class notes, M odwell, copyrighted 9 ECE145a / 18a ower a Deitions Mark odwell University o Caliornia, anta Barbara rodwell@eceucsbedu 85-893-344, 85-893-36 ax
ower a Deitions: ummary class notes, M odwell, copyrighted 9 Transducer a Available a Insertion a s ij s ij s = o ij = o = * T / av, power power available rom erator eral - case ga A ga av, a / av, power available rom ampliier power available rom erator withput matched 1 av, a / av, power delivered to o power available rom erator ga a 5 Ohm enviroment o Operatg a s = * ga ij /, delivered withput matched power power delivered rom erator Maximum Available a MA s = * M A may ij av, a /, delivered not exist = * power available rom amp liier power delivered rom erator ga with both p ortsmatched Ater impedance-matchg: ij,matched s = o = o match ij,raw match 1, matched 11, matched,raw, matched but only i unconditionally stable
Types o -orts To Consider class notes, M odwell, copyrighted 9 The - port might be neither nor 11 a transistor The - port might be transistorwithmatchg built - 11 & a close or equal tozero The - port might be ampliier witharbitrary a eral ij For all o these, we could choose toadd * additional* matchg networks at theerator and at the
Insertion ower a class notes, M odwell, copyrighted 9 From - parameter properties, 1 But i av, / 4 And i / / av, / 4 1 but only i hence 1 power delivered to o power available rom erator o ga a (5 Ohm?) environment
Transducer ower a class notes, M odwell, copyrighted 9 T / av, power delivered to power available rom erator eral - case ga Ampliier put impedance matched to source ( ) Ampliier put impedance matched to enerator impedance o oad impedance o T depends upon both s and
Operatg ower a class notes, M odwell, copyrighted 9 /, delivered power power delivered rom erator Note : /, hence p ga delivered / avg withput matched T i * Ampliier put impedance *is * matched to source( ) Ampliier put impedance matched to enerator impedance o oad impedance o depends upon but not upon s
Available ower a class notes, M odwell, copyrighted 9 A av, a / av, power available power available rom amp liier rom erator Note: hence ava a / avg ga / avg withput matched T i * Ampliier put impedance matched to source ( ) Ampliier put impedance *is * matched to enerator impedance o oad impedance o A depends upon s but not upon
Maximum Available ower a class notes, M odwell, copyrighted 9 av, a /, delivered power available rom amp liier power delivered rom erator Note: hence ava /, delivered imultaneo us put/p ut matchgmay / avg ga with both put and put matched T i ( * and not be possible MAmay not exist * ) Ampliier Ampliier put impedance put impedance *is * matched to source ( *is * matched to ) enerator impedance o oad impedance o depends upon neither s nor
MA Does Not Always Exist class notes, M odwell, copyrighted 9 1 and 1 represent teraction terms betweenput and put I 1 1, then put & put tung become mutually teractive Withsuiciently is not possible large 1 1, simultaneous matchg o put & put In this case, no longer exists This condition corresponds Will becovered later to potentialampliier stability
class notes, M odwell, copyrighted 9 1 Ater Matchg to = MA Beore Matchg 1, matched / avg / o / 4 o but / avg, raw o : 1, matched, raw 11, matched, matched ThedBsertionga o theampliier is thedbmao thetransisto r Implication : network tells examg us thega the transistor M Abeore we design a matchg weshould expect toobta ater matchg
Mason's Unilateral ower a (1) class notes, M odwell, copyrighted 9 1) Cancel device eedback with external losslesseedback ) M atchput and put esultgpower ga is M ason' s U Y 4 overall 1 Y 11 1 Y overall 1 1 1 1 Notecareully the dierence between Y Unilateral a ij and Y overall ij M onolithicamp liiers are not easily made unilateral U mostly o For simplebjt model, In III - s,u showsp eak rom C U hard to use or For bulk CM O, C U should be OK or historical relevance U rolls o at - db/decade U useul or extrap olation to d ds - - extrap olation is sheilded by substrate ds s extrap olation to IC design d teraction M/MA, db 3 U 5 15 Common emitter Common base 1 Common Collector 5 1 1 1 Frequency, Hz
class notes, M odwell, copyrighted 9 Mason's Unilateral ower a (): Additional ots Makes put-put couplg = No teraction o put, put tung networks mostly o historical relevance Mason's ga is variant with respect to embeddg the device a lossless reciprocal network It is the only* unction o the DUT -port parameters which is variant with respect to such embeddg 3 U 5 *except, o course, any other unction which has a 1:1 mappg with U M/MA, db 15 1 Common emitter Common base Mason, "ower a Feedback Ampliier," Transactions o the IE roessional roup on Circuit Theory, vol CT-1, no, pp -5, June 1954 doi: 1119/TCT1954183579 http://ieeexploreieeeorg/stamp/stampjsp?tp=&arnumber=183579&isnumber=34 M upta, "ower ga eedback ampliiers, a classic revisited," IEEE Transactions on Microwave Theory and Techniques, vol 4, no 5, pp 864-879, May 199 doi: 1119/13739 http://ieeexploreieeeorg/stamp/stampjsp?tp=&arnumber=13739&isnumber=374 Common Collector 5 1 1 1 Frequency, Hz
ghakowta's ga class notes, M odwell, copyrighted 9 1) Add external lossless eedback to imize the MA/M, Y, overall overall 1 1 ) tabilize i necessary 3) Match put and put esultg power ga is ghakowta's a, (U 1) U ( U 1) 1/ 1/ This is the highest ga obtaable under conditions o unconditional stability has a 1:1 relationship with U a Capability o Two-port Ampliiers A ghakowta & A Boothroyd International Journal o Electronics olume 1, Issue 6, 1966 http://dxdoiorg/118/71668937931 A ghakowta and A Boothroyd, "On ear Two-ort Ampliiers," IEEE Transactions on Circuit Theory, vol 11, no 1, pp 169-169, March 1964 doi: 1119/TCT19641863 http://ieeexploreieeeorg/stamp/stampjsp?tp=&arnumber=1863 &isnumber=3381 as, db 35 3 5 15 1 5 U, MA/M common emitter MA/M common base 1 1 1 Frequency, Hz
class notes, M odwell, copyrighted 9 Why a and p Matter: Matchg Network Design Circuit simulators (AD, etc) provide contour plots o a vs source impedance and p vs impedance available ga operatg ga These, the a & p circles, show the variation transistor ga as erator and impedance are tuned The center o these circles are the (erator, ) impedances required or imum ga,opt,opt We can then separately design Input & Output Tung Networks to provide these impedances added to device, the ampliier is realized Caution: the above assumes that MA exists; we must exame this critical pot the next lecture
class notes, M odwell, copyrighted 9 imple Matchg Example: Unilateral Device Model gs D m match ds gs m gs ds m ds gs m ds gs m gs gs ava gd C j g C g C g C I g g I C I I C ) ( 1 ) ( rom spection, while, at then match, we impedance- I 4 where 4 4 ) / ( / and because / / device unilateral imple model; 1, 1 1