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BSEE
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July 1944 QST Article

July 1944 QST These 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 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 R

Photos &y Robert E. Cobaugh, W2DTE

Fig.1 - Circuit diagram of the impedance bridge.

C

C

R

R

R

R

R

R

R

R

R

R

R

R

(Note: Odd-size resistance values may be composed of two or more standard-value resistors in series.)

S

S

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

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 S

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.

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.

Referring to Fig. 2-A, the fundamental bridge circuit consists of four resistance arms. Two of these arms, R

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

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

As an illustration, in the instrument shown in the photographs R

, etc.

or, in decimal equivalents, 0.0001, 0.001, 0.01, etc. Since the useful range of R

In the wiring diagram of Fig. 1, R

As R

In use, the unknown resistance is connected to the terminals marked R, the CRL multiplier switch, S

If the bridge is very far off balance when the battery voltage is applied, excessive current may flow through the galvanometer. While R

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 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.

When selector switch S

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

Behind the panel of the impedance bridge. This view shows the multi-tap switches, the fixed standards and the four variable-resistance units.

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

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. 2-B,

p.f. = (R

As an example, we know that the frequency is 1000 cycles and the capacity 0.01 μd. = (0.01) (10

p.f. = (R

= (R

R

In practice, S

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

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.

This table shows how the CRL dial controlling R

This table shows how the D, DQ and Q dials should be marked to be direct reading for each resistance setting of R

When selector switch S

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 R

The smallest multiplying factor is obtained when R

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

When selector switch S

(the factor 10

Thus the range of this circuit in measuring Q is from 0.1 to 10.

When S

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 convenience.

Fig. 3-Method used for winding noninductive resistance standards from copper magnet wire. See text for details.

The standard resistors (R

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.

C

C

S

S

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 R

Once the fixed resistance standards and R

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

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 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.

Posted 12/21/2012