By T. SLONCZEWSKI
The accuracy of a heterodyne oscillator after the low frequency check is made is of the same order of magnitude as th a t of an ordinary type of oscillator in which circuit elements of the same sta bility are used. I t depends on the constants of the variable fre
quency oscillator only. This accuracy can be improved by a ratio of 10 to 1 by adding another and higher check frequency. The tem perature coefficient of the circuit elements can be kept down to less than 6 parts per million. Scale errors can be reduced to a value comparable with the oscillator accuracy by spreading the scale.
A precision oscillator having a frequency range up to 150 kc. and an accuracy of ± 25 cycles including a scale mechanism whereby a large scale spread is obtained on a direct reading scale is described.
In t r o d u c t i o n
T
H E o u tp u t freq u en cy of a h e tero d y n e oscillator is o b tain ed b y m o d u latin g th e o u tp u ts of tw o oscillators of ap p reciab ly higher frequency, one of th e oscillators h av in g a fixed frequency, th e o th er being co n tin u o u sly v a ria b le over a b a n d w id th equal to th e required o u tp u t freq u en cy range.T h e c ircu it consists e ssen tially of th e tw o so-called local oscillators, th e m o d u lato r, w here th e difference freq u en cy is g en erated , a n d an am plifier w here th e m o d u la to r o u tp u t is raised to th e desired level.
T h e e arliest designs of h e te ro d y n e oscillator w ere confined to th e au d io freq u en cy ran g e, b u t re c e n tly carrier-freq u en cy ap p licatio n s hav e becom e m ore num erous. As th e freq u en cy range of th e oscilla
to rs has increased, th e ir p e r ce n t ac cu racy re q u irem e n t has increased also. T h e req u ired freq u en cy ac c u ra cy of th e oscillator is d eterm in ed b y th e m axim um slope of th e frequency ch ara c teristic of th e a p p a ra tu s being m easured. If th is slope is g rea t, as in th e case of a sh arp ly tu n e d circu it a re lativ ely sm all d isp lacem en t of th e frequency will re su lt in a large e rro r in th e v alu e to be m easured. In carrier-freq u en cy system s w here th e signal is displaced upw ard s in th e frequency scale b y m o d u latio n , each channel has to m eet sam e cro sstalk an d tra n sm is
sion re q u ire m e n ts in d e p e n d e n t of its lo catio n in th e c a rrie r b an d . T h erefo re, th e m ax im u m slope of th e c h a ra c teristics is in d e p en d en t of th e freq u en cy a n d an o scillato r used for m easu rin g p urposes h as to m eet a c o n s ta n t freq u en cy e rro r re q u ire m e n t. In ad d itio n th e
accur-407
a c y re q u ire d w hen expressed in cycles is co m p a ra b le w ith t h a t of a u d io freq u e n cy o scillato rs so t h a t th e p e rc e n ta g e a c c u ra c y m u s t b e m uch h ig h er.
T h e a d v a n ta g e s of th e h e te ro d y n e o sc illato r h a v e m a d e it d e sirab le to s tu d y its sources of e rro r to d e te rm in e w h e th e r su ch a n o scilla to r can be d esigned to h a v e sufficient a c c u ra c y for th e se a p p lic a tio n s.
Os c i l l a t o r s Wi t h a Si n g l e Fr e q u e n c y Ch e c k
T h e freq u en c y of a h e te ro d y n e o scilla to r is giv en b y th e e x p re ssio n :
F = f — / , (1)
w here w e will assu m e / ' to be c o n s ta n t a n d / to b e v a ria b le a n d less th a n f w hence th e fre q u e n c y of th e v a ria b le fre q u e n c y o scilla to r is low ered as th e o u tp u t fre q u e n c y of th e h e te ro d y n e o sc illa to r is raised.
T h e v alu e of F is u s u a lly m u ch sm a ller th a n e ith e r f or / a n d re la tiv e ly sm all fre q u e n c y sh ifts in th e local o scillato rs p ro d u c e d b y aging a n d te m p e ra tu re effects u p o n th e e lem en ts of th e ir r e s o n a n t c irc u its a n d changes in v a c u u m tu b e s a n d in th e s tr a y c a p a c ita n c e s of th e c ircu its p ro d u ce larg e re la tiv e v a ria tio n s in th e o u tp u t frequency.
U su ally th e s ta b ility re q u ire d of F a n d th e ra tio f ' / F a re so h ig h t h a t i t is im p ra c tic a b le to design local o scillato rs of sufficient s ta b ility to m eet re q u irem e n ts. In ste a d , in all h e te ro d y n e o sc illato rs a n a d ju s t
m e n t in th e form of a p a d d in g c o n d en se r in th e c irc u it of th e fixed freq u en c y o scillato r is used, w h ereb y its freq u en cy is a d ju s te d sh o rtly before th e m e a su re m e n t u n til th e o sc illato r re a d s c o rre c tly a t th e b o t
to m of its fre q u en cy ran g e. T h e a d ju s tm e n t is m a d e b y th e zero b e a t m e th o d or b y c o m p ariso n w ith a lo w -freq u en cy s ta n d a rd su ch a s a v ib ra tin g reed or th e 60-cycle p o w er su p p ly .
A t th e tim e of th e a d ju s tm e n t th e fre q u e n c y of th e o sc illa to r is
F o = f ' - f „ (2)
w here f 0 is th e v a lu e of / a t th e c h e ck fre q u e n c y F 0. E lim in a tin g / ' betw een (1) a n d (2) we o b ta in
F = F 0 + (/„ — / ) . (3)
T h e freq u en cy of th e v a ria b le o scillato r m a y be ex p ressed as
/ = 1/(2 W L ( C0 + Ca)), (4)
w here Ca is th e change in th e v a ria b le a ir co n d e n se r c a p a c ita n c e from th e v alu e it has a t f 0, a n d C0 is esse n tia lly th e v a lu e of th e fixed c o n
H I G H A C C U R A C Y H E T E R O D Y N E O S C I L L A T O R S 409
denser, u su a lly a good m ica u n it. L is th e in d u c ta n c e of th e re so n a n t circu it.
C o m bining (3) a n d (4) we g et
F = F 0 + 1 /( 2 ttV L Q - 1/(27rV L (C0 + Co)). (5) T h e a cc u ra cy of th e oscillato r will d ep en d on th e v a ria tio n s in th e valu es of F 0, L , C 0a n d Caa n d is in d e p e n d e n t of th e c o n sta n ts of th e fixed freq u en cy oscillator.
B y giving in crem en ts AF 0l AC0, ACa a n d A L to th e c o n s ta n ts F0, Co, Coa n d L we o b ta in a fte r sim plifying th e expressions
A F Fo = A F„, (6)
(7)
^ - ‘êA'A-ÜVAA-m
(8)= <9>
giving th e corresponding freq u en cy e rro rs AFw here f 0 = l / ( 2 x \ L C 0) is th e v a ria b le oscillato r fre q u en cy a t th e check freq u en cy F 0.
A v a ria tio n in F 0will p ro d u ce an e rro r c o n s ta n t over th e whole frequency range. O n F ig. 1 th e o th e r e rro rs are found p lo tte d in p a ra m e tric form . T o find th e e rro r AF co rresponding to a frequency F th e o rd in a te y co rresp o n d in g to th e v alu e of x = ( F — F 0) / ( f o) should be found. T h e n
A F Ca= ycaf<ACa/Ca; A Fco = ycoACo/Coi A F h= y Lf 0A L / L .
I t is found t h a t F 0can be neglected in all p ra c tic a l cases. T h e ratio of th e o rd in a te to th e abscissa gives th e p e rcen tag e e rro r in frequency caused b y a one p e r c e n t v a ria tio n in th e elem en t involved.
A n e x am in atio n of th e cu rv es show s t h a t th e y differ only slig h tly from s tra ig h t lines w hich can be in te rp re te d as m eaning th a t th e errors a re fa irly in d e p e n d e n t of th e choice of f 0. T h is c o n s ta n t should be chosen th erefo re sufficiently low to req u ire in fre q u e n t a d ju s tm e n t a t th e low -frequency end of th e scale. F o r low valu es of f 0such th a t x > .3 difficulties in sh ap in g of th e a ir cond en ser p la te s an d in designing th e m o d u la to r filter begin to ap p e a r. If th e erro rs in an o rd in a ry ty p e of oscillator d u e to c a p a citan ce a n d in d u c ta n c e v a ria tio n s were p lo tte d on th e sam e se t of c o o rd in ates th e curves w ould coincide w ith th e line
y l . T h is m ean s t h a t if elem e n ts of th e sam e a c c u ra cy w ere used, th e h e te ro d y n e o sc illato r w ould be so m ew h at m ore a c c u ra te . I ts to ta l e rro r w ould be re p re se n te d b y y ca + y co + yl- Since ACa/C a a n d A Col C0 will be b o th p o sitiv e a n d of a b o u t th e sam e o rd e r of m a g n itu d e p a rtia l co m p en satio n will o b ta in a n d th e e rro r will be of th e o rd e r of
0 0.04 0 .0 8 0.12 0.16 0 .2 0 0 .2 4 0 .2 8
X
Fig. 1— T he frequency errors in a heterodyne oscillator at a frequency F = xfo + F a after the low frequency check had been m ade can be obtained from th e plot as follows: For a variation A Co in the fixed capacitance Co, AFc„ = y c 0 fa \ for a
Co
variation in the air condenser capacitance Ca, A F ca = yca -pr^/o; for a variation in theA C C a
inductance L , A Fl — Vl-j j fa.
m a g n itu d e of AFl- In th e case of th e o rd in a ry ty p e of o scillato r th e e rro rs d u e to th e c a p a c itan c e a n d in d u c ta n c e v a ria tio n s will be equal a n d of th e sam e sign so t h a t th e e rro r will be of th e o rd e r of m a g n itu d e of 2AF L. F o r au d io fre q u en cy a p p lic a tio n s th is a c c u ra c y h a s been found to be a d e q u a te given sufficient care in th e c o n stru c tio n of th e circ u it elem ents.
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Os c i l l a t o r s Wi t h a Do u b l e Fr e q u e n c y Ch e c k
F o r c a rrie r freq u en cy a p p lic a tio n s th e to lerab le e rro r ta k e s a co n s ta n t v alu e over th e e n tire frequency ran g e an d it is found t h a t if a single frequency check is used it is n o t possible to o b ta in sufficiently stab le elem ents to m a in ta in th e req u ire d a cc u ra cy a t p o in ts on th e scale rem oved from th e check frequency.
A n increase in th e acc u ra cy of h ete ro d y n e o scillato rs has been o b tain ed , how ever, b y a d d in g an a d ju sta b le condenser to C„an d checking th e oscillator a t tw o frequencies, th e low freq u en cy F aan d a t an o th e r, higher, frequency Fa. A d ju stm e n t of th is cond en ser b y AC0 in tro d u ces a frequency change—yc of o^C0/ 2 C 0a d ju sta b le in sign an d m ag n itu d e an d th is can be m ade to cancel th e e rro r AFca + A F L for a t le a st one frequency, th e check freq u en cy Fs. O bviously if th e a d ju s tm e n t is m ade to co rrect for v a ria tio n s in C„ no residual e rro r rem ains. T h e residual e rro rs w hich rem ain a fte r co rrectin g for A Fca an d A F l are shown on Fig. 2. T h e residuals of AF Ca a n d AF L differ from each o th e r
Fig. 2— T he frequency errors in a heterodyne oscillator at a frequency F = xfo + F0 after the low and high frequency checks had been made can be obtained from the plot as follows: For a variation in the air condenser capacitance Ca, AFc„ = y -q-Jo\
for a variation in th e inductance L , A Fl = y /»■
so little t h a t only one se t of curves w as draw n. T h e values of y w ere o b tain e d b y form ing th e sum y = K y Co + y Caa n d choosing K so th a t y = o for x s = (Fs— F„) / f 0.
F o r x s = .1 b e tte r co m p en satio n is o b tain ed a t th e lower end th a n a t th e higher. F o r a v e ry w ide freq u en cy ran g e u p to x = .25 th e b e st
c h eck fre q u en cy w o u ld b e x s = .2. A good p ra c tic a l lim it to x is a t 1.9 a n d h e re a v a lu e of x s a ro u n d .15 is b e st. A f u rth e r im p ro v e m e n t of a b o u t 50 p e r c e n t co u ld be o b ta in e d b y choosing a h ig h e r v a lu e of F 0.
W h en c o m p a rin g F ig. 2 w ith F ig. 1 it should be b o rn e in m in d t h a t th e scale sp re a d for y on F ig. 2 is te n tim es t h a t of th e F ig. 1 w hich show s t h a t an im p ro v e m e n t in a c c u ra c y of a t le a st te n to one is o b ta in e d b y th e a d ju s tm e n t. T h is m ean s, t h a t giv en tw o fre q u e n c y s ta n d a rd s F 0 a n d Fa of sufficient a c c u ra c y a h e te ro d y n e o scillato r can b e b u ilt h a v in g a m u ch h ig h er a c c u ra c y th a n a n o rd in a ry o scillato r h a v in g th e sam e fre q u e n c y ra n g e a n d sam e q u a lity of c irc u it elem en ts. T h is is so m ew h at c o n tra ry to w h a t we are ac c u sto m e d to th in k .
0 10 2 0 30 4 0 50 60 70 80 90 100 110 120 130 140 150 F R EQ U EN C Y IN K ILO CYCLES PER SECO N D
Fig. 3— F requency-output characteristic.
O ne d e ta il in v o lv ed in th e p ro ce d u re of ch ecking th e o scilla to r w hich p e rm its th is high degree of a c c u ra cy to be o b ta in e d n eeds e la b o ra tio n . As C0 is v a rie d d u rin g th e a d ju s tm e n t b y th e a m o u n t A Co th e v a lu e o f/ 0 is ch an g ed a n d th is d e stro y s th e low freq u e n cy a d ju s tm e n t a t F 0. I t is possible to o b ta in th e a d ju s tm e n t b y a process of successive a p p ro x im a tio n s b u t th e p ro ce d u re is te d io u s. T h e difficu lty can be o v erco m e b y th e use of a m echanical device, how ever, as follows. T h e c o n d en ser A Co is ganged to a n o th e r co n d en se r in th e re s o n a n t c irc u it of th e fixed o scillator, a n d th e tw o co n d en sers are so p ro p o rtio n e d t h a t th e change in th e fixed o scillato r freq u e n cy is e q u al to th e ch an g e i n/ 0 a s th e c o n d en se r is a d ju s te d . T h is m ak es th e low fre q u e n c y a d ju s tm e n t in d e p e n d e n t of th e high fre q u e n c y one. T h e o scilla to r is ju s t s e t to th e req u ired read in g a t F, a n d AC0 is a d ju s te d u n til th e fre q u e n c y v a lu e is c o rre ct. T h e o re tic a lly in ste a d of tw o c o n d en sers tw o co u p led in d u c to - m e te rs could h a v e been u sed to a d ju s t th e in d u c ta n c e s in th e re s o n a n t circu its. T h e n e t re su lt o b ta in e d w ould h a v e been th e sam e a n d th e m a th e m a tic a l tr e a tm e n t w ould be like th e one given a b o v e. C o n d e n sers lend th em selv es b e tte r to such c o n s tru c tio n , how ever.
H I G H A C C U R A C Y H E T E R O D Y N E O S C I L L A T O R S 413
en in g of th e air-g ap s. W hen, as u su al, several m a te ria ls a re used in th e
H I G H A C C U R A C Y H E T E R O D Y N E O S C I L L A T O R S 415
settin g , in to an electric co o rd in ate, th e o u tp u t frequency. In p lan n in g th e oscillator design, therefore, it is n ecessary to give as m uch a tte n tio n elem ents.
F o r m axim um scale len g th econom y th e scale should be so subd iv id ed t h a t a frequency in te rv a l equal to th e to le rab le freq u en cy e rro r A F in te rv a l, will v a ry w ith th e m easuring co nditions. F o r well illu m in ated scales on panel m o u n te d eq u ip m e n t to be read c o n v en ien tly a t a r m ’s length an in te rv a l Al of a t lea st .05" is needed. F o r p o rta b le a p p a ra tu s , in te rv a ls as sm all as .02" hav e been used. W ith th e aid of a v ern ier it can be b ro u g h t dow n to .001". Scale sp read s such t h a t a frequency in te rv a l m uch sm aller th a n A F can be read are n o t o n ly uneconom ical b u t are also o b jectio n ab le because th e y encourage th e use of th e in stru m e n t b eyond its acc u ra cy lim its.
H av in g chosen Al a n d th e freq u en cy e rro r A F a t all p o in ts of th e scale, th e scale shape I = / ( F ) can be d e term in ed by th e ap p ro x im atio n
As an exam ple, in au d io frequency ap p licatio n s th e m o st com m on form of frequency ac cu racy desired is t h a t hav in g a c o n sta n t percentage v alu e A F /F = p a t th e u p p e r p a r t of th e scale. A t lower frequencies th is a cc u ra cy is hig h er th a n n ecessary an d th e re q u ire m e n t is changed to a c o n s ta n t AF 0. A sm o o th shape is o b ta in e d b y m aking th e tra n s i
tion p o in t Ft a t such a freq u en cy t h a t AF 0/ Ft = p. T h e scale shape is th e n a p p ro x im ately
T h e scale of com m on ty p e of au d io freq u en cy oscillator can be sp read over a te n inch dial giving a sa tisfa c to ry accuracy.
F o r c a rrie r ap p lic atio n s, w here th e sp re ad of a n y voice b a n d is in d e
p e n d e n t of its position in th e frequency range th e e rro r function tak es th e form of a c o n s ta n t an d th e scale should be linear. U sually th e scale le n g th s involved are m uch larg er th a n in au d io oscillators. T o o b ta in sufficient scale length a precision w orm and gear m echanism h as to be used to d riv e th e tu n in g condenser of th e h etero d y n e oscilla-to th e c o n stru ctio n of th e scale as oscilla-to th e c o n stru c tio n of th e c ircu it
could be read. T h e scale in te rv a l Al corresp o n d in g to th is frequency
for F < Ft
and
to r. I t gives a scale le n g th of 300 inches, th e e q u iv a le n t of a 5-foot
H I G H A C C U R A C Y H E T E R O D Y N E j O S C I L L A T O R S 417
T h e freq u en cy s e ttin g is reco rd ed on a 300-inch film scale such as d escribed above. T h is gives a sp re a d of tw o inches p e r kilocycle.
W ith th e 50-cycle divisions m ark e d d ire c tly th e m echanism can be read ily s e t to a n a c c u ra c y b e tte r th a n 25 cycles. T h e v isib ility of th e scale is g re a tly en h an c ed b y a p ilo t lam p p laced in b a c k of th e scale
&
c
m
**
j
j
Fig. 4— Front view of the oscillator.
w indow w ith an in te rv e n in g opal glass. A c ra n k on th e fro n t of th e panel is used to se t th e oscillator, th e range being covered in 47 rev o lu tions. W hen changing th e freq u en cy s e ttin g even a t a m o d erate ra te th e speed w ith w hich th e film m oves p re v e n ts th e o p e ra to r from observ
ing th e freq u en cy se ttin g . T o m ake th e a d ju s tm e n t m ore convenient, a coarse scale is reco rd ed on a dial w hich can be read easily to one
kilocycle w hile th e m ec h an ism is in m o tion. I t can be seen u n d e r th e
H I G H A C C U R A C Y H E T E R O D Y N E O S C I L L A T O R S 419 b y th e m o d u la to r a n d am plifier; an d th e to p b y th e pow er pack. P e r
fo ra tio n s in th e oscillato r cover p ro v id e v e n tila tio n to reduce w a rm ing-up effects. A close-up giving th e d e ta ils of th e scale m echanism a n d th e shielding is show n on Fig. 5.
Fig. S— D etails of the scale mechanism.
T e sts on th e oscillator show t h a t th e overall frequency accu racy th ro u g h o u t its ran g e can be m a in ta in e d to ± 25 cycles. T h e h a r
m onics are dow n 40 db from th e fu n d a m en tal a t 100-m illiw att o u tp u t.
W ith th e full o u tp u t of one w a tt th e h arm o n ics a re 30 db dow n. T h e to ta l o u tp u t v a ria tio n w ith freq u en cy is show n on Fig. 3.
T h is oscillato r h as found a w ide ran g e of ap p licatio n s as an a c c u rate source of freq u en cy in th e com m u n icatio n s field.
Li s t o f Sy m b o l s
F o u tp u t frequency of th e h etero d y n e oscillator
F 0 s ta n d a rd freq u en cy used to check th e oscillator a t th e low end of th e scale
F s s ta n d a rd freq u en cy used to check th e o scillato r a t th e