

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  






Copyright: 1996  2024 Webmaster:
Kirt Blattenberger, BSEE  KB3UON 
RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling
2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas
and reference material while performing my work as an RF system and circuit design engineer.
The Internet was still largely an unknown entity at the time and not much was available
in the form of WYSIWYG
...
All trademarks, copyrights, patents, and other rights of ownership to images and text
used on the RF Cafe website are hereby acknowledged.
My Hobby Website: AirplanesAndRockets.com

