Stepped-Impedance Microstrip LPF
A stepped-impedance LPF replaces lumped L and C elements with short sections of high-impedance (narrow, inductor-like) and low-impedance (wide, capacitor-like) microstrip. Easier to fabricate than lumped filters above ~1 GHz; the tradeoff is a less sharp roll-off and spurious passbands at higher frequencies.
Equations & Parameters ▸
High-Z (series L): \(\beta\ell = g_k \dfrac{Z_0}{Z_H}\)
Low-Z (shunt C): \(\beta\ell = g_k \dfrac{Z_L}{Z_0}\)
\(\ell = \dfrac{\beta\ell}{\beta_{\rm sub}}\quad \beta_{\rm sub}=\dfrac{2\pi f}{c}\sqrt{\varepsilon_r}\)
Low-Z (shunt C): \(\beta\ell = g_k \dfrac{Z_L}{Z_0}\)
\(\ell = \dfrac{\beta\ell}{\beta_{\rm sub}}\quad \beta_{\rm sub}=\dfrac{2\pi f}{c}\sqrt{\varepsilon_r}\)
| ZH | High-impedance line (narrow trace, acts as series inductor). Recommended: ZH = 100–150 Ω |
| ZL | Low-impedance line (wide trace, acts as shunt capacitor). Recommended: ZL = 10–30 Ω |
| gk | Prototype lowpass element values (Butterworth or Chebyshev) |
| β·ℓ | Electrical length of each section (radians at fc) |
Accuracy improves when ZH/ZL is large. Sections should remain electrically short (β·ℓ < 45°) for good approximation to lumped behavior.
Filter Specification
Ω
Ω
Substrate (for physical dimensions)
mm
Results
Diagram