[Table
of Contents]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. As time permits, I will
be glad to scan articles for you. All copyrights (if any) are hereby acknowledged. |
Here 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 size.
See all available
vintage QST articles.
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.
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
_{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 C-L 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} - 15,000-ohm, wire-wound potentiometer.
R
_{11} - 16,0000-ohm, wire-wound potentiometer.
R
_{12} -165-ohm, wire-wound potentiometer.
R
_{13} - 1600-ohm, wire-wound potentiometer.
R
_{14} - 70 ohms.
(Note: Odd-size resistance values may be composed of two or more standard-value
resistors in series.)
S
_{1} - Sections of 2-gang, 7-position rotary switch.
S
_{2} - Sections
of 2-gang, 4-circuit, 5-position 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. 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 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. 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.
Resistance Measurement Referring to
Fig. 2-A, 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 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, 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 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 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.
Capacity Measurement When selector switch S
_{2} 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,
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 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 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 multi-tap switches, the fixed standards and the four
variable-resistance 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. 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.
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
_{s})
(2
πfC)
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. 2-B. 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. 2-C. The Hay inductance bridge of Fig. 2-D
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. 2-C and 2-D 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. 2-C and 2-D, 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. 2-C,
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. 2-D 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 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 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 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.
C
_{1} - 0.5 μfd.
C
_{2} - 0.1 μfd.
S
_{1} - 4-p.d.t. switch.
S
_{2} - Push-button switch.
B - High-frequency 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 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
_{9}R
_{10} combination. The curve should be checked at as many points over the range of R
_{10}
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 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 smaller-capacity 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 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