Mixed Sal C Des Notes set 4: Broadband Des Techniques Mark odwell University of California, Santa Barbara rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 fax
Gett ore bandwidth At this pot we have learned basics (MOTC etc) How can we et ore bandwidth.? esistive feedback transconductance-transipedance eitter-follower buffers, nefits and headaches eitter deeneration basics eitter deeneration and area scal ft-doubler staes.. distributed aplifiers broadband / peak with LC networks. exaples.
Eitter Deeneration, e Ce e Ce e Eitter deeneration was troduced us only an eitter resistance. We will fd we stead want an C cobation such that C e e C /.
Eitter Deeneration, 2 - C Ce e Ce e Next note that the topoloy is such that we can work with bb, C cb etc reoved, and add the back later...
Eitter Deeneration, 3 1 b C 2-3 e Work fro : 1 But So, and ( 1/ jωc ) (note that the frequency dependent ters cancel) Z bb jωc 2 E C 3 jωc cb /( E E 2 1/ jωc E (1 1 so ) and E ) 3 1 ( * ) etc can now added back...they dont chane E jωc Ce e
Eitter Deeneration, Suary Ccbx Ccbx bb Ccbi bb Ccbi C - - Ce e (1 1 C C E 1, extrsic (1 E ) ) Other eleent values do not chane...
Eitter Deeneration, Unbypassed eitter resistance ex C - C ex - 1, extrsic (1 E ) can shown by eleentary nodal analysis, work throuh Key observation: deeneration by this ethod results a series put resistance, which can crease C char tie.
Eitter Deeneration, cobation case Ccbx bb Ccbi bb Ccbx Ccbi C ex C ext - - Ce ex e C (1 C E ) 1 1, extrsic (1 E )
Eitter Deeneration and Area Scal 1 Consider the CS stae. f then we have a 1 C ( en bb ) C cb eitter area Ae current density Je Current Ae*Jee transconductance put capacitancec collector capacitanceccb base resistancebb we desire a [( )(1 ) ] en bb a A, ext L, ext L L,
Eitter Deeneration and Area Scal 2 eitter area Ae current density Je Current Ae*Jee transconductance put capacitancec collector capacitanceccb base resistancebb Ce e Bier transistor, fore deeneration eitter area kae current density Je Current kae*jeke transconductancek put capacitancekc collector capacitancekccb base resistancebb/k now deenerate: e picked such that (1e)k trsic transconductancek extrsic transconductancek/(1e) put capacitancekc/(1e)c collector capacitancekccb base resistancebb/k
Eitter Deeneration and Area Scal 3 Ce e We have ade the transistor K ties bier, then deenerated by K :1. We are left with the orial and C, but have creased Ccb by K :1and decreased K :1 a a 1 1 C en C en k C cb bb So, appropriate choice of Cbb [ (1 )] kc [ (1 ) ], ext Ccb, and ives the hihest bandwidth bb kc cb en L k bb (1, ext cb bb by ), ext k k exchanes delay ters associated with bb vs L en L L L
Eitter Deeneration and Area Scal 4: Eitter Follower Case Why iht we want to do this?
Eitter Deeneration and Area Scal 5: Eitter Follower Case Ccb1 1 Ccb2 L bb1 C1 bb2 C2 Consider only ters a1associated with the CE stae, bb2 a1... kccb2 out,1 k Note that the undeenerated ( 1 ) bb C bb2 L L C2 k tieconstant of an HBT, ext is several ties1/ 2πf τ, and can a ajor bandwidth liit. Area scal/deeneration as above is one ethod to address this. out,1
Ft-doubler staes.the Darlton evisited 1 L 1 L Q1 Q2 ee ee C1 C2 1 L bb1 bb2 ee C1 C2 ecall the iproveent Dap provided by ee. is there a larer lesson here?
2 Kds of Darlton: en L en L Q1 Q2 Q1 Q2 ee ee EF collector rounded Collectors tied toether f collectors are tied toether: AC collector currents of both transistors contribute to output :) Both transistor Ccb's undero Miller ultiplication :(
Ft-doubler staes 2 c1 out 1 - C1 e1 11 c2 ee1/1 2 22 C2
Ft-doubler staes 3 out ee ee ee ee ee ee ee ee e e c C j C j C C C j C j C j C j C j ω ω ω ω ω ω ω / 2 / hence and 2 / 2 /...so ) ( 1/...hence / such that Choose ) (1 ) / (1 ) /(1 ) / (1,, : Work fro out 2 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 ee1/1 C2 C1 11 1-22 2 c1 c2 e1 out
Ft-doubler staes 4 c1 out 1 C1 - ee1/1 e1 11 2 c2 22 - C/2 C2 out / jωc / 2 and out 2 / jωc..we have doubled f τ! 2 f τ / jf Note that this analysis has ored bb and Ccb...we have certaly not doubled fax, nor will we have doubled overall circuit bandwidth, iven the presence of these other parasitics.
ft-doubler vs Darlton thk ters of current as: H21 (2*H21H21*H21) (1H21) H21(1H21) C2 Current a is Sce / out Y c1 2H out c2 21 / ( H / jf ) Current a varies at lower frequencies as ( 2H 21 1 ) 2 21 ( H 2( f where / jf / jf which ives hih current a but neative put conductance 21 2 τ ) 2 ( ( 1 f f τ τ H 21 2 ) ) 2 2 f τ )... / jf
ft-doubler vs Darlton thk ters of current as: H21 2*H21 (1H21) H21 C2 H21 Current a is Sce / out Y c1 2H out c2 21 / 2H 1 2( f / 21 where H jf ) 2 jf 2 f Current a varies at all frequencies as (2 f τ τ 21 ( jf τ f τ 1 / jf (2πC / jf ) 2 ) / 2)
ft-doubler vs Darlton current as:
ft-doubler correction for Base resistance LCbb/ c1 out 1 - C1 e1 11 c2 ee1/1 LCbb/ bb 2 22 C2 The dicated ductance is necessary for equal current splitt tween the 2 transistors the presence of bb. n this case the put ipedance is C/2 series with bb/2 aa note that this correction is sificant cause bbc>>c/
ft-doubler vs Darlton What is the conclusion of all this? We can view the ft-doubler as a special case of the connected-collector Darlton with heavy eitter-follower load: this case the second-order (resonant) response is entirely suppressed. More enerally we iht vary the EF load to vary the dap. (The particular case of power aplifiers favors the ft-doubler due to efficiency reasons )
Tun: to prevent reflections, to peak a Zo Zo C Zo outzo S 21 1 Zo / 2 jωcz / 2 jωcz / 2 1 0 S11, where Z 1 0 / 2 Zo jωcz jωc The put capacitance has hurt both S11and S21, put atch and a 0
Pi-section put tun. Zo L Zo CxC/2 Zo CC/2 outzo Absorb the transistor put capacitance to a pi -section C C L τz Effective for freqeucies such that the pi - section isshort (hence o C / 2 τ / Z (2C Z o ) Z f0 < 1/ πzoc) o o 2 Ga flatness and atch iproved for f<fo, but ade worse for f>f0
T-section put tun. Zo L/2 Zo Zo L/2 CC outzo Absorb the transistor put capacitance to a T -section C C L τz o C τ / Z (2C Z o ) Z o o Effective for freqeucies such that the pi - section isshort (hence f0 < 1/ πzoc) Note that for a iven C, we have doubled fo relative to the pi -section case...
T-section tun feedback aplifiers Zo L/2 Zo f L/2 CC Zo L/2 Lf Zo Zo outzo CC By Miller Approxiation : L f f Z o (1 A) ( L / 2)(1 A) This is frequently used 50 Oh FBAs...daner is reduced stability.
Brided-T-section put tun. Zo L/2 Zo C/2 Zo L/2 CC outzo C C L τz o C τ / Z (2C Z o ) Z o o nsofar as the transistor has an put ipedance odeled by C, S11is exactly zero.s21 nevertheless rolls off at about the sae frequency as the T -section case...
Brided-T-section put tun. Karthik Krishnaurthi
Tun Networks use Microstrip eleents... Zo L CxC/2 Zo CC/2 Zo L CxC/2 Zo CC/2 Zo L Cx CC/2 Zo
Distributed Aplifiers : Theory synthetic dra le synthetic ate le HEMT put/output capacitances absord to artificial put/output les broadband circuit ; a/bandwidth liited by HEMT resistive parasitics (f ax ) distributed structure Bra frequency put/output transission le sk-effect losses
Synthetic Transission Les transission le section le section ductance le section capacitance HEMT put capacitance synthetic put/output le fored by transission le sections transission le characteristic ipedance Z L/C cutoff (Bra) frequency f B 1/ π LC delay T LC
Transission Le Loss lossless le frequency-dependent loss α 2 2 2 4π f C1 Z0 / 2 frequency-dependent loss α Z0 / 2
HEMT Equivalent Circuit siplified equivalent circuit eleent values scale with HEMT size fτ 2πC s f f r ds / 4r / ax τ i
CS HEMT TWA
CS HEMT TWA--LC equivalent
CS HEMT TWA--SS odel
TWA liits to a and bandwidth... Gate (put)le loss : 2 Nα < 1/ 2...sets a hih frequency liit causeα ω C Dra (output) Le Loss Nα nput - Output Delay Misatch Low - Frequency Ga S 21 N(T d ate < 1/ 2...sets a a liit causeα T N dra ( Z o ) < 90 0...just requires / 2 we et des riht... / 2)(capacitive deeneration ratio)...toether with above liits, sets feasible a - bandwidth Bra Frequency f < 1/ π LC...can ade very hih with lots of very sall transistors...no proble... d Z o ds 2 i...
Undaped Darlton FBA 20 15 S 21 10 5 0-5 S 11-10 -15-20 S 22 0 10 20 30 40 50
Feedback Aplifier with Follower Driv ft-doubler 10 Gas, db 5 0-5 S 21 S 11-10 -15 S 22 0 10 20 30 40 50 60 70 80 Frequency, GHz
80 GHz HBT Distributed Aplifier 15 10 S 21 5 Gas, db 0-5 -10 S 22-15 S 11-20 0 20 40 60 80 Frequency, GHz
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