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. 2. Basic circuit of the transformer bridge.
4. With so many standards involved in the decade
boxes and ratio-arms, calibration is difficult and
often uncertain.
The Transformer Ratio-arm Bridge
The basic circuit of the transformer bridge is shown
in fig. 2. The subscripts u and s refer to the unknown
and standards side of the bridge respectively.
Tx is a voltage transformer to the primary of which
the source is connected. The secondary winding is
tapped to give sections having Nu and Xs turns.
r2 is a current transformer, the primary of which
is tapped to give nu and ns turns, and the secondary
winding is connected to the detector.
Assume at this stage that the transformers are ideal
and that Zs is adjusted to give null indication in the
detector. Under these conditions zero flux is
produced in the current transformer, and there is
therefore no voltage drop across its windings. The
detector sides of both the unknown and standard
impedances are therefore at neutral potential. The
voltages across the unknown and standard are then Eu
and Es respectively. Therefore
and
lu — Eu/Zu
h = Es/Zs
For conditions of zero core flux in the current
transformer, the algebraic sum of the ampere-turns
must be zero. Therefore
Iunu = Isns
Substituting for Iu and Is we have
Eu Es
• nu = — • n.s
7 _ ejl.ll. /
— t=— cs
Es nx
(3)
For an ideal transformer the voltage ratio is equal
to the turns ratio, therefore
z,
\Ns ns i .
(4)
It will be seen from equation 4 that unlike the
conventional bridge, two ratios Xu/Ns and nu/ns are
available. Thus it is possible, by means of a suitable
combination of tappings on the two transformers,
to produce a very high ratio product permitting a
very wide range of measurement.
The Practical Transformer
Before proceeding further, it is necessary to justify
the statement that the actual transformers used in
the bridge may be considered ideal.
Firstly, the transmission loss between the primary
and secondary of the voltage transformers is of no
consequence. The only effect of this loss is to reduce
the sensitivity of the bridge, and this can be
compensated by increasing the gain of the detector. The
important factor is the actual voltage ratio between
the unknown and standard, both of which are tapped
across the secondary windings of the voltage
transformer. This voltage ratio across the bridge windings
is dependent upon three factors:
(a) The turns ratio
(b) The flux linkage
(c) The effective series impedance of the windings
compared with that of the load.
The voltage induced in a coil is proportional to the
number of turns multiplied by the rate of change
of flux. Therefore, provided all the turns of the
bridge windings embrace the same flux, the ratio
of induced voltages is equal to the turns ratio. The
windings are, in fact, wound with precision on a
common core of high permeability material. The
ratio of core flux to air flux is of the order of
1 000 : 1, and the geometrical arrangement of the
windings is such that the air flux is largely common
to the two windings. Even if the windings were so
badly arranged that none of the air flux was
common, the error between the induced voltage ratio and
the turns ratio would be only 0.01 %. If necessary
this error can be reduced to a few parts in a million.
The only error which need be considered is that
caused by the voltage drop in the windings. Ignoring
spurious shunt impedances for the moment, the load
current in the unknown windings is the current in
the impedance being measured. In the measurement
of impedances of 10 to 100 megohms, the total series
impedance of both the voltage and current
transformer windings is approximately 100 ohms. Even if
all this impedance were concentrated in one arm of
Fig. 3. Transformer bridge with the unknown and the
standard impedances divided into their resistive
and reactive components.
1 110 ELTEKN I K 1958
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