[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. 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