------

Journal of Research of the National Bureau of Standards Vol . 59, No.2, August 1957 Research Paper 2776

A Self-Balancing Direct-Current Bridge for Accurate Bolometric Power Measurements

Glenn F. Engen

Un til recently, the most accurate microwave power measurements of the bolometri c t ype have required t he use of a manual d-c bridge. A self-ba lan cin g d-c bridge h as bee n developed t hat preserves t he inheren t accuracy of t he m anual bridge, extends the d y namic range of operation, and greatly simplifies t he operating procedure. A general descrip t. ion of the equipment and operating techniques is given, followed b.v it co mprehensiv e survey of t he sources of error accompanyin g t Ile m ethod a nd t he accuracy achieved .

1. Introduction con tains a random el'l'Ol' of ± 0.005 percen t , it can be shown that for a Lypical bolometer operating at A large amount of th e research effor t expendrd in 200 ohms and requiring 8.5 ma of bifLs (i l = 17 m a) tl10 field of 101'1 level microwave power measurement the error in measuring Prr m ay b e as large as 0.02 , in the past few years has beel1 direcLe d toward a 0. 3, a nd 3 percent at the 10, ], alld 0.1 mw level s, rc­ detC'rmination of bolometer-mount effi ciencies, or spectively , if all oLher sources of rno]' arc neglected. evaluation of lli e validity of the r-f- d-c substitution Tbe small difference beLween it a nd 'i2 at low lcyels pri Ilci plc. I,2,3,4 U n Lil recently Lh e only accessory accounts for the de Lerioratio 11 in accuracy. A instrument of sufficient accuracy to uLilize the r esulls vari.ety of alternative techniques have been p ro'posed of thrse investigations h as been a manually operated and empioyeclwiLh some degrce of success, but it is d I' ~Wli ea tstone bolometer bridge. The usc of thi s not within the scope of t hi.s p aper to examine the dc\'ice is, however, both Ledious and time con­ m a nual technique i n detail or to es tablish the suming; the dynamic range ovcr which the desired maximum accuracy obtainable. In practice, this is accL1l'u,cy is achieved is rather small, a lld t he danger often determi ned hy th e s LabiliLy requirements of barretter humou t cI LI e to a misstep on the p art of imposed on tile g('J1(' rfL tor and m easuring syst em by the operator is ever pl'esC'n t. th e tim e-cons uming JmL Ul'e of Lli I' trcil niq lie, rathrr A ~ self-balancing cI-c bolomctrr bridge has been t ilfLll by more fundamental limitations. developed at Lh e KBS Boulder Laborat.ories, which to a large m eaSUl'e reli eves th ese problem s, while preserving thc accuracy and e.'Lending tbe dynamic range of operaLion. T o d ate, Lhe technique has bern employrd primarily with bane Her-type elemrnts, although on the basis of preliminary resulLs, tlie tccil lli qur should prove equally useful with thrrmis tors, 2. Manual Bridge

One of tho simplest forms of the m anual bridge previoLlsly employed at Lh e Kational Bureau of Standards is shown in figure 1. The r-f power 5 is given by FIG URg L llIanual dil"ecl-ClIl"l'enl bolomeler bridge. (1) 3 . Self-Balancing Bridge where i 1 and i2 are the toLal curren ts reqllirrd to balance the bridge without and wi th r-f pOWE'r The self-balancing d· c bo101110[cr bridge employs a prese nt, r espectively. A precision poteutiometel'­ c1 -c amplifirr in a feedback loop to bala nce the standard resistor combination is used to m easure bolometer bridge. The amplifier is connected in i 1 fLJl cl i 2• If it is assum ed tbat Lhis measurement sueh a manner that. the bridge unbabnce signal is amplified to provide the bridge Cllnen t (fi g. 2). The I R . \\7. B eatty and Frank R eggin, An jmpl'On~d method of JTIefi suring cnicicl1- cirs of ultra-high-frcQuency and microwave bolometer mounts, J . Hcscarch usc of this self-bala ncing circuiL eliminates many of N BS 5~ , 32 t (1955) R P 2594. the timr-consuming featur r s of the technique, but 2 A . C. Ar acpherson and D. l'vL Kerns, A microwave microcalol'imeter, .Rev. Sci. Tnsu·. 26, 27 (1955). Lhe power-measurem en t prohlem is essentially the 3 n . J . Carlin and 1\ fax Sucher, Accuracy of bolol11ctric power measurements, Proe. IllSt . Radio Engrs. ~O , 1042 (Se pt. 1952). sam e. T his problem, at low power levels, is basically 4. D. 1\ [. Kerns, D etermination of e ni ciell cy of micl'owa\'c bolometer mOllnts one of trying to accurately m easure a small change from impedance data, .1. Research N B S ~2 , 579 (1949) HP1995. ' l\ fore correctl y, "the retracted cl·c power". i n a comparatively large d·c po·wer.

101 ometer and standard resistor are e mplo~T ed in place of A [ and A2 to achieve high accuracy. Alternatively, a voltmeter, F, connected as shown , will read (1'0/4) (1:[+ i 2), and the power is given by the product of F and A 2 • These operations may also be combined in a single instrument of the dynamom­ IN DC AMPLIFIER etrr type to ac hieve a dirert reading of t he power. The degree of success obtained wi til this technique is, of co ursc, con tingen t upon the degree of stability achi eved in thc ronstant-current generator. In this case the change in generator output for a complete cutoff of bridge current is less than 1 part in 10 5, resul tin g in a negligiblr error from this source. FIGU RE 2. Basic circuit of selJ-balancing bridge. 4. Performance

CONSTAN T It is shown in a following section that thc over-all CURR ENT acc urac~- in power measuremen t achieved, using a GENERATOR potentiometer to measure the curren t, is about 0.1 percent, wh ereas substitution of a suitable dy na­ mometer to achieve direct reading is expected [,0 y ield an aecurae~T of a bout 0. 3 percent. The instrument thu s provides an increase in accuracy of 10 to 50 times that provided b~T the co mm e reiall~ ' avaiablel aucl iobridges. Other ad vantages over the t.dpica DC AMPLIFIE R audiobridge inelucle : (1) Comparatively simple tec h­ niques arc availa ble for establishing, verifying, and monitoring the specified aceurac.\-, (For example, the bridge balance ma.\- be monitored by a suitabl e galvanometer.) (2) The performance is, to a large degree, independent of t he nominal de terioriation of the vacuum t ubes and other electrollic components. (3) The elimination of the audio b ias power avoids its interaction with the pulse-repet ition frequency in the measuremen t of pulse power. At low power levels the r-f power is approxi­ F r G URE 3. B asic cil'cuit for the determ'inalion oJ tli and power. mately proportional to fli (eq ;3), alld the low-level performance ma~T be d i s p l a~- e cl b~- r ecording thi s cur­ The formula for the J"-f power ma.\- be rewritten rent with the r-f power a l ternatd~- on and off. The s ~~s tem response Lo a ] -p..W signal is given in figure 4. Barring failure of the electronic componen ts, the (2) self-balancin g operation eliminates the clanger of bolometer burnout clu e to exc('ssive bias current, whereas protection against an )"-f overload ma.\ ~ also (3)

where fli = i[ -i2 . The difficul t factor to m easure accuratel\T is fli . A constant-current ge nerator of high stabiii ty has been developed for use in co njllnction with a differ­ ential current-measuring technique, which enables a dir'ect and accurate determination of fli. The circ Ll i t is illustrated in figure 3 a nd operates as foHows: Firs t, with no microwave power presell t in the bolometm', i[ is deLermined by ammeter A I, a nd tho output of the constant-current generator is adjusted with the aid of ammeter A2 to equal i[ (ammeter A2 reads zero) . Then, with microwave power applied, A2 will read fli di rer tl~-, and the power may be FIGURE 4. Bridge l'es ponse to a I -micTOwatt signal. determined from eq (:3 ). In practice, a potenti- (Rad iofrequency on and on ror I-minute inLeryals)

102 l<'lGUR," 5. Prololl/pe model oJ self-balancing bridge, front and real' views. br proyideci th rough usc of n s uitable rday to tum ofl' the r-f sourcr '\'hl'll th e' po\\'('r illput to the boloml'ler ('xcr('cis n prl'scri lwei 11moulll. a = (ib l-1bJ/(igl- ige) = CtIlTe n L amplification of The d-c amplifier emploYl'd ill this applicntioll is a amplifier commerciall.," uyail abk instrumellt of e:\cept iOllul 7 = fraclional deviation of the lower bridge arm gu ill , zero stnbilit .\·, Hlld phnsl' ]"('SPOIlSl', which was from t he ynllle 1'0 modified by the additioll of a cathocle follo\\'er to 1'1 = r<'sistnllr(' of holometer leads providl' the requ ir l'C1 output CUITl'Ill. Th(' current 1' = tlwrmaJ (or otl1er) ('111f in nmpli(i('l' input amplificntion of the nmpl ifier, as thus moelifiecl. is ?b = total hridge CU ITl'llt appro:\imately 100,000. Compellsatioll for the ig = nmplifiel' illput ClII'rellt tilermnllng of the bolometer is provided ill the feed­ fJ!'o = amplifiel' inpu t rl'S istaIIC!' back loop b.\" ml'HIl S of a cOlldellse'r , as illdicated ill 'Y = "ohms per ,,"aU " \)olol11et er coefficiC'u t. figure 2, but the' ac hi(,Y (,Il1(' llt of s tn!>\(> operatioll with this large amplifi('atioll is primaril.\· It tribute to For a typical bolomctrr opera ~ il1g in tile ° to 10- the nmpl ifin phasl' respollse. The consta 11 t-CUITl'n t m,\' n'gioll, lilt' following values may !w assigned: gelH'J'U tor emplo.\"s H secolld ampli fier of the same type, which, with modifieatioll, maintains a C'ollsta nt­ 1'0 = 200 ohms output current by referellce against a mercu1'.\- cell. 1' = 4.5 ohms/mw A protot~ ' pe moclrl of this equipmellt is shown in i b1 = 17 rna figu re 5 1b2>8 rna

5. Analysis of Errors S lIhsLituting tllesc values in tho above expre"sion yields the resul t Tlle practical problems involved in making an ac­ curate dclermillation of th e power, using eq (1) to (:)), have been noted. But use of these formulas implies that tbe bridge is rxactly bnlanceci, the bridge arms are eq ual to /'0, etc. IL is shown in the appendix Lhat a more complete rxpl'essioll for the power is

wherr tile last three (,erms in the bracket, reflect the inahility of the d-c am plifier to balance the bridge exactly. The characteristics of the d-c amplifier employed in this application arc such th at the foll owing values

103 obtain:

g= 1/4 (amplifier input resistance 50 ohms)

(currcnt amplification)

0< i g di bl < 2X 10- 5 1 0< i g2 < 10 - 7 ~ (amplifirr zero stability). lel< 10 - j Substituting these values in the last three terms gives a value for th eir sum of about 0.0002. The bolometcr lead resistance can be m easured with littlc effort and the correction appli ed, so the error from this source is negligible, whereas the value of IZI can ordinarily bc h eld to 0.0001 or less. Finally, it is possible to m easure current by m eans of a precision poten tiometer-standard resistor com­ FIGURE 6. Bridge circuit used in the evaluation oj errors. bination to an accuracy of a few parts in 104 ; thus the first factor in eq (4) may be determined by the technique discussed earlier to an accuracy of about 0.06 percent.. In summary, the total limits of error are as follows :

D eviation of bridge arms from valu ero ______0. 01 percent. Fail ure of bridge to be exactly bala nced ______. 02 percen t. The failure of the expression for power to have a M easurement of ib1 + i w______. 03 percent. first-order dependence on X or Y is explained as M easurement of i b1 -ib2-______. 03 percent. Bolometer lead resistance ______. 00 percent. follows: A prescribed , small valu e for X or Y will Amplifier noise and instabili ty cause a first-order variation in bolometer resistance (experimen tally observed)__ 0.1 }.tW. 1', as indicated in eq (7), but also produces an unequal Tot,d______. 09 percent+ 0.1 }.t W. division of current in the two sides of the bridge. These two sources of error cancel to a first approxi­ 6. Appendix mation. The only general requirement on t he upper bridge arms is that they be equal, and if they have a From figure 6 - the power may be expressed 111 nominal value of To, it can be shown that they may the form differ from each other by as much as 2 percent and produce , 'an error in th e power measurement of only 0.01 percen t. (5) At a constant ambient temperature and assuming equivalence of d-c and r-f heating,6 the power , P , dissipated in the bolometer will be a fun ction of its where X , Y, and Z are the deviations of each of the resistance, 1': bridge arms from t he value To, iy and e are the detector current and thermal (or other) emf, re­ P j (1'). spectively, and 1' 1 the resistance of the bolometer leads. B ecause the bolometer is nearly a ~ square-law Assuming a knowledge of the bolometer resistance detector, one ma~- in the neighborhood of an ar­ law, an exact expression for the second term could bitrarily se l ec t ed~ operating resistance To, write be derived, but the labor required suggests the fol­ lowing approximate treatment. By hypothesis, the variables X ... 1'1 and f(X .. . 1'1) are small, and f(X ... 1'1) may, to a good approximation, be written as the sum of the first-order corrections for each of these qua ntities, where the correction for each of where Po is tbe power required to bring the bolometer the variables is determined with the other variables to the resistance To at the given ambient temperature, equal to zero. P is the sum of the d-c and r-f power, P = Pdc + Prh Application of this technique to the circuit in and aP/ar is the reciprocial of the " ohms-per-watt" figure 6 yields the following first-order expressions for the d-c power dissipated in the bolometer, and 6 'rhe r.f-d-c substitution error is assumed to-be negligible in this discussion. the bolometer resistance For a treatment of this problem, see footnotes 2:and 3.

104 bolometrr coefficient, i. c., (oP/or) = (l /'Y). Then is subject to change with the application of r-f power. Substituting eq (G) alld (7) in eq (8) gives the desired result

Po- may be determincd by measuremenLs III the absence of r-f power: I , \ P o~ Pdc-- \.1'1 - 1'0), 'Y where where the subscript 1 has been used to indi cate the a = -~b.--l -~b2.- · value of quantities measured in the absence of r-I ~gl-~g2 power, whereas the subscript 2 will indicate values with r-f present. The formula for r-f power i.s then Thr author extends his thanks to R. IV. BraLLy and John E. Laucr for thcir valuable criticisms and suggestions in the prcparaL ion of Lhi.s paprr, and to RaS" R. Rumfelt for his assistance in the dcsign n,nd co nstrucLion of this equipmenL. In thr given applicaLion, onl~- i g of Lhe variables X ... l't has a Iu nctional dependence upon iv, or BOULDER, COLO., November 28, 1956.

105