Calculator Inputs
The synthesis model assumes a practical parallel-coupled band-pass filter. For production hardware, always verify layout with EM simulation and manufacturing rules.
Example Data Table
| Example Parameter | Sample Value | Notes |
|---|---|---|
| Filter Family | Chebyshev | Useful when a sharper roll-off is preferred. |
| Order | 4 | Higher order increases selectivity and layout complexity. |
| Center Frequency | 2.45 GHz | Common ISM design target for RF prototypes. |
| Bandwidth | 120 MHz | Gives a moderate fractional bandwidth. |
| Substrate | εr = 4.40, h = 1.60 mm | Representative FR-4 style starting point. |
| Expected Output | Width around 3 mm, resonator length near 18 mm | Final values vary with losses and coupling targets. |
Formula Used
1) Fractional bandwidth
FBW = BW / f0
2) Effective dielectric constant
For microstrip width-to-height ratio u = W / h, the code uses the standard quasi-static effective dielectric estimate. It transitions between narrow and wide trace behavior automatically.
3) Guided wavelength
λg = c / (f0 √εeff)
4) Quarter-wave resonator length
L ≈ λg / 4 − 2ΔL
5) Coupling inverter values
The calculator derives low-pass prototype coefficients gk from the selected family and order, then converts them to inverter terms J/Y0 for a parallel-coupled band-pass implementation.
6) Even and odd mode impedances
Zoe = Z0(1 + J/Y0 + (J/Y0)²)
Zoo = Z0(1 − J/Y0 + (J/Y0)²)
7) Coupling coefficient
k = (Zoe − Zoo) / (Zoe + Zoo)
8) External Q estimate
Qe ≈ g0g1 / FBW and Qe,out ≈ gngn+1 / FBW
These equations are appropriate for early synthesis. Accurate copper roughness, enclosure effects, radiation loss, and exact coupling usually require EM tuning.
How to Use This Calculator
- Choose the filter family and order that match your selectivity target.
- Enter center frequency and required bandwidth for the passband.
- Provide substrate dielectric constant, thickness, and copper thickness.
- Set the reference impedance, loss tangent, conductor loss, and fabrication tolerance.
- Click Generate Design to calculate widths, resonator lengths, coupling targets, and the response plot.
- Review the section table to pick a first-pass width and gap layout.
- Export the design using CSV or PDF when you need documentation.
- Move the layout into an EM tool for final optimization before fabrication.
Frequently Asked Questions
1) What kind of microstrip filter does this tool synthesize?
It targets a practical parallel-coupled microstrip band-pass structure. The results are intended for first-pass dimensions and coupling estimates before electromagnetic optimization and layout cleanup.
2) When should I choose Butterworth instead of Chebyshev?
Choose Butterworth for a flatter passband and smoother amplitude shape. Choose Chebyshev when sharper selectivity matters more and you can allow controlled passband ripple.
3) Why does filter order matter so much?
Higher order improves rejection and steepens transition regions, but it increases size, sensitivity, and tuning complexity. More sections also demand tighter control over spacing and fabrication tolerances.
4) Why are the gap values labeled as starting estimates?
Microstrip coupling is strongly affected by conductor thickness, enclosure, discontinuities, and nearby metal. The gap values are meant to start layout work, not replace electromagnetic verification.
5) What does effective dielectric constant tell me?
It reflects how the electric field splits between air and substrate. That value directly changes guided wavelength, resonator length, and the frequency shift you should expect in layout.
6) Can I use FR-4 for microwave filters?
You can prototype with FR-4 at lower microwave frequencies, but loss tangent variation and dielectric tolerance often reduce repeatability. Dedicated RF laminates usually perform better.
7) Why is the estimated loss only approximate?
The loss model is simplified. It does not fully include roughness, radiation, connector launch effects, solder mask changes, finite ground issues, or enclosure coupling.
8) Do I still need an EM simulator after using this calculator?
Yes. This tool speeds up synthesis and layout planning, but final performance should be verified with an EM solver to tune resonator lengths, gap spacing, and real manufacturing effects.