Full resolution (JPEG) - On this page / på denna sida - 1958, H. 8 - The Transformer Ratio-arm Bridge, by Raymond Calvert
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Fig. 14. Measuring transfer admittance.
The method is a general one and can be applied to
any complex impedance in the range zero to, say,
10 ohms. For simplicity it is shown in fig. 15 applied
first to a pure resistance and then to a pure
reactance, the unknown being r.
The two resistors R are standards of known value.
Let the current leaving the network be Iu,
remembering that at balance there is zero voltage across
the current transformer. The voltage across r is IUR.
The current through r is IuR/r. The current through
the first resistor of the network is IuR/r + Iu. The
input voltage Eu is therefore
Eu = IUR (1 + R/r) + IUR
and
EJIu = fi2/r + 2 R
If R is very large compared with r (say 1 000 times),
the second term can be ignored and we have a close
approximation.
EJIU = RVr
But EJIU is the ratio that would be obtained by
connecting a resistor Ru straight across the bridge
instead of the T-net\vork. That is to say the bridge
will measure the T-network as though it were a
resistor of value Ru ohms. So we can put
r = RVRU
where Ru is the resistance read on the bridge.
Alternatively, if the bridge reads conductance directly, we
have
r = R"G
Several ranges can be provided by switching R in
pairs, or by range changing on the transformer taps,
or both. In this way it is possible to make
measurements down to a few microhms without undue diffi-
Fig. 15. Measuring impedances up to 10 ohms.
116 ELTEKNIK 1958
culty. If r is replaced by an inductance L and the
above argument repeated, we have
EJIU = R2/j co L
In this case the bridge measures the T-network
as though it were a capacitance of value L/R2, so
we have
L = R2C
where C is the capacitance measured on the bridge.
Again, it is a simple matter to arrange a number of
switched ranges, and inductance down to the order
of one millimicrohenry can be measured.
Conclusions
It has been shown that the attributes of the
transformer ratio-arm bridge are such that complicated
measurements can be quite simply made which
would be very difficult, if not impossible, with a
conventional bridge arrangement.
The advantages of the transformer bridge may be
summarized as follows:
1. The measurement is dependent upon the
product of the current and voltage ratios for each fixed
standard used. Both of these ratios are easily
obtained with great accuracy, increasing the possible range
of measurement to a figure well beyond the scope
of impedance arms. Voltage and current ratios each
of 1 000 : 1 are possible, giving an overall ratio of
one million to one.
2. Since the ratios depend only upon the number
of turns on the transformer windings, they are
permanent and calibration is unnecessary.
3. Only one standard is required for each decade.
Furthermore, the transformer ratios may be used to
set the standard in one decade against that in
another, so that only two fixed standards of known
accuracy are required, one resistive and one
reactive.
4. The standards need not be pure. The effects of
a reactive term associated with a reactance standard
and of a reactive term associated with a resistive
standard can be removed entirely at a given
frequency.
5. The measurement of very small capacitances by
conventional means is extremely difficult, due to the
effect of stray capacitance and the difficulty in
obtaining a standard of sufficiently low value. By
means of the transformer bridge, it is possible to
measure capacitors of the order of 0.0002 pF at the
ends of leads having some thousand times this
capacitance.
6. As the sign of a voltage or current can be
reversed simply by reversing the connections to the
relevant transformer winding, measurements can be
made in all four quadrants of the complex plane.
The bridge can therefore be used to measure transfer
impedance as well as direct impedance.
7. The bridge will measure the impedance between
any pair of terminals of a three-terminal network.
In situ measurements are possible on impedances
remote from the bridge and on components wired
into a circuit. The capacitance of long connecting
leads and spurious impedances connected to the
unknown terminals are completely counteracted by the
appropriate use of the third terminal of the bridge.
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