Maxwell’s bridge measures an unknown inductances in terms of a known capacitor.
The Maxwell bridge circuit diagram is as shown in
figure. Maxwell bridge are of the ratio arms has a resistance and a capacitance
in parallel.
The Maxwell bridge circuit is as shown in figure below.
The unknown inductance is connected in the fourth arm of the bridge.The four bridge arms Z1, Z2, Z3
and Z4 are impedances and the detector is represented by headphones.
When the bridge is balanced, the detector response
is zero or indicates a null. Balance adjustment to obtain a null response is
made by varying one or more of the bridge arms.
The conditions for bridge balance requires that the
potential difference from point A to C be zero. This will be the case when the
voltage drop from B to A equals the voltage drop from B to C, in both magnitude
and phase.
I1Z1 = I2Z2
.......................
(1)
For zero detector current (the balance condition),
the currents are
I1 = E / Z1 + Z3
and I2 = E / Z2 + ZX
Substitution of above equation in equation (1),
gives
E / Z1
+ Z3 * Z1 = E / Z2 + ZX * Z2
Z1 / Z1Z3 + Z2
/ Z2+ZX
(or)
Z1ZX = Z2Z3
ZX = Z2Z3 / Z1
= Z2Z3Y
.................... (2)
Here Y1 = 1/Z1 = 1/R1
+ JωC,
Z2 = R2, Z3 = R3
and ZX = RX + JωLX
Substitution of these values in equation (2) gives
RX
+ JωLX = R2 R3 (1/R1 + JωC)
RX + JωLX = R1R3
/ R1 + JωC, R2R3
Separation of the real and imaginary terms, we get
RX = R2R3/ R1
..........................
(3)
And LX = R2 R3 C1 ............................ (4)
The equation (4) is used to calculate the unknown
inductance in terms of a known capacitance.
The Maxwell bridge is limited to the measurement of
medium. Q coils
(1<Q<10). The usual procedure for balancing
the Maxwell bridge is by first adjusting R3, for inductive balance
and then adjusting R1 for resistive balance.
Also Q = WLX / RX = WC1R2R3
/ R2R3 * R1 = WC1R1.
APPLICATIONS:
It is used for inductances measurements.
The bridge can be made to read directly in Q.
LIMITATIONS:
Using a fixed capacitor has the disadvantage that
there is an interaction between the resistance and reactance balances.
Only low Q values can be measures.
It is independent of the excitation frequency.
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