2 Frequency & Wavelength
Professional EMC engineers must understand signal frequency f [Hz] and wavelength λ [m] — because the boundary between lumped-circuit and transmission-line behavior occurs where wavelength becomes comparable to circuit dimensions. Misjudging this regime is the root cause of most unintended emissions and immunity failures:
EMC and Frequency.
In general, EMC issues occur with signals of frequency f > 9kHz. This is the reason why most EMC Standards do not consider signals with f < 9kHz.
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Conducted Emission. Conducted emissions dominate at f < 30MHz.
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Radiated Emission. Radiated emissions dominate at f > 30MHz.
Wavelength: Calculation.
The frequency f [Hz] of a sinusoidal signal and its wavelength λ [m] have the following relationship [2.1]:
where v [m/sec] is the propagation velocity of the signal and f [Hz] is the frequency of the signal. Critical for EMC: Propagation velocity v [m/sec] differs significantly by medium:
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Free space: v ≈ c ≈ 3⋅10⁸ m/sec
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Cables and PCB traces: v = c ⋅ "velocity factor" (typically VF≈0.66)
This affects whether your circuit behaves as lumped elements or as a transmission line.
Example: A 100MHz signal in free space has wavelength λ=3⋅10⁸m/sec/100MHz=3m. In a shielded cable with velocity factor VF≈0.66, the same signal has λ≈2m.
Wavelength in any media.
Transverse electromagnetic (TEM) is a mode of propagation where the electric and magnetic fields are all restricted to directions normal (transverse) to the direction of propagation (neither electric nor magnetic field in the direction of propagation). Plane waves are TEM waves.
The frequency f [Hz] of a sinusoidal electromagnetic TEM wave and its wavelength λ [m] have the following relationship [2.5]:
where v [m/sec] is the propagation velocity of the signal, f [Hz] is the frequency of the signal, β [1/m] is the propagation constant of the media, ε' [F/m] is the real part of the complex permittivity ε=ε'+jε'', ε'' [F/m] is the imaginary part of the complex permittivity ε=ε'+jε'', µ' [H/m] is the real part of the complex permeability µ=µ'+jµ'', µ'' [H/m] is the imaginary part of the complex permeability µ=µ'+jµ''.
Remember: For lossy media or dispersive materials where conductivity and loss tangent are significant, wavelength must account for complex permittivity and permeability. However, in typical EMC applications (PCB traces, shielded cables), the velocity factor approximation (VF≈0.66) is sufficient.
Wavelength in vacuum.
Understanding free-space wavelength is essential for predicting radiated emissions and designing antennas for EMC testing. In the case that an electromagnetic wave travels through vacuum (and approximately air), the wavelength λ [m] of such a sinusoidal electromagnetic wave with frequency f [Hz] can be written as [2.5]:
where c [m/sec] is the speed of light (2.998·10⁸m/sec), ε0 [F/m] is the permittivity of vacuum (8.854·10⁻¹² F/m), µ0 [H/m] is the permeability of vacuum (12.57·10⁻⁷ H/m).
Example: A 100MHz radiated emission has wavelength λ=3·10⁸m/sec/(100MHz)=3m in free space. This is why antennas for 100MHz EMC testing are ~1.5m long (λ/2 dipole).
Wavelength in insulating media.
In the case that an electromagnetic wave travels through an insulator (μr'= 1) with negligible dielectric and magnetic losses (ε''=0, μ''=0), the wavelength λ [m] of such a sinusoidal electromagnetic wave with frequency f [Hz] can be written as [2.5]:
where v [m/sec] is the propagation velocity of the signal, f [Hz] is the frequency of the signal, c [m/sec] is the speed of light (2.998·10⁸m/sec), ε0 [F/m] is the permittivity of vacuum (8.854·10⁻¹² F/m), µ0 [H/m] is the permeability of vacuum (12.57·10⁻⁷ H/m) and εr' is the relative permittivity (dielectric constant of the insulator).
Example: In an FR-4 epoxy PCB substrate with εᵣ≈4, a 1GHz signal through a stripline (embedded in FR-4) has wavelength λ≈3·10⁸/(10⁹·√4)≈0.15m (compared to 0.3m in free space). When trace length approaches λ/10 (≈15mm here), transmission-line behavior begins to dominate the design.
Wavelength in good conducting media (e.g. in shields).
In the case that an electromagnetic sinusoidal wave travels through a good conductor (penetrating through, not traveling along), e.g., through a shield) with negligible magnetic losses
(µ'' = 0), the characteristic decay wavelength can be calculated as [2.5]:
where f [Hz] is the frequency of the sinusoidal signal, µ'=µr'µ0 [H/m] is the real part of the complex permeability (µ=µ'-jµ'') and σ [S/m] is the specific conductance of the medium where the wave is propagating through.
Example: For aluminum at f=1GHz, the characteristic decay wavelength in the conductor can be calculated:
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Conductivity: σ ≈ 3.77·10⁷ S/m
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Permeability: μ' = μ₀ = 4π·10⁻⁷ H/m (aluminum is non-magnetic)
λ=√(4π/(fμ₀σ))=√(4π/(10⁹·4π·10⁻⁷·3.77·10⁷))≈16.3μm. This wavelength λ [m] is directly related to the skin depth δ≈λ/(2π)≈2.59μm (λ=2π·δ). The electromagnetic field inside aluminum decays exponentially as e^(−x/δ), with 20·log₁₀(e^(−δ/δ))=8.7dB attenuation per skin depth. Over one characteristic wavelength λ (≈2π·δ), the field attenuates by approximately λ/δ·8.7dB≈2π·8.7dB≈55dB.
Practical implication: A 1mm thick aluminum sheet contains approximately 1000μm/2.59μm≈385 skin depths. With 8.7dB attenuation per skin depth, the total shielding effectiveness SE is (theoretically): SE≈385·8.7dB≈3350dB. To consider:
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Real-World SE Limit (~100–120 dB): High-performance solid aluminum enclosures typically top out at 100dB to 120dB of shielding effectiveness. Attenuation beyond 120–140dB is virtually impossible to measure or achieve due to dynamic range limits of test equipment and leakage pathways.
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Apertures and Seams: Real enclosures require seams, screw holes, display windows, connectors, and ventilation slots. The overall SE of an enclosure is dictated by electromagnetic leakage through these mechanical openings, not by the thickness of the metal.
Wavelength of signals traveling long blank wires vs. cables & PCB traces.
It is important to understand that the signal propagation velocity v [m/sec] depends on the transport medium through which the electromagnetic field is traveling. Therefore, the same signal with the same frequency f [Hz] has a different wavelength λ [m] in a blank wire (surrounded by air) than in a cable or PCB trace (surrounded by insulation material). The wavelength λ [m] is calculated the following way [2.1]:
where v is the signal propagation velocity in [m/sec], c is the speed of light (3E8 [m/sec]), f is the frequency of the sinusoidal signal in [Hz], εr is the relative permittivity and μr is the relative permeability of the media through which the electromagnetic field is propagating. VF is called the velocity factor.
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Wavelength in a blank wire. The wavelength λ of a signal with frequency f along a blank wire (or antenna surrounded by air) depends only on the speed of light c and the signal frequency f (v=c, because εr = 1 and μr =1 and therefore VF=1) [2.1]:
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Wavelength in cables & PCB traces. The wavelength λ of a signal with frequency f along an insulated copper wire or a cable or a Printed Circuit Board (PCB) trace is [2.1]:
Where c is the speed of light (3E8 [m/sec]), f is the signal frequency [Hz], εreff the effective dielectric constant (relative permittivity) through which the electromagnetic wave is propagating. The effective dielectric constant εreff is defined as the uniform equivalent dielectric constant for a transmission line, even in presence of different dielectrics (e.g. FR-4 and air for a microstrip line, see picture below).
The relative permeability μr is assumed to be equal to 1.0 for cables and PCBs because the insulation materials are non-magnetic. Thus, the velocity factor VF depends primarily on the effective relative permittivity (also called effective dielectric constant) εreff of the insulation or PCB material.
The calculation of the effective dielectric constant εreff [1] depends on the insulation material and the geometry of the transmission line (e.g. ribbon cable, microstrip, coplanar waveguide, etc.), because the amount of the electric field lines in the different media depending on the geometry of the transmission line (e.g. see the microstrip line below).
The Excel sheet below contains a calculator for calculating the effective dielectric constant εreff [1] (effective permittivity) for some of the most common transmission lines:
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PCB-traces. Microstrip, stripline, coplanar waveguide with a reference plane.
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Cables. Ribbon cable, twisted pair.
The velocity factor VF of a transmission medium is the ratio of the velocity v [m/sec] at which a wavefront of an electromagnetic signal passes through the medium, compared to the speed of light in vacuum c [3E8m/sec]: VF=v/c. Thus, the smaller the velocity factor VF, the smaller the wavelength λ [m]. The table below shows the approximate velocity factors for different insulation and PCB materials and different transmission line types [2.2, 2.3, 2.4].
The table below shows some rough approximations of wavelengths in different conductors (cables, PCBs) compared to free-space (air). Possible assumptions for wavelength λ in PCBs (FR-4) and cables are:
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PCB. λPCB≈0.5*λair (assumption εreff ≈3.0...4.5 → VF≈0.5).
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Cables. λCable≈0.7*λair (assumption εreff ≈1.5...3.0 → VF≈0.7).
