An Inexpensive Impedance Bridge
July 1944 QST Article
is an amazingly detailed article on how to construct and operate
a near-lab-quality impedance bridge out of relatively inexpensive
components. 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 smaller-range 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 home-built 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
July 1944 QST
articles are scanned and OCRed from old editions of the ARRL's QST magazine. Here is a list
of the QST articles I have already posted. All copyrights are hereby acknowledged.
An Inexpensive Impedance Bridge
The Principles and Construction. of a Laboratory-Type 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 laboratory-type precision
measuring equipment. It is safe to say that the post-war ham
will be far more "instrument-conscious" 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 650-A Impedance Bridge, the best "out" is
to build an impedance bridge which will do the work.
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 G-R 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 hard-to-get item is the galvanometer.
Panel view of the impedance bridge. The large dia in the center
is the CRL dial, which controls R10
. In the upper
corners are the knob. for (left) the selector switch, S2
and (right) the multiplier switch, S1
. In the bottom
row from left to right are the Q dial controlling R12
the DQ dial controlling R11
and the D dial controlling
. 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 C-L terminals, to which unknown capacities
or inductances are connected, are at the right.
Robert E. Cobaugh, W2DTE
Fig.1 - Circuit diagram of the impedance bridge.
- 0.01μfd. mica (see text).
- 10,000 ohms, wire wound.
- 1000 ohms, wire wound.
- 1 ohm, wire wound.
ohms, wire wound.
- 100 ohms, wire wound.
- 100,000 ohms, wire wound.
- 41,000 ohms, wire wound.
- 1600-ohm, wire-wound potentiometer.
- 70 ohms.
(Note: Odd-size resistance
values may be composed of two or more standard-value resistors
- Sections of 2-gang, 7-position
- Sections of 2-gang, 4-circuit,
5-position rotary switch (Centralab 2515).
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
In Fig. 1, when selector switch S2
is in the position marked R, the circuit is that of the Wheatstone
bridge, shown in Fig. 2-A. 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. 2-B. Any capacity between
100 μfd. and 10 μμfd. connected across the C-L terminals
can be measured with either of these arrangements. This circuit
also provides for two ranges of power factor, 0 to 0.1 with S2
in the CD position and 0 to 1 with S2 in the CDQ position.
With the switch thrown to the LDQ position, the circuit
is that of the Maxwell bridge shown in Fig. 2-C. 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. 2-D. 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.
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.
Referring to Fig. 2-A, the fundamental bridge circuit
consists of four resistance arms. Two of these arms, Ra
and Rb, are made up of fixed resistance values which
are selected by a dual tap switch, S1. The third arm,
Rv consists of a calibrated variable resistor (in this
case the resultant of R9 and R10 in parallel,
because a variable unit of proper taper could not be obtained),
while the fourth arm is composed of the unknown resistance, Ru.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 Rb has three times the
resistance of Ra, then the unknown resistance, Ru,
must have three times the resistance of the variable resistor, Rv,
when the latter is set for zero galvanometer current. Since Rv
is calibrated, it is a simple matter to determine the value of the
From this reasoning we can set down
the following proportion for the condition of zero current through
From this we obtain
It is apparent that the unknown resistance, Ru, must
always be equal to the value of resistance at which the variable
resistor, Rv, is set, times a multiplying factor represented
by the ratio Rb/Ra. lf some fixed value is
selected for Ra, then a change in Rb alone
will change the multiplying factor. Thus, the several resistances
(R3, etc.) represented by Rb may be considered
as multipliers for the range of Rv.
As an illustration,
in the instrument shown in the photographs Rv is 10,000
ohms, Ra is also 10,000 ohms (except for the highest
resistance range, G in Fig. 1), while the tap switch, S1,
changes Rb 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 Rv are, therefore,
or, in decimal equivalents, 0.0001, 0.001, 0.01, etc.
Since the useful range of Rv 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 Rb = 1 ohm; from 100
X 0.001 = 0.1 ohm to 10,000 X 0.001 = 10 ohms when Rb
= 10 ohms; from 100 X 0.01 = 1 ohm to 10,000 X 0.01 = 100 ohms when
Rb = 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 Rb selected by the tap
the wiring diagram of Fig. 1, R1 and R2 are
the resistors represented by Ra, while R3
to R8 are the resistors represented by Rb.
Rv represents the resultant of R9 and R10
in parallel. When S1 is turned to the last tap (G), Ra
is changed from R1 (10,000 ohms) to R2 (1000
ohms). In this position, Rb (which represents R8)
has a value of 100,000 ohms. The .multiplying factor for this range
As Rv is varied from 100 to 10,000 ohms, the resistance-measuring
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, S1,
is turned to the approximate value and the CRL dial, controlling
R10, is adjusted for zero galvanometer current, The CRL
dial reading is taken and the multiplying factor indicated by the
position of S1, 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 R14 serves to limit this current, a push-button
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
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 low-resistance measurements. The
1,000-cycle a.c. source and headphones may be used for measuring
the higher resistance values as well as for inductance and capacity.
switch S2 is in the CD position, the circuit becomes
that of the capacity bridge shown in Fig. 2-B. 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, Cu, and opposite it a known capacity,
Cs. 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
1000-cycle 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 Rv/Rb
is the multiplying factor to be applied to the standard capacity
to obtain the unknown value, Cu. The highest capacity
range is made available when Rb is set at one ohm. The
multiplying factor then becomes
when Rv = 100 ohms, and
= 10,000 when Rv = 10,000. At the other end
of the range, when Rb is set at 100,000 ohms the multiplying
factor is reduced to
= 0.001 when Rv = 100 ohms and
= 0.1 when Rv = 10,000 ohms. The standard
represented by Cs is C2 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
to 0.00001 μfd. = 10 μμfd. when
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 S1.
Behind the panel of the impedance bridge. This view shows the
multi-tap switches, the fixed standards and the four variable-resistance
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
(R11 or R13 in Fig. 2-B) until the circuit
is in balance. The setting of the series resistance for balance
thus serves as a means for measuring the power factor.
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. 2-B,
p.f. = (Rs)
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. = (Rs)
(6.28) (1000) (0.01) (10-6)
= (Rs) (0.0000628)
Rs represents either
of the variable resistances, R11 or R13, in
the standard arm in Fig. 2-B. R11 is in the circuit when
S2 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 S2 is in the CD position the circuit is the
same except that R13, with a maximum resistance of 1600
ohms, is substituted for R11. R13 is controlled
by the dial marked D. When R13 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, S1 is first
set to the appropriate range for the capacity to be measured. The
CRL dial controlling R10 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.
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, S1
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.
Q measurements on the Q dial, multiply the dial reading by 100.
This table shows
how the CRL dial controlling R10
should be marked
to be direct reading for various resistance settings. For example,
when the parallel combination of R9
in Fig. 2 is adjusted to a resistance of 1500 ohms, the CRL
dial scale should be marked 1.5.
This table shows
how the D, DQ and Q dials should be marked to be direct reading
for each resistance setting of R13
(Fig. 2), respectively.
When selector switch
S2 is turned to the LDQ position, the circuit becomes
that of the Maxwell inductance bridge shown in Fig. 2-C. The Hay
inductance bridge of Fig. 2-D is obtained with S2 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. 2-C and 2-D is given by
From this we see that the product of RbRv
is the factor by which the numerical value of Cs 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. 2-C and 2-D,
Cs represents C1, which has a capacity of
0.1 μfd., while Rv may be varied from 100 ohms to
10,000 ohms and Rb from 1 ohm to 100,000 ohms, as before.
The smallest multiplying factor is obtained when Rv
and Rb are at their minimums of 100 ohms and 1 ohm respectively.
Then the factor becomes 100 and Lu = (100) (0.1) = 10 μh.
(μh. because Cs is expressed in μfd.). The largest
multiplying factor is obtained with the maximum values of resistance
for both Rv and Rb, which are 10,000 ohms
and 100,000 ohms, respectively. The factor at this end of the range
is (10,000) (100,000) = 109 and Lu = (109)
(0.1) = 108 μh. = 102 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, Cs
is given by
When selector switch S2 in Fig. 1 is in the LDQ position
for the Maxwell bridge circuit of Fig. 2-C, Cs = C1
= 0.1 μfd. and R = R11, 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 R11,
Thus the range of this circuit in measuring Q is from 0.1 to
When S2 is in the LQ position to give the
Hay bridge circuit of Fig. 2-D the procedure is the same, except
that R12, which has a useful range of 16.5 to 165 ohms,
is substituted for R11. 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 1000-cycle source can be included in the unit for greater
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 (R1
through R8) must be of the noninductive type. Fig. 3
shows the method used in winding the lower-value 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 half-lengths 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 100-ohm standards.
For the 1000- and 10,000- ohm units half-inch 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 1,000-ohm units and 2500 ohms per pie for the 10,000-ohm
unit. Two 50,000-ohm meter multipliers, rated at 1 per cent accuracy,
were connected in series to provide the 100,000-ohm standard.
Fig. 4 - Circuit of tbe 1000-cycle tone source.
- 0.5 μfd.
- 0.1 μfd.
- 4-p.d.t. switch.
- Push-button switch.
B - High-frequency buzzer.
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 wire-wound 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 R9R10
combination. The curve should be checked at as many points over
the range of R10 as possible. If a 10,000-ohm 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 R9 and R10 was used to obtain an approach
to the desired logarithmic characteristic.
Once the fixed
resistance standards and R10 are calibrated, it is a
relatively simple matter to calibrate R11, R12
and R13 by simply connecting them to the R terminals
of the bridge. These three units preferably should also have a logarithmic
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. C1 may be made up of a combination
of smaller-capacity units in parallel, if necessary.
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 1000-cycle 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 sound-proof box.