Definition
Group delay τ_g(f) is defined as the negative rate of change of transmission phase φ with respect to angular frequency ω:
τ_g(f) = −dφ/dω = −(1/2π) · dφ/df Units: seconds (ns for most RF components) φ: phase of S21 in radians
An ideal transmission medium has constant (flat) group delay — every frequency component of a signal experiences the same time delay, so a pulse or waveform passes through undistorted. Variation in group delay (group delay ripple) causes different frequency components to arrive at different times, distorting modulated signals.
Typical Group Delay Values
| Device | Typical Group Delay | Group Delay Ripple |
|---|---|---|
| Ideal transmission line (1 m) | ~5 ns/m (air), ~8 ns/m (FR4 microstrip) | 0 (perfectly flat) |
| SAW filter (cellular) | 50–500 ns | ±5–20 ns in passband |
| BAW/FBAR filter | 1–10 ns | ±0.5–2 ns |
| LC bandpass filter (5th order Chebyshev) | 5–50 ns at center | Large at band edges |
| Bessel filter (5th order) | Maximally flat | <5% across −3 dB BW |
| Waveguide (below cutoff) | Very high, diverges at f_c | Highly dispersive |
| SMA cable 1 m (RG58) | ~5 ns | <0.1 ns (very flat) |
Impact on Digital Modulation
In digital modulation schemes like QAM, OFDM (LTE, 5G), and WLAN, group delay ripple causes inter-symbol interference (ISI) and degrades EVM (Error Vector Magnitude). The critical parameter is:
Maximum tolerable group delay variation ≈ 1/(4 · symbol_rate)
LTE 20 MHz channel (15 kHz subcarriers, 66.7 µs symbol):
Acceptable Δτ_g < ~16 µs (much larger than filter delay)
But within a single OFDM symbol: Δτ_g < CP length = 4.7 µs
Practical filter spec: Δτ_g < 2–5 ns across passband
Calculating Group Delay from S21
Given S21 phase φ(f) in degrees: τ_g(f) = −Δφ / (360° · Δf) [in seconds] Example: φ changes from −45° to −50° over 1 MHz: τ_g = −(−50° − (−45°)) / (360° · 1 MHz) = 5° / (360° · 10⁶) = 13.9 ns
Bessel vs Chebyshev Group Delay
Filter type strongly affects group delay profile:
- Butterworth: moderately flat delay, increases at band edges
- Chebyshev: larger group delay ripple especially near cutoff
- Bessel (Thomson): maximally flat group delay at expense of slower roll-off
- Elliptic: worst group delay distortion due to finite transmission zeros
RF View: RF View plots group delay directly from any .s2p file — just select "Group Delay" in the plot type menu. Add markers to measure delay at specific frequencies and use the Delta Marker to quantify ripple.