AC Network Analysis
AC Bridge Networks
Measurements of inductance, capacitance, and of some other quantities may be made by AC bridges. The number of AC bridge networks known is very large. A few only will be considered here as a means of illustrating the method of treatment, which is not limited to the bridges described.
The simple form of AC bridge bears a strong resemblance to the DC Wheatstone bridge: it consists of four impedances (arms), a power supply, and a balance detector. The power source furnishes alternating current of the desired frequency and suitable magnitude to the bridge. This bridge is shown in the figure below.
Balance is achieved by adjustment of one or more of the bridge arms. Balance is indicated by zero response of the detector D, which means that points b and d are at the same potential at all instants. Then writing down the equation for the voltage drops around the circuit abda at balance
where I1, I2, etc. are the phasor expressions for the currents and Z1, Z2 etc. are the complex numbers representing the impedances. Similarly, for the circuit bcdb, at balance
Since at balance the current through the detector is zero,
To satisfy this condition, it is necessary to satisfy simultaneously the two conditions
i.e. the impedance magnitudes must be in the correct ratio and the phase-angle differences must be equal.
It can be observed from this that it is not necessary for the four impedances to have identical phase-angles, nor even for the impedances to be of the same kind, so long as the phase-angle differences satisfy the above condition. Each of the four impedances can be made up in several different ways and the various AC bridges of this class result from a consideration of the ways which enable the phase-angle conditions to be satisfied.
Usually, two of the bridge arms serve the purpose of fixed ratio arms. These ratio arms are commonly resistances, since these can be made with high accuracy and very small residual inductance and capacitance.