An Inexpensive Impedance Bridge
July 1944 QST Article 
July 1944 QST
Table
of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from ARRL's
QST, published December 1915  present. 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. 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
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).
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
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.
Fig. 3Method used for winding noninductive resistance standards
from copper magnet wire. See text for details.
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.
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.
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.
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.
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
12/21/2012 






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