No.

STX-107

Moy,1968

THE UNIVERSAL IMPEDANCE BRIDGE 1. Why can" we simply measure L and C instead of L, or Lp and C, or Cp7

2. Why does a universal impedance bridge measure series resistance or parallel conductance?

D

and Q instead of the equivalent

3. When is the null good enough to take advantage of the accuracy b u i l ~into the bridge? 4, When does the nulling procedure converge rapidly? Is there a cure for an extreme case of '"tiding null"?

5. 1s there a better balancing procedure than flailing about with the controls7 6. Bridges require a certain amount of skill and knowledge of the operator. Why, then, does one use a bridge instead of one of the direct-reading instruments such as ohmmeters and inductance meters?

IMPEDANCES AND ADMITTANCES AND T H E I R EQUIVALENT CtRCUlTS

A two-terminal device can be characterized by either ~ t impedance s

or its admittance.

Z = R + j,Y

(1)

Simply by inspecting these equations and equating real and jmaginary parts, We can write down all the relations between the 2- and 1'-components:

(2)

Y=C+jR

R=-

G

c24- H'

I

x=-

(7)

G=-

R R' + ' X

18)

-B

c2+ B~

Notice also that

1

argZ = arg ; = a r g Y. X argX = tan-' R

(3)

arg Y = tan-'

nG

(4)

Since the device's ~mpedanceand admittance are reciprocals of each other, we have R+jX

1 G - 'Lj =--,=L C+JR

and

GZ + R Z

(11)

I

(5'

The characterization of a device in terms of its irnpedancP suggcsts that we can repreznt it bv an equivalent circuit consisting of a resistance and reactance in series, while characterization of the same device by i t s admittance implies an equivalent circuit r h a t consists of a conductanc~and susceptance in perallel.

,u.

Question: Usually we talk about the plain "capacit a n c e " ~ €a capacitor, nat CS or Cp. Strictly speaking, does such a quantity exist? Mow much difference is

-1

there between Cs and Cp if the capacitor i s fairly lo= less/11=0.001,say)7

Exercise: Show that

Q=

-"1 ZW

average enerfy stored irl Ls or Lp average power dissipated in Rs or Gp

Why does this formula differ by a factor of 2 from the similar formula that gives the Q of a resonant

INDUCTORS

circuit? The series and parallel equivalent circuits for inductive devices are THE BRIDGE BALANCE CONDITION The general circuit of a bridge is shown i n Figure 1. If we assume that the meter impedance is infinite we may regard Z1 and Zq a5 one voltage divider and Z3 and Z2 as another. It is then apparent that

The Q of an inductive device is given b y

and in terms of Q,

We can easily obtain the relations between the t w o equivalent circuits just as we did above in the capacitive case.

The bridge will "balanceu- the output voltage will be zero when the numerator of (31 ) is zero.

balance condition: Z1Z2 - X3Za = O Question: When we talk abouta"lOmH~hake," do we mean that L, = 30 mH or that Lp = 10 MH?

Exercise: A particular ferritc bead choke has an im pedance at 100 MHz of 115 ohms. I f the resistive component of this impedance is f 00 ohms, what is Q? What i s Ls? What are Lpand R p 7

-

Question: Ferrite bead chokes look like short circuits at dc. Why is the series ac resisrance Rs at 100 MHz so much higher than the dc resistance?

1321

Since no current flaws in the meter branch at balance, our assumption that the meter impedance is infinite is not necessary for ( 3 2 ) to be valid. The balance condition does not depend on eithcr the generator or the meter. The complex balance condition (32) yields t w o real equations. Equating magnitudes and angles, we have

and

Equations 33 and

34 must both be satisfied when the b r i d q ~

is balanced.

basic components are switched, depending on the nature of the unknown irnmittance that is t o bc measured, into one of the configurations shown in Figure 4. Capacitive unknowns whose dissipation factors are not too large are regarded as serie~equiva'ent circuits and t h e bridge c ~ fFigure 4a measUFPS Csx and D x . Capacitive unknowns w~Fhl a r g ~loss are treated as pirallel-equivalent circuits and rhe bridge of Figure 4b measures Cp and D x . Conversely, low-loss inductive unknowns are treated as paraklel-equ~valen t circuits and bossy inductances as series-equivalent circuits. The bridges of Figures 4c and 4d measure respectively L s x , Qx and L p x , Qx. R e sistance and conductance are measured by the bridges of Figures4e and 4f.

Equation 34 tells us what combinations af bridge arms have a chance of rratancing. For example, the arrangement of Figure 2 can't posibly balance because arg2, is positive, argZ3 is negative, and argZ2 and argZa are zero, so that a r c , + a r c 2 could never equal arM3 + argZd. The bridge of Figure 3, on the o t h e r hand, could balance ~f the element values were proper1y adjusted.

I ~TI'7V.I>

FIGURE 4a

FIGURE 3

THE StX BRIDGE CONFlGURAf IONS Accurate variable inductors and capacitors are very costly, so we don't want to use them in a br~dge~f we can help it. Inductors are never very ideal; they have distributed capacitance, thev have low Q at low frequenc~es,and the re sistive part of either of their equivalent circuits i s likely to be frequency dependent. Therefore we don't want to use f ~ x e d inductors either, With these constraints on the choice af parts to use i n ttre arms, all universal bridges turn out about the same. two variable resistors, a fixed capacitor, and several fixed resistors. In the General Radio Type 1650 Bridge, these

FIGURE 4b

I 511-11.11

FIGURE 4c

FIGURE 4f

Let us look a t the balance condition of the series capacitance bridge of Figure 4a. Compar~sonwith Figure 1 shows that

so that the balance equation 32 becomes S T L * f i Y 15

(Isx -i&)

.)pcGRL i b a

+ = (,DO

FIGURE 4d

(ball j -

I )RR, WC~T

whence, equating real and imaginary parts, we get

and

Equation 37 shows that when the bridge is balanced, Csx i s determined from the balance setting of only one of the bridge varisbles, hence the CCRS dial can be calibrated so as to read C,, d~rectly. But R S x depends upon + the balance settings of both bridoe variables, R C G R Land 4 R o n ; so we cannot read R s , directly from a single dial on the bridge. Howwer if we multiply equation 38 by w C s x ,

ZCGRL;

FIGURE 4e

FIGURE 5 The General Radio Type 16508 Impedance Bridge.

+ and at the same time get rid of RcGRL(ball by substituting from (37),we have

Turning now to the parallel-capacitance bridge of Figure 4b,we see that

which shows that at kalance the B of the unknown is equal t o the D of the CSTRDo2ranch. Since D x is proportional t o the balance setting of R,, and also to the frequency, the DQdial can be provided with a scale that i s proportional to D x divided by the frequency. On theType 1650 Bridgethe reading on the series capacitance Dscale is equal t o Dx /f{ k Hz}. Equation 39 also helps explain why the series capacitance configuration is not used when D x is large. Large values of would be needed to balance unknowns with large D's. But if i s made too large, the unavoidable stray capacitance in the DQ rheostat would introduce a non-negligible shunt capacitance branch into Z 3 , equation 36 would have t o be modified. and equation 37 would no longer be + valid. Thus R D a must be limited to reasonable values for the sake of accuracy in the CGRL-dial reading.

The balance equation, which i s now

z,

&,

gives us the two relations

balanced. Taking the series-capacitance bridge as our example,

(42)

we shall calculate the sensitivity of the null to small adjust-

143'

ments of the CGRL and DQ dials. We supzose that the bridge is very near balance. Let -RCGR_Land dm differ from the balance sett~ngs_RcGRLiball + and RDalball by small amounts A R C E ~ Land ARoa. I f we make the substitution

144)

and

and

+

z o o = ~ D a ( b a l -I) dOa Equation 42 for CPX is identical with equation 37 for Csx, so a single scale on the CGRL dial reads both Csx when the bridge is in the series capacitance configuration and CpX when it is in the parallel capacitance configuration. But equaZion 44 is not the same as equation 39. This time Dx is inversely proportional to the balance setting of and t o the frequency. This is why the paral !el-capacitance Dscale reading on The 1650 is equal t o D x f { k H z ) , and why i t s readings increase in the opposite direction from those on the seriep capacitance Dscale. Equation 44 also shows that the parallelcapacitance bridge is used far unknowns with large values of D for exactly the same reason that the series capacitance bridge is used for low-Y-D unknowns: to a v o ~ dlarge values of

Spa

in the bridge arsm impedances (35) and then put these irnped ances into (311, we shall obtain an expresion for VDu, as a function of GcGRL and d o a . We can save ourselves considerable work i f we exploit the fact that near balance the numerator of equation 31 is almost zem. The differential of a fraction is by

and if N is very small we have approximately

4

Ron.

Calculations s~milar to the ones we have just gone through lead to the iofilowing balance relations for the seriesand parallel-inductarce bridges of Figures 4c and 4d, the resistance bridge of F~gure4e, and the conductance bridge of Figure 4f.

AZ,-,,~

~x~~

Thus we may ignore the effect of and on the denominator of (31 + . l When we substitute (351,I57 1, and (52) into (311, leaving hRCGRLand d,, out of the denominator and noting that most of the terms in the numerator cancel because of the balance condition (361, we have

4

L P X= R R ~ s T R c G ~ ~ ( ~ ~ ~ ) para1tel inductance

Qx =

1 + LdCsTRoQ(ba1)

G -X

L

I ~

s

(48)

+ R = O R L (ball

~

R

conductance

150)

NULLS Thus far in 0 8 j r discussion we hwe assumed that the bridge is already balanced; now let us look a t the way i t gets

The bridw detector does not measure V,,,: it meas.1 I f w multiply equation 53 by i t s complex conjugate, we can obtain, after considerable arranging of terms and some substi'tutions from equations 37,38, and 39, UPS

Iv,,,

{6:GRL

2

D~ [ ~ C G R-L 6i30)21lVgonl2

+ c ~ R ~ / Rand~ 6Q0 ~ =~ ~ Z ~ oa ( l T~ t D~a I ) (bal). Equation 54 expresses the bridge output volfage as a function of the fractional deviations SCGRL and 8.. of the CGRL and DQdials from their balance settings. where 6 C ~ R =L ~

-

5. Measure the capacitance of a reversebiased diode or transistor collector-t~basejunction on t h e Cs bridge as a function of bias voltage, which can be applied t h r o u g h the bridge's bias connection. Note from t h e bridge schematic t h a t any diode leakage currenf must flow through the bridge ratio arm. On t h e 10BpF range, R R is 1 Ma, SO t h a t 1 pA of leakage current causes a 1-volt drop in series with t h e bias supply.

6. Connect a capacitor and resistor in wries to obtain a D of about 0.2. Measure Cs and D on the Cs bridge and Cp and D on the Cp bridge. Do the two D readings agree? Are t h e measured Cs and Cp in agreement with (181 and (19)? What should D be a t 10 kHz7 Using an external oscil!ator to drive t h e bridge, measure D a t 10 kHz.

R

++L I* C

r

p , ? , =" 53

.

1"y.

6\ ,v>" ...

,,$bwNltH


,

one

, E i 1

cGRL

/' "\

=

pU'

(. :;

I

I.+ K

-,

.

a, T u r n GENERATOR switch PO B A T CHECK position. If the meter pointer i s not i n rhe BAT sector, replgcethe batteries,

bm,T ,,

pointer i s not i n the BAT sector, replace the batteries. b- Turn GENERATOR s w i t c h t o AC E X T E R N A L or AC I N T E R N A L

GENERATOR or A t

EXTERNAL

to

y,-

Turn PARAMETER switch t o Cr. d. Connect the unknown so that

AC

J



1

MULT ,!?A

100 1

1 10

TO

TOa

100 1k

1 lot

L: 10

lOOL

100 IM

a. Check mechanical zero of meter. b. Turn GENERATOR s w i t c h t a the BAT CHECK position. If the meter painter is not in the BAT sector,

The

p.TurnGENERATORswitchOFF.

.FIN

\:.,$:,

cli'lr

OR THO NULL^

,

*'

...5:,5m>.

,.3.-

OUT. f. Turn OSC LEVEL clockwise. p n e l control affects only the internal o s c i l lator. g. Turn DQ d i a l near 0.2 on the HtGH D scale. h . T u r n CGRL d i a l near 11. i. Adiust D E T SEN5 for about 6 d i v i s i o n s deflection, i. Turn MULTIPLIER switch for minimum meter reading. k. Alternately adiust, f i r s t the DQ dial, then the C G A L d i a l for the DET best null, increasing the SENS a s needed. I. ORTHONULL@ switch should be SettoIN iftheDQdialreading times l / f (kHz) approaches or exceeds 1. m. If fhe DQ d i a l reaches the stop at 0.1, the unknown should be rneasured a s Cs. n, She capacitance of the unknown equals the prcrduct of the CGR t - d i a l reading and the M U L T I P L I E R - s w i t c h setting. c. The D equals the reading on the DQ d i a l times 1Jf (kHz).

vVm:, x+-

P.**4,,%

INTERNAL

for greater occurocy. d. Connect the unknown so that most stray capacitance i s between the LOW terminal and the 1650-6 case, e m f urn switch t o

1

..,

. T ., o.~\~ /7

c. Turn PARAMETER switch t o Cp, Large e l e c t r o l y t i c s sheuld be rnensured a t o low frequency (120 Hz)

1 kHz.

,

LC

1 kHz.

F.

'

L Z e2\ p / v

.,

-uL'c'b'

>

UYIINWH

urrumw*

r;~TvYM*3U9

"'oo#9y6:" ,, ::i " -'b

,/

,*--

=pdw '

hU'5.

>:

.

--

-a -4 -

9-5c

*'I I I b.?%

I

.

1

replore the barteries. c. Turn GENERATOR s w i t c h t o the desired generator source, The OSC L E V E L control affects only the intetnal o s c i l lator. d, T u r n ORTHONULL@ s w i t c h t o OUT and PARAMETER switch t o R. e. Turn CGRL d i a l near 11. f. Adiust DET SENS control for about 6 d i v i s i o n s deflection, g. Turn M U L T I P L I E R s w i t c h for minimum reading to the l e f t of center if making o dc meosuremerrt. Nullasusualifmakinganocmeosurernent. (DQ rheostat not in the circuit.) I?. Adiust CCRL d i a l for best ac null, or zero the pointer if u s i n g dc. If ac n u l l i s n o t sharp, a rea c t i v e bolcrnce may be necessary, see instruction manual. i. The unknown resistance i s the CGRL-dia t reading m u l t i p l i e d by the M U L T I P L I E R s w i t c h setting. i. Turn GENERATOR s w i t c h t o

OFF.

-

OPERATING -*-->t o w 0 coo? i o lor

---10 MULT 100 I ,.I/

>, H

MULT 3~

TOO I

m 11

1 10

II

10

100

100

lk

1 10 1 0 ~ IOOE

100IM

Turn GENERATOR switch t e BAT CHECK. If the meter pointer

0.

isn't in the BAT sector, replace the batteries. b, T urn GENERATOR s w i t c h t o 4C EXTERNAL or AC INTERNAL 1 kHz. A i r core rf chokes should be measured a t a high frequency (10 kHz) t o get o reasortable Q. c. Turn PARAMETER s w i t c h t o Ls. d. Connect unknown so that most stray capacitonce i s between the LOW terminal and the 16504 case. e. Turn O R T H O N U L L @ switch t o

./

"llt

r,.Tr

,,

-

- 'I.,, t

OUT.

u.-b

,

.'I

f, Turn OSC L E V E L clockwise, *I'

r

MULT

100

1

PA