How do I calculate the effective dielectric constant of a microstrip line versus a stripline?
Microstrip vs Stripline Dielectric
In microstrip, the signal trace sits on top of the dielectric substrate with air (εr=1) above. The electromagnetic field extends both into the substrate and into the air, experiencing a weighted average dielectric constant. This effective dielectric constant determines the propagation velocity and wavelength of signals on the line.
The effective dielectric constant increases slightly with frequency because higher-frequency fields are more tightly confined to the substrate. This frequency dependence causes dispersion: different frequency components of a wideband signal travel at different velocities, distorting the signal pulse shape. For FR4, the dispersion is modest below 10 GHz but becomes significant above 20 GHz.
For stripline, the trace is fully enclosed between two ground planes with dielectric filling the entire space. All of the field propagates in the dielectric, so εeff equals the bulk εr exactly (assuming uniform dielectric). This makes stripline non-dispersive: εeff is constant with frequency. This is an important advantage for wideband designs where phase linearity matters.
FR4 (εr=4.4), 50Ω line (W/h≈2):
εeff ≈ 3.3
vphase = c/√εeff = 1.65×10⁸ m/s
Stripline: εeff = εr = 4.4
vphase = c/√εr = 1.43×10⁸ m/s
Frequently Asked Questions
Why does εeff matter for design?
εeff determines the physical length of quarter-wave transformers, stubs, and resonators. A quarter-wave section at 10 GHz on microstrip (εeff=3.3) is 4.1 mm long. On stripline (εeff=4.4), it is 3.6 mm. Using the wrong εeff causes the structure to resonate at the wrong frequency.
How accurate are the closed-form equations?
The Hammerstad-Jensen equations are accurate to about ±0.2% for εeff and ±1% for Z0 when W/h is between 0.1 and 10 and εr is between 1 and 16. Outside these ranges, or at very high frequencies, full-wave electromagnetic simulation is needed.
Does the solder mask affect εeff?
Yes. Solder mask (εr ≈ 3.5-4.5) applied over the microstrip trace replaces some of the air above the trace with a higher-εr material, increasing εeff by 2-5% and lowering the impedance by 1-3 Ω. For impedance-critical designs, either remove the solder mask over RF traces or include it in the impedance model.