Normal-mode and common-mode interference
An amplifier with 120 dB of common-mode rejection is useless if one of the lines has 10 kΩ more than the other: the imbalance converts the common mode into signal before it reaches the input.
01Two ways of getting into a measurement
Interference is any voltage that adds to the one you want to measure. Depending on how it appears at the instrument’s terminals, two modes are distinguished:
- Normal mode (or differential): the interference is in series with the signal, between the two input terminals. The instrument has no way of separating it from the signal by its connection; only by its frequency or its shape.
- Common mode: the interference appears equally on both terminals with respect to ground. An ideal differential instrument ignores it, because it measures only the difference; a real one lets a fraction through.
In a measurement of millivolts near the 220 V mains, 50 Hz interference can be thousands of times larger than the signal. Measuring well is, in large part, knowing where it comes from and how it is rejected.
02How interference couples in
| Coupling | Mechanism | Remedy |
|---|---|---|
| Capacitive | The electric field of a conductor at a given voltage injects current into a high-impedance circuit through the capacitance between the two | Shield grounded at a single point; lower the circuit impedance |
| Inductive | The magnetic field of a conductor carrying current induces a voltage in any loop it crosses: \( V = \omega B A \) | Reduce the loop area with a twisted pair; move away; magnetic shielding |
| Conductive | Two devices grounded at different points: the potential difference makes current flow through the grounds | Single-point ground, galvanic isolation |
| Radiated | Radio-frequency fields that a cable receives like an antenna and a semiconductor rectifies | Complete shielding, filters at the inputs |
The twisted pair works because each twist reverses the direction of the loop: the voltage induced in one twist cancels with that of the next. A cable shield, on the other hand, protects against the electric field, but very little against the low-frequency magnetic field.
03Ground loops
If a sensor is grounded at one end of a plant and the instrument at the other, there can be a volt or more between the two grounds, because of the currents flowing through the installation. That difference appears in common mode at the input, and if the cable shield joins the two grounds, a current flows through it that converts it into normal mode. The solutions are to break the loop: ground at a single point, measure with differential inputs, use floating instruments or galvanic isolators (isolation amplifiers, optocouplers, transformers).
04Common-mode rejection
The common-mode rejection ratio (CMRR) of a differential amplifier says how many times less it amplifies the common voltage than the differential one. But there is a second mechanism, often worse: if the impedances of the two lines are not equal, the common voltage produces different drops in each and is converted into a differential one before reaching the amplifier:
The guard technique attacks the second mechanism: a shield around the lines is connected to the common-mode voltage, so that there is no potential difference across the leakage capacitances and no current flows through them.
05Normal-mode rejection
Normal-mode interference can only be separated by its frequency. If the signal is slow, such as a temperature, a low-pass filter removes it. Integrating converters do something finer: if they integrate for a whole number of mains cycles, the 50 Hz interference and all its harmonics average to zero.
A thermocouple gives 5 mV, about 120 °C for type K. Between its ground and the instrument’s there is a 50 Hz common-mode voltage, the loop of the cables picks up 10 mV in normal mode and each input has 10 pF and 1 GΩ to ground. The bars, on a logarithmic scale, compare each error with the signal and with 41 µV, which is 1 °C.
06In the laboratory
Measure with the oscilloscope the 50 Hz picked up by two parallel 1 m wires, by a twisted pair and by a shielded cable, near a transformer. Compare the protection against the electric and the magnetic field.
With an instrumentation amplifier, inject 1 V of common mode and measure the output with balanced lines and with 10 kΩ in series in only one of them.
Set a bench multimeter to 1, 10 and 100 mains cycles of integration and measure a DC voltage with 50 Hz superimposed.
07Common mistakes
- Grounding the shield at both ends. It closes a ground loop through the shielding.
- Relying only on the amplifier’s CMRR. The imbalance of the lines can dominate.
- Setting the instrument for 60 Hz on a 50 Hz mains.
- Leaving high-impedance inputs open. They pick up all the electric field of the environment.
08Self-assessment
What error does 1 V of common mode produce in an amplifier with 80 dB of CMRR?
\( 1\ \text{V} / 10^4 = 100\ \mu\text{V} \), about 2.4 °C on a type K thermocouple.
What 50 Hz rejection does a converter that integrates for 16.7 ms have?
\( |\sin(0.833\pi)/(0.833\pi)| = 0.19 \): about 14 dB.
Why does the twisted pair reduce inductive coupling?
Because the voltages induced in successive loops have opposite signs and cancel.
Where is the shield of a low-frequency signal cable grounded?
At a single end, usually the instrument’s, so as not to form a ground loop.
09Further reading
- Ralph Morrison. Grounding and Shielding: Circuits and Interference. 6th ed., Wiley-IEEE Press, 2016. The reference book on grounding, shielding and ground loops.
- Henry W. Ott. Electromagnetic Compatibility Engineering. Wiley, 2009. The coupling mechanisms and their remedies, with numbers.
- Keithley Instruments. Low Level Measurements Handbook. 7th ed., Keithley, 2014. Guarding, ground loops and interference rejection in very low-level measurements.