Shielding, grounding and noise in measurements

Why it matters

A thermocouple gives about 40 μV per °C; a strain-gauge bridge a few millivolts. The 230 V, 50 Hz wiring a metre away can couple volts into an unshielded high-impedance input. Whether a measurement is meaningful depends far more on shielding, grounding and differential inputs than on the meter's nameplate accuracy. These are also the first questions asked in any plant-instrumentation interview.

Key ideas

Interference versus noise.

• Interference comes from outside: mains wiring, motors, relays, switching converters, radio transmitters. In principle it can be eliminated by good layout.
• Inherent noise is generated inside components and can only be minimised:
  • Thermal (Johnson) noise: random motion of charge carriers in any resistance; white (flat spectrum); proportional to √(TRB).
  • Shot noise: random arrival of discrete charges across a junction; proportional to √(IB).
  • Flicker (1/f) noise: dominant at low frequencies in semiconductors and carbon resistors.

Coupling mechanisms and their cures.

• Capacitive (electric-field) coupling: stray capacitance from a high-voltage conductor to a high-impedance node injects a current that develops a noise voltage across the node's resistance. Cure: an electrostatic shield (conducting foil or braid) around the signal conductors, connected to the signal reference at one point only, so the injected current flows to ground through the shield instead of the circuit. Lower circuit impedance also helps.
• Inductive (magnetic-field) coupling: a changing current nearby links flux with the loop formed by the signal wires, inducing V = M·dI/dt. Cure: minimise loop area (run go and return together; twisted pairs, where successive twists induce opposing voltages), increase distance, and use magnetic shielding — high-permeability material (mu-metal) at low frequencies, conducting (eddy-current) shields at high frequencies.
• Conductive coupling / ground loops: if a signal circuit is earthed at two points (sensor end and instrument end), the potential difference between the two earths drives current around the loop and appears in series with the signal. Cure: single-point grounding, a floating (isolated) input or an isolation amplifier, and differential measurement.
• Radiated RF: filters, ferrite beads, metal enclosures, short leads.

Common-mode and differential-mode signals.

• A differential-mode voltage appears between the two signal wires — this is the wanted signal, and any noise that gets in this way cannot be separated from it.
• A common-mode voltage appears equally on both wires with respect to ground — typically from ground-potential differences and capacitive pickup.
• A differential (instrumentation) amplifier amplifies the difference and rejects the common-mode voltage. Its quality is the common-mode rejection ratio (CMRR). Unbalanced source or lead impedances convert some common-mode voltage into differential mode, so keep both lines balanced.

Guarding. A guard conductor driven at (nearly) the same potential as the signal conductor surrounds it, so no leakage current or capacitive current flows from the signal conductor. Used in high-resistance measurements and high-impedance DVM inputs.

Other remedies. Low-pass filtering to the signal bandwidth (noise power ∝ bandwidth), averaging repetitive measurements (random noise reduces as √N), integrating ADCs with mains-period integration, lock-in (synchronous) detection, and keeping signal and power cables in separate trays crossing at right angles.

Formulas

Vn = √(4·k·T·R·B) (thermal noise, RMS) k = 1.38 × 10⁻²³ J/K; T = absolute temperature (K); R = resistance (Ω); B = noise bandwidth (Hz); Vn in V.

In = √(2·q·I·B) (shot noise, RMS) q = 1.602 × 10⁻¹⁹ C; I = DC current (A).

SNR (dB) = 10·log₁₀(Ps/Pn) = 20·log₁₀(Vs/Vn)

CMRR = Ad / Acm ; CMRR (dB) = 20·log₁₀(Ad/Acm) Vo = Ad·Vd + Acm·Vcm = Ad·(Vd + Vcm/CMRR) Ad = differential gain; Acm = common-mode gain; Vd = differential input; Vcm = common-mode input (V). Vcm/CMRR is the input-referred error.

Vn ≈ ω·R·C·V (capacitive coupling, valid for ω·R·C ≪ 1) C = stray capacitance (F); R = resistance from the victim node to ground (Ω); V = source voltage (V).

Vn = ω·M·I (inductive coupling, sinusoidal) M = mutual inductance (H); I = RMS interfering current (A).

Worked examples

Example 1 — thermal noise. A 100 kΩ source resistance feeds an amplifier with a 10 kHz noise bandwidth at 300 K. Find the RMS thermal noise voltage and the SNR for a 1 mV RMS signal.

1. Vn = √(4 × 1.38 × 10⁻²³ × 300 × 10⁵ × 10⁴).
2. = √(1.656 × 10⁻¹¹) = 4.07 × 10⁻⁶ V = 4.07 μV.
3. SNR = 20·log₁₀(1 × 10⁻³ / 4.07 × 10⁻⁶) = 20·log₁₀(245.7) = 47.8 dB.

Answer: Vn ≈ 4.07 μV RMS; SNR ≈ 47.8 dB. Reducing B to 100 Hz would cut Vn tenfold.

Example 2 — common-mode rejection and capacitive pickup (GATE level). (a) A thermocouple signal of 2 mV rides on a 1 V, 50 Hz common-mode voltage. The instrumentation amplifier has Ad = 1000 and CMRR = 80 dB. Find the output signal, the output error due to Vcm, and the output SNR. (b) An unshielded input node has 1 MΩ to ground and 10 pF stray capacitance to a 230 V, 50 Hz conductor. Estimate the induced voltage.

1. (a) CMRR = 10^(80/20) = 10⁴. Signal output = 1000 × 2 mV = 2 V.
2. Common-mode output = Ad·Vcm/CMRR = 1000 × 1/10⁴ = 0.1 V.
3. SNR = 20·log₁₀(2/0.1) = 26.0 dB.
4. (b) ωRC = 2π × 50 × 10⁶ × 10 × 10⁻¹² = 3.14 × 10⁻³ ≪ 1, so Vn ≈ ωRC·V = 3.14 × 10⁻³ × 230 = 0.72 V.

Answer: (a) 2 V signal, 0.1 V error, SNR 26 dB; (b) about 0.72 V of hum — hundreds of times the thermocouple signal, which is why a grounded electrostatic shield is essential.

Common mistakes

• Grounding a cable shield at both ends at low frequency — it creates a ground loop. (At RF, multi-point shield grounding is used; know which regime you are in.)
• Expecting a copper or aluminium shield to block 50 Hz magnetic fields; it stops electric fields, but low-frequency magnetic fields need high-permeability material or reduced loop area.
• Writing thermal noise as kTB (that is noise power into a matched load, in watts) instead of √(4kTRB) volts.
• Using 10·log for a voltage ratio or 20·log for a power ratio.
• Assuming a high CMRR fixes everything; unbalanced lead resistances convert common-mode voltage into differential error.
• Forgetting temperature must be in kelvin in noise formulas.

For GATE IN

Expect NAT questions on thermal noise voltage, SNR in dB, CMRR and the resulting output error, and capacitive or inductive pickup estimates. MCQs test which shield stops which field, single-point grounding and ground loops, twisted pairs, guarding and the nature of thermal, shot and flicker noise. Practise dB conversions both ways quickly.

Quick check

1. Thermal noise of a 10 kΩ resistor at 300 K in a 10 kHz bandwidth?
2. CMRR = 100 dB and Vcm = 10 V. Input-referred error?
3. Which noise has a 1/f spectrum?
4. Why are twisted pairs effective against magnetic interference? Answers: 1. 1.29 μV RMS; 2. 10/10⁵ = 100 μV; 3. flicker noise; 4. adjacent twists form small loops of opposite orientation, so induced voltages cancel and the net loop area is small.