June 1931 Radio-Craft
Wax nostalgic about and learn from the history of early electronics.
See articles from Radio-Craft,
published 1929 - 1953. All copyrights are hereby acknowledged.
This reactance measuring bridge circuit employs a very unique
element for generating an alternating current: an electromechanical
buzzer which doubles as an audio source. Sure, it doesn't produce
a pure sinewave, but for the method used here to determine inductance
and capacitance it does not matter. Rather than attempting to
measure an absolute value of inductance or capacitance, a known
reactance is used as part of a balanced bridge. This is by no
means a precision instrument since accuracy depends on the user's
interpretation of the presence or absence of an audible 'buzz'
in a pair of headphones, but in an era when 'real' test equipment
was beyond the budgets of many (maybe most) hobbyists, the scheme
was better than nothing at all.
Measuring Inductance and Capacity
How the Experimenter May Utilize a Reactance Bridge
By James A. Dowie*
In the February issue of Radio-Craft appeared a description
of the construction of a Wheatstone bridge which could be used
to measure unknown resistances, such as are used in radio work.
("A Home-Made Slide-Wire Bridge," by
A. W, Bonser, page 482). The object of this article is
to show how the Wheatstone bridge may be used also to good advantage
by radio-tricians and Service Men for making various measurements
of inductance and capacity - two important factors necessary
for satisfactory reception of radio signals. Inductances, as
used in radio work, function under alternating current; therefore,
measurements should be carried out with alternating current.
Fig. 1 - The simple bridge, with buzzer and
phones, for measurement of inductance.
Fig. 1 shows the circuit arrangement used in this bridge.
In series with the battery "B," a buzzer is placed; and the
combination is utilized to give an alternating current through
the various arms of the bridge. (A high-frequency buzzer or
a vacuum-tube A.F. oscillator, such as have been described in
Radio-Craft, may also be used for this purpose.) With this arrangement
a pair of phones serves as the indicating device; they are connected
as shown in the diagram. If audio-frequency current flows through
the phones, a sound will be heard; while, if no alternating
current flows, no sound is heard. The Wheatstone bridge is then
balanced by sliding the contact c over the arms m, n of the
bridge until a minimum of sound is heard; this is the condition
(Note: "Minimum" sound is specified; because it may be impossible
to obtain a zero sound-balance with this apparatus, on account
of induction and stray capacity effects. Knowing this, we will
now consider the case of measuring the inductance of a coil
by means of such an arrangement.).
Measurement of Inductance
In the circuit arrangement of this bridge used for inductance
measurements, m and n are the slide-arms of the bridge; c is
the sliding contact; L the known inductance, and X is an unknown
coil whose inductance is to be measured.
This circuit is in theory the same as that used in the resistance
measurement, described in the preceding article; when the slider
c is moved along m and n until a balance is obtained, a minimum
sound will he heard in the telephones. Then the following relation
Thus, if a single standard inductance L and a slide-wire
bridge with phones, battery and buzzer are available, the values
of unknown inductances may be easily measured.
This relationship is only true in practice when the unknown
inductance X is of the same order of magnitude as the standard
inductance L. By this it is meant that inaccuracies will arise
in these measurements if the standard inductance is about 0.1
millihenry, for instance, while the unknown inductance is 10
millihenries; because the ratio of m to n would then be too
great to obtain an accurate balance. If the ratio of m and n
is about 1 or 2, then a sharp balance will be had.
The following notes should be of interest to radio-tricians
interested in accurate measurements with a bridge:
The formula given above for inductance is sufficiently accurate
for all practical purposes; however, it does not take into consideration
the resistance of the inductance coils. If there is a great
discrepancy between the resistances of the two coils L and X,
it is quite possible that a sharp balance will not he obtained.
Balancing a Wheatstone bridge circuit is something like tuning
a radio receiving circuit; since resistance in a resonant radio
circuit makes for extremely broad tuning.
Balancing a Wheatstone bridge is equivalent to reducing the
resistance, and thus enables sharp balance or tuning. If the
resistances of the coils are not balanced, a sharp balance will
not be secured and, therefore, the accuracy of the measurement
will be destroyed; since the accuracy of the measurement in
a Wheatstone bridge depends upon the sharpness of the balance.
Correction for Resistance
Since all inductance coils have some resistance, a better
arrangement of the bridge is shown in Fig. 2, where each coil
has its compensating resistance (R3, R4) in series.
For precision measurements, it is necessary to strike a balance
for both the inductances and the resistances of the coils. The
inductance balance is secured by means of the buzzer and headphones;
while the resistance balance is secured by a voltmeter and the
battery B2 for the source of supply. In this bridge, Fig. 2,
we use two double-pole double-throw switches (S1 and S2); one
is used for switching on either the voltmeter V or the phones
PH for the balance indicator. (The potentials of B1 and B2 must
be found by experiment).
The buzzer and phones are used for the A.C. inductance balance,
with switches S1, S2 thrown left; the battery and voltmeter,
for securing a D.C. resistance balance, the switches thrown
right. The variable resistors, R3, R4, placed in series with
each of the inductances enable us to balance the inductance
arms for resistance.
Fig. 2 - The bridge arrangement for balancing
inductance and resistance to obtain a true reading of the former.
The following gives the method used for operating this type
of bridge circuit. First, a balance is obtained for the A.C.
signal; the double-pole, double-throw switches are both thrown
to the left, to use the buzzer and phones. The sliding contact
c on the wire m-n is varied until a balance is obtained. The
switches are then thrown to the right to place the battery and
voltmeter in the circuit. With the sliding contact c fixed at
the position previously obtained, vary the resistance of R3
and R4 until the voltmeter v indicates a balance, by zero deflection.
Now switch over again to the buzzer and phones, and vary the
position of the sliding contact until a balance is obtained,
as indicated by a minimum sound in the phones. Again switch
back to battery and voltmeter, keeping the sliding contact c
fixed in the new position previously found; and very the resistors
R3 and R4 until a balance is obtained. Alternate this way until
a very sharp balance is obtained on both D.C. and A.C. - then
note the values of m and n and apply the formula previously
It will be noted that the important adjustment of the sliding
contact c was not changed in balancing the resistances of R3
and R4; since the important adjustment of the slider determines
the inductance measurement. The above formula is absolutely
correct and is based upon both types of balance thus obtained.
Measurement of Capacity
The Wheatstone slide-wire bridge may be used also to measure
unknown capacities, there being required in this circuit but
one known capacity. Fig. 3 illustrates the connections for this
bridge; in which C is the known capacity and CX the unknown
capacity, while m and n are the lengths of the two arms of the
slide-wire, which are adjusted for a balance by a minimum sound
in the phones.
Fig. 3 - Use of the bridge for capacity measurements,
with the necessary compensation for zero setting.
It is evident that, with this arrangement, the resistance
in one arm of the bridge is balanced against the impedance of
the condenser in the adjacent arm. (The impedance of a condenser
is the resultant of resistance and reactance but, as the resistance
is so very low, compared to the reactance, it can be disregarded
and the entire impedance considered as reactance.)
The reactance of a condenser varies inversely as its capacity;
while the reactance of an inductance varies directly, and therefore
the preceding formula must be rewritten and used in the following
For example, the scale has 100 divisions and the sound is
minimum in the phones at a point on the wire 25 divisions from
E (Fig. 6); leaving 75 divisions for n, between F and c. Assuming
that we use a standard capacity value of 0.002-mf. for C, we
may substitute these values, giving
In all these measurements using a buzzer to supply the alternating
current to the bridge, it is advisable to set the buzzer at
some distance from the bridge, or muffle it in some wav; for
otherwise it will be difficult to determine whether the sound
is coming from the phones and due to the current passing through
them, or whether it is direct noise from the buzzer. (A "high-frequency"
buzzer is more quiet. See Fig. 4.)
Fig. 4 - The circuit connections of a Wheatstone
bridge using a high-frequency buzzer, for accurate measurements
An excellent source of A.C. voltage for measuring inductance
and capacity is a vacuum-tube audio-frequency oscillator which
does not have the above-mentioned fault of buzzers. The terminals
of the oscillator are connected to the points E arid F of the
bridge. (See Fig. 5) Resistor R1 controls the amount of A.C.
fed to the bridge.
In these measurements, a calibrated variable (air dielectric)
condenser may be used as the standard C; with this, a very large
range of unknown capacities may be very simply measured.
First, the slider is set at the mid-point of the length of
resistance wire, thus making m equal to n. The variable condenser
C is then adjusted until a balance is obtained. Then, the dial
reading of the standard condenser C will indicate the capacity
of the unknown condenser CX; since m and n are equal.
Fig. 5 - The most satisfactory operation
of the bridge is obtained with an A.C. oscillator giving a good
A midget condenser, C1, is necessary in this measurement
so that a balance (at the minimum capacity of C) may be had,
and the zero reading of C taken without the unknown condenser
CX in the circuit. It is required also to bring the balance
point further up the scale on C when measuring small values
The effective resistance of the condensers enters into the
measurement of capacities exactly as in the measurement of inductances;
but, in the case of condensers using air as the dielectric,
this is not very important because the resistance of such condensers
is almost zero. However, where condensers have different dielectrics,
(for instance, air, and "mud" compositions), there will be a
considerable difference in their resistances; which means that
it will be impossible to get a silent point in the telephones.
However, a fair balance point can usually be secured.
Fig. 6 - A wooden base, 8 x 45 inches, will
mount a one-meter rule as shown; or the "reciprocal" scale of
the February article may be used.
Because of the insulating properties of condensers, the circuit
will be open; therefore, it is impossible to balance this bridge
with direct current. However, a good balance, with fair accuracy,
is generally found when using the fundamental circuit shown
in Fig. 3.
In order ·to secure a more accurate balance with this bridge,
it is necessary to connect a variable resistor R in one or the
other of the condenser arms, (X1 or X2, Fig. 3.); the proper
place is found by trial. This will compensate for any resistance
effect introduced by the condenser in the other condenser arm.
The readings of this resistance, with and without the condenser
CX, are indicative of the losses in the condenser under test.
This is a check-up of "leaky" condensers.
Construction of a Slide-Wire Bridge
The connections between the components of the bridge are
made on the top of the wooden base by means of brass straps
1 1/2 inches wide and 1/4-inch thick (Shown in Fig. 6.). The
holes for the terminals are tapped the correct size.
The wire used for m and n may be of any standard make of
resistance wire (such as nichrome, German silver, constantin,
etc.) and its gauge from No. 24 to No. 28 B & S.; as these
are the most convenient sizes with which to work. (Note: Be
careful to secure uniform wire, for the resistances of the two
arms of the bridge m and n are proportional to their lengths
only if their cross sections are equal.)
The resistance wire is stretched taut almost flat on the
board, and securely fastened at E and F to the brass strap at
each end of the bridge. The meter-scale is mounted directly
beneath the resistance wire, thus positioning the slide-wire
about 1/16-in. above the meter-scale. The contact slider c may
be one of the sharp edges of a 1/4-in. brass rod; the opposite
edge being soldered to a length of rubber-covered lamp cord.
Compare Fig. 6 with Fig. 2.
* Chief Instructor, National Radio
Posted August 25, 2015