is above as generationscaling/de Area limit.bandwidth major a becan and , 2/1 timesseveral is
HBTan ofconstant time tedundegenera that theNote
1...
stage, CE with theassociated a1in only terms gConsiderin
1,2
2,1,2
21
τπfCR
Rk
RCRRgRk
RkCa
bebb
outbb
beLLextmoutbb
cb
++
++
++=
R1RL
Rbb1Rbb2
Ccb1Ccb2
Cbe1Cbe2
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Ft-doubler stages….the Darlington Revisited
R1 RL R1 RL
Q1Q2
Cbe1 Cbe2Ree Ree
R1 RL
Rbb1
Rbb2Cbe1 Cbe2
Ree
Recall the improvement in Damping provided by Ree….…is there a larger lesson here ?
ECE194J /594J notes, M. Rodwell, copyrighted 2011
2 Kinds of Darlington:
If collectors are tied together:AC collector currents of both transistors contribute to output :)Both transistor Ccb's undergo Miller multiplication :(
Rgen RL
Q1Q2
Ree
RgenRL
Q1Q2
Ree
Collectors tied togetherEF collector grounded
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Ft-doubler stages 2
Ree=1/gm1
Cbe2
Cbe1gm1Vbe1
Vbe1
+
-
gm2Vbe2
Vbe2
Vin
Iin Ic1
Ic2Ie1
Iout
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Ft-doubler stages 3
beminoutbembein
inbebebebeeembe
meembeeebeee
eebe
mbeeebemeebeeeebe
mbebemebemcbebein
CjgIIVgICjIVVVVVRgV
gRgCRCRRCjgCjRVgRCjRIV
gCjVgIVgIVCjI
ωω
ωωω
ωω
/2/ hence and 2/2/ so...)(
/1 hence.../ such that Choose)1()/1()1/(
)/1( , , :V fromWork
out
21112
1
112
111111
be1
=======
==+
+=+=
+===
Ree=1/gm1
Cbe2
Cbe1gm1Vbe1
Vbe1
+
-
gm2Vbe2
Vbe2
Vin
Iin Ic1
Ic2Ie1
Iout
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Ft-doubler stages 4
.parasiticsother theseof presence given the bandwidth,circuit overall doubled have wenor will fmax, doublednot certainly have Ccb...we and Rbb ignored has analysis that thisNote
! doubled have ..we/2/2/
and 2/ out
τ
τωω
fjffCjgII
VgICjI
beminout
bembein
====
Ree=1/gm1
Cbe2
Cbe1gm1Vbe1
Vbe1
+
-
gm2Vbe2
Vbe2
Vin
Iin Ic1
Ic2Ie1
Iout
+
-
Cbe/2gmVin
Vin
ECE194J /594J notes, M. Rodwell, copyrighted 2011
ft-doubler vs Darlington…thinking in terms of current gains:
econductancinput negativebut gain current high giveswhich )/( as sfrequencielower at sgain varieCurrent
...)/()/(2)(2
/
)( Since/ where)(2/ isgain Current
2
222121
212121
212
2121
jffjffjff
gHH
gYVI
VgVVgVgVgIIIjffHHHII
mmininin
inmbebembembemccout
inout
τ
ττ
τ
=+
=+
==
=+=+=+==+=
Iin H21Iin
(1+H21)Iin
Cbe2
H21(1+H21)Iin
(2*H21+H21*H21)Iin
ECE194J /594J notes, M. Rodwell, copyrighted 2011
ft-doubler vs Darlington…thinking in terms of current gains:
)/2( as sfrequencie allat sgain varieCurrent
)2/2(2)/(22
/
)( Since/ where2/ isgain Current
21
212121
2121
jff
Cjff
jfgjff
gHgYVI
VgVVgVgVgIIIjffHHII
bemmm
ininin
inmbebembembemccout
inout
τ
ττ
τ
π=====
=+=+=+===
Iin H21Iin
(1+H21)Iin
Cbe2
H21IinIin
H21Iin
2*H21Iin
ECE194J /594J notes, M. Rodwell, copyrighted 2011
ft-doubler vs Darlington…current gains:
ECE194J /594J notes, M. Rodwell, copyrighted 2011
ft-doubler …correction for Base resistance
Ree=1/gm1
Cbe2
Cbe1gm1Vbe1
Vbe1
+
-
gm2Vbe2
Vbe2
Vin
Iin Ic1
Ic2Ie1
Iout
L=CbeRbb/gm
Rbb
L=CbeRbb/gm
The indicated inductance is necessary for equal current splittingbetween the 2 transistors in the presence of Rbb. In this case theinput impedance is Cbe/2 in series with Rbb/2…again notethat this correction is significant because RbbCbe>>Cbe/gm
ECE194J /594J notes, M. Rodwell, copyrighted 2011
ft-doubler vs Darlington
What is the conclusion of all this ? We can view the ft-doubler as a special case of the connected-collector Darlington with heavy emitter-follower loading: in this case the second-order (resonant) response is entirely suppressed. More generally we might vary the EF loading to vary the damping. (The particular case of power amplifiers favors the ft-doubler due to efficiency reasons…)
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Tuning: to prevent reflections, to peak gain
gain andmatch input S21, and S11both hurt has ecapacitancinput The
1 where,2/1
2/
2/12/
0
011
021
=
+=
+−
=
CjZZ
CZjCZjS
CZjZgS
oin
om
ωωω
ω
Cin
Rin=Zo
Zo
Rout=Zo
Zo
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Pi-section input tuning….
)/1 (henceshort issection -pi thesuch that freqeuciesfor Effective
)2(2/2/
section-pi a into ecapacitancinput r transisto theAbsorb
0 CZf
ZZCZLZCCC
o
ooino
obein
π
ττ
<
=====
Cin=C/2
Rin=Zo
Zo
Rout=Zo
Zo
Cx=C/2
L
Gain flatness and match improved for f<fo, but made worsefor f>f0
ECE194J /594J notes, M. Rodwell, copyrighted 2011
T-section input tuning….
case...section -pi the torelative fo doubled have weCin,given afor that Note
)/1 (henceshort issection -pi thesuch that freqeuciesfor Effective
)2(/
section-T a into ecapacitancinput r transisto theAbsorb
0 CZf
ZZCZLZCCC
o
ooino
obein
π
ττ
<
=====
Cin=C
Rin=Zo
Zo
Rout=Zo
ZoL/2
L/2
ECE194J /594J notes, M. Rodwell, copyrighted 2011
T-section tuning in feedback amplifiers
stability. reducedisger FBAs...dan Ohm 50in used frequently is This
)1)(2/(
)1(:ionApproximatMiller By
ALLAZR
f
of
−=
−=
Cin=C
Rin=Zo
Zo
Rout=Zo
ZoL/2
L/2
Cin=C
ZoZo
L/2 Lf
Rf
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Bridged-T-section input tuning….
case...section -T theasfrequency same about theat off rolls ssneverthele S21 zero.exactly is S11 Cbe,by
modeled impedanceinput an hasr transisto theasInsofar )2(/
ooino
obein
ZZCZLZCCC
=====
ττ
Cin=C
Rin=Zo
Zo
Rout=Zo
ZoL/2
L/2C/2
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Bridged-T-section input tuning….
Karthik Krishnamurthi
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Tuning Networks use Microstrip elements....
Cin=C/2
Rin=Zo
Zo
Cx=C/2
L
Cin=C/2
Rin=Zo
Zo L
Cin=C/2
Rin=Zo
Zo
Cx
L
Cx=C/2
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Distributed Amplifiers : Theory
synthetic drain line
synthetic gate line
• HEMT input/output capacitances absorbed into artificial input/output lines• broadband circuit ; gain/bandwidth limited by
HEMT resistive parasitics (fmax)distributed structure Bragg frequencyinput/output transmission line skin-effect losses
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Synthetic Transmission Lines
transmission line section
line section inductance
• synthetic input/output line formed by transmission line sections• transmission line
characteristic impedancecutoff (Bragg) frequency delay
line section capacitanceHEMT input capacitance
L/CZ =LCfB π/1=
LCT =
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Transmission Line Loss
lossless line
frequency-dependent loss
frequency-independent loss
2/4 02
122 RZCfπ=α
RZ 2/0=α
ECE194J /594J notes, M. Rodwell, copyrighted 2011
HEMT Equivalent Circuit
• simplified equivalent circuit
gsm Cgf π=τ 2/ ids rrff 4/max τ=
• element values scale with HEMT size
•
ECE194J /594J notes, M. Rodwell, copyrighted 2011
CS HEMT TWA
ECE194J /594J notes, M. Rodwell, copyrighted 2011
CS HEMT TWA--LC equivalent
ECE194J /594J notes, M. Rodwell, copyrighted 2011
CS HEMT TWA--SS model
ECE194J /594J notes, M. Rodwell, copyrighted 2011
TWA…limits to gain and bandwidth...
problem... rs....no transistosmall very of lotshigh with very made be...can /1
Frequency Braggbandwidth-gain feasible sets limits, aboveer with ....togeth
)ratioon degenerati capacitive)(2/(GainFrequency -Low
right...design get werequires...just 90)MismatchDelay Output -Input
2/ becauselimit gain a sets...2/1NLoss Line (output)Drain
... becauselimit frequency high a ...sets 2/1N:loss e(input)lin Gate
21
0
d
22g
LCf
ZNgS
TN(T
RZ
RC
om
draingate
dsod
ig
π
αα
ωαα
<
=
<−
=<
=<
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Undamped Darlington FBA
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50
S22
S11
S21
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Feedback Amplifier with Follower Driving ft-doubler
-15
-10
-5
0
5
10
0 10 20 30 40 50 60 70 80
Gai
ns, d
B
Frequency, GHz
S21
S11
S22
ECE194J /594J notes, M. Rodwell, copyrighted 2011
80 GHz HBT Distributed Amplifier
-20
-15
-10
-5
0
5
10
15
0 20 40 60 80
Gai
ns, d
B
Frequency, GHz
S21
S22
S11
ECE194J /594J notes, M. Rodwell, copyrighted 2011
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