Bridges and component measurement
At bridge balance no current flows through the detector, so the result does not depend on the detector or on the source: only on the reference components.
01Measuring by comparison
A bridge measures a component by comparing it with other known ones. Instead of reading a voltage on an instrument, the known components are adjusted until a detector reads zero. At this balance no current flows through the detector and the result does not depend on its accuracy or on that of the source: only on the reference components. That is why bridges were for a century the most accurate method for measuring resistances, capacitances and inductances. The basic impedance measurement methods are presented in the technician program, in impedance measurements.
02DC bridges
The Wheatstone bridge has four resistors in a diamond, a source between two opposite vertices and a galvanometer between the other two. It is balanced when the two dividers give the same voltage:
For resistances below 1 Ω, the resistance of the leads and contacts adds to the unknown. The Kelvin double bridge eliminates it with a second pair of arms that takes the voltage directly across the resistor, with the same idea as the four-wire measurement used by precision multimeters.
03AC bridges
In AC the arms are impedances and the balance condition \( Z_1 Z_4 = Z_2 Z_3 \) is an equality of complex numbers: it requires two things to match at once, the real parts and the imaginary parts. That is why an AC bridge needs two adjustments, and each configuration is designed so that the two are independent.
| Bridge | Measures | Reference |
|---|---|---|
| Maxwell | Inductances of low or medium Q (1 to 10) | A capacitor in parallel with a resistor |
| Hay | High-Q inductances | A capacitor in series with a resistor |
| Schering | Capacitors and their dissipation factor, also at high voltage | A standard capacitor |
| Wien | Frequency, or capacitors | RC networks |
The Maxwell bridge measures a real coil, with inductance \( L_x \) and series resistance \( R_x \), using a capacitor as the reference, which is easier to make accurate than a standard inductance:
A Maxwell bridge with \( R_2 = R_3 = 1 \) kΩ, fed with 1 V at 1 kHz. You choose the unknown coil and adjust \( C_1 \) and \( R_1 \) until the detector voltage is nulled. The graph shows the detector voltage in decibels; the bridge is considered balanced when it falls below 1% of the voltage across the coil.
04The Q meter
The Q meter measures the quality factor of a coil by resonance. The coil is connected in series with a calibrated variable capacitor and excited with a small known voltage \( V_i \). When the capacitor is adjusted to resonance, the reactances cancel, the current is maximum and the voltage across the capacitor is \( Q \cdot V_i \): a voltmeter across the capacitor is graduated directly in Q. From the capacitance value at resonance the inductance follows, \( L = 1/(\omega^2 C) \). It works at radio frequencies, where bridges lose accuracy because of parasitic capacitances.
05The modern LCR meter
Current LCR meters use a self-balancing bridge: an amplifier holds the voltage of a node at zero by injecting just the right current, and the instrument measures the voltage across the component and that current with a synchronous detector that separates the in-phase and quadrature parts. It obtains instantly what the manual bridge achieved with two adjustments, and at frequencies from 20 Hz to several megahertz. The connection is four-terminal (Kelvin), two for the current and two for the voltage, so that the leads do not add to the result.
06In the laboratory
Build a Wheatstone bridge with a resistance decade box and a galvanometer or an amplifier with instrumentation, measure resistors from 100 Ω to 100 kΩ and compare with a 6½-digit multimeter.
Measure an air-core coil with a Maxwell bridge at 1 kHz and compare L and Q with an LCR meter.
Measure a 0.1 Ω resistance with two wires and with four wires, and explain the difference.
07Common mistakes
- Adjusting both controls at once on an AC bridge. It is better to alternate: one to the minimum, the other to a lower minimum, and repeat.
- Measuring low resistances with two wires. The leads and contacts can be worth more than the unknown.
- Forgetting the measurement frequency. An electrolytic capacitor or a cored inductor changes a lot with it.
- Ignoring parasitic capacitances. At high frequencies they add to the bridge arms.
08Self-assessment
A Wheatstone bridge balances with R₁ = 200 Ω, R₂ = 1 kΩ and R₃ = 470 Ω. What is the unknown?
\( 1000 \cdot 470 / 200 = 2350\ \Omega \).
A Maxwell bridge with R₂ = R₃ = 1 kΩ balances with C₁ = 47 nF and R₁ = 100 kΩ. What are the inductance, the resistance and the Q of the coil at 1 kHz?
\( L_x = 47 \) mH and \( R_x = 10\ \Omega \). The quality factor is \( Q = \omega R_1 C_1 \approx 29.5 \).
Why does an AC bridge need two adjustments?
Because the balance condition is a complex equality: the real part and the imaginary part have to be matched.
In a Q meter, with 10 mV of excitation, the voltmeter across the capacitor reads 1.2 V at resonance. What is the Q?
120.
09Further reading
- Albert D. Helfrick and William D. Cooper. Modern Electronic Instrumentation and Measurement Techniques (Spanish edition: “Instrumentación electrónica moderna y técnicas de medición”). Prentice Hall, 1990. DC and AC bridges with their balance conditions and sources of error.
- Keysight Technologies. Impedance Measurement Handbook. 6th ed., Keysight, 2016. Modern impedance measurement methods, the self-balancing bridge and the four-terminal connection.
- Ernest O. Doebelin and Dhanesh N. Manik. Measurement Systems: Application and Design. 6th ed., McGraw-Hill, 2011. Bridges as part of measurement systems, with their sensitivities.