Design and Simulation of a Stepped-Impedance Low Pass Filter using Altair Feko
A stepped-impedance filter is a popular design approach for realizing a low pass filter as it is relatively simple to design and occupies less space in comparison with stub-based filters. These filters are typically used in applications that do not require a sharp cut-off. A stepped-impedance filter consists of an alternating section of very high and very low characteristic impedance microstrip or strip lines. The design stage begins with identifying the equivalent circuit of such short lengths of transmission lines. Typically, the equivalent circuit of these filters have a series of inductors and parallel (shunt) capacitors in a repetitive fashion. The series inductors represent the high-impedance transmission line sections and the shunt capacitors represents the low-impedance transmission line sections. The electrical lengths of these short sections (series inductors and shunt capacitors) are determined by eq (1) and eq (2) respectively.
Where,
For example, a stepped impedance low-pass filter having a maximally flat response and a cutoff frequency of 2.5 GHz is designed with more than 20 dB insertion loss at 4 GHz. The filter impedance is 50 Ω, the highest impedance is 120 Ω, and the lowest is 20 Ω. The substrate chosen for this filter has a thickness of 1.58 mm, dielectric constant of 4.2, and loss tangent of 0.02. Using (1) and (2) and table 8.3 from [1], the electrical lengths along with physical microstrip line widths and lengths are calculated and shown in Table 1.
Table 1: Design Parameters for a 6-section stepped impedance low-pass filter
The final filter schematic with the microstrip structure is shown in Fig 1 and the filter response is shown in Fig 2.
Fig 1. Schematic of the stepped impedance low pass filter.
Fig 2. Low pass filter response for the designed filter.
Reference:
[1] "Microwave Engineering," by David.M.Pozhar.