So far the series has dealt with noise generated inside devices. Interference is different: unwanted signals that originate from external sources, are more structured than intrinsic noise, and can usually be traced back to a specific source. This lecture models how interference gets into a circuit — by capacitive, inductive, conductive or radiative coupling — and how each path is blocked.
Interference exists only when three components exist in order: a noise source, a coupling medium, and a receiver that reflects the coupled noise. Breaking or weakening any one link mitigates the interference.
Interference is usually studied separately from intrinsic noise. Intrinsic noise is typically continuous and stochastic; interference is more structured, e.g. the 50 Hz hum riding on an ECG trace.
Identifying the type of noise is the first step in designing the right mitigation, and three bench instruments cover most cases:
Any two conductors separated by a dielectric form a capacitor — two wires separated by an air gap, or even a single wire, since any wire has a stray capacitance to the (conductive) earth. Capacitive coupling causes interference and crosstalk between nearby wires and traces. Aggressors include high-voltage lines (the mains grid) and high-frequency lines (PCB traces around switching supplies).
Consider a low-impedance aggressor wire 1 (e.g. a power line carrying 230 VRMS at 50 Hz, whose voltage vn is spread over the whole wire without attenuation) running parallel to a victim wire 2 with a resistive load RL (e.g. the input impedance of an amplifier stage sensing a signal). The stray capacitances to ground are C1,G and C2,G, and the capacitance between the wires is C1,2.
This resembles the output of a high-pass filter: the higher the noise frequency, the greater the chance of coupling. It has two useful limits:
Digital signals may have small source voltages, but their fast switching edges can cause crosstalk between parallel signal lines running close together. If the aggressor itself has a high source impedance RS, the voltage at the coupling point is a low-pass-filtered version of vn and the strength of coupling goes down: the pass bands of that low-pass filter (f < fLP) and the subsequent high-pass filter (f > fHP) must overlap for coupling to occur, so if RS is large enough that fHP > fLP there is no overlap and coupling is weak at all frequencies.
Shielding blocks external interference by encasing cables and equipment in conductive material (foil, metallic braiding, or a combination) kept at a fixed potential — the idea of a Faraday cage. Maintaining a single potential is typically done by grounding the shield, though shields can also be actively driven (e.g. driven guard rings). Reducing coupling also follows directly from C = εA/d: increase distance, minimise overlap, and use low-permittivity material between conductors.
Inductive (magnetic) coupling is the magnetic counterpart of capacitive coupling. A changing current in one conductor (the aggressor) creates a changing magnetic field; where that field passes through a loop of another circuit (the victim) it induces a voltage (Faraday’s law) that appears in series with the victim loop. The victim is the loop, not the wire — what matters is the area enclosed between the signal path and its return. Typical aggressors are large or fast-changing currents: mains and power cables, transformers, motors, switching-converter current loops.
Every term is a lever for mitigation: distance (the field falls as 1/r); loop area (twist the aggressor’s outgoing and return conductors together so their fields cancel; keep the victim’s signal and return paths close together); and orientation (the induced voltage is zero when θ = 90°, so route sensitive loops at right angles to the field — for example, cross a mains cable at 90°).
The induced voltage rises in proportion to the aggressor’s frequency, which is why fast edges are such a problem:
Example. A wire carries 50 Hz mains current (1 A RMS) and has a mutual inductance of 100 nH with a nearby conductor: vn(t) = 100×10−9·d/dt(1√2 sin(2π×50t)), giving Vn,RMS = 100×10−9 × 2π × 50 × 1 = 31.4 µV.
A switching converter carrying the same 1 A RMS at f = 1 MHz with the same coupling gives Vn,RMS = 0.63 V — a 20 000-fold increase, and a practical concern for switching power supplies. Even when they carry lower currents than the AC mains, their sheer switching frequency couples a lot of interference.
Voltage induced in a cable by external magnetic fields drives interference currents in the signal wires. Twisting the pair makes the induced current direction alternate from one twist to the next, so adjacent loops cancel each other out and the interference is cancelled.
Electric fields are easy to shield — almost any thin, grounded conductor works. Low-frequency magnetic fields are harder: they penetrate conductors and are attenuated mainly by absorption as they pass through the thickness x of the shield:
where f is the interference frequency and μ and σ are the permeability and conductivity of the shield. The field falls to 37% at one skin depth. At 50 Hz copper has a skin depth of about 9 mm, so a 0.5 mm copper shield is almost transparent; steel’s high permeability shrinks the skin depth to under 1 mm, which is why steel is used for low-frequency magnetic shielding, while 0.5 mm of copper only becomes effective in the hundreds of kHz and above. Practical message: at mains frequency it is usually much easier to reduce inductive pickup with distance, small loop areas, twisting and orientation than with a shield.
| Aspect | Capacitive coupling | Inductive coupling |
|---|---|---|
| Coupling field | Electric field (E) | Magnetic field (B) |
| Coupling element | Stray capacitance C1,2 | Mutual inductance M1,2 |
| Aggressor | Node with a large or fast voltage change (dv/dt) | Conductor with a large or fast current change (di/dt) |
| Typical aggressors | Mains wiring near the patient, switch nodes, clock lines | Power and mains cables, transformers, motors, switching-converter loops |
| Noise in the victim | Current injected into the victim node: in = C1,2 dv1/dt | Voltage in series with the victim loop: vn = M1,2 di1/dt |
| Model coupled noise as | Current source (high source impedance) | Voltage source (low source impedance) |
| Most vulnerable victims | High-impedance nodes (electrodes, op-amp inputs) | Low-impedance circuits with a large loop area |
| Geometry that matters | Spacing and parallel length of conductors | Loop area, distance, orientation |
| Shielding | Thin grounded conductor works well | Thin conductors are poor at low frequency (needs steel or mu-metal) |
| Main fixes | Grounded shield, spacing, lower victim impedance | Twisting and small loops, distance, orientation |
Conductive coupling happens when current from one circuit (a complete loop) flows through some impedance it shares with another circuit. Any practical wire or PCB trace has a non-zero impedance: purely resistive at low frequencies, with inductive reactance added in series at high frequencies. If a single wire or trace is shared between two subcircuits, currents from both flow through it and a potential drop appears across its length: at low frequency ΔV = I × R; at high frequency ΔV = I × (R + jωL).
Shared ground return. Two sub-circuits share one ground trace on a PCB, with impedance Z1,2. A potential difference ΔV = v1 − v2 = Z1,2(iA + iB) appears across it. If the current iA of sub-circuit A is large, then even though the bulb in sub-circuit B is powered by a DC source VB, it will begin to flicker at the frequency of A’s source va(t). The fix is to give each sub-circuit its own return path (no shared impedance), as in the PCB lecture.
Ground loops occur when multiple ground connections close a loop. The potential differences within the loop come from two sources: EMF induced by magnetic flux through the loop area (inductive coupling), and ground-potential differences from other circuits’ currents flowing in shared ground impedance (conductive coupling). Those potential differences drive currents inside the loop and into connected nodes. Ground connections are especially susceptible because a ground is almost always a network of nodes connected at different points; improper grounding, multiple ground points connected inappropriately, long ground connections, and devices powered from separate-ground sources that are interconnected can all create ground loops.
Long ground conductors are prone to all three kinds of interference: higher impedance gives larger potential drops; a larger enclosed area picks up more magnetic field (and because ground conductors have low impedance, the induced EMF drives a large circulating current); and the stray capacitance grows with length, so capacitive coupling increases as well. Ground loops exist at large scale (between devices) and inside a single PCB.
For a shield to work against capacitive coupling it should be connected to the signal reference node — but connecting it to the reference at both ends can form a ground loop. Potential differences between the two grounding points then drive a current through the shield, whether picked up magnetically or from other circuits through a shared ground with non-zero impedance. This adds directly in series with the signal if the shield doubles as the signal return (e.g. a coaxial cable) or if source and receiver end sit on a shared ground rail at separate points.
A large-scale example is audio hum: the source (mixer/PC) is earthed through its power socket, a powered speaker is earthed through a separate socket at another location, and a shielded cable connects them with the shield grounded at both ends — the earth and shield complete a loop, with 50 Hz current flowing and magnetic fields inducing more. In medical devices such as EEG and ECG systems, ground loops introduce low-frequency noise into delicate µV–mV-level measurements.
Mitigation techniques for ground loops: single-point grounding (effective at low frequency, but long ground leads have high impedance at high frequency); isolation (transformers, optocouplers); differential inputs with high common-mode rejection; short, thick ground wires; and twisted pair cables with careful cable routing.
A well-designed grounding system distinguishes two kinds of ground: safety grounds (usually at earth potential; they carry fault currents and must not be used as signal grounds) and signal grounds (which may or may not be at earth potential — a battery-powered device may not have its reference tied to earth).
| Signal-ground scheme | Description | Pros | Cons | Use case |
|---|---|---|---|---|
| Single-point | All modules connect to ground at a single common point | Eliminates ground loops at low frequency; simple | Long return paths cause high inductance at high frequency; ineffective for RF/EMI | Low-frequency analog, audio |
| Multipoint | Each module connects directly to a ground plane at multiple points | Very low impedance; excellent for RF and digital | Can create ground loops at low frequency; can cause hum in audio | High-frequency digital, RF |
| Hybrid | Single-point at low frequency, multipoint (capacitive coupling) at high frequency | Reduces low-frequency loops; low impedance at high frequency | More complex; needs careful capacitor selection and layout | Mixed-signal (analog + digital), EMI-sensitive equipment |
Isolation breaks the conductive (galvanic) path between two circuits but still passes the signal or power across a barrier. The ground-potential difference VG then appears across the barrier, not in the signal path — so no ground-loop current flows — and the barrier doubles as a safety barrier against dangerous currents and high voltages.
| Method | Crosses the barrier as | Typical use |
|---|---|---|
| Transformer | Magnetic field | AC signals, power (isolated DC–DC) |
| Optocoupler | Light (LED → photodetector) | Digital and control signals |
| Capacitive isolator | HF carrier across small capacitors | Fast digital buses (SPI, UART) |
Limits: the barrier still has a few pF of capacitance, so fast common-mode transients can couple across it, and the isolated side needs isolated power too (an isolated DC–DC converter or a battery). Medical devices isolate the patient-connected part from the mains to meet µA-level leakage limits (IEC 60601-1). A battery-powered wearable is isolated by design — but not while it is connected to a PC or charger by USB.
Any pair of lines v1, v2 (measured to ground) splits into a wanted differential part and an (usually unwanted) common part:
A differential amplifier ideally responds only to vDM, but a practical one responds to both: vo = GDM vDM + GCM vCM. Shifting both inputs by the same amount moves vCM but leaves vDM unchanged. The figure of merit is the common-mode rejection ratio:
CMRR is measured by tying the inputs together to get GCM, and driving vDM alone to get GDM.
Almost every op-amp has a differential pair as its first stage with a tail current source (IEE). The pair only steers the fixed tail current between its two transistors, so a differential input moves the collector voltages by the factor GDM = gmRC/2. For a common-mode input the ideal tail source resists any change in total current, so the common-mode gain would be zero. A practical tail source (e.g. a biased transistor) has a finite output resistance REE, so raising both inputs lets some current flow through it:
An ideal current source (REE → ∞) therefore gives infinite CMRR. CMRR also falls with frequency because stray capacitance across the tail source lowers its impedance — check the datasheet curve at 50 Hz.
For the classic difference amplifier (v2 through R1 to the inverting input with R2 feedback; v1 through R3 to the non-inverting input with R4 to ground), superposition gives vo = A v1 − B v2 with A = (R4/(R3+R4))(1+R2/R1) and B = R2/R1. Substituting v1,2 = vCM ± vDM/2:
With perfectly matched resistor ratios R2/R1 = R4/R3 = G the common-mode gain is exactly zero — but real resistors have tolerances. If the two ratios differ by a fraction δ the CMRR is limited to about (1+G)/δ, so even a perfect op-amp is limited by its resistors, and source impedances can further destroy the matching.
Differential signalling transmits a signal on two complementary lines (one is the inverted version of the other); the receiver subtracts them, and with high CMRR any common-mode noise, which acts similarly on both lines, is cancelled. It is especially useful over longer distances, where long wires pick up more common-mode interference, and works best when the lines are matched and routed together (twisted pairs, differential PCB pairs). Examples: USB, Ethernet, RS-485 — and the instrumentation-amplifier input of an ECG.
Electromagnetic interference (EMI) is electromagnetic disturbance, radiated or conducted, from an external source — natural (lightning, solar flares) or artificial (motors, transformers, electronic devices). It is mitigated by shielding (conductive or magnetic enclosures) and filtering (capacitors, inductors, ferrite beads) to remove what the shield could not attenuate.
Power-line interference (PLI) is EMI from the mains wiring, coupling capacitively, inductively and conductively. Appliances and machinery can directly shift ground levels via conductive coupling, including 50 Hz noise and its harmonics. Conductively coupled PLI is mitigated by transformer isolation, power-line filters (for higher-frequency conducted noise) and proper grounding; the capacitive and inductive paths use the techniques above (shielding, twisted pairs, ground-loop mitigation).
Conducted noise travels in two modes. Common mode flows in the same direction on live and neutral and returns through protective earth via stray capacitance (e.g. nearby lightning induces nearly the same voltage on both and can lift the local earth relative to the transformer’s remote earth). Differential mode flows in on live and returns on neutral; live/neutral imbalance converts part of a common-mode disturbance into differential mode.
Power-line filters are passive LC low-pass filters fitted at the AC inlet of mains equipment (often built into the IEC power-entry module). They stop interference from the grid reaching the device, and the device’s noise from reaching the grid. They do not remove the 50 Hz line voltage — they pass 50 Hz and attenuate conducted noise from about 10 kHz to 30 MHz. Inside:
A data-acquisition (DAQ) system converts physical phenomena into digital data. Noise can enter at every block — and noise added early is amplified by the later stages. Sources include internal noise (thermal, shot, flicker), power-supply noise (ripple currents, switching noise) and noise picked up in the signal transmission line (e.g. capacitively coupled noise). Fixes: shielding and layout, low-noise parts, decoupling, short twisted leads.
An N-bit ADC rounds each sample to one of 2N levels with step q = VFS/2N (1 LSB), where VFS is the full-scale voltage. The rounding error lies within ±q/2 and behaves like white noise. Assuming the error is uniformly distributed between −q/2 and +q/2, its RMS value is:
ECG example. With VFS = 3.3 V: a 12-bit ADC has a quantisation noise floor of 3.3/(212√12) ≈ 233 µVRMS, so a gain of a few hundred is needed to bring it below 1 µV at the input — but at that gain the electrode offset voltage would saturate the amplifier. A 24-bit ADC has 3.3/(224√12) ≈ 56 nVRMS, already negligible (though a real ADC’s floor will be much higher because of its inherent thermal noise).
Design rule: refer the ADC noise to the input (divide by the front-end gain) and keep it below the analog noise.
VFS is set by the reference voltage VREF (usually VFS = VREF for unipolar ADCs such as those in microcontrollers; VFS = 2VREF for bipolar types such as the ADS1292). Noise on VREF is reflected in every sample on top of the other noise in the signal. Therefore: never use VDD straight from a switching converter as the reference; using the separate AVDD is not recommended either; use the ADC’s internal stable reference if it has one, otherwise a reference IC powered from AVDD; and add a decoupling capacitor on the reference pin (value usually given in the datasheet).
Filtering is the last resort for noise and interference that could not be mitigated by other means: low-pass to remove high-frequency noise, high-pass to remove low-frequency noise, band-pass to keep a certain frequency band, and notch (band-stop) to remove a narrow band such as 50 Hz.