How to Analyze a Low-Pass RF Filter

LPF Analysis Overview

A low-pass filter passes signals from DC to cutoff frequency f_c and attenuates above. Complete LPF characterization requires: cutoff frequency verification, passband insertion loss, stopband rejection at specific frequencies, port return loss, and group delay.

Step 1: Find Cutoff Frequency

  Load LPF .s2p → S21 dB view
  BW Marker set to −3 dB threshold:
  RF View finds f_c (where S21 first drops 3 dB from DC level)
  Example: 1 GHz LPF → BW Marker reads f_c = 1.02 GHz ✓

Step 2: Verify Passband Insertion Loss

  Set marker at low frequency (e.g., 100 MHz for 1 GHz LPF):
  Read S21: −0.4 dB → IL = 0.4 dB ✓ (spec: <0.5 dB in passband)

  Note: LPF IL should be nearly flat from DC to ~0.8 f_c
  If IL increases toward f_c: filter is lossy or resonating

Step 3: Measure Stopband Rejection

  Single markers at key stopband frequencies:
  At 2f_c (2 GHz): S21 = −52 dB → rejection = 52 dB ✓ (5th order Cheby spec: >50 dB)
  At 3f_c (3 GHz): S21 = −68 dB → rejection = 68 dB ✓

  For harmonic filter application at 2.4 GHz:
  Marker at 4.8 GHz (2nd harmonic): S21 should be <−42 dB for FCC compliance

Step 4: Check Port Match

  S11 in passband: target >14 dB return loss (VSWR <1.5)
  S22 in passband: same target
  Switch to VSWR view: both ports should show <1.5:1 in passband

Step 5: Group Delay Characterization

LPF group delay should increase monotonically from near-zero at DC to a maximum near f_c (Butterworth/Chebyshev) or remain nearly flat (Bessel). A sharp group delay spike at f_c indicates a high-Q resonance at the cutoff — characteristic of elliptic filter stopband poles.

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