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Substrate Integrated Waveguide (SIW) Calculator RF
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Substrate Integrated Waveguide (SIW) Calculator

Synthesize low-loss planar waveguides on PCB substrates, calculate Cassivi equivalent widths, TE10 mode cutoff frequencies, and verify via pitch radiation leakage rules.

Relative Permittivity ε_r:
Substrate Thickness h (mm):
Loss Tangent tan δ:
Copper Cladding (oz / μm):
Via Spacing Ratio (p / d):
-

SIW Mode & Waveguide Dimensions

Equivalent Width (a_eff) -
TE10 Cutoff Freq (f_c) -
Operating Band Window: -
Guide Wavelength (λ_g): -
Dielectric Loss (α_d): -
Conductor Loss (α_c): -
Total Attenuation (α_total): -
Microstrip Taper Length (L_taper): -

Via Array Radiation Leakage Rules

Rule 1 (p < 2·d): -
Rule 2 (d < 0.2·λ_g): -
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Substrate Integrated Waveguide (SIW) Fundamentals

A Substrate Integrated Waveguide (SIW) synthesizes a classic rectangular metallic waveguide within a planar printed circuit board (PCB) substrate. The top and bottom copper cladding act as the broad conductive walls, while two parallel rows of metallic plated through-hole (PTH) vias form the narrow side walls. SIW bridges the gap between bulky, expensive rectangular metal waveguides and planar microstrip circuits, providing high Q-factors, high power handling, and zero radiation leakage at millimeter-wave frequencies (24 GHz to 100 GHz).

Cassivi & Wu Equivalent Width Formulation

Due to the cylindrical geometry of the via fences, electromagnetic fringing fields penetrate between adjacent posts. The effective electrical width $a_{eff}$ of an equivalent solid-wall rectangular waveguide is calculated using the established Cassivi empirical formula:

\[ a_{eff} = w - 1.08 \frac{d^2}{p} + 0.1 \frac{d^2}{w} \]

Where:

  • $w$: Transverse spacing between the centers of the two via rows.
  • $d$: Via diameter.
  • $p$: Longitudinal center-to-center pitch between adjacent vias along the propagation axis.
  • Fundamental $TE_{10}$ Mode Cutoff: \[ f_{c10} = \frac{c}{2 \cdot a_{eff} \cdot \sqrt{\varepsilon_r}} \]

Design Rules to Eliminate Radiation Leakage

To ensure that the periodic via fences behave as a continuous metallic wall without radiative leakage, two strict geometric criteria must be satisfied:

  1. $p \le 2 \cdot d$ (or $p/d < 2.0$): Keeps the gap between adjacent vias small enough to prevent electromagnetic wave leakage into the substrate.
  2. $d < 0.2 \cdot \lambda_g$ (or $d < \lambda_0 / (5 \sqrt{\varepsilon_r})$): Ensures individual vias do not act as parasitic radiating dipole antennas.

Frequently Asked Questions

Why does SIW exhibit lower loss than standard microstrip at millimeter-wave frequencies?

Microstrip lines suffer from open radiation losses, surface wave excitation, and high conductor current concentration along the strip edges. SIW completely shields the fields between copper planes and via fences, eliminating radiation loss and spreading current across broad copper walls, achieving 3x to 5x higher unloaded Q.

What is the recommended operating frequency range for an SIW channel?

Like conventional rectangular waveguides, the recommended single-mode operating band is 1.25 · f_c ≤ f_0 ≤ 1.90 · f_c. Operating below 1.25 f_c introduces excessive dispersion and guide attenuation; operating above 2.0 f_c excites higher-order modes (TE20).

How is a 50 Ω microstrip line transitioned into an SIW?

A linear tapered microstrip transition is used. The 50 Ω microstrip line widens gradually over a length L_taper ≈ λ_g / 4 to match the wave impedance of the SIW mode (Z_SIW ≈ Z_TE10), providing broadband return loss better than 20 dB.