Can one apply the Wheatstone Bridge formula with inductors or capacitors as impedances?

 Can one apply the Wheatstone Bridge formula with inductors or capacitors as impedances?

The Wheatstone Bridge is an old circuit topology that continues to be very useful where small changes exist in a much larger, constant signal. In this circuit from Hackaday dot com, the resistor R2 is adjusted until there is a null measured on the meter G:

When a null is reached, the ratio of R1/R2 = R3/Rx and so Rx can be calculated. If R1 and R3 are equal, then it can be reduced to simply Rx = R2 at null. This same configuration is used still in things like strain gauges and in circuits where a very small signal is riding on a much larger, constant signal. Thanks to AllAboutCircuits dot com for this schematic of one possible strain gauge Wheatstone Bridge configuration:

To measure reactance and impedance, an AC signal source of a frequency appropriate for the devices being measured is used rather than a DC source. R1 and R2 above would remain resistors, R3 will be replaced with a reference capacitor for measuring capacitors, or reference inductor for measuring inductance. Thanks to Play-Hookey dot com for the image:

AC Applications of the Wheatstone Bridge

The output will be AC so it must be rectified to show on a meter or magic eye tube. Minor circuit changes may be made to change the balanced, floating Null signal into a single-ended signal that is easier to amplify and display.

In this old tube based Heathkit IT-28 capacitor analyzer, it uses 60Hz AC to drive it and a magic eye tube as a null indicator. It can also take an external reference inductor. Thanks to the California Historical Radio dot com page:

Later transistorized version Heathkit IB-5281 has internal reference inductors, thanks to EEVBlog for the image:

An RX Noise Bridge is a device used to analyze antennas and other complex impedances. It uses your radio receiver as the device used to measure the null, and a broadband white noise source as the AC signal source. A variable resistor and variable capacitor are adjusted for a null in noise volume. It is just a Wheatstone bridge. Thanks to RFCafe dot com for this schematic of the Palomar RX Noise Bridge, everything to the left of T-1 is just a noise source and amplifier:

Thanks to Palomar-Engineers dot com for this picture of the device itself, note the markings in Ohms of Xc, Xl, and R:

Another device used for measuring frequency curves and impedance is called a Return Loss Bridge or RLB. It is again just a Wheatstone Bridge, used with a signal source and a radio receiver. It can also be used with a broadband noise source and one of those RTL SDR $15 wideband radio receivers to make a simple network analyzer/spectrum analyzer.

Thanks to RTL-SDR dot com for these sample screenshots of an RTL SDR receiver being used to measure the pass characteristics of filters using a RLB and noise source:

Tuning an HF Antenna with an Airspy, SWR-Bridge and Noise Source

Using the Airspy as a Network Analyzer for Characterizing Antennas

Thanks to K8IQY dot com for the schematic of a RLB:

A slightly different version that is functionally the same from VK2ZAY dot com:

These are well-suited to measuring SWR of an antenna or load. The transformers are there only to change the balanced Null signal into a single-ended signal for easier measurement.