EMC Grounding and Bonding Analysis

That's the story in the low-frequency world. For DC or 50/60 Hz, a single thick ground wire is sufficient. However, what becomes a problem in EMC is the wide frequency band from several kHz to several GHz. In this band, the inductance of even a few centimeters of wiring cannot be ignored.

The inductance of wiring is roughly 10 nH/cm as a guideline. For example, a 5 cm ground wire has about 50 nH of inductance. At 100 MHz:

If there is a 31 Ω ground impedance, a noise current of just 1 mA will cause a 31 mV ground potential difference. Considering that the signal level of high-speed digital circuits is around 1 V, this erodes more than 3% of the noise margin. This is the essence of the "grounding problem" in EMC.

Exactly. Let's organize the definition of ground in EMC:

• Safety Grounding (Protective Grounding): Prevents electric shock during leakage. Requires low resistance (a few Ω or less) at 50/60 Hz.
• Signal Grounding (Signal Ground): Reference potential for circuits. Requires low impedance across the signal bandwidth.
• EMC Grounding: Controls the return path of noise currents to optimize radiation and immunity. The core point is that the optimal grounding topology changes depending on frequency.

And Bonding is the electrical connection of two conductors with low impedance. The "connection method" between enclosures, between boards and chassis, between cable shields and connectors—these determine EMC performance.

Good question. The issue is how to determine that boundary frequency. The basic criterion is the electrical length of the ground wiring.

Here, $\ell$ is the physical length of the ground wiring, and $\lambda$ is the wavelength at the frequency of interest. For example, if the ground wire length is 30 cm:

In other words, if handling frequencies above 50 MHz, grounding with a single 30 cm wire is dangerous. You need to switch to multi-point grounding or shorten the wiring.

Because multi-point grounding forms ground loops. At low frequencies, wiring inductance is small, so the loop impedance is also low. This allows large noise currents to flow within the loop due to fluctuations in external magnetic fields.

With single-point grounding, the loop does not physically exist, so noise from magnetic field coupling can be eliminated. However, at high frequencies, the ground wire itself risks becoming an antenna, so multi-point grounding via short paths becomes more advantageous.

You ground only at a single point for low frequencies and place bypass capacitors at various locations for high frequencies. For example, a 10 nF capacitor is about 16 Ω at 1 MHz, but 0.16 Ω at 100 MHz. At low frequencies, the capacitor appears open, not creating a ground loop, while at high frequencies, the capacitor appears shorted, functioning as multi-point grounding. This is a technique often used in automotive ECUs.

Let's consider the equivalent circuit of a bonding strap. Even a simple metal strip has the following elements:

• $R_{DC}$: DC resistance. Determined by cross-sectional area and material. For copper, it's on the order of a few mΩ.
• $R_{skin}(f)$: Increase in AC resistance due to skin effect. Increases proportionally to $\sqrt{f}$.
• $j\omega L_{self}$: Self-inductance. Determined by the strap's shape (length/width/thickness), and the impedance increases proportionally to frequency.
• $C_{stray}$: Stray capacitance with surrounding structures. Its influence becomes apparent in the GHz band.

At low frequencies, $R_{DC}$ is dominant (mΩ order), but as frequency increases, $\omega L$ becomes dominant, and the impedance changes rapidly near the resonant frequency.

At the series resonant frequency of L and C, the impedance takes a minimum value (ideally only the R component). However, at the parallel resonant frequency, the impedance takes a maximum value, resulting in a state effectively equivalent to the bonding being "open-circuited".

For example, if $L = 20$ nH, $C = 5$ pF:

If the enclosure bonding impedance spikes at 503 MHz, the shielding effectiveness in that band degrades dramatically. This is the reason for using FEM to sweep the impedance of the grounding structure over frequency and design to avoid resonance points.

They are very different. The self-inductance of a flat strap with width $w$, thickness $t$, and length $\ell$ is approximately:

The key is to make it wider and shorter. For the same cross-sectional area, a flat strip (strap) has lower inductance than a round wire. Doubling the width reduces inductance by about 30-40%. That's why flat straps, not round wires (jumper wires), are recommended for EMC bonding.

A typical case is when two separate devices are connected by both a signal cable and a power ground. This forms a closed loop. According to Faraday's law, a time-varying magnetic flux linking the loop induces an electromotive force:

If a sinusoidal magnetic field $B_0 \sin(\omega t)$ uniformly links a loop area $A$:

For example, in a factory environment with $B_0 = 1\;\mu\text{T}$ (near 50 Hz power cables) and loop area $A = 0.1\;\text{m}^2$:

31 μV might seem small, but for a measurement system where sensor signals are on the order of hundreds of μV, it significantly degrades the SNR. Since the noise voltage increases proportionally to $\omega$ as frequency rises, it becomes severe near high-frequency noise sources.

That is one of the most effective countermeasures. Specifically:

• Keep signal lines and return lines close together (the principle behind twisted pairs).
• Route cables along walls/surfaces (minimizes loop area).
• Use shielded cables (shields external magnetic fields).
• Adopt differential transmission (removes common-mode noise).

In CAE, we model the actual wiring routes in 3D and numerically evaluate coupling with external magnetic field sources. FEM is powerful in cases where simply estimating loop area is insufficient—for example, optimizing routing in non-uniform magnetic fields.

Transfer impedance $Z_t$ is an indicator of "how much external noise current leaks to the inside." It is defined as:

For a shielded cable, it's the ratio of the voltage $V_{inner}$ induced between the inner conductor and the shield when a current $I_{outer}$ flows on the external surface. For an ideal perfect shield, $Z_t = 0$, but in reality, due to the shield's DC resistance, apertures (gaps in the braid), and imperfections at joints, $Z_t$ has a finite value.

Enclosure seams and bonding joints also have "transfer impedance." For example, at a location where two panels are fastened with bolts, EMI leaks through the gaps between bolts. Quantifying this leakage is the transfer impedance of the joint.

For a solid metal plate, if the thickness exceeds the skin depth $\delta$, $Z_t$ decays rapidly with frequency (about 8.7 dB/skin depth). However, at bolted joints:

• Contact resistance: Depends on surface roughness, oxide films, tightening torque.
• Leakage from gaps: If the bolt spacing exceeds $\lambda/20$, it radiates as a slot antenna.
• Gasket degradation: $Z_t$ increases due to aging of conductive gaskets.

We evaluate these with FEM to determine specifications like bolt spacing and tightening torque.

The basis is Maxwell's equations, but in grounding analysis, frequency-domain electromagnetic field equations are central. Assuming time-harmonic ($e^{j\omega t}$):

Here, $\mathbf{A}$ is the magnetic vector potential, $\phi$ is the electric scalar potential, $\sigma$ is conductivity, and $\mathbf{J}_s$ is the external current source.

The impedance of the grounding structure is calculated by exciting a port with unit current:

for each frequency. $R(\omega)$ is the resistive component (energy dissipation), and $X(\omega)$ is the reactive component (energy storage).

The PEEC (Partial Element Equivalent Circuit) method decomposes conductor structures into equivalent circuits. Comparing them:

For overall optimization of a grounding network, PEEC is computationally efficient. However, to accurately evaluate electromagnetic field distribution inside enclosures or leakage from slots, FEM or FDTD is necessary. In practice, a two-step approach of overall design with PEEC → local verification with FEM is often used.

There are three main challenges:

1. Multi-scale Problem
Bonding strap thickness is a few mm, skin depth is a few μm (GHz band), and enclosures are tens of cm to several meters. A scale difference of over 6 orders of magnitude needs to be covered. Discretizing everything with 3D solid elements is computationally impractical.

Related Topics