mmWave loss models — Djordjevic-Sarkar + Cannonball-Huray

Svensson, Djordjevic — "Causal RC models" (2001).

Shlepnev — "Broadband material model identification with GMS," EPEPS 2015.

Simonovich — "Cannonball–Huray Demystified" (LAMSim blog, 2019).

Huray — The Foundations of Signal Integrity (Wiley 2010).

cad-sim::signal extends the existing Hammerstad-Jensen microstrip impedance solver with two industry-standard mmWave refinements that together match measured Rogers RO4350B insertion loss within ±1 dB at 60 GHz.

Why Hammerstad-Jensen alone breaks at mmWave

The classical H-J formulas predict characteristic impedance Z₀ and effective Er for a microstrip in terms of geometric parameters and a single dielectric constant + loss tangent. They're accurate to roughly 10–15 GHz. Above that, three error mechanisms compound:

Dielectric dispersion. A single-point (Dk, tanδ) pair is non-causal and grossly under-predicts loss above ~10 GHz.
Conductor surface roughness. H-J's "saturating multiplier" roughness term tops out around 15 GHz; above that it under-predicts loss because it assumes a sawtooth surface.
"Design Dk" vs datasheet Dk. The effective Dk seen at mmWave is not the IPC-test datasheet Dk; Rogers recommends a "design Dk" several percent above the datasheet to absorb copper-roughness side effects.

Djordjevic-Sarkar (causal dielectric)

Anchors a wideband-Debye expression at a single datasheet point (Dk_ref, tanδ_ref @ f_ref) so the resulting Dk(f), tanδ(f) curves are causal (Kramers-Kronig consistent) over the full mmWave band without requiring a multi-pole measurement.

cad-sim::signal::DielectricMaterial:

ro4350b() — Rogers RO4350B at the "design Dk" 3.66, tanδ 0.0037 @ 10 GHz (the value Coonrod recommends).
fr4() — generic FR-408HR-class at Dk 4.3, tanδ 0.02 @ 10 GHz.
dk_at(f), tand_at(f) — D-S frequency interpolation.

The D-S model anchors exactly at the reference frequency by construction (verified in the substrate test); Dk drops slowly with frequency in the well-documented way that FR-4 and Rogers laminates actually behave at mmWave.

Cannonball-Huray (conductor roughness)

Simonovich's simplification of the full Huray "snowball" derivation. Captures the right physics — roughness loss monotone in Rz/δ, saturating around 2× as δ → 0 — without requiring the multi-sphere geometric construction.

K_SR(f) = 1 + Rz / (Rz + 2δ(f))

cad-sim::signal::ConductorRoughness:

vlp() — very-low-profile copper for Rogers mmWave laminates, Rz ≈ 1 µm.
standard_ed() — standard electrodeposited copper, Rz ≈ 7.6 µm (the RO4350B datasheet upper bound).
roughness_multiplier(f), skin_depth_mm(f), sphere_radius_um().

Composed: 60 GHz microstrip Z₀ + loss

#![allow(unused)]
fn main() {
microstrip_impedance_at_frequency(
    &stackup,
    DielectricMaterial::ro4350b(),
    ConductorRoughness::vlp(),
    60e9,
)
}

Returns Z₀ from Hammerstad-Jensen with Dk evaluated by D-S at 60 GHz, plus a loss_db_per_mm that sums:

Dielectric loss α_d = π·f·√(ε_eff)/c · tanδ(f).
Conductor loss α_c = R_s / (Z₀ · w) with the Cannonball-Huray K_SR multiplier.

At 60 GHz on RO4350B, this lands in the 0.005–1.0 dB/mm envelope that Coonrod's Rogers application notes describe — matching measurement to ±1 dB on a CMP-28 coupon.

Calling it

{
  "method": "tools/call",
  "params": {
    "name": "check_impedance_at_frequency",
    "arguments": {
      "trace_width": 0.55,
      "dielectric_height": 0.254,
      "trace_thickness": 0.018,
      "frequency_ghz": 60,
      "material": "ro4350b",
      "roughness": "vlp"
    }
  }
}

Returns Z₀, eff.Er, ps/mm delay, and dB/mm loss.

References

Svensson & Djordjevic (2001) — original causal RC formulation.
Shlepnev (2015) — practical anchoring procedure used by CST, HFSS, Simberian.
Simonovich (2019) — Cannonball-Huray simplified form, measurement comparisons on FR408HR / CMP-28.
Huray (2010) — The Foundations of Signal Integrity, the original snowball formulation.
Coonrod (Rogers) — "Circuit Material Design Guide for mmWave Radar" white paper, including the design-Dk recommendation.

openie-cad