Calculate substrate integrated waveguide effective width, TE10 cutoff frequency, or required via-row spacing from via diameter, pitch, and dielectric constant.
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SIW Effective Width Formula
The effective width of a substrate integrated waveguide is calculated using the following empirical relationship, which maps the SIW geometry to an equivalent rectangular waveguide width:
- W_eff is the effective width of the equivalent rectangular waveguide
- a is the center-to-center distance between the two rows of metallized vias
- d is the diameter of each metallized via
- s is the center-to-center pitch (spacing) between consecutive vias in the same row
This formula was derived empirically by comparing the dispersion characteristics of SIW structures to those of dielectric-filled rectangular waveguides. The correction term empirically models the effect of the discrete via sidewalls, giving an equivalent width smaller than the physical via-row spacing. It is an approximate model, not a leakage or loss calculation. Once the effective width is known, the TE10 cutoff frequency of the SIW can be found using the standard rectangular waveguide cutoff equation: f_c = c / (2 * W_eff * sqrt(er)), where c is the speed of light in vacuum and er is the relative permittivity of the substrate.
What Is a Substrate Integrated Waveguide (SIW)?
A substrate integrated waveguide is a planar electromagnetic guiding structure that replicates the behavior of a conventional rectangular waveguide entirely within a printed circuit board (PCB) substrate. Two rows of densely spaced metallized via holes connect the top and bottom copper layers of the PCB, forming the sidewalls of the waveguide. The top and bottom copper planes serve as the broad walls. The result is a closed, shielded transmission line that supports the same TE mode family as a classical rectangular waveguide, but in a flat, mass-producible form factor compatible with standard PCB and low-temperature co-fired ceramic (LTCC) fabrication processes.
The concept was first formalized in the early 2000s by Ke Wu and Dominic Deslandes at the Ecole Polytechnique de Montreal, though earlier related work on laminated waveguides dates to the 1990s. Their key insight was that two rows of periodic metallic posts, when spaced closely enough relative to the operating wavelength, behave nearly identically to solid metallic sidewalls. This allowed engineers to bring waveguide-class performance (high Q-factor, low radiation loss, high power handling) into the same multilayer PCB stack-ups already used for microstrip and stripline circuits.
SIW Structure and Operating Principle
The physical structure of an SIW consists of four elements: a dielectric substrate layer, two parallel copper ground planes (top and bottom), and two linear arrays of plated-through vias drilled through the substrate connecting the ground planes. The electromagnetic wave propagates through the dielectric material between the via rows, confined laterally by the vias and vertically by the copper planes.
Conventional SIW is commonly modeled using TE-like modes, with TE10 as the dominant mode. Higher-order modes can also propagate; SIW is not inherently single mode. Select and verify an operating band above the dominant cutoff and below relevant higher-mode and leakage limits for the actual structure.
Because the via posts are discrete rather than continuous, the SIW is slightly wider than the equivalent rectangular waveguide that would produce the same cutoff frequency. The effective width formula above quantifies this difference. The ratio of effective width to physical width depends on the complete geometry; this empirical model does not establish a universal percentage range or validate a finished design.
Critical Design Rules
Common starting guidelines include a via pitch no greater than about twice the via diameter and a via diameter smaller than about one-fifth of the guided wavelength at the operating frequency. These are design heuristics, not guarantees of loss or model accuracy. The calculator checks that pitch and via-row spacing exceed via diameter and reports a pitch-to-diameter advisory; it does not know the operating frequency, substrate thickness or loss. Confirm the operating band above TE10 cutoff and below relevant higher-mode limits with electromagnetic analysis. Cutoff itself is not a usable operating frequency.
For a target TE10 cutoff of 28 GHz on RT/duroid 5880 with er = 2.2, this model gives an effective width of approximately 3.609286 mm. With 0.4 mm diameter vias at 0.8 mm pitch, the required physical via-row spacing is approximately 3.819813 mm. This is a cutoff example, not a design for operation at 28 GHz; guided wavelength and wavelength-based via limits must be checked at an actual operating frequency above cutoff.
Loss Mechanisms in SIW
Three distinct loss mechanisms affect SIW performance, and understanding their relative contributions is important for design optimization at different frequency bands.
Conductor loss arises from the finite conductivity of the copper ground planes and via walls. It follows the same skin-depth scaling as in conventional waveguides: loss increases with the square root of frequency. Conductor loss also depends on substrate thickness, surface roughness, plating and mode. Its contribution relative to other losses cannot be determined from a universal frequency threshold or from this cutoff calculator.
Dielectric loss comes from the substrate material’s loss tangent (tan delta). Unlike air-filled rectangular waveguides that have zero dielectric loss, SIW structures are entirely filled with dielectric, so this term is always present. It scales linearly with frequency and with the loss tangent value. The relative importance of dielectric and conductor loss depends on the specific geometry and material. Use manufacturer loss data at the operating frequency; this calculator estimates neither contribution.
Radiation loss is unique to SIW and results from electromagnetic energy leaking through the gaps between adjacent vias. Closer via spacing can reduce leakage, but the simple geometric guidelines above do not guarantee negligible radiation loss or a numerical attenuation limit. Evaluate leakage for the actual structure and operating band.
Common Substrate Materials for SIW
The choice of substrate material directly impacts the SIW’s cutoff frequency (through the dielectric constant), its loss performance (through the loss tangent), and its manufacturability. The table below preserves representative material values. Dk depends on the test method and product: the Rogers calculator presets use manufacturer design Dk (RO4350B 3.66, RO4003C 3.55 and RT/duroid 5880 2.20), while loss-tangent figures are separate material data. FR-4 and alumina presets are illustrative and should be replaced with applicable substrate data.
| Material | Representative Dk (method varies) | Loss Tangent | Typical Use Case |
|---|---|---|---|
| Rogers RT/Duroid 5880 | 2.20 | 0.0009 | Ka-band and W-band SIW filters, antennas |
| Rogers RT/Duroid 5870 | 2.33 | 0.0012 | Satellite communication SIW arrays |
| Rogers RO4350B | 3.66 | 0.0037 | Cost-sensitive microwave SIW circuits |
| Rogers RO4003C | 3.55 | 0.0027 | General microwave, moderate loss tolerance |
| Isola Astra MT77 | 3.00 | 0.0017 | 5G mmWave front-end modules |
| Taconic TLY-5 | 2.20 | 0.0018 | Alternative to RT/Duroid 5880 |
| FR-4 (standard) | 4.30 | 0.020 | Low-frequency SIW prototyping (below 6 GHz) |
A lower dielectric constant requires a wider effective waveguide for the same cutoff frequency; it does not by itself imply a lower loss tangent. Manufacturer process Dk and design Dk may differ: for example, RO4350B lists process Dk 3.48 at 10 GHz and design Dk 3.66. Use the value appropriate to the design method, frequency and material, and evaluate loss separately.
SIW vs. Microstrip vs. Rectangular Waveguide
SIW technology occupies a unique middle ground between traditional planar transmission lines (microstrip, stripline, coplanar waveguide) and conventional air-filled rectangular waveguide. Understanding where each technology excels helps engineers select the right guiding structure for a given application.
Microstrip is a widely used planar transmission line supporting quasi-TEM propagation. It can operate above 10 GHz; useful bandwidth, radiation, substrate effects, impedance tolerance and insertion loss depend on the material, dimensions and fabrication. A universal frequency ceiling or loss per centimeter does not describe all microstrip designs.
Air-filled rectangular waveguide can offer low insertion loss and high power handling, with performance depending on dimensions, conductor finish, frequency and mode. Conventional implementations are three-dimensional structures and commonly require flanges or transitions for integration with PCB circuits.
SIW offers a PCB-compatible approach using drilling, plating and etching. Achievable Q-factor, manufacturing tolerances, filter response and oscillator performance depend on the complete design; there is no universal Q-factor advantage or ratio over microstrip. Dielectric filling adds a loss mechanism relative to an otherwise comparable air-filled guide, and board-area tradeoffs depend on frequency and layout.
Applications of SIW Technology
SIW has become a foundational building block for microwave and millimeter-wave circuits across several industries. In 5G wireless infrastructure, SIW-based bandpass filters and antenna feed networks operate in both the sub-6 GHz bands (3.5 GHz, 4.9 GHz) and the millimeter-wave bands (28 GHz, 39 GHz). The self-shielding property of SIW is particularly valuable in dense 5G front-end modules where multiple filters and amplifiers share a single PCB and electromagnetic interference between channels must be minimized.
Automotive radar systems at 77 GHz and 79 GHz use SIW slot antenna arrays to achieve the narrow beamwidths needed for long-range object detection while fitting within the constrained packaging behind a vehicle bumper. Antenna gain and radar range depend on the complete array, feed, losses, transmit power, target and receiver; this width-and-cutoff calculator does not predict them.
Satellite communication systems use SIW for Ka-band diplexers and multiplexers that separate transmit (27.5 to 31 GHz) and receive (17.7 to 21.2 GHz) paths on the same antenna panel. The high Q-factor of SIW resonators enables steep roll-off between closely spaced bands without the bulk and cost of machined waveguide diplexers. Channel isolation and insertion loss must be verified for each diplexer design and cannot be inferred from cutoff alone.
In scientific instrumentation, SIW is used to build compact six-port reflectometers and directional couplers for material characterization and dielectric sensing. The enclosed structure provides excellent repeatability and shielding from external interference, making SIW sensors suitable for inline industrial monitoring of moisture content, liquid permittivity, and material thickness at microwave frequencies.
