The bridge circuit is used for medium inductance and can be arranged
to yield results of considerable precision. As shown in figure 1, in the
two arms, there are two pure resistances so that for balance relations,
the phase balance depends on the remaining two arms. If a coil of
unknown impedance Z1 is placed in one arm, then its positive phase angle ɸ1 can be compensated for in either of the following two ways:
- A known impedance with an equal positive phase angle may be used in either of the adjacent arms (so that ɸ1 = ɸ2 or ɸ1 = ɸ4), remaining two arms have zero phase angles (being pure resistances). Such a network is known as Maxwell’s a.c. bridge or L1/L4 bridge.
- Or an impedance with an equal negative phase angle (i.e. capacitance) may be used in opposite arm (so that ɸ1 + ɸ3 = 0). Such a network is known as Maxwell-Wien bridge or Maxwell’s L/C bridge.
Hence, we conclude that inductive impedance may be measured in terms
of another inductive impedance (of equal time constant) in either
adjacent arm (Maxwell Bridge) or the unknown inductive impedance may be
measured in terms of a combination of resistance and capacitance (of
equal time constant) in the opposite arm (Maxwell-Wien bridge). It is
important, however, that in each case the time constants of the
two impedance must be matched.As shown in figure 1.
Z1 = R1 + jX1 = R1 + jωL1…….unknown;
Z4 = R4 + jX4 = R4 + jωL4….…known;
R2,R4 = known pure resistances; D = detector
The inductance L4 is a variable self-inductance of constant resistance, its inductance being of the same order as L1. The bridge is balanced by varying L4 and one of the resistance R2 or R3. Alternatively, R2 and R3
can be kept constant and the resistance of one of the other two arms
can be varied by connecting an additional resistance in that arm.
The balance condition is that Z1Z3 = Z2Z4
(R1 + jωL1)R3 = (R4 + jωL4)R2
Equation the real and imaginary parts on both sides, we have
Z1 = R1 + jX1 = R1 + jωL1…….unknown;
Z4 = R4 + jX4 = R4 + jωL4….…known;
R2,R4 = known pure resistances; D = detector
The inductance L
4 is a variable self-inductance of constant resistance, its inductance being of the same order as L
1. The bridge is balanced by varying L
4 and one of the resistance R
2 or R
3. Alternatively, R
2 and R
3
can be kept constant and the resistance of one of the other two arms
can be varied by connecting an additional resistance in that arm.
The balance condition is that
Z1Z3 = Z2Z4
(R1 + jωL1)R3 = (R4 + jωL4)R2
Read more...