Microwave Engineering
`
`APPLE ET AL. EXHIBIT 1017
`
`1
`
`

`

`Microwave Engineering
`
`Second Edition
`
`David M. Pozar
`Univerdy OF Massachusetts at h h e r s t
`
`@
`
`JOHN W a E Y & SONS, INC.
`New York
`Chichester Weinhei~n
`Brisbane a Singapore Toronto
`
`2
`
`

`

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`
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`
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`the numhrr 111 [rceh cut each !'rdT d u ~ s lint exceed the ,Inlt~uni of IWW g r ~ w t k
`
`r l f m y FIT d
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`thlr voA bcqoad that pcermirtcd b j SFC~IOI~S
`107 untl 108 ~rf rhe 1976 Unitcd Snleh
`Act u i t h o ~ t thc prmlssaon or the cop?ijght
`oa'ncr i.; unldwful. R e q u e u ~ ror pcrm~w.in~l
`or i'nnhrr mfurrn~~~rm h w l J h t ndclrc,tc.il lu
`rhr Ptrrn~~?,siuflk kpnr?rncr~i. Julm l\'~lrk & Srmg, 1 " ~ .
`
`Cthrm. (f Cflnge~s Lbbf@~r$ or F~Mrc-a~in?d
`))ttfd,
`Prw;tr. Uavtd M
`Microwave t.ng1rlwrine / D;l\iJ hl k m r -. ed,
`p. m ,
`ISBN 0-471- I7Wh-5 ( C I L H ~ : nlb ppperi
`1. M~~rt)wrtvrs. ?. hhsronare deu'im,
`I- Tkfc.
`77i;7876.P6Y
`I B W
`671 31 1'3-dc20
`
`j , Mcr~a~vfi mui15,
`
`97-2W8
`=F
`
`3
`
`

`

`Contents
`
`1 - ELECTROMAGNETIC THEORY
`
`1
`
`2 . A Short History nf Microwave
`
`1
`
`I. 1
`
`I
`
`.
`
`Inrroduction tn Mjcrowave Engineerjng
`Rpplicalions of Microwave hglneerinp
`3
`EZdgirteerirrg
`1.2 Maxwell's Equations
`5
`1.3
`Fields in Media and Bnufldw Conditions
`Fields ar a D i e l e c ~ c
`11
`Fields at a Gencraf Mntcrial Intcrfnce
`Fields at the interface with a Perfecl Conductor (Electric
`lnre+ice
`14
`' h e Magnetic UtalI Boundary condition
`15
`14
`Wall 1
`I
`Tke Radiaciut~ C~aditi~a 15
` The Wave Equation and Basic Plane Wave Solutions
`16
`I'he Helrnhnl~z Equation
`Plane Waves in a Lossless
`16
`Plane Waves in a Genera Lossy Medium
`16
`Medium
`a
`Plane Waves in 3 Good Conductor
`I 4
`t .5 GeneraI Plane Wave Solutions
`21
`Circularly Polarized Plane Waves
`23
`1.6 Energy and Pu~:s:cr 26
`29
`Pnwer Abwrbed by a Grlod Conductor
`1.7 Plane W a v e Reflectinn from a Media Interface
`31
`Lossless Medium
`General Mrdium
`36
`34
`PerfectConductor
`Conductor
`[mpcdance Concept
`36
`1.8 Oblique Incidcnce at a Dielectric lnlerface
`39
`Perpendicular Polari~alion
`PardlIel Polarization
`40
`43
`Total Reflection a d Surface Waves
`1.9 Some UseIul Theorems
`45
`4.5
`The Reciprocrry Theorem
`The Uniqueness Theorem
`49
`
`9
`
`18
`
`30
`32
`
`Gmd
`TheSur-facr
`
`4 1
`
`Image 7heoq
`
`47
`
`4
`
`

`

`2
`
`TRANSMISSION LINE THEORY
`
`56
`
`2. I
`
`j B
`
`r
`
`Pt~in~crfM~w~:D~.eih-~!!s
`
`76
`
`r
`
`T l ~ c Slomd
`
`8 3
`
`The Multiple Rzflec~ion Lriewpoinr
`
`35
`
`Thc Lumpcd-Ekmznl Circuit Mullel for a Trmsmisisirm Lint.
`56
`Wave Propaeation on R Tmmissi~li\ Line
`58
`7hc Loss1c.s~ 1.inc
`2.2 Fir Id Analysis (IT Tr;insmission I-incs
`5'3
`'l'he Tslegrapher E i p a t i t r n h ncnved
`Trat~s~nisr;irrn Line Panrne~ers
`~ I I r
`from Field Analysis af a Curtvial Line
`Proparalion Con&@,
`h:+
`Itnptldnncc, a1111 Power Flow tbr the Lo~desa Ctyaxial Line
`64
`2.3 The Tenninared Lossless Linu
`65
`SpzcialCa~esoILos~lt~aTrminaltrdI-incs b8
`7-1
`i ~ ? f L i tVL~pfl3
`2.4 Tile S ~ ~ i j t l i C'liarr
`73
`Thc Camhincd Inlpedmce-Adrllimc'c Smirh C ' h a
`78
`Line
`2.5 The QWXL~T-WAY~ Trn~ftrrner
`
`83
`T h c 1mprd;mce Viewpoint
`2.6 Gerwrator and 1.md 1Misrnaiches
`87
`Grneralrw Mntuhcd lo 1,oadcd
`Imad Matchcd to Line
`88
`fi9
`C u n j ~ g a e M;it~-hing X9
`Line
`2.7 Lossy Transmission tincs
`91)
`ThrLi~n-LussI-ins
`E)I)
`Terminalcd 1,ussy Line
`94
`Anenuntion
`
`The Distortiotilesi; Line
`92
`The
`ThePenlrrharionMethildfnrClalcularing
`43
`0
`The W11eeitr tncremsnral Induc~wcc Rulc
`96
`
`3
`
`TRANSMISSION LINES AND WAVEGUIDES
`
`104
`
`105
`L
`
`1 1 1
`
`113
`
`TF M d r s
`
`1 17
`
`3.1 Genmd Solutit~ns r~)r TEhI. TI',. and TM Wa\-es
`TE Wo\,es
`TEM W a ~ c k
`109
`107
`I Ill
`Th1 Waves
`Attenuation Due ul DieIectric Loss
`l t 2
`3 -2 Pard lcl Plate Waveguide
`TEh1 Modes
`112
`TM M d e s
`r
`3.3 Reclangular Wavepnide
`120
`TE,,,, Mt&i ~f a-Part-d Iy
`TE Modcs
`?'%I Mudeh
`1 3 3
`+
`125
`131
`PoinroJln~erest-: WrnegadideFEunge~'
`Loaded Waveguide
`3.4 Circuliir Waveguide
`I T Modes
`13r
`3.5 Coaxial Line
`141
`TEM Modcs
`I 4 I
`ITighcr-Order hlodes
`!r~llfyr.e~s[: Corr.xicd C(~nrtcc~~lrs 14fi
`
`1 3U
`132
`TM M O ~ S 137
`
`142
`
`r
`
`Prririi of
`
`5
`
`

`

`Contents
`
`147
`
`Puinf rf Int~resr:
`
`3.6 Surface Waves m a Grounded Dielectric Slab
`Thl Mndes
`TE Modes
`15I1
`147
`152
`Ror)r-k-i'irtdilip A / K ~ r ; t / t f l ~ s
`153
`3.7 Siriplinc
`Formula5 for h)pagatiua Corrsml. Clldrncteristic Tmpe&nce. and
`An Appmxi~mte Eleclrostarir. Salufinn
`I54
`Attcnu~ttion
`0
`3.8 Microsrrip
`I(itl
`Fumwlas fur Effective D i c l ~ ~ r i c C o m ~ n ~ . Charactcrislic lmpzilancr. and
`An Appmximate Elecrrostatir Solulion
`1
`Arrenuritjon
`3.9 The Transvcrsc Resonance Technique
`167
`TMModesI'or~t.l'mjlelPlatcWavg~~ide 168
`Partially Landed Rectangular LVnveguidz
`1 h9
`3.111 WAI e Velocities and Dispersion
`171)
`170
`Group V~locity
`3.1 1 Surnmq- of Transmission LLres and Waveguides
`173
`P n i ~ ~ i r ~ ~ ~ ~ ~ ! ~ ~ ~ ~ ~ r ; P u n ? ~ ~ ~ @ & @
`Oth~.rT~lpz.+~fLirle~andC.~uide.s 174
`w
`uf T
`i
`
`176
`L
`
`Thl, Modes of a
`
`157
`
`164
`
`MICROWAVE NETWORK ANALYSIS
`
`182
`
`190
`
`I97
`
`A Shifi in Reference
`Pairir of
`+
`ZIW
`
`ltnpedance and Equivalent Voltagch and Currenrs
`I 83
`Equivalei~t Volragcs and Cmrnts
`181
`The C?unrept
`Even and Odd Prupcrtles of ZIii) and rid)
`1187
`(11- Imprclmce
`Impcdawe and Adn~mmcr Matrices
`191
`Kecliprucal hTetkf,c~rks
`Losslcss Networks
`19.1
`196
`The Scattering Mtttri.~
`i H
`Rcriprocal N c ~ ~ l n r k r and Lussless Nctwnrks
`Gencr~1izt.d Scat~eri ~rg Paramctcra
`Pimeri
`201
`Irt re r.e.1~: The Verlo r Ncq~rjurk Ann l p i -
`205
`The Transn~iquion (ABCD) Matrix
`206
`Relatioil to Lmprdaacg M , ~ i x 2119
`N E I W U ~ ~ S 210
`2 13
`Slgnrtl Flow Graphs
`Dccnmpasition of Signal T;lr)u. Graphs
`217
`A ~ l a l y ~ r Calibration
`Micrf>nlaiv C i ~ * r ~ f { $ 222
`Discontinuiries and hIodal Analysis
`221
`hlt~dal 22nalyqi~ ur 3n ICPIarir: Step in Rectanguls Waveguide
`Micro.uriJ) L ) i ~ ~ r ~ n t i d ~ i p
`~ ? { I ~ ~ I P ~ E I
`CCnrnJt~scrriu~ 229
`Excitation r r f Waveguides-Electric
`and Magnetic Cumnts
`Curren~ Sheets -l-llat Escire Only One Waleguidt h.Iode
`230
`Excitatinn from an Arbitra~y Flcc~l-ic nr Magnetic Cumnt Source
`
`E q u l v g l c ~ ~ Circuits (or 'L'wu-Port
`
`Application lo TRI, Network
`2 1-1
`r
`Pr~inr r.!/' Inreresr: Cnnaputer-Aided Derig?? for
`
`325
`
`Puirll
`
`230
`
`232
`
`Made
`
`6
`
`

`

`Contents
`
`4.8 Excitation o i Waveguides-hperr ure Coupling
`237
`Crlupling Through an Aperture ill rr Traosveme Waveguide Wall
`
`C ' u u ~ l i r ~ g 'I'hrnugh ail :\lirrti~rc in thc Broad Wall uf a U:lvesuids
`
`140
`23.3
`
`5
`
`IMPEDANCE MATCHING AND TUNING
`
`251
`
`254
` 257
`
`Pt)i!ti tf
`
`Sencc Sruhs
`
`262
`
`Analytir. Solutiufl
`271
`273
`
`2711
`
`I
`
`I
`
`~
`
`~
`
`~
`177.
`
`~
`
`~
`
`c
`
`~
`
`~
`
`o M ~
`
`285
`
`Matchi t~g with Lumpcd Elcments ( Networks)
`752
`hnalj~ic S d u r i o ~ 253
`Smith Chm Solutions
`o r M
` f
`i
`i
`s
`P r
`i
`
`I
`.
`:
`Single-Stub Tuning
`258
`2rL)
`Shunt Stubs
`Dcluhle-Stub Tunirlg
`266
`S~niEh Chart S~ilutiun ?hh
`Thc Qumcr-%'aye Transfmner
`'I'hc 'Theory of Snlull Reflections
`~
`~
`Srnglc-Sccti0n Traforrrier
`17fi
`Biiionlial Mulf isect ion Witching Transl'onncrs
`278
`Cheb) shcv Multi.sct.ri~~n Matching Transfom~ers 181
`De3ign of Cbebyshev Transformzrs
`283
`Chebysher Polyrrt~rnids
`288
`Tapered Line5
`Lxpont3nti;rl 1-aper
`290
`Trrprr
`29[
`The Bode-Frtno ri-i tcri on
`
`Triangular Taper
`
`28 I
`
`I
`
`KIapfe1t~e.h
`
`2115
`
`6
`
`MtCROWAVE RESONATORS
`
`300
`
`6 . Series and ParalIel Rrsunwt Circuits
`1300
`Series Rescmmr Circuit
`a
`IJl~lutyled Q
`306
`I.uarlcci ~ i ~ d
`6.2 Transmissicm Line Resonators
`Shnrr-Circuitcd
`'2 1,in~'
`30h
`3 1 1
`Opcii-Circu ited X,'2 Line
`6.3 Rcrlmgular Waveguide Cavities
`3 1
`Resonanr Freqliencies
`6.4 Circdar Waveguide Cavities
`Resamrs~ Freqrrencic~
`3 1 E
`323
`6.5 Dittlcccric Resonators
`re son an^ Frequencies of TGjr+ Made
`6.6 Fobry-Rrul Kcso~~atnrs 328
`338
`Stabiliiy ol Opcn Resunators
`
`30U
`I'nrnllel Rrhonwl I'ircuit
`
`303
`
`306
`
`Shorl-I:ircuited A!'Q 1 . h
`
`? 1.0
`
`a
`
`3 13
`Q r ~ t ' he TEII,, Motic
`
`3 15
`
`318
`w
`
`(2 ~ j f the 'E,,,Y Mude
`
`320
`
`374
`
`7
`
`

`

`Contents
`
`332
`
`6.7
`
`Excitation of Resonaiurs
`332
`Crihcal Couplmg
`Resonator
`4
`c
`6.8 Cavity Perturbarions
`Material Perturbation.,
`
`A Gap-Vuuylcd Micr~strip
`337
`.An Aprrlure-Louplcd Cavity
`340
`340
`
`hshp?brh&ms
`
`349
`
`7
`
`35 1
`Four-R)rt Networks t Directional
`J'j7
`i
`
`0
`I
`
` M
`
`-
`
`3fi(
`
`U W U ~ Power D ~ b ~ s i o u and .l--Ww
`
`368
`374
`U e ~ i g ~ ~ f M n I t ~ h o l e C o u p l ~ ~ ~
`379
`
`POWER DIV1DERS AND DIRECTIONAL
`COUPLERS
`351
`7.1 Hasic Propeltics of Dividers and Couplers
`Three-Pori Nerworkc IT-junctiodsl 351
`$5)
`Couplcrl; I
`I
`I
`7.2 Thr 1'-Junction Pc)i\cr Divider
`339
`I,r,sdzsh Div~dcr
`Kzsirtitr' Divider
`360
`363
`7.3 The U'ilkinsun Power Divider
`36.;
`Elen-Odd Mudc r\nulvsls
`U7ilkinac,n Dj~idrrs
`l h 7
`- 4 Wavcgu~dr: Direction~l Couplers
`Bcrhc I ir)le r o ~ ~ p l c r 3hV
`7.5 The Quadrature (90") Hybrid
`Evcn-Odd Mode Anrrlys&
`380
`7 6 Coupltd Line Dircctiunal Coupler3
`383
`Coupled Line T h a q
`384
`Design iti' Coupled Lrne
`Ursipn r j f ' hlultisacrion Coupled Line Couplers
`Couplers
`389
`7.7 Thc Lange C.'uulilrr
`3'38
`40 I
`7-8 The 180 Hybrid
`EI en -LWcl htude A nalj ,qjs gf &r Riny H y W
`Analysis oF UIP Tapred Cnupld Ltnc lT>trtid
`41 1
`Magic-T
`4 I I
`7.9 Other Couplcr5
`Pnirrl of Jrri~r~st: l'Jte Rejiei.trl~)zrlcr
`
`3~)4
`
`403
`4117
`
`E r e n - W : M ~ d k
`8 Waveguide
`
`J l J
`
`8
`
`MICROWAVE FtLTERS
`
`422
`
`423
`8 . I PrrinJ~c Struc1urr.s
`Andju.; o i Infmiie Psri~tdic Structure$
`424
`Tcrmtnared Penodic
`k- i Dbgranls and '&;lie Veltrcluzs
`478
`Smctttre?.
`427
`43 I
`8.2 Filter Design by rhu lmage Paranletcr Melhod
`Irnagc In~pudancec and ?-rnn\fc.~. Functronh fbr Two- Furl ks;ctwc~rb
`43 1
`nr -lltrived Fihea* 5ccti:tions
`Co~js~ant-k Filtr~ Scci~ons 43?
`Cumposrte Filters
`440
`
`436
`
`8
`
`

`

`Contents
`
`8.3 Filter &sign Ay the Inseltioh Lass Metlmd
`143
`Maximally Flat Low-Paas Filler
`Characteriza~inn by Piwer Loss Ratio
`444
`Equal-Rippie Low-Paw Filter Prototype
`347
`Protorygc
`350
`Linear Phase Low-Pass Filter Pruraypes
`45 1
`452
`8.4 Filler Trr-tnsforinations
`Impedazlcc and Frequency Scaling
`Transforrnauons
`357
`462
`8.5 Filler [nlplemcntation
`Richard's Transformalion
`462
`Irnpedancr: and ,4dm~~lancc
`Inverters
`8.6 Stepped-Impedance Low-Pas Filters
`470
`Approximate Equivalent Circuirg for Short Trwsmissian Line Sections
`474
`8.7 Coupled Line Filters
`Filter Pruper~ies of a G>upled Lint Section
`Bandpass Filters
`477
`8.8 Filters Llsing Cocrpled Resonarors
`486
`Bandstup and Bandpass Filters U3ing Quarler-Wave Rcsonat~rs
`4W
`Bandpass Filters Using Cupxitively Coupled Resnnators
`Direct-Coupled Waveguide Cavity Filters
`493
`
`170
`
`474
`
`r
`
`Design o f Conpled Line
`
`486
`
`1
`
`454
`
`Bandpms and Bmdstop
`
`Kuroda's Tdentiries
`
`464
`
`a
`
`r
`4hX
`
`9
`
`. THEORY AND DESIGN OF FERRIMAGNETIC
`COMPONENTS
`497
`
`5 1 1
`512
`
`r
`
`S I 8
`
`9.1 Basic Properties of Ferrirnagnetic Materials
`498
`498
`The Fcrmeahility Tensor
`Circularly Polarized fie&
`Effect of Loss
`506
`Demagnetization Factors
`508
`51 0
`Interrst: Pernrn~rent M0gnt.r~
`9.2 PIme Wave Propagation in a Ferrite Medium
`Prupagation in Direction of Bias (Faraday Rotation)
`Transverhe to Bins IBirefi-inge~~ce) 5 13
`Y .S Pr'ropugarion in a Fcmte-Loaded Rectangular Waveguide
`x,,, Modes of Waa~eglride ufith a Single Fe;lrrtile Slab
`518
`of Waveguide with T w o Symmetrical Ferrite Slabs
`52 1
`523
`9.4 Ferrite lsulators
`Rrscmmct: lsolaturs
`$23
`530
`9.5 Ferrite P11ase Shifters
`Nonrecipmcal Latuhmg Phase Shifter
`The Gyrator
`S h i f ~ r s 533
`9.6 Ferrite Circulators
`535
`Pmpenies d a Mismatched Circulator
`
`Poirrr of
`
`Propap;uiun
`
`T&,M&
`
`527
`
`Thc Field Displaccmznt Isdaror
`
`r
`
`Other Types of Ferrire Phdse
`
`530
`53.5
`
`537
`
`J ~ c t i o n Circulator
`
`537
`
`9
`
`

`

`t o - ACTIVE MICROWAVE CIRCUITS
`
`Cantents
`
`547
`
`Noise Power and Equivalen~
`548
`Mensurement of Noisc Temperature by tllc
`Noise Figure nf a
`575
`NoiscFig~re
`
`r
`
`10.1 Noise in Microwave Circuits
`538
`Dynamic Range and Sources nf Noisc
`Nnise T e m p c r i ~ c ~ r ~ 550
`Y-Gctnr AJc~hod
`35-3
`Cascaded Syrletn
`557
`10.2 Detectors and Mixers
`559
`Single-Ended Mixer
`DiMe Rtxuers and Delec~nn
`559
`5155 Bdmced
`Other Tl'pes uf Mixers
`+
`571
`M i x e ~
`Intcmr>dulatiun
`568
`Poi111 (?j'irr,ere.vr: nllr~ Sprrrridm A~wL?;,-pr 573
`574
`Products
`576
`10.3 PIN D i d e Control Circuits
`577
`Single-Pvlr Switcheh
`10.4 M i c r o w a ~ e Integrared Circuits
`583
`Hybrid Microwave I n t e p t e d Circuits
`581
`584
`htegrawd Cixuits
`0 . 5 Overview of Microwave Sour~*cs
`Solid-State Snurces
`5E9
`
`. PIN &de %asc Shifterg
`
`?do
`
`+ Monolithic Microwave
`
`988
`Tubes
`~ i c r o w ~ v ~
`
`593
`
`11
`
`DESIGN O f MICROWAVE AMPLIFIERS AND
`OSCILLATORS
`600
`1 1.1 Characterisrics of Microwave Transistors W 1
`Micro1va~-e Fieid Effzcr Trnnhisro-rs / FETs)
`bD1
`Transistors
`604
`11.2 Gain and Stability
`606
`TWO-PO~ Power Gains
`Stahili1)-
`606
`1 1.3 Single-Stage Transisror Amplif~er Design
`6 18
`61 8
`Design fur htaxilnum Gain !Ci.mju;atc Matclfirrsj
`Ckcles and Design for Specrfid Gain (Unilateral Device)
`628
`Arnplifjzr Design
`1 1.4 Brodbmd Transistor Aioplificr Design
`6-12
`632
`Distributed A~nplihefi
`Balanced Arnpliliers
`11.5 Osciilatar Design
`641
`Tmnsistor
`641
`One-Pi~ri Negative Rcs~hvace OscilIa~ors
`Diclechic Resona~or Oscillators
`648
`6.M
`Oscillri~on
`
`Mim~rruaw B i p l s r
`
`61 2
`
`Constminl Gain
`Low-Noise
`
`622
`
`h35
`
`12 - lNTRODlJCTlON TO MICROWAVE SYSTEMS
`
`655
`
`655
`12.1 System Aspecth of hnlenntls
`Dtfifilli~ of Imporram Antenna Parameren
`655
`h t m n a mrn Chamccerisucs
`65fi
`Antennas
`a
`Efficiency. Gain. and Tempewhm
`661
`
`Basic Type of
`6.56
`
`Anrerina
`
`10
`
`

`

`xv t
`
`Contents
`
`663
`
`12.2 hlicrowavc Communication Syslerns
`Types of Communication Systrrns
`The Friis Power Transmission
`t>67
`I'msmirters and Receivers
`+ M i ~ m ~ a v e
`663
`656
`Formula
`Noisc Chariiclerizarion of a M j ~ r ~ ~ n v c
`667
`Rccciver
`Frequenr y -Multiplexed Systems
`670
`12.3 R u d x Systems
`672
`-1'tlr Radar Equation
`673
`Pul.qc Radar
`RacfxCrussSectio~~ 678
`Ra&ar
`677
`12.4 Kadiv~nctn,
`679
`Theory md Applicalions of Radiometry
`679
`The Dicke Radir~rnewr
`h8 1
`Radir~melcr
`t2.S Micron-avepropagatinn
`68.5
`685
`Arrnospheric Effects
`688
`Efects
`12.5 Orher Applications and Topics
`689
`E n e r ~ ~ Transfer
`Micrtm;lvz Hzaing
`683
`Biological Effec~s ;sad Sdety
`69 I
`Wartare
`
`675
`
`Doppler
`
`'I'otal Puwer
`684
`
`GroundEffecrs
`
`AX7
`
`Plasma
`
`690
`694
`
`Eiectrunic
`
`APPENDICES
`
`697
`
`698
`Prefixes
`Vector Analysis
`698
`700
`Besxl Functionti
`Other Mathematical Results
`Physical Constants
`7114
`Canductivities for Some Malcrialb
`704
`Dielectric Constam and Lass Tangents fur Some Materials
`Properties o f Some Micmwave Ferrjte Marerids
`705
`Standard Rec.tangu1 ur Waveguidr D;ira
`706
`707
`Standard Coaxial Cable Data
`
`303
`
`705
`
`INDEX
`
`709
`
`11
`
`

`

`10.2 Detectors and Mixers
`
`noise figure of the transmission line-amplifier cascade. What would be the noise
`figure if the amplifier wert placed a1 the anlenna eliminating the umsmissiun
`line'! Assume all components are at an ambient temperature of T = 3M) K.
`
`Snlrstinl~
`The loss factor of h e coaxial line is L = 10~1'' = 1 +58. so from ( 10.16) the
`noisc figure of the line is
`
`F y n (IU.l1), W noise figure of the amplifier is
`c
`150
`F Q = l + - = l + - = 1.52 = 1 .$1 dB.
`To
`290
`Then (10.21) gives the noise figure of the cascade as
`
`since l/Gr = L = l+58 for h e coaxial line. Withour the transmission line. the
`noise figure would be that uf the amplifier itself. w 1.81 dB. So wc see that
`the effect of the lossy feedline reduces the noise iigure: c ~ f the system by nbuut-
`2 d B a subsranrial amount. Snrnetimes such a line cannot be avoided in the
`front end of a receiver. Its effect. however. will be deleterious. because not only
`does the line icser add noise bur. since its gain is less than unily. i t increases
`0
`b e effect of rhe noise of the next stage.
`
`DETECTORS AND MIXERS
`Detectors and mixers use a nonlinear device to achieve frequency com~tersion of an
`input signal [I]. Microwave diodes are most comsnonIy used as the nonlinear clement, but
`Wansistcrrs can also be used. Figure 10.10 illiistrates he three basic frtqucncy conversion
`functions of rerrtification. detection, and mixing. We will first discms the nonlinear
`voltage-current chaacreristics of a diode. and then use a s m a l l - s i p d analysis 10 describe
`the operation of vario~s circuib that perform these hoctions.
`
`Diode Rectifiers and Detectors
`A diode is basically a nonlinear resislor, with a DC V-1 cbmctwistic tba can be
`expressed a<
`
`where a = q/nkT, and q is the charge of an electron, k is B o l m a m ' s consml, T is
`temperature, n- is the idedty factor, and 1, is the saturation current [4l, I5l- TYPicAly,
`
`12
`
`

`

`560
`
`Chapter 10: Active Microwave Circuits
`
`FIGURE 10.10 Basic operations of recfification, detection, and mixing. (a) Diode r e c ~ e r .
`(b) D i d e detector. (c) Mixcr.
`
`is between I o - ~ and 1 0- A. and n = q/nk'T is approximately I 425 mV) for
`T = 290K. The idealty factor. ra. depends on the stmcLure of the diode itself. and can
`vary froin 1.2 for Schuttky barrier h i d e s to about 2.0 for painr-cont;ncl silicim diodes-
`Figure la 11 shows a typical diode V - I characteristic. NOW let the diode voltage be
`
`is a DC bias voltage and r . is a smali AC signal vnltage. Thcn (10.24) can be
`where
`expanded in a Taylor series about I..b as I~llows:
`
`13
`
`

`

`10.2 Detectors and Mixers
`
`56?
`
`f i r
`
`-
`
`1, 1 -
`t
`FIGURE 10.11 V-1 charac~eristics of a diode,
`
`v
`
`where lu = Iwo) is the DC bias currenl. The firsr derivative can be evaluated as
`
`which defines Ri, the juoctiun resistance of thc diode, and Gd = 1 /Rj, which is c d e d
`the dynamic conductmw of he diode. The second derivative- is
`
`Then (10.26) can be rewritten as the sum of the DC bias cment, ID,
`and an AC current, i:
`
`Thc three-tern1 approxiniation for the diode current in (10.29) is called the .r,trrrl(-signu/
`appro~~imariun, md will be adequa~e for most of uur purposes.
`The small-signal approxi~na~ion is based on the DC vultage-cmnr relationship of
`(10,24), and shows thar thc equivalent circuit of a diode will involve a nonlinear re-
`sistance, Ln practicc, however, the AC characteristics of a diode also involve r e d v e
`effects duc to the smcture and packaging of thc diode. A typical equivalent circuit for
`a diode is shown ia Figure 10.1 1. The lcads and contracts of the dinde package lead to
`a series inductance. L,. a d shunt capslcllmcc, C,. The series resistor. R,, accounts for
`
`IrlGIJKE 10.12
`
`q v j v d e n t AC circuit model for a d i d e .
`
`14
`
`

`

`562
`
`Chapter 10: Active Micmwave Circuits
`
`contact and current-spreading resistance. Cg aad Rj are h e junction cqacitace
`resistance. and are bias-dependent.
`
`I
`
`FX.AhfPT,E i0.4
`
`D i d e Package Eflects
`A diode in m axial-lead packase has the following equivalent c h i t parameters:
`- -
`Cp = 0.10 pF. L , = 2.0 HH, Cj 7 0.15 pF, R, = 1051. ~d T5 = 0.1
`CalculaIe and plot Lhe in~pdance 01 this diode from 4 to 14 GHz. for a bias
`current lo = O and In = 60pA. Ignore the change in Cj with bias, and assume
`a -- I /(25 mV].
`
`s~!idrif~ll
`From 110.27) the junction resistance for the two bias states is
`1
`75 mV
`=--
`for = 0, R j = -
`r~[I[l f I,) 0. I /r A
`- - -
`-
`for lD = HI ,ilA, H j =
` + 1
`(60 c 0. I ,
`I
`(
`7'klr h e inp~rt impedance can be calculated from tlsr equi vdent circuit of Fig-
`ure 10.12; the resuit is pintled versus frequency on a 50 61 Smith chxt in Fig-
`0
`ure 10.13.
`
`- 2.5 x lc9 fl,
`
`= 41752.
`
`15
`
`

`

`10.2 DeteEtow and Mixers
`
`563
`
`3 rectifier application, a diode is used lo convert a fraction of an RF input s i ~ a l
`tn DC power. Rectificarion is a very common function. and is used for power rnoni-
`to;, automatic gain control circuits, and signal strength indicators, If the diode voltage
`consists of a DC bias voltage and a small-sigal RF voltage,
`
`then (10.29) shnws that h e d i d e current will he
`
`ID is the bias current and r~iG2/4 is the DC rectified cun.en1. The output also contains
`AC signals of frequency ;L~o. and 2ufl [and higher-ibrder harmonics), which are usuaUy
`filtered uut wih a simple Iow-pass filter. A current sensitivity, ,dl. can be defined as a
`measure of the change in DC output current for ;x given inpur RF power. From ( ! U.29)
`
`the RF input power is J ; G ~ / ~ (using only the: first [em). while { 10.3 I ) shuws the change
`in DC current is $Ck/4. The current sensitivity is then
`
`An open-circuit voltage sensitivity, ,ij,:;, can be defined in lerms of the voltage drop across
`the junction rmlstmce when ?he diude is open-circuitd. Thus,
`
`Typical values for the voltage sensitivity uf a diode range fronl 400 to 7500 mVlmW.
`In a derector application the nonlinearity of a diwde is uscd to de~noduIale an m-
`pIitude moduIated RF carrier. For ~s case, the diode volbge can be expressed as
`u(t) = LU(I + rn cos dmtj cos dot.
`10.34
`is the modulation frequency, % is the RF carrier frequency (uu > > w,,,], and
`where w,
`,m. is defined as the modula~ion index (0 5 m 5 1). Using (10.'34) in (10.9) gives the
`diode current:
`$(t) = u D G ~ ( 1 + m cos w,t)
`
`,
`cos wilt + -Gd(l + m cas w, tj2 cos 'uoi
`?:;
`2
`
`- dm)t $. 3 cOS 2#ot
`m,?
`-
`$- m. C W S ( ~ ~
`-I+ i~,,)t -k ~ c u s ( ~ ~
`
`16
`
`

`

`564
`
`Chapter 10: Active Microwave Circuits
`
`The bequency spectrum of this c)ulpat is show11 in Figure 10.14- The nutput cuneni
`r m s ~vhich are linear in the diode voltage (terms fiwlriplying q G d ) have frequencies of
`4 0 and + d m . while the t r m s that are proportional to thc square of the diode voltage
`(tem~s mul~iplying I:;G>/ZI include h e frequencies and relative mpliludes listed in
`Table i O , I .
`The desired demodulated output of frequency dm is eaily sepzrated from the un-
`desired cornpo~lents with a Ii~w-pass filter. Observe hd he amplitude of this current
`is msdG&/2, which is proportional to ihc power of the inpul signal. Ths y ~ m r r - / u w
`behavior is the usual npcrating co~~dition for detectw diodes, but can be obtained onIy
`over a restricted rmzc of input powers. If the input power is too large, small-signal
`conditions will not apply. and the output will berrr~me saturi~ed and approach a linear.
`and then a constanl. i i:ersus P chxacteristic. Az very low signal levels fie input signal
`will be lost in the noise fluor of h e device, Figure 10,I5 shuws the typical zl,,
`versus
`P,,, characteristic. where rhe tlutpur voltapr: can be cunsidered as the voltage drop across
`a resistur in series with the diode. Squue-law operatian is p~ticularly important for
`appiications w h e ~ power levels are inferred from detector vultage, as in SWR indicaton
`and signal level indicators. Derectors may be DC biased to an operaring point that
`provides the besi sensitivity.
`
`TABLE 10.1 Frequencies arid Retati~e Amplitudes of the Square-Law Output of a
`Detected AM SignaI
`
`Frequency
`
`Relalive Amplitude
`
`17
`
`

`

`10.2 Detectors and Mixers
`
`FIGURE 10.15
`
`Square-law region fur 3 typical diode deteclur.
`
`log Ph
`Id&ml
`
`Single-Ended Mixer
`A mixer uses the nonlinearity of a diode to generate an output spectrum consisting
`of the sum and difference frequencies of two input signals. In a receiver application. a
`low -1evd RF signal md an RF Iwai uscillatw (LO) signal are mixed logether 10 prducc
`an intermediate frequency (IF). frF = ~ R F -JLoy and a much higher frequency, fw + fW.
`which is filicrcd o u ~ . See Figure 10.16i, The IF signal usuafly has a frequency betwee0
`1U and ! W MHz, and rill be amplified with a low-mist m~plifie~. This is called
`a heterodyne receiver. and is usefill because it has much better sensitivity and noise
`characteristics (using an IF ~n~plifier lninimizcs I /$ noise) than the direct detectinn
`scheme discussed in the previous scciion. A heterodyne syslern also has h e advantage
`of being ab!e to tune over a band by simply chanpng the LO freqirency. withour the
`need for a high-gain, widehand RF anlplilie~,
`As shown *m Figure 1#.16b, a mixer c m also be used in a m s n l i t t e r to offser he
`hquency of an RF signal by an amount equal to fF. This is a convenient technique.
`as it allows [he use o f identical local oscjlla~nrs in the transmitter and receiver; a single
`oscillator may senre this purpose in a radar or transceiver system.
`There are several vpes of mixer circuits. but Ihe shpIest is ihe single-e~dd mi-rer;
`single-cnded mixers often are used at; pad of nwrs sophisticated mixers. A typical
`single-ended mixer cireuir is shown i n Figure 1U. 17, where an RF signal,
`
`is combined with m LO signal.
`
`ura(t) = e~fl cas ; ~ o i , .
`
`10.37
`
`and fed into a diode. The combiner may be a simplc T-junction combiner. or a direcrional
`coupler. AQ RF matching circuit may precede the dicdc, and the diode may be biased
`r h ~ o ~ i p h c 3 v . k ~ ~ * a d ~ w DC to pass whik blocking RE;. Frorn I t0.29). h e d i d e c m e n I
`
`18
`
`