Elliptic Filter Overview
Elliptic (Cauer) filters achieve the maximum possible rolloff for a given filter order by using equiripple in BOTH the passband and stopband. Transmission zeros (finite-frequency notches) are placed in the stopband to create extremely steep skirt selectivity.
Elliptic Filter S21 Characteristics
|H(jω)|² = 1 / [1 + ε²·Rn²(ω, ξ)] where Rn = rational Chebyshev function with ξ controlling stopband ripple Passband: equiripple with ripple Rp (design parameter) Stopband: equiripple with minimum rejection As (design parameter) Transition band: STEEPEST of all filter types for same N Shape factor (5th order, 0.5 dB/−60 dB elliptic): BW₋₆₀dB / BW₋₃dB ≈ 1.15 (only 15% wider to get 60 dB!) Compare Butterworth: ≈ 2.0 (100% wider for same rejection)
Elliptic vs Butterworth Comparison (N=5)
| Property | Elliptic (0.5 dB/60 dB) | Butterworth |
|---|---|---|
| Attenuation at 1.2ωc | >60 dB | ~20 dB |
| Attenuation at 1.5ωc | >60 dB | ~48 dB |
| Group delay at ωc | Large spike (very poor) | Moderate |
| Component sensitivity | High (sharp notch tuning) | Low |
| Best for | Duplexer RX filter (tight duplex gap) | General RF |
Where Elliptic Filters Are Used
Duplexers require very high TX-RX isolation with minimal frequency separation (duplex gap). For LTE Band 3 (TX: 1710–1785, RX: 1805–1880, gap = 20 MHz), only an elliptic or near-elliptic SAW/BAW design can achieve >50 dB TX→RX isolation while maintaining <2 dB RX insertion loss.
RF View: Load elliptic filter .s2p and view S21 — the characteristic steep stopband skirt with multiple transmission zeros (notches) is immediately visible. Group Delay shows the signature peaking at band edges. Free on Android.