Stepped Impedance Filter
Overview
Lowpass filter topology using alternating high and low impedance transmission line sections to emulate series inductors and shunt capacitors. Compact implementation suitable for microstrip realization.
Principle
Series inductors are replaced by high-impedance (narrow) TL sections, and shunt capacitors are replaced by low-impedance (wide) TL sections. The electrical lengths are chosen such that the TL sections approximate lumped elements at the design frequency.
Design Equations
Impedance Assignment
For a CLC topology (shunt-first):
Shunt capacitor → Low-impedance line
Series inductor → High-impedance line
For an LCL topology (series-first):
Series inductor → High-impedance line
Shunt capacitor → Low-impedance line
Line Length Calculation
For low-impedance sections (capacitor replacement):
l = (gₖ × Z_{low}) / (β × Z₀)
For high-impedance sections (inductor replacement):
l = (gₖ × Z₀) / (β × Z_{high})
Where:
Parameter |
Description |
|---|---|
gₖ |
normalized lowpass prototype coefficient |
β = 2πfc / c |
propagation constant at cutoff frequency |
Z₀ |
System impedance |
c |
speed of light |
Input Parameters
Parameter |
Range |
Default |
Description |
|---|---|---|---|
Minimum Z |
1 – 40 Ω |
10 Ω |
Low-impedance line (Z_{low}) |
Maximum Z |
50 – 400 Ω |
200 Ω |
High-impedance line (Z_{high}) |
Cutoff freq (fc) |
— |
1 GHz |
Lowpass cutoff |
Order (N) |
2 – 10 |
3 |
Number of sections |
References
Pozar, D. M. (2012). Microwave Engineering (4th ed.), Section 8.5, pp. 424–426. Wiley.