July 1944 QST
Table
of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
QST, published December 1915  present (visit ARRL
for info). All copyrights hereby acknowledged.

Here is an amazingly detailed article on
how to construct and operate a nearlabquality impedance bridge out of relatively
inexpensive components. It appeared in a 1944 issue of QST magazine. A
bridge is used to determine the precise value of a resistor, capacitor, or inductor.
Prior to modern, easily affordable digital impedance meters, both amateurs and professionals
relied on such devices for lab and field work. Why might you need to measure the
value of a component when most are marked with a value? One common application is
when a variable version of a component (or components) is soldered into the circuit
while tweaking for optimal performance, and then the variable is replaced either
with a single fixed component or a fixed component with a smallerrange variable
component (the latter provides adjustment, but over a smaller range of values).
It is not uncommon when doing the initial tuning on a complete homebuilt transceiver
to have many variable components in place initially, and then solder in fixed versions
later. This design centering process provides good reference values for future designs
and makes the final product more affordable and compact, since variable are almost
always more expensive and larger in physical size.
An Inexpensive Impedance Bridge  The Principles and Construction
of a LaboratoryType Instrument for C, L and Measurements
By Athan Cosmas*
Many amateurs who have gone into advanced radio work, either
in the armed forces or as civilians in industry, are becoming acquainted with the
usefulness of laboratorytype precision measuring equipment. It is safe to say that
the postwar ham will be far more "instrumentconscious" than he was in prewar days.
He will consider an inexpensive but accurate Impedance bridge, such as the one described
in these pages, an almost indispensable item of station equipment.
Into the life of every ham there comes a time when the exact measurement of some
value of C, L or R is required. It may be of a resistor which is to be used with
a delicate relay, a coil for some type of filter, or perhaps a condenser which is
needed in a special circuit. What to do? If there is no school laboratory handy,
or if there are no friends who happen to own an expensive instrument such as the
General Radio Type 650A Impedance Bridge, the best "out" is to build an impedance
bridge which will do the work.
The bridge shown in the accompanying photographs will enable the making of all
the measurements which usually are required in ham work. It has many of the fine
features of the GR bridge which it emulates. It will, of course, lack several of
the fine points which contribute to the nicety and high accuracy of the expensive
laboratory instrument i but it may be made from inexpensive parts, most of which
the average ham has on hand, and it will have high enough accuracy for the average
type of amateur measurements. The only hardtoget item is the galvanometer.
Panel view of the impedance bridge. The large dia in the center
is the CRL dial, which controls R_{10}. In the upper corners are the knob.
for (left) the selector switch, S_{2}, and (right) the multiplier switch,
S_{1}. In the bottom row from left to right are the Q dial controlling R_{12},
the DQ dial controlling R_{11} and the D dial controlling R_{13}.
The generator or battery input terminals are located at the bottom, and the detector
terminals at the top. The R terminals, to which unknown resistances are connected,
are at the left, and the CL terminals, to which unknown capacities or inductances
are connected, are at the right. Photos &y Robert E. Cobaugh, W2DTE
Range
The complete circuit diagram of the instrument is given in Fig. 1. It includes
a switching arrangement whereby any of the basic bridge circuits shown in Fig. 2
may be obtained.
In Fig. 1, when selector switch S_{2} is in the position marked
R, the circuit is that of the Wheatstone bridge, shown in Fig. 2A. With this
arrangement any resistance value from 0.01 ohm to 1 megohm can be measured when
it is connected across the terminals at the right marked R.
When the switch is turned to either of the positions marked CD or CDQ, the circuit
is that of the capacity bridge shown in Fig. 2B. Any capacity between 100 μfd.
and 10 μμfd. connected across the CL terminals can be measured with either
of these arrangements. This circuit also provides for two ranges of power factor,
0 to 0.1 with S_{2} in the CD position and 0 to 1 with S_{2} in
the CDQ position.
With the switch thrown to the LDQ position, the circuit is that of the Maxwell
bridge shown in Fig. 2C. This circuit is used to measure the inductance of
coils having values of Q up to 10. In the LQ position, the circuit is changed to
that of the Hay inductance bridge shown in Fig. 2D. With it, coils having
values of Q up to 1000 can be measured. The inductance range is from 10 microhenries
to 100 henries with either circuit.
For the benefit of those who have not had occasion to work with bridge circuits
of this sort R, in the past, a brief explanation of the operating principles will
be given.
Resistance Measurement
Referring to Fig. 2A, the fundamental bridge circuit consists of four resistance
arms. Two of these arms, R_{a} and R_{b}, are made up of fixed resistance
values which are selected by a dual tap switch, S_{1}. The third arm, R_{v}
consists of a calibrated variable resistor (in this case the resultant of R_{9}
and R_{10} in parallel, because a variable unit of proper taper could not
be obtained), while the fourth arm is composed of the unknown resistance, R_{u}.G
is a d.c. galvanometer which, in effect, indicates the voltage differential between
the midpoints of the upper and lower branches.
The object in adjusting the bridge is to arrive at a balanced condition where
no current flows through G. In order that no current shall flow through G, it is
obvious that its terminals must be at the same voltage. For this to be true, the
galvanometer must have each of its terminals connected at the same percentage of
the total resistance in each arm. For instance, if R_{b} has three times
the resistance of R_{a}, then the unknown resistance, R_{u}, must
have three times the resistance of the variable resistor, R_{v}, when the
latter is set for zero galvanometer current. Since R_{v} is calibrated,
it is a simple matter to determine the value of the unknown resistance.
From this reasoning we can set down the following proportion for the condition
of zero current through the galvanometer:
From this we obtain
Fig. 1  Circuit diagram of the impedance bridge.
C_{1}  0.01μfd. mica (see text). C_{2}  0.001μfd.
mica. R_{1}, R_{7}  10,000 ohms, wire wound. R_{2},
R_{6}  1000 ohms, wire wound. R_{3}  1 ohm, wire wound.
R_{4}  10 ohms, wire wound. R_{5}  100 ohms, wire wound.
R_{8}  100,000 ohms, wire wound. R_{9}  41,000 ohms, wire
wound. R_{10}  15,000ohm, wirewound potentiometer. R_{11}
 16,0000ohm, wirewound potentiometer. R_{12} 165ohm, wirewound
potentiometer. R_{13}  1600ohm, wirewound potentiometer. R_{14}
 70 ohms. (Note: Oddsize resistance values may be composed of two or more
standardvalue resistors in series.) S_{1}  Sections of 2gang, 7position
rotary switch. S_{2}  Sections of 2gang, 4circuit, 5position rotary
switch (Centralab 2515).
It is apparent that the unknown resistance, R_{u}, must always be equal
to the value of resistance at which the variable resistor, R_{v}, is set,
times a multiplying factor represented by the ratio R_{b}/R_{a}.
lf some fixed value is selected for R_{a}, then a change in R_{b}
alone will change the multiplying factor. Thus, the several resistances (R_{3},
etc.) represented by R_{b} may be considered as multipliers for the range
of R_{v}.
As an illustration, in the instrument shown in the photographs R_{v}
is 10,000 ohms, R_{a} is also 10,000 ohms (except for the highest resistance
range, G in Fig. 1), while the tap switch, S_{1}, changes R_{b}
in steps of 10 to 1; i.e., 1 ohm, 10 ohms, 100 ohms, etc., up to 100,000 ohms. The
multiplying factors which can be applied to the resistance setting of R_{v}
are, therefore,
, etc.
or, in decimal equivalents, 0.0001, 0.001, 0.01, etc. Since the useful range
of R_{v} is assumed to be from 100 to 10,000 ohms, the successive ranges
of resistance measurements which can be made by the bridge are from 100 X 0.0001
= 0.01 ohm to 10,000 X 0.0001 = 1 ohm when R_{b} = 1 ohm; from 100 X 0.001
= 0.1 ohm to 10,000 X 0.001 = 10 ohms when R_{b} = 10 ohms; from 100 X 0.01
= 1 ohm to 10,000 X 0.01 = 100 ohms when R_{b} = 100 ohms etc.
Therefore, with the particular values selected for this bridge, the maximum resistance
measurable in each range is equal to the value of R_{b} selected by the
tap switch, S_{1}.
In the wiring diagram of Fig. 1, R_{1} and R_{2} are the
resistors represented by R_{a}, while R_{3} to R_{8} are
the resistors represented by R_{b}. R_{v} represents the resultant
of R_{9} and R_{10} in parallel. When S_{1} is turned to
the last tap (G), R_{a} is changed from R_{1} (10,000 ohms) to R_{2}
(1000 ohms). In this position, R_{b} (which represents R_{8}) has
a value of 100,000 ohms. The .multiplying factor for this range is, therefore,
As R_{v} is varied from 100 to 10,000 ohms, the resistancemeasuring
range runs from 100 X 100 = 10,000 ohms to 10,000 X 100 = 1,000,000 ohms = 1 megohm.
In use, the unknown resistance is connected to the terminals marked R, the CRL
multiplier switch, S_{1}, is turned to the approximate value and the CRL
dial, controlling R_{10}, is adjusted for zero galvanometer current, The
CRL dial reading is taken and the multiplying factor indicated by the position of
S_{1}, as shown in Table I, is applied to the CRL dial reading to obtain
the value of the unknown resistance.
If the bridge is very far off balance when the battery voltage is applied, excessive
current may flow through the galvanometer. While R_{14} serves to limit
this current, a pushbutton switch may also be incorporated in series with the galvanometer
so that the battery voltage may be applied only momentarily until the arms are adjusted
for an approximate balance.
Fig. 2  Basic bridge circuits. A  Wheatstone bridge used
for resistance measurements. B  Capacity bridge for measuring capacity and power
factor. C  Maxwell inductance bridge. D  Bay inductance bridge.
Labels on components refer to similar components and labels in Fig. 1 and
to designations in the text. The respective dials controlling each variable unit
also are indicated. In A, a DeJur student galvanometer or its equivalent is suitable
for G. The galvanometer is strictly necessary only for lowresistance measurements.
The 1,000cycle a.c. source and headphones may be used for measuring the higher
resistance values as well as for inductance and capacity.
Capacity Measurement
When selector switch S_{2} is in the CD position, the circuit becomes
that of the capacity bridge shown in Fig. 2B. This arrangement is similar
to the Wheatstone bridge circuit used for resistance measurements except that two
of the arms contain capacities  one the unknown capacity, C_{u}, and opposite
it a known capacity, C_{s}. The principle of obtaining a balance is much
the same as that described for the Wheatstone bridge. In order to obtain voltage
drops across the condensers, it is obvious that an a.c. source must be used instead
of a battery. This is provided by a 1000cycle generator. In place of the galvanometer
a pair of headphones is used as an indicator, and the bridge is balanced when the
arms are adjusted to give minimum response in the headphones.
Since the impedance of a condenser is in inverse proportion to its capacity,
the expression for a balance becomes
From this we obtain
From the above, we see that the ratio R_{v}/R_{b} is the multiplying
factor to be applied to the standard capacity to obtain the unknown value, C_{u}.
The highest capacity range is made available when R_{b} is set at one ohm.
The multiplying factor then becomes when R_{v }= 100 ohms,
and = 10,000 when R_{v} = 10,000.
At the other end of the range, when R_{b} is set at 100,000 ohms the multiplying
factor is reduced to = 0.001 when R_{v = }100 ohms
and = 0.1 when R_{v} = 10,000 ohms.
The standard represented by C_{s} is C_{2} in Fig. 1. It has
a value of 0.01 μfd., to which the above multiplying factors are applied when
determining the value of the unknown capacity. The total capacity range varies from
100 μfd. when = 10,000 to 0.00001 μfd. = 10 μμfd.
when = 0.001. Table I shows the factor by
which the CRL dial reading should be multiplied to obtain the capacity in μfd.
for each of the ranges set by S_{1}.
Behind the panel of the impedance bridge. This view shows the
multitap switches, the fixed standards and the four variableresistance units.
Power Factor
When making capacity measurements with the bridge it will be found impossible
to obtain a complete balance unless the power factor of the condenser under measurement
happens to be the same as that of the standard condenser, because of the difference
in phase shifts. A condenser with a power factor greater than zero may be represented
by a pure capacity (a condenser without losses) in series with a resistance. Therefore,
if the losses of the condenser used as a standard are negligible, the power factor
of the arm containing the standard may be made the same as the power factor of the
arm containing the unknown capacity by adding resistance (R_{11} or R_{13}
in Fig. 2B) until the circuit is in balance. The setting of the series resistance
for balance thus serves as a means for measuring the power factor.
A close approximation of the power factor of a condenser is given by the ratio
R/X, which is known as the dissipation factor. Here R is the equivalent series resistance
and X the reactance of the condenser. The latter is equal to
where f is the frequency of the applied voltage
in cycles and C the capacity of the condenser in farads. Therefore, in Fig. 2B,
p.f. = (R_{s}) (2πfC)
As an example, we know that the frequency is 1000 cycles and the capacity 0.01 μd.
= (0.01) (10^{6}) farads. Substituting these values, we obtain
p.f. = (R_{s}) (6.28) (1000) (0.01) (10^{6})
= (R_{s}) (0.0000628)
R_{s} represents either of the variable resistances, R_{11} or
R_{13}, in the standard arm in Fig. 2B. R_{11} is in the circuit
when S_{2} is in the CDQ position. It has a maximum resistance of 16,000
ohms and is controlled by the dial marked DQ. At full scale the power factor of
the standard arm is (16,000) (0.0000628) = 1. When S_{2} is in the CD position
the circuit is the same except that R_{13}, with a maximum resistance of
1600 ohms, is substituted for R_{11}. R_{13} is controlled by the
dial marked D. When R_{13} is set at maximum the power factor indicated
is 0.1. If the DQ dial is marked 0 to 10, its readings should be multiplied by 0.1
to obtain the correct power factor. (See Table III.) Similarly, the D dial reading
should be multiplied by 0.01.
In practice, S_{1} is first set to the appropriate range for the capacity
to be measured. The CRL dial controlling R_{10} is then varied for minimum
response in the headphones. Finally, the D or DQ dials and the CRL dial must be
carefully juggled back and forth for minimum response. When the positions giving
the lowest possible response are found, dial readings of capacity and power factor
can be made.
Table I
This table shows the multiplying factors which must be applied
to the readings of the dial calibrations given in Tables II and III.
Depending upon the position of tile multiplier switch, S_{1}
in Fig. 1, CRL dial readings should be multiplied by the factors shown below
to give the correct values in the units indicated.
When making p.f. measurements on the D dial, multiply the dial
reading by 0.01.
When making p.f. measurements on the DQ dial, multiply the dial
reading by 0.1.
When making Q measurements on the DQ dial, multiply the dial
reading by 1.
When making Q measurements on the Q dial, multiply the dial reading
by 100.
Table II
This table shows how the CRL dial controlling R_{10}
should be marked to be direct reading for various resistance settings. For example,
when the parallel combination of R_{9} and R_{10} in Fig. 2
is adjusted to a resistance of 1500 ohms, the CRL dial scale should be marked 1.5.
Table III
This table shows how the D, DQ and Q dials should be marked to
be direct reading for each resistance setting of R_{13}, R_{11}
and R_{12} (Fig. 2), respectively.
Inductance Measurement
When selector switch S_{2} is turned to the LDQ position, the circuit
becomes that of the Maxwell inductance bridge shown in Fig. 2C. The Hay inductance
bridge of Fig. 2D is obtained with S_{2} in the position marked LQ.
The circuits are the same insofar as the measurement of inductance is concerned;
they differ only in the ranges of Q which may be measured.
Since the impedance of a coil is proportional to its inductance while that of
a condenser is in inverse proportion to its capacity, the condition for balance
in the circuits of Fig. 2C and 2D is given by
From this we see that the product of R_{b}R_{v} is the factor
by which the numerical value of C_{s} must be multiplied to obtain the value
of the unknown inductance. Both inductance and capacity are expressed in units of
similar order; i.e., in henries and farads. In the circuits of Figs. 2C and 2D,
C_{s} represents C_{1}, which has a capacity of 0.1 μfd., while
R_{v} may be varied from 100 ohms to 10,000 ohms and R_{b} from
1 ohm to 100,000 ohms, as before.
The smallest multiplying factor is obtained when R_{v} and R_{b}
are at their minimums of 100 ohms and 1 ohm respectively. Then the factor becomes
100 and L_{u} = (100) (0.1) = 10 μh. (μh. because C_{s} is
expressed in μfd.). The largest multiplying factor is obtained with the maximum
values of resistance for both R_{v} and R_{b}, which are 10,000
ohms and 100,000 ohms, respectively. The factor at this end of the range is (10,000)
(100,000) = 10^{9} and L_{u} = (10^{9}) (0.1) = 10^{8} μh.
= 10^{2} h. = 100 h. Therefore, the range of the instrument on inductance
measurements is from 10 μh. to 100 h.
As in the case of capacity measurements, it will be found necessary to balance
resistive components as well as reactive components in the nonresistive arms. The
amount of resistance which must be added in the capacitive arm to obtain minimum
response in the headphones may be used as a measure of the Q (or X/R) of the coil.
Since the reactance of the standard condenser, C_{s} is given by
When selector switch S_{2} in Fig. 1 is in the LDQ position for
the Maxwell bridge circuit of Fig. 2C, C_{s} = C_{1} = 0.1 μfd.
and R = R_{11}, which is the variable resistor controlled by the DQ dial
and which has a useful range of 160 to 16,000 ohms. The frequency is, of course,
1000 cycles, as before. Substituting these values in the above equation,
(the factor 10^{6} in the above denominator being necessary in converting
to farads). At the other end of the range of R_{11},
Thus the range of this circuit in measuring Q is from 0.1 to 10.
When S_{2} is in the LQ position to give the Hay bridge circuit of Fig. 2D
the procedure is the same, except that R_{12}, which has a useful range
of 16.5 to 165 ohms, is substituted for R_{11}. This gives a range of Q
from 10 to 1000.
Constructing Resistance Standards
Most of the constructional details may be observed from the photographs. If the
case is made of sufficient size, the galvanometer, battery and 1000cycle source
can be included in the unit for greater convenience.
The absolute accuracy of measurements made with the bridge naturally will depend
upon the accuracy of the fixed resistors and condensers used as standards, as well
as the calibration of the variable resistors. Ordinary copper magnet wire may be
used in constructing homemade fixed resistance standards of values up to 10,000
ohms. Reference to the wire table in the Handbook (see pages 401 and 427 in the
1944 edition) will show the approximate resistance of copper wire of various sizes.
For instance, the table shows that No. 28 wire has a resistance of 66.2 ohms per
1000 feet, or 0.0662 ohms per foot. Therefore, a length of about 16 feet will have
a resistance of approximately 1 ohm.
Fig. 3  Method used for winding noninductive resistance
standards from copper magnet wire. See text for details.
The standard resistors (R_{1} through R_{8}) must be of the noninductive
type. Fig. 3 shows the method used in winding the lowervalue resistors on
a thin strip of Bakelite. The two ends of the wire first are soldered to the terminals
at one end of the strip. The two halflengths of wire are then wound in opposite
directions around the Bakelite strip and the loop end fastened to the other end
of the strip.
This method was used in making the 1, 10 and 100ohm standards. For the 1000
and 10,000 ohm units halfinch Bakelite rod was used, grooves being cut in the
rod so that the windings could be made in pies. Each pair of adjacent pies was wound
in opposite directions. Resistance wire rated at 80 ohms per foot was used, wound
250 ohms per pie for the 1,000ohm units and 2500 ohms per pie for the 10,000ohm
unit. Two 50,000ohm meter multipliers, rated at 1 per cent accuracy, were connected
in series to provide the 100,000ohm standard.
Calibration
The most accurate means available should be used in checking the resistance of
the standards. A local serviceman or a school laboratory may have a resistance bridge
which can be borrowed to make the calibrations. The wirewound units can be adjusted
to exact values by removing the insulation from the loop end and twisting the loop
until the correct value is obtained.
An accurate calibration must also be obtained for the R_{9}R_{10}
combination. The curve should be checked at as many points over the range of R_{10}
as possible. If a 10,000ohm resistor with a logarithmic taper is available it may
be used to replace the parallel combination. When building this unit a potentiometer
of this type could not be obtained locally, and so the combination of R_{9}
and R_{10} was used to obtain an approach to the desired logarithmic characteristic.
Fig. 4  Circuit of tbe 1000cycle tone source.
C_{1}  0.5 μfd. C_{2}  0.1 μfd.
S_{1}  4p.d.t. switch. S_{2}  Pushbutton switch.
B  Highfrequency buzzer.
Once the fixed resistance standards and R_{10} are calibrated, it is
a relatively simple matter to calibrate R_{11}, R_{12} and R_{13}
by simply connecting them to the R terminals of the bridge. These three units preferably
should also have a logarithmic taper.
Condensers having capacities as close as possible to..the required values of
0.1 μfd. and 0.01 μfd. should be used for the capacity standards. Both should
be of the mica type, to minimize loss errors. C_{1} may be made up of a
combination of smallercapacity units in parallel, if necessary.
The accompanying tables (II and III) show how the dials should be marked to be
direct reading.
Fig. 4 shows the circuit of an inexpensive generator suitable for the 1000cycle
signal source required for measuring capacity and inductance. The frequency can
be checked with sufficient accuracy by matching it up with the second B above middle
C on a correctly tuned piano. The buzzer should be enclosed in a soundproof box.
Posted July 20, 2021 (updated from original post on 12/21/2012)
