Trace Loss (Insertion Loss) Calculator

Insertion loss of PCB traces in dB per inch and over the full length: conductor loss with copper roughness and dielectric loss from a 2D field solver, for microstrip, stripline and differential pairs, with laminate Dk/Df modelled across frequency.

Method, formulas and references

How the loss is calculated

The loss of a line has two parts: resistive loss in the copper and polarisation loss in the dielectric. Both are computed from the 2D field solution of the actual cross-section, the same solver the impedance calculator uses.

Dielectric loss

The solver splits the stored electric energy between the regions of the cross-section: laminate below and above, solder mask and air. The effective loss tangent is the energy-weighted average, and the attenuation follows from it:

(1)tanδeff = Σ εr,i tanδi pi / εeff,   αd = π f √εeff tanδeff / c

On a surface microstrip part of the field is in air, so the effective loss tangent is lower than the laminate's. In a stripline it equals the laminate's.

Laminate Dk and Df versus frequency

Datasheets give Dk and Df at one frequency. The tool fits the Djordjevic–Sarkar wideband model to that point. The model is causal, so the loss and the permittivity stay consistent: Df is nearly flat across the band and Dk falls slightly as frequency rises. The impedance and εeff shown are at the frequency of interest. Checked against datasheets that list several frequencies (Shengyi S1141, Isola FR408HR), the fitted Dk stays within 1.5 % from 1 to 10 GHz. Ultra-low-loss laminates whose Df rises steeply with frequency are best entered at the frequency you care about.

(2)ε(ω) = ε∞ + Δε / (m2 − m1) · log10( (ω2 + jω) / (ω1 + jω) ),   ω1 = 104, ω2 = 1012 rad/s

Conductor loss

Wheeler's incremental-inductance rule gives the skin-effect resistance of any cross-section. The solver recedes every copper surface (trace sides, top, bottom and the planes) by a small depth, and the change in the air-filled impedance gives the resistance:

(3)R′ = (Rs / η0) · ∂Z0,air/∂n,   Rs = √(π f μ0 ρ),   αc = R′ / (2Z0)

This includes the current crowding at the trace edges, the return current in the planes, trapezoidal etching and the coupling of a differential pair. Below the frequency where the skin depth is comparable with the copper thickness, the resistance blends into the DC value: R = √(Rdc² + Rac²). For a differential pair the tool reports the odd-mode loss, which is the differential insertion loss (SDD21) per unit length.

Copper roughness

The treated copper surface makes the current path longer at high frequency. The skin-effect resistance is multiplied by a factor K:

  • Hammerstad: K = 1 + (2/π)·atan(1.4 (Rq/δ)²). This is the classic model; it saturates at 2 and underestimates very rough foils above about 10 GHz.
  • Groiss: K = 1 + exp(−(δ / 2Rq)1.6). It fits measured data better for moderate roughness, and also saturates at 2.
  • Huray: K = 1 + 1.5·SR / (1 + δ/a + δ²/2a²). This models the surface as spheres of radius a. It does not saturate, and it is the most accurate model when the parameters come from the foil maker or a measurement.

Accuracy

The automated tests check the dielectric loss against the exact stripline result and the quasi-static microstrip formula (within 3 %). The conductor loss is checked against Pozar's incremental-inductance stripline formula (within 4 %) and against the Hammerstad–Jensen microstrip derivative (within 5 %). In practice the input data limits the accuracy more than the solver does: laminate Dk/Df vary with resin content and glass style, and foil roughness varies from lot to lot. Datasheet values are typical; for a tight loss budget, ask the fabricator for the values of the actual construction.

References

  1. H. A. Wheeler, “Formulas for the Skin Effect,” Proc. IRE, vol. 30, 1942.
  2. D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012, sections 3.7–3.8.
  3. A. R. Djordjevic et al., “Wideband Frequency-Domain Characterization of FR-4 and Time-Domain Causality,” IEEE Trans. EMC, vol. 43, no. 4, 2001.
  4. E. Hammerstad, Ø. Jensen, “Accurate Models for Microstrip Computer-Aided Design,” IEEE MTT-S, 1980.
  5. S. Groiss et al., “Parameters of Lines on Rough Substrates,” Proc. European Microwave Conf., 1996.
  6. P. G. Huray et al., “Impact of Copper Surface Texture on Loss: A Model that Works,” DesignCon 2010.

Data sources

  1. Shengyi S1141 technical data sheet CN-TDS-2101-03
    Dk 4.4, Df 0.013 at 1 GHz (IPC-TM-650 2.5.5.9, 1.6 mm 8×7628); Tg 140 °C.
  2. Shengyi S1141 line-up table CN-LU-2106-S03 (SPDR)
    Dk/Df per prepreg glass style and resin content at 1/3/5/10 GHz.
  3. Shengyi S1000-2M technical data sheet CN-TDS-1911-03
    Dk 4.6, Df 0.018 at 1 GHz (2.5.5.9, 1.6 mm 8×7628); Tg 180 °C (DSC).
  4. Nan Ya NP-155F data sheet (rev. 2025-10-27)
    NP-155FR: Dk 4.2–4.4, Df 0.014–0.016 at 1 GHz (2.5.5.9, 0.062" laminate); Tg 155 °C. The library uses the middle of each range.
  5. Isola 370HR data sheet (Rev C/D, 2021)
    Dk 4.04, Df 0.021 at 2 GHz (Bereskin stripline); Tg 180 °C.
  6. Isola FR408HR data sheet (Rev E, 2021)
    Dk 3.65, Df 0.0095 at 10 GHz (Bereskin); Tg 190 °C.
  7. Isola I-Speed data sheet (Rev F, 2021)
    Dk 3.63, Df 0.0071 at 10 GHz (Bereskin); Tg 180 °C.
  8. Isola Tachyon 100G data sheet (Rev H)
    Dk 3.02 (2.5.5.5), Df 0.0021 (Bereskin) at 10 GHz; Tg 215 °C.
  9. TUC TU-872 SLK data sheet DS1801013A
    Dk 3.8, Df 0.009 at 10 GHz, resin content 50 %; Tg 200 °C (DSC).
  10. Panasonic MEGTRON 4 R-5725 data sheet (2020)
    3313 core, resin 57 %: Dk 3.80, Df 0.007 at 10 GHz (2.5.5.5); Tg 176 °C.
  11. Panasonic MEGTRON 6 R-5775 data sheet (2021)
    Resin 54 % cores (3313/2116): Dk 3.61, Df 0.004 at 10 GHz (2.5.5.5); Tg 185 °C.
  12. Panasonic MEGTRON 6 R-5775(N) data sheet (2022)
    Low-Dk glass, 0.75 mm: Dk 3.34, Df 0.0037 at 13 GHz (BCDR); Tg 185 °C.
  13. Panasonic MEGTRON 7 R-5785(N) data sheet (2024)
    Low-Dk glass, 0.75 mm: Dk 3.31, Df 0.0023 at 14 GHz (BCDR); Tg 200 °C.
  14. Rogers RO4000 series data sheet (RO4003C, RO4350B), 2022
    Design Dk 3.66 (RO4350B) / 3.55 (RO4003C) for 8–40 GHz; Df 0.0037 / 0.0027 at 10 GHz.
  15. Rogers RO3000 series data sheet, 2024
    RO3003: design Dk 3.00, Df 0.0010 at 10 GHz.
  16. Rogers RT/duroid 5870/5880 data sheet, 2022
    RT/duroid 5880: Dk 2.20, Df 0.0009 at 10 GHz.
  17. Taiyo America PSR-4000 BN DI series TDS (Feb 2024)
    Solder mask: Dk 3.9, Df 0.027 at 1 GHz.
  18. Taiyo America PSR-4000 HFX DI TDS (Jun 2020)
    Solder mask: Dk 3.5, Df 0.019 at 1 GHz.
  19. Rogers “Copper Foils for High Frequency Circuit Materials” (Pub. 92-243, 2021)
    Measured RMS roughness Sq of rolled, ED, RTF and LoPro foils.
  20. Furukawa Electric copper foil product pages (GTS, FV-WS, FZ-WS)
    Rz of standard (GTS-MP), HVLP (FV-WS) and HVLP2 (FZ-WS) foils.
  21. Circuit Foil HFZ-B data sheet (2016)
    RTF foil, treated side Rq ≤ 1.1 µm.
  22. B. Simonovich, “Cannonball-Huray Model Demystified,” white paper, 2019
    Rz ≈ 2√3·Rq; Huray sphere radius r ≈ 0.06·Rz with 14 spheres on a 36r² tile (surface ratio 4.89).
  23. DuPont Pyralux AP data sheet EI-10124
    AP9121: Dk 3.2, Df 0.003 at 10 GHz, ASTM D2520.
  24. DuPont Pyralux HP adhesive data sheet EI-10208
    HP250000: Dk 2.8, Df 0.0035 at 10 GHz, ASTM D2520.
  25. DuPont Pyralux HP coverlay data sheet EI-10209
    HP252500 composite coverlay: Dk 3.0, Df 0.0045 at 10 GHz, ASTM D2520. Use for the complete film/adhesive composite, not each constituent.

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