RF Passives › Distributed Filters

Coupled-Line Bandpass Filter

Design parallel coupled-line bandpass filters for microstrip PCB. Enter substrate, centre frequency, bandwidth and order — get even/odd mode impedances (Zoe/Zoo), trace widths, gaps and physical lengths. Direct to layout.

// PCB Substrate Parameters
// Filter Specifications
MHz
%
Ω
J-inverter coupling values:
J0,1/Y0 = √(π·FBW / (2g1))
Jk,k+1/Y0 = π·FBW / (2√(gkgk+1))  (middle)
Jn,n+1/Y0 = √(π·FBW / (2gngn+1))

Even/odd impedances:
Zoe = Z0(1 + J/Y0 + (J/Y0)²)
Zoo = Z0(1 − J/Y0 + (J/Y0)²)

Physical length: each resonator is λ/4 at f0
// Filter Layout View (top view)
Top view — parallel coupled λ/4 resonators. All resonators same length, gaps vary.
// Frequency Response
// PCB Layout Rules
① Gaps are tighter than widths. The first and last sections (input/output coupling) typically have the tightest gaps. The minimum manufacturable gap on standard PCB is 0.1–0.15 mm (4 mil). If any gap is below this, reduce FBW or increase f0.

② All resonators same physical length. Each resonator is λ/4 at f0 on the substrate. Keep lengths identical — only the gaps and widths vary per section.

③ Even/odd mode dispersion. The even and odd mode effective permittivities differ on microstrip (unlike stripline). This causes the electrical lengths to differ slightly, degrading the response. Rogers substrates with lower εr have less dispersion.

④ Open ends are not exactly at the edge. The open-circuit end of each resonator has a small end-effect (fringing capacitance). Shorten each resonator by Δl ≈ 0.412h·(εeff+0.3)/(εeff−0.258)·(W/h+0.264)/(W/h+0.8) to compensate.

⑤ Box shielding. Couple the filter in a metal enclosure (cavity or lid) to prevent radiation loss and suppress surface waves. Ground via fences on each side.

Coupled-Line Bandpass Filter — Design Guide

The parallel coupled-line bandpass filter is one of the most widely used microstrip filter topologies in RF PCB design. It consists of n+1 sections of quarter-wave coupled transmission lines, where adjacent lines are brought close together to achieve electromagnetic coupling. The coupling coefficient at each section is controlled by the gap between the lines.

Even and Odd Mode Impedances

When two transmission lines are closely coupled, the system supports two fundamental modes: the even mode (currents flow in the same direction) and the odd mode (currents flow in opposite directions). Each mode sees a different characteristic impedance — Zoe (even) and Zoo (odd). The coupling coefficient J/Y0 determines how far apart these two impedances are. Tight coupling (small gap) gives a wide bandwidth; loose coupling (large gap) gives a narrow bandwidth.

Fractional Bandwidth and Realisation

FBW = BW/f0. Very narrow FBW (<1%) is difficult to realise because the required gaps become extremely small — below PCB manufacturing limits. Very wide FBW (>20%) degrades the approximation because the J-inverter model assumes narrow-band behaviour. Practical FBW for PCB realisation is 3–15%. Below 3%, consider cavity or ceramic resonator filters instead.

Insertion Loss

The minimum insertion loss of a coupled-line BPF depends on the substrate loss tangent, conductor loss and resonator Q. On FR4 at 2.4 GHz, a 3-section filter with 5% FBW typically has 2–4 dB insertion loss. On Rogers 4350B, the same filter achieves 0.5–1.5 dB. For low-loss applications, use Rogers or PTFE substrates and minimise the order (n≤3 or 4).