MICROWE ND RF DESIN Case Stuy: Osc2 Design of a C-an CO Pesente by Michael Stee 4.4 to 5.5 Hz Oscillato Case Stuy Osc2: Design of a C-an CO tune 3.6nH 0.5pF D1 D2 D3 D4 0.5pF 47.5 Ca 2k 2.2nH out 2.2pF Z L L CHOKE cc I cc Reaing: Chapte 20, 20.5,6 Inex: CS_Osc2 ase on mateial in Micowave an RF Design: Systems ppoach, 2 n Eition, by Michael Stee. SciTech Publishing, 2013. Pesentation copyight Michael Stee Slies copyight 2013 M. Stee. 2 Outline Reflection oscillato pinciples Common base Colpitts oscillato Reflection oscillato opeation Resonato an active netwok topologies Point of oscillation Reflection oscillato Y = +j Γ Γ Y = +j t the fequency an amplitue of oscillation: Y Y 1 1 ll equivalent. When the oscillation signal is small, i.e. fo oscillation stat-up: gets smalle as the oscillation signal buils up. 3 4
Common base Colpitts oscillato The C R an L R cicuit is calle a esonato but esonate at a fequency below the oscillation fequency so the netwok looks like an effective capacitance. in C 1 L 3 H L tune C 2 Lchoke out Colpitts Oscillato Feeback Fom C R L R L 3 L C Colpitts Tansisto Configuation Output R L Dain souce Capacitance (coul also a aitional C 1 capacitance) Feeback output C 2 5 tune Lchoke C R Y = +j Reflection oscillato opeation L R L C One pot oscillato Output R L Y = +j Conuctance Susceptance Ieal mplitue Ieal Fequency, f s the amplitue of the oscillation inceases, the magnitue of the evice conuctance, eceases while the conuctance of the tank cicuit, is constant. s the fequency of the oscillation inceases the susceptance of the tank cicuit,, changes while, (ieally) oes not change. 6 Y = +j ctive evice ieal esponse One pot oscillato Y = +j Results in constant amplitue acoss the tuning ange. Results in low phase noise. Common base oscillato tune Y = +j Lchoke C R Γ L R Γ Y = +j L C Output R L Fequency, f mplitue Results in low phase noise. small vaiation in with espect to fequency is ok (an unavoiable at RF). lso often necessay fo oscillato stat up., especially fo COs tune Resonato netwok 3.6nH 0.5pF D1 0.5pF D2 D3 D4 ctive netwok 47.5 Ca 2k 2.2nH out 2.2pF Z L L CHOKE cc I cc 7 8
Resonato netwok tune Lchoke C R L R Inuctos ae RF open cicuits. L C Output R L tune 3.6nH Resonato netwok 0.5pF 0.5pF ctive netwok 47.5 2k 2.2nH out 2.2pF Z L 50 L CHOKE 47.5 cc I cc tune Resonato eflection coefficient 4 Hz tune 3 D1 tune D2 D3 D4 Inceasing fequency Stacke vaacto ioes incease RF beakown voltage. (aactos have tunable capacitance.) Tansmission line eplaces L R an has lowe loss. 9 10 ctive netwok Ieal tune Resonato netwok 3.6nH 0.5pF 0.5pF ctive netwok 47.5 2k 2.2nH out 2.2pF Z L 50 L CHOKE 47.5 cc I cc ctive evice eflection coefficient out Z L cc mplitue RF SHORT out Z L cc RF OPEN C b RF SHORT Inceasing fequency Inceasing signal level RF SHORT an C b ajust so that 0 1/ (Small signal) 11 12
Y = +j Γ Γ Oscillation point Y = +j 4 Hz Inceasing amplitue Y = +j Γ Γ Oscillation point Y = +j 4 Hz Lage amplitue Intesection efines oscillation fequency an amplitue. Want just one intesection fo single fequency oscillation. Rotation in opposite iections an with paallel tajectoies esults in low phase noise. (3 ) Inceasing fequency Intesection Inceasing fequency 13 Y f Y 0 f Oscillation conition: Note that 0 So phase noise is even bette than ieal situation. Inceasing fequency (3 ) Inceasing fequency Intesection 14 Topology outline. Summay Case Stuy Osc2: Pat Oscillation Conitions Initial esign objective state. oal is stable single fequency oscillation with low phase noise an high efficiency. To consie next: Detaile esign stategy. Oscillato stat-up equiements. Stategies fo avoiing multiple oscillations. Y = +j Y = +j If stable single fequency oscillation occus, then an That is, 1, 1/, o 1/ 1. Oscillation conition (vaiation of conuctance an susceptance) Known as Kuokawa oscillation conition 2. Conitions fo stat up of oscillation Slies copyight 2013 M. Stee. 15 D 16
Kuokawa oscillato conition Kuokawa conition fo stable singlefequency oscillation: 0 0, 0 The subscipt 0 efes to the opeating point. Descibes a single cossing of the eflection coefficient cuves Fo a fixe fequency RF oscillato is vey small so secon tem is negligible. Kuokawa conition simplifies to: 0 0, 0 Fo an RF CO, is not small ue to vaacto loss. So esign can be complex. Y = +j mplitue Fequency, Y = +j f 17 Kuokawa oscillato conition fo micowave CO esign Kuokawa conition fo stable singlefequency oscillation: 0 0, 0 Y = +j Y = +j chieving single-fequency oscillation can be a challenge fo micowave fixe fequency oscillato esign, an the esign complexity is much highe fo a micowave CO. Design using the full Kuokawa conition is foun to be too limiting at micowave fequencies. Thee ae othe consieations such as minimizing phase noise, e.g. we want the fequency of oscillation to be inepenent of the oscillation amplitue (this minimizes phase noise). minimizing DC powe consumption. conitions fo oscillato stat-up. 18 Kuokawa oscillato conition simplification Kuokawa conition fo stable singlefequency oscillation: 0 0, 0 Y = +j Y = +j Simplifie Kuokawa oscillato conition Kuokawa conition fo simplifie esign: 0, 0 0 Y = +j Γ Γ Y = +j So in CO esign the esign poceue must be kept simple, an this opens up the esign space to enable optimization of othe chaacteistics. Micowave CO esign stategy: choose a topology that Has an effective evice susceptance that is inepenent of signal amplitue (i.e., / = 0). Has a loae esonato conuctance that is inepenent of fequency (i.e., / ω = 0). Kuokawa conition fo simplifie esign: 0, 0 0 19 Design evice netwok so that 0 Design tank netwok so that 0 Recall unmoifie Kuokawa conition: 0, 0 0 20
ltenative simplifie Kuokawa oscillato conition Kuokawa conition fo simplifie esign: 0, 0 0 Y = +j Γ Γ Y = +j Simplifie Kuokawa oscillato conition Fixe fequency oscillato ey little loss in esonato oltage contolle oscillato Significant esonato loss (ue to vaacto ioes) 21 22 Common base Colpitts oscillato Lchoke tune Output C C R L R R L L Γ Γ Colpitts point of oscillation Resonato netwok ctive netwok tune 3.6nH 0.5pF 0.5pF D1 D2 D3 D4 47.5 Ca 2k 2.2nH out 2.2pF Z L L CHOKE cc I cc 1 2 POINT OF OSCILLTION HERE OR HERE Fo a fixe fequency oscillato eithe egion of oscillation is suitable. Fo a micowave CO egion 2 is equie because of esonato loss. 23 24
Resonato netwok tune Lchoke C R L R Inuctos ae RF open cicuits. tune L C Output R L tune D1 D2 D3 D4 3.6nH Resonato netwok 0.5pF 0.5pF ctive netwok 47.5 2k 2.2nH out 2.2pF Z L 50 L CHOKE 47.5 cc I cc Inuctos ae RF open cicuits. tune Simulate eflection coefficient of the esonato, Γ, of the C-ban CO. 3. (1 ) 4 Hz Stacke vaacto ioes Stacke vaacto ioes 25 26 Reflection coefficient of the esonato at iffeent biases Legen (1 ) 4.5 Hz (3 ) 4.5 Hz 4.2 Hz 4.5 Hz 4. 3. 4. 3.7 Hz (1 ) 4.4 Hz 4.7 Hz Compaison of oscillation points Oscillato Case Stuy #1 Oscillato Case Stuy #2 3. (1 ) 4 Hz (3 ) tune 4.8 Hz 4.5 Hz 20 Hz 15 Hz 4.7 Hz 4.9 Hz 4. 27 Point of oscillation in this egion. Point of oscillation in this egion. 28
Y = +j Conuctance Requie angle of evice Y = +j R P = 1/ Summay oscillation conitions 1. Kuokawa conition fo stable single-fequency oscillation: 0 0, 0 2. Simplifie Kuokawa conition (easy to esign to): 0 0, 0 Requie that ( / = 0) an ( / ω = 0). (If lossy esonato.) oltage contolle oscillato Significant esonato loss (ue to vaacto ioes) mplitue Want high R P = 1/ so is small. (a) Γ = 1.4 (b) Γ = 2 (c) Γ = 4 vesus the evice eflection coefficient angle. () is the oscillato Q fo Γ = 2. 29 3. Conition fo oscillato stat up (fo a CO with a lossy esonato). 30 Case Stuy Osc2: Pat C Resonato Design Y = +j Y = +j t oscillation Kuokawa oscillato conition simplification Kuokawa conition fo stable singlefequency oscillation: Y = +j 0 0, 0 Kuokawa conition fo simplifie So, ieally want esign: 0 0 an 0, 0 Γ Γ Y = +j 0 tune lso want Keeps phase noise low as oscillation fequency oes not epen on amplitue. - an is +ve so must be +ve Slies copyight 2013 M. Stee. mplitue mplitue 31 32
Resonato chaacteistic Resonato chaacteistic Γ Γ Γ Γ So, must be +ve 0 Y = +j Y = +j Line of constant conuctance Y = +j Y = +j lso No epenence on amplitue Conuctance mplitue Inceasing fequency 33 lso tunable, must be able to otate by vaying a tuning voltage. Oscillato stat up. 34 Resonato esign Γ Γ Lchoke tune C C R L R L tune Lchoke C R Resonato netwok esign Γ L R Γ L Inucto is an RF open cicuit. DC block Wie (low impeance) micostip tansmission line. 1. Keep esonato as a simple paallel LC cicuit. 2. L R an C R esult in high an can contol magnitue. 3. R comes fom L R (tansmission line) an C R (vaacto). 4. Depenence of an on amplitue comes fom vaacto. 35 + I Cj evese biase ioe is a vaiable capacito. tune vaacto ioe D 36
aacto ioe, tune aacto stack euces 0 tune D RF signal. Want negligible cuent flow (low shot noise). + I I tune I 0 tune RF signal. D tune RF signal. 1. Choose tune to minimize DC cuent. 2. Minimize cuent flow an. 3. ut a goo esonato will have a lage RF voltage swing. 4. Make sue tune minimizes cuent flow. RF signal. Cj tune RF signal. Cj RF signal. C eff What if RF voltage swing is too lage? Recall that we want 0 tune 4 tune RF 37 38 aacto stack euces an aacto stack inceases tuning ange tune tune tune tune + I I eate tuning ange since high cuent egions can be avoie. I + I I eate tuning ange since high cuent egions can be avoie. I 4 4 I 0 RF I 0 RF I 0 RF I 0 RF Cj C eff Cj C eff tune RF tune RF 4 tune RF tune RF 4 39 40
Final esonato justments tune RF chokes Capacitance ajustment (also DC block) justable shot cicuit tune DC block C Moel C TL TL Povie impeance tansfomation. 41 42 tune Reflection coefficient of the esonato at iffeent biases If cossove of an 1/ is as shown by then changing the tuning voltage fom 1 to 3 changes the oscilaltion fequency fom 4.5 Hz to 4.8 Hz. Legen (1 ) 4.5 Hz (3 ) 4.5 Hz 4.7 Hz 3. (1 ) (3 ) 3.7 Hz 4.2 Hz 4.5 Hz 4.9 Hz 4. 4. 4. 4.8 Hz 4.4 Hz 4.7 Hz 4.5 Hz 43 Summay: final esonato netwok tune Tansmission line euces loss compae to an inucto aacto stack euces esonato conuctance. aacto stack euces epenence of esonato amittance on signal amplitue. D1 D2 D3 D4 TL C 1 justments povie by, an C fixe afte layout 44
Case Stuy Osc2: Pat D ctive Netwok Design Y = +j Y = +j t oscillation tune Lchoke C R Reflection oscillato opeation L R L C Output R L Conuctance Ieal mplitue s the amplitue of the oscillation inceases, the magnitue of the evice conuctance, eceases while the conuctance of the tank cicuit, is constant. out Z L cc Y = +j One pot oscillato Y = +j Susceptance Ieal s the fequency of the oscillation inceases the susceptance of the tank cicuit,, changes while, (ieally) oes not change. Slies copyight 2013 M. Stee. Fequency, f 45 46 ctive netwok opeation L C Output R L mplitue Keep inepenent of amplitue to euce phase noise. ctive netwok Ieal The esistos ae equie fo biasing. L R L C Output R L RF SHORT tune 3.6nH Resonato netwok 0.5pF 0.5pF ctive netwok 47.5 2k out Z L cc RF OPEN 2.2nH out 2.2pF Z L 50 L CHOKE 47.5 cc I cc Y = +j One pot oscillato Y = +j (b) (a) Fequency, f Cuve (a) is simple ieal esponse, cuve (b) esponse is even bette. 47 RF SHORT RF SHORT C b an C b ajust so that 0 an ( f ) is paallel to ( f ). 48
Kuokawa oscillato conition Kuokawa conition fo simplifie esign: 0, 0 0 Y = +j an Γ Γ Design evice cicuit so that Y = +j 0 0 Small an lage signal 1/ Want 1. Lage at (fast stat up of small signal oscillation) levels. ( 1/ is small at a small signal level). 2. (low phase noise) 0 3. (unifom 0 amplitue of oscillation acoss tuning ange ) Oscillation statup 49 Inceasing fequency Inceasing amplitue 50 Reflection coefficient shaping Legen = 0.5 pf, C b = 0 = 0.5 pf, C b = 0.5 pf CC = 0, C b = 0.5 pf DD = 0, C b = 0 1/ C 4 Hz D Inceasing amplitue 4 Hz 1/ 3.7 Hz 3.7 Hz Inceasing Simulate eflection coefficient of the esonato, Γ, an the invese of the small signal eflection coefficient of the active evice, 1/Γ, of the C ban CO fo vaious values of the compensation capacitos an C b. 1/ C (3 ) D 51 Simulate eflection coefficient = 0.5 pf C b = 0.5 pf. (3 ) 1/ oscillation level 52
Multiple cossings out Z L cc 4 Hz 1/ 3.7 Hz Multiple simultaneous oscillation 4 Hz 1/ 3.7 Hz Measue Simulate eflection coefficient of the esonato, Γ, an the invese of the small signal eflection coefficient of the active cicuit, 1/Γ, with = 0.5 pf an without C b. (3 ) 1/ Inceasing level 53 (3 ) 1/ Inceasing level 54 ctive netwok Summay: active netwok esign out Z L cc C b ctive netwok nees to be optimize using measuements (cannot moel sufficiently). an C b enable shaping of 1/ out Z L cc Cicuit at RF: out Z L RF OPEN cc Nee to avoi multi oscillation. Nee inepenent of fequency. (Constant amplitue oscillation.) Pi attenuato (with 294 Ω esistos in the shunt legs an a 17.4 Ω seies esisto). The output filte is a 50 Ω PF. 55 C b Nee lage fo fast statup. 56
Case Stuy Osc2: Pat E Final Iteation on CO Design CO schematic tune 3.6nH Resonato netwok 0.5pF 0.5pF ctive netwok 47.5 2k 2.2nH out 2.2pF Z L 50 L CHOKE 47.5 cc I cc (a) justable featues out Z L cc (b) L tune Slies copyight 2013 M. Stee. (c) 57 58 Final CO cicuit Resonato an active evice cicuits. Resonato netwok ctive netwok Resonato netwok ctive netwok justable featues 59 60
Measuement of the active netwok Measuement of the active cicuit with a 50 Ω test fixtue at the inteface of the esonato an active netwoks. The ca was cut at the inteface to make the connection. The 35 ps elay is ue to the length of the SM connecto is equie to efeence measuements to the cicuit ca ege. The peio of a 5 Hz signal is 200 ps. Resonato measuements Measue Γ at 3. Raw 5. Coecte 3.8 Hz So the connecto has an electical length of 63 o. The eflection coefficient is otate by 126 o. So measuements must be coecte. The SM connecto also has paasitic capacitance an inuctance. Coection will not be pefect. 61 ctual measuements otate by 126 o 62 Measuement Measue Γ at 3. = 0.5 pf an C b = 0. 1/Γ moves to the ight as the signal level inceases. The intesection of 1/Γ an Γ etemines the oscillation fequency an the signal level. 4.8 Hz 5. 5.4 Hz 4.4 Hz 3.8 Hz 4 Hz Compaison 3.7 Hz Inceasing level 4.8 Hz 5. 5.4 Hz 4.4 Hz 3.8 Hz 1/ Small signal Simulate = 0.5 pf an C b = 0. tune = 3 Small signal 0.4 S 2.5 Measue 64
Simulation an measuement accuacy Lage signal chaacteistic Simulation fielity Measuement fielity Lage signal 10 m RR RR Locus of oscillation 5. 5. 21/2 D EM simulation use but sie wall capacitances not taken into account. Moel limitations. Connection esistances ae not accounte fo. Full effect of SM connecto not accounte fo. Paasitics of connecto Γ fo 0 (cuve a) to 9 (cuve g) Lage signal 1/Γ. e f 4.5 Hz a b c g 3.5 Hz 4.5 Hz 4.8 Hz Fiel lines teminate on flange. 65 66 Resonato ajustments D1 D2 Cicuit at RF: ctive netwok ajustments an C b enable shaping of 1/ out Z L cc D3 D4 C justments povie by, an C C C b C b 67 68
Measue tuning cuve Measue output powe an hamonics t out (befoe the banpass filte) inicating low level hamonic content. 69 70 Phase noise measue Summay: C ban (5 Hz) CO tune 3.6nH 0.5pF 0.5pF 47.5 2k 2.2nH out 2.2pF Z L 50 L CHOKE 47.5 cc I cc Micowave CO esign is a methoical pocess. Simulation togethe with measuements leas to a methoical esign pocess. uil in ajustability in esign. Micowave cicuits nealy always equie tuning of each item. 71 72