54 Philips ech. Rev. 38, 54-68, 1978/79, No. 2 Frequency-dividers for ulra-high frequencies W. D. Kasperkoviz To derive from a periodic elecrical signal anoher periodic signal wih wice, he period a logic circui is ofen used. A high frequencies - 1000 MHz and above - however, he ransiions beween he high and low volage levels of a logic signal ake up a no inconsiderable porion of he period. One way of explaining his is o say ha, mainly because of he parasiic capaciances and he delay imes in he ransisors, he circui is unable o pass he higher harmonics of he ideally recangular signals. A reducion in he number of ransisors and oher componens o he absolue minimum helps o shif his limiaion asfar as possible owards he higher frequencies, bu even hen here is sill à ransiion region a he highes frequencies in which he operaion of he circui can be described equally well as analog or digial. The auhor gives a series of examples of circuis ha he has reduced o an ofen elegan simpliciy, which ogeher form a complee progressionfrom digial o analog. The 'ravelling-wave divider' is applied in a digial uning sysem for elevision receivers. Inroducion In various branches of elecronics here is a need for circuis ha will operae as frequency-dividers a ulrahigh frequencies - and even above 1000 MHz - or a any rae a frequencies approaching he ransiion frequency of he ransisors now available (he frequency a which he curren gain has fallen' o uniy). Such circuis, would be useful in professional measuremen and conrol equipmen, digial uning sysems for elevision and radio and in quarz-conrolled elecronic waches. Each applicaion has is own special requiremens for he highes frequency o be divided, he supply volage, he curren required and he inpu sensiiviy. The emperaure range is also of significance. The degree o which he circui can be inegraed is very imporan. Someimes he circui mus operae wih sinusoidal inpu volages even hough i forms a par of a digial sysem; his is he case where he minimum curren is required, for insance in waches. There is no esablished mehod for ranslaing he requiremens for a paricular applicaion ino a circui. Neiher is i 'possible in mos cases o ell beforehand wheher he requiremens can be me. I is however relaively simple o give some general rules for he componens of he circui. For example, i seems very reasonable - hough unproved - ha he ransiion frequency of he ransisors should be higher han he Dr.-Ing. W. D. Kasperkoviz is wih Philips Research Laboraories, Eindhoven. highes frequency o be divided, paricularly for circuis of high inpu sensiiviy. Similar semi-quaniaive reasoning applies for he parasiic capaciances and inducances presen in any circui: he RC ime consan associaed wih each parasiic capaciance and he L/ R ime consan for he parasiic inducance should be less han he shores period or lowes pulse-widh of he inpu signal. R represens he inernal impedance of he circui, which varies srongly from node o node. I is ofen difficul or even impossible o makean esimae 'of his impedance, because i depends on he sae of he circui. In addiion o keeping he number and value of he frequency-limiing parasiic elemens as small as possible, i is desirable, where possible, o choose he inernal impedance levels such ha he maximum inpu frequency is no deermined by a single RC or L/R ime consan ha dominaes he circui. Where his is he case i is ofen possible o increase he sensiiviy or he maximum frequency by changing resisance values or bias currens. The rules given above have o serve in he absence of a proper design procedure. They allow he designer considerable freedom in he opological arrangemen of he circui. This is more so wih inegraed circuis han wih circuis made from discree componens, since hese are inerconneced by wires a leas a few millimeres in lengh, which have an inducance of a
- --- - ----------------~-----------------, Philips ech. Rev. 3S, No. 2 FREUENCY-DIVIDERS FOR UHF 55 few microhenries. In inegraed circuis he parasiic inducance of he inerconnecions is usually negligible on accoun of he small dimensions; bu here again i is desirable o keep he number ofinerconnecions small, because beyond a cerain degree of complexiy he number of crossovers increases, and so does he number of parasiic capaciances (usually of a few picofarads). In boh inegraed and discree circuis, keeping he number and value of he parasiics as low as possible hus corresponds o keeping he number of inerconnecions as low as possible. A small number of inerconnecions in general means a small number of componens, paricularly of componens wih hree or more erminals. In frequency-dividers, which consis of resisors, capaciors and ransisors, hese are he ransisors. A comparison of he parasiics in he differen componens also shows ha he ransisors should be limied in number, since he Miller capaciance and he base-emier capaciance of he ransisors are usually much more significan han he parasiics in he resisors and capaciors in boh inegraed circuis and hose wih discree componens. A number of dividers for high frequencies will now be described. One approach ha will be followed is ha L DEI DE 2 DI I D 2 2 I r, al r T 2 0. 2 I-- V r Vf V n_ru r I I I I I I I I I I I I I I I I Val I I I I ~ I I I I I I I I I I I I V Ö2 I I I I ls!mlsiml I I I I I 1 2 3 4 -f Fig. 1. a) Block diagram of a binary divider-by-wo using he maser-slave principle. This consiss of wo laches wih single exciaion DEl and DE2. These are bisable when he volage a inpu T is a he high level (maser sae), bu only pass he level of inpu D o he oupu if he volage a T is low (slave sae). Complemenary rigger volages VT. Vi', which serve as inpu signals o he divider, are applied o he inpus Tl and T2. b) Waveforms of he rigger volage VT and he oupu volages V1 and V2. The period of he oupu volages is doubled. M maser sae. S slave sae. ime. of he reducion in complexiy, in paricular in he number ofransisors [11. Anoher approach shows ha here is no sharp disincion beween digial and analog: he operaion can no longer be compleely described by referring o high and low logic levels, bu i is essenially deermined by he naure of he ransiions via inermediae levels. Eiher approach can lead us o he 'ravelling-wave divider', a cyclic circui wih a circulaing periodic signal a half he frequency of he inpu signal. In oher circuis deliberae use is made of he volaile-memory operaion ha is presen in parasiic elemens such as he base-emier capaciance of a ransisor. This gives he circuis a dynamic characer and hey do no necessarily operae a low frequencies. To make he operaion ofhe various frequency dividers easier o follow he survey will sar wih he descripion of a convenional frequency-divider for binary signals. Binary frequency-divider using he maser-slave principle The block diagram of a frequency-divider using he maser-slave principle [21 is shown infig. la. I consiss ofwo laches wih single exciaion or D-ypeflip-flops - bisable circuis ha can be in eiher he 'maser sae' or he 'slave sae'. This depends on he volage a he rigger inpu T. If his volage is a he high level he lach is in he maser sae; he oupu volage a hen only depends on he logic sae of he elemen. If he volage a T is low, he lach is in he slave sae; oupu hen has he same logic level as inpu D. The wo laches in fig. la are riggered by wo complemenary volages V T and V:r,so ha one is always in he maser sae and he oher in he slave sae. Fig. lb shows he effecs ofhis on he oupu volages V l and V2. In he ime inerval I VT is high and VT low; lach 1 is herefore in he maser sae (M) and lach 2 in he slave sae (S). If we now assume ha l is high, hen D2 - and consequenly 2 - is high also. The complemenary oupu 2 is hen low, and so is Dl. In inerval 2 he roles are reversed. Lach 2 is now in he maser sae. I is sill a he high level. Lach I has gone ino he slave sae and oupu l has herefore followed Dl o he low level. This change-over ook place while VT was falling. While Vf is falling - and hence VT is rising - here is a similar changeover in lach 2, which hen goes ino he slave sae and remains here during ime inerval3. As shown in fig. lb, he reciprocal inerchange of in- [1] Improvemen of performance by reducion in he number of ransisors is also discussed by Z. E. Skokan, Emier funcion logic -logic family for LSI, IEEE J. se-s, 356-361, 1973. [2] A. Richardson and R. C. Foss, New binary couner circui, Elecronics Leers 1, 273, 1965.
56 ~... - W. D. KASPERKOVITZ Philips ech. Rev. 38, No. 2 This is due in par o he raher complicaed srucure of he lach circui, and also o he use of wo separae lach elemens ha conrol one anoher alernaely. However, by applying oher principles i is possible o make à divide-by-wo circui wih only one bisable elemen, and his implies a considerable simplificaion. One such approach will now be described. This is a dynamic circui, where unlike he previous one deliberae use is made ofhe shor-erm memory effec presen in he base-emier capaciance of he ransisors. Fig. 2. Circui of a binary divider-by-wo using he maser-slave principle. An oupu signal a half he frequency of he conrol signal VT, VT can be aken in complemenary form from he oupus l, l or 2, 2. Each lach circui DEl, DE2 consiss of a cross-coupled differenial amplifier (Tl,T2) ha funcions as a bisable memory elemen when he common emier curren hl is equal o I (maser sae), and a buffer differenial amplifier (T3,T4) conneced o he same collecor resisances, which is enabled when Is = I (slave sae). formaion coninues and afer wo ime inervals or wo periods of VT he oupu sae is reached again. Two periods of he inpu signal correspond o one period of he oupu signals Vl and V2 and he circui herefore works as a divider-by-wo. A more deailed circui diagram of he divider is shown infig. 2. The circui consiss enirely of differenial amplifiers, and all he signals are herefore applied in complemenary form. Each of he laches consiss of a cross-coupled differenial amplifier n,t2 funcioning as a bisable circui, a buffer amplifier T3,T4 and an inpu amplifier T5,T6. The inpu amplifier swiches he curren I supplied by a curren generaor eiher as hi o he bisable differenial amplifier Tl,T2 or as Is o he, buffer amplifier T3,T4. The curren goes o Tl,T2, when VT is high and Ts conducs, and o T3,T4 when VT is high and TG conducs. In he firs case he bisable differenial amplifier is acivaed ('enabled') and he buffer amplifier is no operaing ('inhibied'); he oupu signal depends only on he logic sae of he bisable differenial amplifier, and he elemen is herefore in he maser sae. If Vi is high, he buffer amplifier T3,T4 is enabled; he signals a he inpus D and ÏJ are immediaely passed on o he oupus while he bisable pair Tl,T2 is inhibied. The lach is now in he slave sae. As can be seen from fig. 2, his circui based on he maser-slave principle is raher complicaed; he many inerconnecions beween he nodes make i difficul o make a pracical version wih few parasiic elemens. Dynamic frequency-dividerwih only one bisable elemen Fig. 3a shows a dynamic divide-by-wo circui ha conains only one bisable elemen. This is he crosscoupled differenial amplifier Tl,T2 wih a common emier curren Ibi. The circui also conains a differenial amplifier T3,T4, which has negaive feedback via he exernal base resisances RB. ls common emier curren is Is. Boh differenial amplifiers have he collecor resisances Rc in common, so ha he oupu signals are added. The rigger volage VT and is complemen VT, which also form he inpu signal of he divider, are presened o he common emiers via he coupling capaciances C. In he absence of he rigger volage hi = I and Is = I'; I and l' are supplied by curren generaors. Their magniudes are chosen such ha he gain of he cross-coupled differenial amplifier is higher by more han one han ha of he differenial amplifier wih negaive feedback: his gain is proporional o he emier curren hrough he ransisors.
Philips ech. Rev. 38, No. 2 FREUENCY-DIVIDERS FOR UHF 57 This condiion is saisfied if Wih he bias-curren seings indicaed above, and in he absence of a rigger signal, he gain of he wo coupled amplifiers is greaer han uniy and he circui is herefore bisabie. A general picure of he volage variaions is shown in fig. 3b. The ransiion of he oupu volage V - V from one level o he oher always occurs a he railing edge of VT. In he maser-slave principle of fig. 1 he swiching process is acuaed by a second bisable circui, which does no change sae during he railing edge. The funcion of his second circui is aken over here by he base-emier capaciances of he ransisors T3,T4; he sae previous o he railing edge is sored emporarily in hese capaciances [31. The effec of hese capaciances will be shown in a deailed descripion of he operaion wih he aid of fig: 5. The ime axis is expanded in his figure; fig. Sa shows he railing edge of he rigger signal. During he falling edge of he rigger signal he charging and discharging currens of he coupling capaciors Care added o Ibi and Is; he coupling capaciors are of he same order of magniude as he base-emier capaci- I-I' > 2kT, Ree where k is Bolzmann's consan, T is he absolue emperaure o-"?-----+--..._ and e he elecronic charge. This can be seen from he following analysis. The curren i hrough he base-emier juncion of a ransisor.is given by c ~Ibi ~Is Vr 0 which approximaes i = IR ( exp VZ~ - 1), o VBEe I RI hl, exp kt ' where IR is he reverse-bias curren and VBEhe volage beween base and emier, see fig. 4. If he base curren is negleced, he collecor curren is also i. The change in collecor curren i wih he base-emier volage VBEis given by di e VBEe e. dvbe= kt IR exp kt = kt I. The volage gain A of he ransisor sage is he raio of he volage drop Vc across he collecor resisance o he base-emier volage: I Vf o--------j C ~I ~I' A = dvc = Re ~ = Ree i. dvbe dvbe kt We can consider he ransisor sage as half of a differenial amplifier. In fig. 3 he half of a differenial amplifier has a bias curren of I or r. If he bisable pair in fig. 3 is o have a gain Abl ha is greaer by more han one han As for he pair wih negaive feedback, hen his leads o he condiion ~c.;(i-i') > 1, which corresponds o he relaion saed a he beginning. -- Fig. 3. a) Dynamic divider-by-wo wih a single bisable circui insead of wo. The bisable circui is he cross-coupled differenial amplifier Tl,T2. The differenial amplifier T3,T4 has negaive feedback via he base resisances RB. The base-emier capaciances of T3,T4, in conjuncion wih he resisances RB, funcion as a dynamic memory, which makes a second bisable circui unnecessary. I' is so much smaller han I ha he gain of he combinaion of he wo differenial amplifiers, one cross-coupled and he oher wih negaive feedback, is greaer han 1. b) Waveforms of he rigger volage VT and he oupu volage V - V. The oupu is a half he frequency of VT and he volage only changes polariy a he falling edge of VT. A! he rising edge a peak appears in he oupu volage; his peak decays exponenially wih he ime consan of he baseemier circui of T3,T4. Fig. 4. Volage gain of a ransisor sage. VBEbase-emier volage. vc collecor volage. i collecor curren and emier curren, aken as equal here, wih he base curren negleced. Rc collecor resisance. (3] In H. H. Muller and W. J. Wu, A GHz IC couner using Isoplanar Il, 1974 IEEE In. Solid-Sae Circuis Conf. Dig. ech. Papers, pp. 20-21, a fas divider-by-wo ha only uses a single bisable circui is described. This circui operaes in he 'race mode', in which he oupu from is invered in a separae amplifier, hen coupled direcly o D o provide feedback. The inverer sage also funcions here as a shorerm memory. This circui conains abou hree imes as many ransisors as he one in fig. 3a, parly because i was necessary o derive pulses of fixed widh from he rigger signal.
58 W. D. KASPERKOVITZ Philips ech. Rev. 38, No. 2 ance of T3 and T4. The curren Ibi becomes smaller because of his superposiion, ~nd Is becomes larger by he same amoun. The effec of his is ha he condiion ha he gain in he bisable pair should be greaer by one han he gain in he pair wih negaive feedback is emporarily no longer saisfied, and he circui is emporarily monosabie insead of bisable (fig. 5b). Le us assume ha in he iniial sae before swiching hi = I flows hrough T2 and Is = I' hrough T3; he volages a he oupus are hen V = - If Re and V = -IRe (fig. 5c). The addiion ofhe charging and discharging currens from he coupling capaciors C produces immediae and corresponding changes in he collecor currens. The collecor curren of T2 falls and V consequenly rises; he curren hrough T3 increases and consequenly V falls. Because of he increase in V ransisor Tl sars o conduc, bu afer a small delay owing o he presence of he base-emier capaciance. The fall in V will sop T3 from conducing, bu here he presence of RB is responsible for a much longer f. Vr I I...J I ~----~ I IL _ ~-----=--- -IRe ---- --- - (I+I')Rc - Fig. 5. Diagram showing he variaion ofhe currens and volages in he dynamic divider-by-wo (fig. 3) during he falling edge of he rigger volage VT. The ime axis has been grealy expanded. a) Falling edge of VT. b) Variaion of he common emier currens hl and Is. For a shor ime hl is smaller han Is and he circui is no dominaed by he bisable differenial amplifier; i is hen monosable. c) Variaion of he collecor volages V and V when i is assumed ha he collecor currens of T3 and T4 have no ye changed. Since he curren in T2 changes over o Tl and T4 was no conducing, he curren hrough he righhand collecor resisance Rc is zero for a shor ime and V reaches he value O. The paern of evens for V is he mirror image of his. In fac he swiching of.he curren Is from T3', o T4 sars immediaely, alhough i is slower, and he acual volage variaion is shown by he hin lines. ime consan and hence a much longer delay. For he momen T3 remains conducing, so ha he sum of I and If flows in he lef-hand collecor resisance and V assumes a minimum value. In a similar way T4 sill remains non-conducing for a shor ime inerval, so ha no curren flows in he righ-hand collecor resisance and V reaches a maximum. Afer a delay, however, he bases of T3 and T4 go o heir new poenial. This is higher for T4 han for T3, so ha Is evenually passes hrough T4. This makes he siuaion exacly he opposie of ha a he sar. In fac he base-emier volages of T3 and T4 really begin o change o heir new values righ a he sar of. he swiching ime. This causes he peaks in fig. Se o be rounded off, as shown by he hin lines. I has been shown above how, saring from a divider-by-wo based on he maser-slave principle, a simplificaion can be made by leaving ou one of he bisable circuis and making use of dynamic sorage of informaion. However, his is no he only simplificaion possible. The nex secion shows how a simplificaion can also be obained, while reaining he maserslave principle and saic operaion, by changing he coupling beween he wo bisable circuis. Saic frequency-divider wih negaive feedback Fig. 6 shows a divider-by-wo ha is based on he maser-slave principle like he circui in fig. 2, bu has a fixed coupling beween he wo bisable circuis ha is independen of he rigger signal [41. The bisable elemens here are he cross-coupled differenial amplifiers TI,T2 and T3,T4; hese amplifiers are enabled in urn a a periodic rigger signal VT by he collecor currens Ib112 and Ibi34 of he differenial amplifier T7,Ts. This brings he bisable circuis Tl,T2 and T3,T4 alernaely ino he maser or he slave sae. 'Slave sae' does no mean quie he same here as in he circui of fig. 2, since here are no laches. In he slave sae of he ransisor pair T3,T4 he collecor volages are simply he collecor volages of Tl,T2' reduced bya volage divider. The wo bisable elemens are coupled symmerically via he resisances Ree; boh elemens affec one anoher in he same way hrough his pah. There is also a direcional coupling from he pair T3,T4 o Tl,T2 via differenial amplifier T5,TG wih common emier curren Is. Seen from 1',T2 his direcional coupling looks like a negaive feedback from he oupu signal IJ. V12, in which he feedback signal is also dependen on he sae of T3,T4. The wo forms of coupling work in he opposie sense. In schemaic erms he symmerical coupling wih Ree ries o make he polariy of he oupu <' ",;b
~. --.---~~---------------------------------------------------------------.~ I_ Philips ech. Rev. 38, No. 2 FREUENCY-DIVIDERS FOR UHF 59 volages /).VIZ and /).V34 he same, while he direcional coupling via differenial amplifier T5,T6 ries o force he pair TI,Tz ino a sae in which he oupu volage /). VIZ has he opposie polariy o /).V34. The special feaure of his configuraion is ha he asymmerical coupling beween T3,T4 and TI,Tz brings he differenial are in he maser sae. Le us assume ha in he saring condiion /).V34 is negaive. Because of he effec of he direcional coupling via T5,T6 he volage /).VI2 is hen posiive. This siuaion is sable unil VT sars o rise. Ibi34 is hen reduced o zero and Ibil2 increases from zero o I. While T6 was,already in he conducing Rc Fig. 6. Simplified saic divider using he maser-slave principle wih wo bisable differenial amplifiers Tl,T2 and T3,T4. The amplifiers are symmerically coupled via he resisances Ree. Furher coupling from T3,T4 o Tl,T2 is provided via differenial amplifier Ts,To. The circui has fewer ransisors han he one in fig. 2 and has beer high-frequency performance. amplifier T5,T6 o a sae such ha i helps o make T3,T4 change over when his pair goes ino he slave sae. The volage variaion is shown in fig. 7. When he rigger volage VT has he low logic level, Ibil2 = 0 and Ibi34 = I, so ha T1.T2 are in he slave sae and T3,T4 V T - Fig. 7. Volage waveforms in he simplified divide-by-wo circui (fig. 6). The slighly delayed reacion of differenial amplifier Ts,T6 is he cause of he peaks in he volage l!. V12; hese peaks help he bisable pair T3,T4 o swich over quickly. sae, T2 now sars o conduc, so ha /).VIZ increases. The rapid increase in /).VI2 o a high value makes he bisable pair T3,T4 swich over quickly, before Ibi34 has quie fallen o zero. However, once his has happened he differenial amplifier Ts,T6, which reacs wih some delay owing o he base-emier capaciances, also swiches over. Finally, T5 and T2 become conducing. The difference volage /).VI2 decreases a his las changeover, bu remains posiive. A he falling edge of VT, Ibil2 decreases. When hil2 has fallen o abou Is he lef-hand half of he circui becomes monosabie. The ransisor pair TI,T2 now swiches o a sae deermined by differenial amplifier T5,T6 and hence opposie o ha of T3,T4. The circui described here has been made up experimenally wih BFR92 microwave ransisors on a ceramic subsrae wih evaporaed resisors. The sensiiviy o sinusoidal rigger signals has been measured as a funcion of frequency for his experimenal version; here again he rigger signal is he inpu signalof he divider. The resuls are shown in fig. 8. The increase wih frequency of he smalles inpu ampliude for correc operaion is parly due o parasiic elemens, bu is of course also relaed o he ransiion frequency of he ransisors, which was beween 2 GHz and 3 GHz for he bias curren used. The circui also works a low (4) W. D. Kasperkoviz, U.S. Paen No. 3 996478.
60 W. D. KASPERKOVITZ Philips ech. Rev. 38, No. 2 300mV.----------------r----------~ Vi 500 1000 1500MHz -f Fig. 8. The minimum inpu volage Vi for correc operaion of he simplified saic divider-by-wo, as a funcion of he inpu frequency f The curve was measured for an experimenal circui using BFR92 microwave ransisors. The rise of he curve a he higher frequencies is due o he parasiic elemens in he circui bu is also conneced wih he ransiion frequency IT of he ransisors, which is beween 2 GHz and 3 GHz for he operaing poin used. Like he logic-circui frequency-divider wih wo laches, he divider wih negaive feedback described here is based on wo bisable circuis ha are alernaely in he maser and he slave sae. If circui 1 is in he maser sae, circui 2 is consequenly brough o a slave sae of similar polariy, bu if circui 2 is in he maser sae, circui 1 is brough o a slave sae of opposie polariy. Boh frequency-dividers herefore possess an essenial asymmery in he coupling beween he wo bisable circuis, and his asymmery is paricularly noiceable in he divider wih negaive feedback. However, in opimizing he many parameers of such a circui i is paricularly desirable o make he circui as symmerical as possible. In general an increase in he symmery no only reduces he number of free parameers, bu also gives more cerainy ha he maximum inpu frequency will no be deermined by a single RC or L/ R ime consan and could herefore be increased by a beer choice of componens. Fig. 9. Travelling-wave divider. The wo differenial amplifiers TI,Ta and T2,T4 are 'inerwoven' and are coupled by he resisances Rbi and Ra. The circui forms a closed-loop srucure in which here is a circulaing collecor-volage wave ha has half he frequency of he rigger signal VT, VT". frequencies, as would be expeced for a saic circui ha alernaes beween sable saes. The small increase in inpu signal required on going owards he lower frequencies can be explained by he decrease of he change in volage wih ime in a sinusoidal inpu volage of decreasing frequency. Since he operaion of he circui is in par dependan on cerain buil-in ime consans, oo slow a change.in he currens Ibi12 and hi34 resuls in an incorrec ransfer of informaion. This can be prevened by making he ampliude ofhe sinusoidal signallarger on decreasing he frequency. In he nex secion a frequency-divider is described ha has a maximum of symmery wih a drasic reducion in he number of ransisors. Divider-by-wo based on he ravelling-wave principle The principle on which he frequency-divider shown in fig. 9 depends can be called he ravelling-wave principle [51. The circui consiss of hree differenial amplifiers: he rigger or inpu amplifier T5,T6 and wo differenial amplifiers Tl,Ta and T2,T4 wih complemen-
Philips ech. Rev. 38, No. 2 FREUENCY-DIVIDERS FOR UHF 61 Fig. 10. In he explanaion ofhe operaion ofhe ravelling-wave divider (fig. 9) i is assumed ha he common emier currens Ii» and 124 decrease linearly from I o zero and increase linearly from 0 o I during he ime fs associaed wih he swiching. g Va + I I K -»> "",," o.ssr;... V r-, <,; - es, ors, Fig. 11. The collecor volage Vc and he base volage VB of he ransisors Tl, T2, T3 and T4 ofhe ravelling-wave divider during one sep of he swiching process. Afer four seps he saring posiion is reached again. Rb! and Rs are assumed equal. a) Sar of he swiching process; = O.The oal curren I flows hrough Tl. b) Afer a quarer of he swiching ime; = 0.25 fs. T2 sars o ake over he curren. c) f = 0.5 fs. A curren i flows in Tl and T2. d) = 0.75 fs. The greaer par of he curren has ransferred o T2; T2 also has he highes base volage. e) End of he swiching sep; f = fs. The oal curren I flows hrough T2. Transisor T3 has he same base volage as T2 and is hus prepared o ake over he curren in is urn. ary conrol. The collecor and base erminals of ransisors Tl o T4 are conneced o one anoher in a cyclic manner via coupling resisances Rbi and Rs; The operaion of he circui shown here can be described by considering i as wo closely coupled and 'inerwoven' bisable differenial amplifiers ha are brough alernaely o a maser and a slave sae. However, here are advanages in using a descripion ha pus less emphasis on he digial swiching beween maser and slave saes, bu pays more aenion o he smooh ransiions of he currens in he various branches of he circui. This will show more clearly ha he circui is parly analog in naure. Since he circui has a cyclic configuraion i is only necessary o describe he operaion during a quarer of he period of he oupu volage V - Vii, and o discuss he variaion of he collecor and base volages during his quarer-period. The volages during he remaining hree-quarers of he period can be derived from he volages during he firs quarer by cyclic inerchange of he numbers of ransisors Tl o T4. In many cases he inpu signal o he circui will be a sinusoidal conrol volage. To simplify he descripion of he operaion, however, he variaion of he drive currens ha and 124during he swiching of differenial amplifiers T5,T6 will be approximaed by a linear variaion (fig. la). The swiching ime a is deermined by he rise ime of VT. Fig. 11 shows he collecor and base volages-of he ransisors Tl o T4 a five successive insans during he swiching ime; he lengh of ime beween he successive 'snapshos' is always s. The following values are assumed: Rc = 100 n, Rbi = Rs = 50 n, 1= 10 ma. Fig. Ila illusraes he siuaion a he sar of he swiching process: = 0, ha = I, Iz«= 0 (see fig. 10). I is assumed ha ha flows only hrough Tl. The greaer par of he collecor curren of Tl flows hrough is collecor resisance Rc. A cerain fracion flows via he coupling resisances Rbi and Ra hrough he collecor. resisances of T2 and T4, however, and an even smaller fracion hrough he collecor resisance of Ta. The resul is ha Tl has a low collecor volage (abou - 450 mv), Ta a high collecor volage (abou - 150 mv) and T2 and T4 inermediae collecor volages' (abou -200 mv). The poins represening hese volages in fig. 11a are conneced by sraigh lines, which can be considered as he represenaion of he volage drop across he coupling resisances Rbi and Ra. Since hese are assumed o be equal, he base volages of Tl o T4 are half-way [5) D. Kasperkoviz and D. Grenier, Travelling-wave dividers: a new concep for frequency division, Microelecronics and Reliabiliy 16, 127-134, 1977 (No. 2).
62 W. D. KASPERKOVITZ Philips ech. Rev. 38, No. 2 beween he collecor volages. The poins represening he base volages in fig. 11 are joined by dashed lines. A = 0.25 s (fig, lib) ha = 0.751 and Iz«= 0.251. The curren 1 flows only hrough T2, since his ransisor has a higher base volage han T4. The collecor volage of T2 has herefore decreased. The collecor volage of Ti has increased because of he decrease in ha. Half-way hrough he swiching ime ( = 0.5 s) boh drive currens are equal (ha = Iz«= 0.5 I). ha sill flows only hrough Tl and 124 hrough T2 giving equal base volages for Tl and Ta (fig. lie). The fac ha ha neverheless sill coninues o flow only hrough Tl can be explained by he rapidiy of he swiching process; he ransisors have an inernal swiching ime of he same order of magniude as so Fig. lid shows he siuaion a = 0.75 s. I has been assumed here ha he grealy reduced common emier curren ha = 0.25 1 of differenial amplifier TI,Ta sill coninues o flow hrough Tl, alhough he base volage of Ti is abou 100 mv lower han he base volage of Ta. Such a siuaion only occurs for very shor swiching imes so If s is of he same order of magniude as he inernal swiching ime of he ransisors, some of he common emier curren ha swiches from Tl o Ta. This decreases he collecor volage of Ta, and increases he collecor volage of Tl, by he same amoun. The resul of his is an increase in he base volage of T4 and a decrease in he base volage of T2. This makes he condiions less favourable for conducion of he curren h4 hrough T2 only, which should afer all be he resul a he end of he swiching process. We have herefore reached he mos criical momen in he ransfer of he informaion. If he swiching ime s is greaer han a criical swiching ime sc, he base volages of T2 and T4 will approach one anoher oo closely and he circui will no longer work properly as a divider-by-wo. Fig. lie shows he siuaion a he end of he swiching ime so Curren h4 = I flows only hrough T2. The base volage of T2 is 150 mv higher han ha of T4; he siuaion is herefore sable. The curves in fig. 11 can be considered as a collecor-volage wave and a base-volage wave; in a single swiching ime hey ravel one posiion o he righ. Afer four swiching imes, i.e. wo periods of he rigger volage VT, hey will have gone hrough one cycle; he circui herefore works as a divider-by-wo. As can be seen from fig. 1la he wo differenial amplifiers n,ta and T2,T4, which ogeher form he circui, have he same inpu volages (VBI - VBa = VB2 - VB4) a he sar of he swiching process. This comes abou because of he assumpion ha Rb! and Rs were equal. However, for opimum circui behaviour Vc Fig. 12. The base volages a he ime = 0 for wo values of r = Ra/(Rbl + Ra}. For higher r he inpu volage VB2 - VB4 of differenial amplifier T2,T4 is higher, so ha he curren ransfers more readily from Tl o T2; he swiching is herefore faser. 300mV'~--------------------------~ Vi 200 500 1500MHz -f Fig. 13. The minimum inpu volage Vi for correc operaion of he ravelling-wave divider, as a funcion of he frequency f. The curves were measured for wo inegraed versions wih r = 0.75 and r = 0.8. There is a disinc minimum in he curves a he frequency of maximum sensiiviy; for r = 0.8 he minimum is a a higher frequency bu he sensiiviy a low frequencies is reduced. he wo inpu volages should be differen. The inpu volage of differenial amplifier TI,Ta should be as small as possible because i mus change polariy during so On he oher hand he inpu volage of differenial amplifier T2,T4 should be as large as possible, since he common emier curren 124 mus evenually flow hrough T2 only. Boh requiremens can be saisfied by changing he raio of Rb! o Rs. In he example discussed hese wo resisances were he same, so ha r = Rs/(Rb! + Rs) = 0.5. Fig. 12 shows how he base volages in he saring condiion a = 0 change if r is made equal o 0.75 while he sum Rb! + R«remains consan. The resul is wofold: he inpu volage VBl - VBa of differenial amplifier TI,Ta, which passes curren, has been reduced from 150 mv o 90 my, whereas he inpu volage VB2 - VB4 of differenial amplifier T2,T4, which does no passcurren, hasincreased from 150mV o 260mV. The decrease in he inpu volage of differenial amplifier TI,Ta and he increase in he inpu volage of differenial amplifier T2,T4 causes boh differenial ampli-
L Philips ech. Rev. 38, No. 2 FREUENCY-DIVIDERS FOR UHF 63 he same ime he sensiiviy a low frequencies has decreased. ' A comparison of fig. 13 wih fig. 8 shows ha he sensiiviy of he ravelling-wave divider a high frequencies is considerably higher han ha ofhe simplified saic divider-by-wo. However, his advanage is obained a he expense of a lower sënsiiviy a lower frequencies. The ime a signal akes o ravel around r he cyclic srucure deermines a preferred frequency o which he ravelling-wave divider can be considered o be uned (see he minima in he curves of fig. 13). The circui does in fac end o oscillae a hese frequencies, bu oscillaion is impossible while a rigger signalof sufficien srengh is presen; he divider hen follows his rigger signal. Adapive ravelling-wave divider Fig. 14. Adapive ravelling-wave divider. Two ravelling-wave dividers are conneced o he same collecor resisances Rc and operae in parallel. The upper divider (/1 o le) represens he limiing case r = 0 and is opimum for low frequencies; he lower one (Tl o Te) represens he limiing case r = 1 and is opimum for high frequencies. The upper ravelling-wave divider consiss of wo separae cross-coupled differenial amplifiers. The wo common emier currens ibi and Is, and hence.he share of each half in he operaion of he complee circui, are independenly adjused. This allows he band of highes sensiiviy o be shifed along he frequency scale. fiers o swich more rapidly o heir new saes. An increase in r hus gives an increase in he inpu sensiiviy a high frequencies and an. increase in he highes divisible frequency. On he oher hand he danger of an incorrec ransfer of informaion wih he drive currens changing slowly becomes greaer because of he reducion of he inpu volage VB! - VB3 of differenial amplifier Tl,T3. There is a criical swiching ime sc ha mus no be exceeded. This criical swiching ime is made shorer by he increase of r. A low frequencies he ampliude of sinusoidal inpu volages has o be increased; he circui is hus less sensiive a low frequencies. The sensiiviy o sinusoidal inpu volages has been measured for wo versions of he ravelling-wave frequency-divider described here, boh made in inegraedcircui form for applicaion in a digial uning sysem for elevision receivers. In one version r was 0.75, and in he oher r was 0.8. I can be seen fromfig. 13 ha he frequency responses of he wo versions are appreciably differen; he small change in r has shifed he maximum sensiiviy from 850 M;E-Jzo 1050 MHz. A In he ravelling-wave divider jus described he parameer r allows he designer o locae he maximumsensiiviy par of he response anywhere wihin a wide range. This choice, which also deermines he sensiiviy a low frequencies, canno be alered once he circui has been inegraed. However, he abiliy o aler he, sensiiviy would be vèry useful in a number of applicaions. If his variaion in sensiiviy auomaically followed he inpu frequency i would be possible o obain a high sensiiviy over a wide frequency band and a he same ime o increase he maximum.inpu frequency. A circui whose frequency response can be varied by making an exernal adjusmen of currens is shown in fig. 14. I consiss of a combinaion of he wo limiing cases of he ravelling-wave divider; he lower half in he figure is he opimum limiing case for high frequencies wih r = 1, he upper half is he low-frequency limiing case wih r = O. The upper half consiss of nohing more han wo bisable cross-coupled differenial amplifiers. Boh halves have he collecor resisances in common and are coupled in his way. The emier currens ibi of he upper half and Is of he lower half can be independenly adjused. The collecor currens and base volages of he eigh ransisors are ploed in fig. 15 in a similar way o ha used in fig. 11 for he simple ravelling-wave divider. Here, however, he collecor currens are ploed insead ofhe collecor volages, because hese are always he same for each pair of ransisors. Fig. 15a shows he siuaion in which VT is high, so ha T6 and s are conducing. Is flows only hrough Tl, ibi hrough s. In addiion, he wo common emier currens Is and ibi are assumed o be equal. In his condiion, and considering he cenre of he fla op of he base-volage wave as is maximum, he base-volage wave is 45
64 W. D. KASPERKOVITZ Philips ech. Rev. 38, No. 2 ahead in phase of he collecor-curren wave. From fig. 11 i can be seen ha he same phase difference arises in a simple ravelling-wave divider if he raio of he coupling resisances is r = 0.5; his is anoher siuaion midway beween r = 0 and r = 1, hough in anoher way. As was shown earlier, increasing r gives an increase in he frequency for maximum sensiiviy. An increase in r can be brough abou by reducing he share of he halfwih r = 0 in he behaviour ofhe complee circui. Fig. 15h shows a siuaion in which ibi = 0.25.Is. The phase difference has increased from 45 o abou 70. Besides he faciliy of adjusmen by curren variaion, he circui includes a mechanism ha gives a furher auomaic increase in he phase advance of he base-volage wave wih respec o he collecor-curren wave, provided ha he inpu frequency is high enough. This frequency-dependen mechanism depends on he base resisances RB in he upper half of he circui. The resisances RB are eiher added o he ransisors s. o 4, or, in an inegraed version, included in hem by a suiable choice of heir surface-area raios. The base resisances ogeher wih he base-emier capaciances of he ransisors.cause a delay in he signal. A a sufficienlyhigh frequency his delay inerferes wih he cyclic swiching of he common emier curren ibi from i1 o z, ec. Insead, each ransisor akes a quarer of ibh so ha he collecor-curren wave of he upper half degeneraes o a sraigh line. The collecor volages and hence he base volages of he complee circui are now deermined by he lower half only, he limiing case of a ravelling-wave divider wih r = 1. In his siuaion he phase difference beween base volage and collecor curren has increased o 90. The minimum inpu signal required for an inegraed adapive ravelling-wave divider has been measured as a funcion of frequency. Two curves are shown infig.16, one for ibi = 0.5 Is and one for ibi = 0.2 Is. As migh be expeced, he curve for ibi = 0.2 Is has a minimum a higher frequencies, bu gives a lower sensiiviy a low frequencies. f 1 f 2 3 4 VB! ie ibi -Reibi I ~ Ic Is -ReIs I Ti 72 7j T". _::: -- ----...... /...... '" /...1-/ _. 700 /V '" ----...... i'- -,...... /...... /, /, / - - '" " v... '"7 90..., ~/ '" r-,... <,, 1-/ '" Fig. 15. Collecor currens and base volages in he adapive ravelling-wave divider. ic collecor curren, VB base volage of ransisors 11o 4 (upper half of he circui in fig. 14); Ie collecor curren, VB base volage of ransisors Tl o T4 (lower half of circui). a) Bias currens equal, Ïbl = Is. The basevolage wave is 45 ahead ofhe collecor-curren wave in phase. b) ibl = 0.25 Is. The base-volage wave is abou 70 ahead of he collecor-curren wave; he circui is faser. c) The upper, slower half of he circui canno followa higher frequencies. The four collecor currens hen all assume he same value, libl. The resulan base-volage wave is 90 ahead of he lower half of he circui in phase. 300mV.---------------------------, Vi 0 VB + The ransisors Tl o Te in his inegraed circui have wo emier fingers and hree base conacs, while he ransisors 11 o e have only one base conac and one emier conac of he minimum permied lengh. Wih his arrangemen, no only is he major par of he base resisances RB inegraed in a compac way, bu a he same ime he parasiic load on he collecor conacs of Tl o T4 is kep o a minimum because he collecor-base and collecor-emier capaciances of 1 o 4 are kep small. An examinaion of he frequency-dividers ha have been discussed so far clearly reveals a gradual ransiion from purely digial circuis wih he associaed digial inpu and oupu signals (fig. 2, fig. 3) o circuis wih Fig. 16. The minimum inpu volage Vi for correc operaion of he adapive ravelling-wave divider as a funcion of he frequency j: The wo curves were measured for an inegraed circui. The curve for ibl = 0.2 Is has a higher sensiiviy a high frequencies and a lower sensiiviy a low frequencies han he curve for ibl = 0.5 Is.
Philips ech. Rev. 38, No. 2 FREUENCY-DIVIDERS FOR UHF 65 inpu volages ha are sinusoidal and oupu volages ha raher resemble sine waves (fig.9, fig. 14). An exrapolaion of his rend suggess ha i migh well be possible o complee he paern by designing frequency-dividers wih sinusoidal inpu and oupu signals. indicae ha he conversion loss of he mixer is equal o he gain of he amplifier and he loop gain is herefore uniy. In his version here was no lowpass :filer in he loop. The :filering was provided by he bandwidh-limiing elemens in he mixer and he amplifier. By using an amplifier of greaer bandwidh he highes Dynamic frequency-divider wih mixer sage The block diagram of a frequency-divider for sinusoidal signals is shown in fig. l7a. The circui includes a mixer sage, in which he inpu signal is muliplied by a 'pump signal' a wice he frequency. This is followed by a wide-band amplifier and a lowpass filer. There is a closed loop in his arrangemen; he oupu signal from he lowpass filer, which is also he oupu signalof he divider-by-wo, serves as he inpu signal for he mixer. Fig. 17b shows he waveforms. The muliplicaion of he pump signal, which we shall represen by cos Zca, and he fundamenal cos oo of he inpu signal produces he signal (cos oo + cos 3oo). The firs erm has he desired half frequency. This signal is now amplified, by a facor of wo in he figure. The producion of higher harmonics as a resul of disorion mus be prevened here. The lowpass filer aenuaes he unwaned componen a angular frequency 300; i has been assumed for he figure ha he aenuaion of he filer is zero for signals a frequencies up o 00 and is proporional o he square of he frequency for signals a higher frequencies (he response has a slope -of -12 db' per ocave above (0). The oupu signal is now fed back o he inpu of he mixer. The aenuaed hird harmonic in his signal gives rise o a fifh harmonic in he mixing process, bu his is aenuaed even more srongly by he filer han he hird harmonic. The assumpion ha he volage gain is equal o wo is only valid for he seady sae. When he divider is swiched on he gain is higher han wo and he loop gain is herefore greaer han uniy for he signal cos w. This signal is presen in he noise and increases exponenially unil limiing in he mixer or amplifier brings he gain back o uniy. This happens only for he signal cos on wih he phase shown in fig. 17b; for oher signals he phase relaions are no correc and here is no posiive feedback wih a loop gain greaer han uniy. Two experimenal versions of he divider in fig. 17a have been made. One has a mixer ha makes use of Schoky diodes and will operae up o 4 GHz. This is combined wih an amplifier of bandwidh 1.3 GHz. The highes divisible frequency is 2.9 GHz. This is exacly wice he frequency a which he specificaions rvvco~2w îp'c7 L cos a Î ~ ~(cos w«cos3w! Fig. 17.a) Block diagram of a dynamic frequency-divider wih mixer sage. The circui operaes wih sinusoidal signals and consiss of a closed loop conaining a mixer M, a wide-band amplifier and a lowpass filer. b) Waveforms a various poins in he circui. When a 'pump signal' Vp = cos 2ro is muliplied by a signal Vl = cos ro a produc V2 = (cos ro + cos 3ro) is produced. This is amplified wice, and he hird harmonic is hen aenuaed in he lowpass filer. For simpliciy i is assumed in his diagram ha Vl only conains he fundamenal cos ro of V4. divisible frequency can of course be increased furher. The oher experimenal version was based on a double-balanced modulaor, shown in he schemaic circui of fig. 18. A circui of his ype also has gain, and since he base-emier capaciances of he ransisors give sufficien aenuaion of he higher har-
66 W. D. KASPERKOVITZ Philips ech. Rev. 38, No. 2 monies he oupu can be dirécly conneced o he inpu o form he closed loop of fig. 17a. This gives he very compac circui of fig. 19. This circui was buil as an experimen from discree resisors and ransisors (he microwave ransisor BFR90). Fig. 20 shows he minimum inpu volage as a funcion of frequency. Comparison wih similar measuremens made on he circuis discussed earlier revealed wo noable feaures: his 'analog' divider-bywo does no work a low frequencies, and he minimum inpu volage increases linearly wih he inpu. frequency over pracically all of he operaing band. This effec can be êxplained direcly from he block diagram of fig. 17a. Since he loop gain decreases wih increasing frequency because of he acion of he filer, he pump signal from he mixer has o increase o produce he criicalloop gain of uniy. The lower limi of he operaing band is also deermined by he filer. If he pump or inpu frequency 2w decreases o below he cu-off frequency of he filer, he aenuaion of he componen a frequency 3w becomes progressively smaller wih respec o ha of he componen a frequency w. Below a cerain criical pump frequency wo frequencies wih comparable loop gain are presen a he same ime. The preference for he frequency cois hen los and he circui no longer operaes properly as a divider-by-wo. I is ineresing o compare he circui described here wih he circui of fig. 3a, which also depends on he base-emier capaciances of he ransisors for is cor-: ree operaion. Excep for he base resisances RB in fig. 3a he connecions beween he ransisors Tl o T4 are he same in boh circuis. The variaions in he currens [bi,!s and h2,ia4 also correspond: one grows larger a he expense of he oher and vice versa 'in ime' wih he inpu frequency. There is however a marked difference in he average values of hese currens; in fig. 3a hey are unequal o make he amplifier wih posiive feedback dominan, whereas in fig. 19 boh currens are equal. This difference corresponds o he difference beween saic and dynamic behaviour. The circui of fig. 3a operaes a frequencies down o o Hz, while he circui of fig. 19 canno operae a low 'frequencies because i conains nohing ha can funcion as a saic memory. To summarize, hen, a paricularly simple and symmerical divider-by-wo for sinusoidal inpu and oupu signals has been described ha will operae a very high inpu frequencies. However, he circui canno be used a low frequencies. In he nex secion an exension of he same principle will be described ha has also been derived by assuming sinusoidal inpu and oupu volages, ye will operae as a divider-by-wo a low frequencies because of a gradual change in he waveform. +------0 Va 0------+ Fig. 18. Schemaic circui of a double-balanced modulaor. The oupu signal V o is he produc of he inpu signal Vi and he pump signal V p All signals are balanced o earh. Fig. 19. Compac dynamic divider-by-wo wih mixer sage, derived from he double-balanced modulaor (fig. 18) by direcly connecing he oupu o he inpu. 300mV~--------------------------~ Vi 200 100 500 1000 1500MHz --f Fig. 20. The minimum inpu volage Vi for correc operaion of he dynamic divider-by-wo wih a mixer sage as a funcion of he frequency f. The curve was measured for an experimenal version wih BFR90 microwave ransisors. The linear increase wih frequency of he inpu volage required is due o he lowpass naure of he circui. If on he oher hand he inpu frequency is so low ha he higher harmonics are no longer adequaely suppressed operaion of he divider is no longer possible.
Philips ech. Rev. 38, No. 2 FREUENCY-DIVIDERS FOR UHF 67 Frequency-divider wih wo mixer sages Fig.21a shows he circui of fig. 17a exended by he addiion of a second mixer sage. The new dividerby-wo consiss of a cascaded arrangemen of wo mixers wih a common pump signal, a broad-band amplifier and a lowpass filer, ogeher forming a closed loop. I is no difficul o see ha. he operaion of his circui is essenially he same as ha of he earlier circui wih a single mixer, provided ha he pump and loop signals are sinusoidal. Le us assume ha he pump V p signal for he wo mixers is cos 2w and he inpu signal o he firs mixer is cos w. The oupu signal from he firs mixer hen conains he frequencies w and 3w. Furher mixing wih he pump signal hen ~ produces a signal including he frequencies w, 3w and 5w a he oupu ofhe second mixer. The componens a frequencies 3w and 5w are aenuaed wih respec ~ o he componen a frequency a by he lowpass filer. When he loop is closed he dominan componen 'in he circulaing signal is herefore he one a frequency w. ~ The grea difference beween he wo circuis becomes eviden when he pump signal is given a fre- - quency significanly lower han he cu-off frequency of he filer. The loop signal hen consiss of a number Fig. 21. a) Block diagram of a dynamic frequency divider wih of componens spaced a frequency inervals of 2w, wo mixer sages MI and M2. The addiion of he second mixer produces he correc phase relaion for he division-by-wo of since each componen is shifed by ± 2w in each approximaely square-wave signals a low frequencies and hus mixing process. To show simply ha he circui of gives an exension of he operaing range o lower frequencies. The signal is muliplied by he same pump signal V p in boh fig. 21 will also work a low pump frequencies i is mixers. b) Schemaic represenaion of he waveforms. VI inpu easies o sar by assuming waveforms ha approximae o a square wave, since such waveforms only con- signal o he firs mixer. V2 oupu signal from he firs mixer and inpu signal o he second mixer. Va oupu signalof he divider, equal o VI. ain he fundamenal wand he odd harmonics a a frequency spacing of 2w. This provides a naural ransiion from analog o digial; he square-wave volages can now be reaed as signals in which i only maers wheher hey are a he high level or he low level. Fig. 2lb shows schemaically how a double muliplicaion of an inpu signal of 'nearly-square' waveform bya pump signalof similar waveform and wice he frequency gives an oupu volage of he same waveform and phase as he inpu signal. Thefigure can be immediaely verified by assigning Fig. 22. Schemaic circui diagram of a dynamic divider-by-wo wih wo mixer sages, each aking he form of a double balanced modulaor. This circui, when buil wih BFR90 microwave ransisors, operaes as a divider-by-wo for frequencies beween several MHz he value' l' o he high level, and 1.2 GHz. Vp pump signal. Va oupu signal. for example, and he value