RF Design

De-Embedding (EM)

Q: When should I use EM de-embedding instead of TRL calibration?

Use EM de-embedding when you cannot build a clean set of physical calibration standards or when the fixture geometry is too complex for an analytic model. TRL calibration requires fabricating a thru, a reflect, and one or more delay lines on the same substrate as the device, which is impractical for a soldered surface-mount fixture, a bond-wire transition, or a coax-to-microstrip launch with an irregular keep-out. EM de-embedding instead builds a full-wave model of the fixture in a solver such as HFSS, CST, or ADS Momentum, exports its 2-port or 4-port S-parameters, and removes it numerically. It excels above 40 GHz where standard fabrication tolerances make discrete standards unreliable, and it lets you de-embed a single asymmetric structure that has no measurable counterpart. The accuracy ceiling is set by how faithfully the model captures dielectric constant, conductor roughness, and connector parasitics, so material characterization matters more than with measurement-based methods.

Q: How does T-parameter cascading remove the fixture from measured data?

S-parameters do not multiply when networks are cascaded, so the measured data is first converted to transfer scattering parameters, or T-parameters, which do multiply. If the measured cascade is T_meas = T_left times T_DUT times T_right, where T_left and T_right are the simulated fixture halves, then the device is recovered as T_DUT = inverse(T_left) times T_meas times inverse(T_right). The result is converted back to S-parameters for reporting. This is mathematically exact when the fixture model is exact and the fixture and device share matched reference impedances at the de-embedding planes. Any error in the EM model, such as a wrong substrate height or an unmodeled launch discontinuity, propagates directly into the recovered device response, which is why a 2x-thru sanity check is run first: de-embedding half the thru from itself should yield a near-ideal zero-length connection.

Q: What error sources limit EM de-embedding accuracy above 50 GHz?

The dominant limits are material uncertainty and reference-plane definition. Substrate dielectric constant and loss tangent vary by 2 to 5 percent lot to lot, and conductor surface roughness adds frequency-dependent loss that a smooth-conductor model underestimates by 0.1 to 0.3 dB per centimeter at 60 GHz. Mesh convergence in the solver must be tightened until S-parameters change by less than 0.01 dB and 0.5 degrees between adaptive passes. Higher-order moding in the fixture, port de-normalization errors, and an ambiguous reference plane at a tapered launch each add error. In practice a well-characterized EM de-embedding holds magnitude accuracy near 0.1 dB and phase accuracy near 1 to 2 degrees through 67 GHz, degrading as the unmodeled physics grows toward 110 GHz.

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Rather than fabricating physical calibration standards, this method builds a full-wave electromagnetic model of the test fixture, launch, or interconnect that surrounds a device, then numerically removes it to expose the device's intrinsic response. The simulated fixture S-parameters are converted to cascadable T-parameters, inverted, and multiplied against the measured cascade so the recovered data lands at the true reference plane. EM de-embedding is the workhorse for millimeter-wave characterization above 40 GHz, where soldered fixtures, bond-wire transitions, and tapered launches defy the discrete-standard approach used in TRL calibration. A 2x-thru self-test validates the fixture model before any device data is trusted.

Category: RF Design

Typical Band: 40 to 110 GHz

Phase Accuracy: 1 to 2° to 67 GHz

How a Simulated Fixture Replaces Physical Standards

Every measured device sits behind a fixture: a coax connector, a probe tip, a microstrip launch, a bond wire, or a soldered footprint that contributes loss, phase delay, and reflections of its own. Measurement-based correction methods such as TRL or SOLT remove those effects by fabricating known standards on the same substrate and back-solving the error terms. EM de-embedding takes the opposite route. The engineer constructs a geometrically accurate model of the fixture inside a full-wave solver, drives it with the same port impedances and modes used in the measurement, and exports an S-parameter file that describes the fixture alone. Because no physical standards are built, the technique applies to one-of-a-kind asymmetric structures that have no measurable calibration counterpart.

The removal itself relies on a property of cascaded networks: scattering parameters do not multiply, but transfer scattering parameters do. The measured data and both simulated fixture halves are converted to T-parameter matrices, the fixture inverses are placed on the left and right of the measured cascade, and the matrix product collapses to the device sitting alone at its true terminals. Converting that product back to S-parameters yields the de-embedded result. The procedure is exact in principle, so its real-world accuracy is governed entirely by how well the model matches the hardware, which makes substrate and conductor characterization the decisive step rather than an afterthought.

This dependence on model fidelity is also the method's main hazard. A wrong dielectric constant, an unmodeled via stub, or a smooth-conductor assumption that ignores surface roughness all leak directly into the recovered device parameters with no measurement to catch them. The defensive habit is the 2x-thru: simulate a back-to-back fixture pair, de-embed one half from the measured thru, and confirm the result approximates a lossless zero-length connection. Any deviation flags a model error before a real device is misjudged.

Governing Math: T-Parameter Cascade Inversion

Measured cascade (transfer parameters):
[T_meas] = [T_L] × [T_DUT] × [T_R]

De-embedded device:
[T_DUT] = [T_L]⁻¹ × [T_meas] × [T_R]⁻¹

S ↔ T conversion (2-port):
T₁₁ = −det(S) / S₂₁, T₁₂ = S₁₁ / S₂₁
T₂₁ = −S₂₂ / S₂₁, T₂₂ = 1 / S₂₁

Reference-plane phase shift per fixture length:
φ = β × ℓ = (2πf / c) × √ε_eff × ℓ

Where T_L, T_R = simulated left/right fixture halves; T_DUT = intrinsic device; det(S) = S₁₁S₂₂ − S₁₂S₂₁; β = phase constant; ε_eff = effective permittivity; ℓ = de-embedded length. Example: a 6 mm microstrip launch on ε_eff ≈ 6.5 at 60 GHz adds φ ≈ 1,100° that the inverse removes.

EM De-Embedding vs. Other Fixture-Removal Methods

Method	Standards Needed	Best Frequency	Handles Asymmetric Fixture?	Limiting Error Source
EM de-embedding	None (full-wave model)	40 to 110 GHz	Yes	Material & mesh fidelity
TRL calibration	Thru, reflect, line(s)	2 to 67 GHz	No	Line length / band ratio
SOLT calibration	Short, open, load, thru	DC to 50 GHz	No	Load & open model error
Port extension	None (length only)	Any (phase only)	No	Ignores loss & mismatch
2x-thru (AFR)	One back-to-back thru	1 to 50 GHz	Symmetric only	Fixture asymmetry

Common Questions

Frequently Asked Questions

When should I use EM de-embedding instead of TRL calibration?

Reach for EM de-embedding when clean physical standards are impractical: soldered surface-mount fixtures, bond-wire transitions, or coax-to-microstrip launches with irregular keep-outs. You build a full-wave model in HFSS, CST, or ADS Momentum and remove it numerically. It shines above 40 GHz where fabrication tolerances make discrete TRL standards unreliable, and it can de-embed a single asymmetric structure that has no measurable counterpart. The accuracy ceiling is set by how well the model captures ε_r, conductor roughness, and connector parasitics.

How does T-parameter cascading remove the fixture from measured data?

S-parameters do not multiply across cascaded networks, so the measured data is converted to transfer (T) parameters, which do. With [T_meas] = [T_L][T_DUT][T_R], the device is recovered as [T_DUT] = [T_L]⁻¹[T_meas][T_R]⁻¹, then converted back to S-parameters. It is exact only when the fixture model is exact and the de-embedding planes share matched reference impedances, so any model error feeds straight into the result. A 2x-thru self-check catches that first.

What error sources limit EM de-embedding accuracy above 50 GHz?

Material uncertainty and reference-plane ambiguity dominate. Substrate ε_r and loss tangent drift 2 to 5% lot to lot, and conductor roughness adds 0.1 to 0.3 dB/cm of extra loss at 60 GHz that smooth-conductor models miss. Mesh must converge until S-parameters shift under 0.01 dB and 0.5° between adaptive passes. Done well, magnitude accuracy stays near 0.1 dB and phase near 1 to 2° through 67 GHz, degrading toward 110 GHz as unmodeled physics grows.

Related Terms

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