A Resonance Bridge is an AC bridge circuit used for measuring an unknown inductance, an unknown capacitance, or an unknown frequency, by balancing the loads of its four arms. Figure 1 below shows a diagram of the Resonance Bridge.

Figure 1.  The Resonance Bridge

As shown in Figure 1, three arms of the resonance bridge has a resistor each (R1, R2, and R3), while the fourth arm has a series RLC circuit (R4, C1, L1). The values of R1, R2, R3, and R4 are all known. If L1 is the unknown variable, then C1 must be adjustable. If C1 is the unknown variable, then L1 must be adjustable. 

Like other bridge circuits, the measuring ability of a resonance bridge depends on 'balancing' its circuit. Balancing the circuit in Figure 1 means adjusting C1 (if L1 is the unknown) or L1 (if C1 is the unknown) until the current through the bridge between points A and B becomes zero.  This happens when the voltages at points A and B are equal.  When the resonance bridge is balanced, it follows that R2/R1 = R3/Z wherein Z is the total impedance of the RLC circuit of the fourth arm. Thus, Z = R4 + 1/(2πfC1) + 2πfL1.

The resonance bridge got its name from the fact that it becomes balanced when L1 and C1 are in resonance with each other. A series LC circuit that is in resonance, i.e., excited by a signal at its resonant frequency, exhibits zero reactance. The frequency at which resonance in a tuned LC circuit occurs is given by the following formula:

fr = 1 / [2π(sqrt(LC))] where

fr = resonant frequency (Hz);

L = the inductance (H); and

C = the capacitance (F).

Thus, when a resonance bridge is balanced, the combined reactance of L1 and C1 becomes zero, and Z simply becomes equal to R4.  The equation for a balanced resonance bridge therefore simplifies to R2/R1 = R3/R4, or R4 = R3R1/R2. The frequency f at which the resonance bridge becomes balanced is given by: f = 1 / [2π(sqrt(L1C1))].  The source frequency must therefore be known in order to measure L1 (or C1) in terms of C1 (or L1).

See Also:   Bridge Circuits;  More Articles