MEASUREMENTS LAB
Introduction of Maxwell
Inductance Bridge
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INTRODUCTION
The alternating current bridges are mainly designed to
measure the electrical quantities such as inductance and
capacitance. These AC bridges are the improved versions of
Whetstone Bridge. These bridges in their basic form consist of
normally four arms, an AC power source and a detector. The
Maxwell’s Inductance Bridge is one such type of bridge
normally used for measurement of inductance whose 'Q'
values lies below '10'.
MAXWELL'S INDUCTANCE BRIDGE
The Maxwell's Inductance Bridge is most commonly used
bridge for measurement of inductance so f Q value below 10.
A typical Maxwell’s bridge consists of an inductance measured
in comparison with a capacitance in laboratory operations. The
input for the bridge is given through a standard 1 KHz
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oscillator circuit which produces a 1 KHz sine wave at constant
amplitude. The basic circuit diagram is as shown below.
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Now let us see the derivation for calculating the
unknown value
Let
L4 = Unknown inductance
R4 = Effective resistance of inductor L1.
R2, R3,R4 = Known non - inductive resistances
C2 = Variable standard capacitor.
At balanced condition,
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→R4R2 + jω L4R2 = R1R3 + jωR1R2R3C2
Now separating real and imaginary terms, we have
The expression for Q factor is given by
The Maxwell's bridge is limited to the measurement of
medium Q coils (1<Q<10). This can be shown by considering
the second balance condition which states that the sum of the
phase angles of one pair of opposite arms must be equal to the
sum of the phase angles of the other pair. Since the phase
angle of the resistive elements in arm 2 and arm 3 add up to 0,
the phase angle of high Q coil will be very nearly positive
which requires that the phase angle of the capacitive arm must
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also be very large indeed which can be very impractical. High Q
coil are therefore generally measured on Hay's bridge.
The main advantage of the bridge is that the two balance
equations are independent if we choose R2 and C2 as variable
elements and also the frequency does not appear in any of the
equations.
The main disadvantages of the bridge are that it requires
a variable standard capacitor which is very expensive so fixed
standard capacitors are used normally. To compensate this,
balance adjustments are done by both varying R1 and R2 or by
putting an additional resistance in series with the inductance
under measurement and then varying this resistance and R2.
The bridge also has a disadvantage of limited measurement of
low or coil (1<Q<10) and is also unsuited for measurement of
low 'Q' coils i.e., below 1. Hence the Maxwell's bridge is used
only for the measurement of medium 'Q' coils.
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The unit has an inbuilt 1 KHz oscillator circuit for giving
input to the bridge and an output is find the CRO in the
balance condition output is zero.
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