Group Delay¶

Group delay vs frequency, derived from S21 phase or read directly from an S2VNA capture.

Group delay analysis

What you need¶

A 2-port VNA capture: Touchstone .s2p or S2VNA .csv with S21(s) column

What "group delay" means¶

$$\tau_g = -\frac{d\phi_{21}}{d\omega}$$

The negative slope of S21 phase with respect to angular frequency. For an antenna pair, $\tau_g$ measures the propagation delay through the antennas plus the air path.

Metrics RFlect computes¶

Metric	Definition
`mean_ns`	Average group delay over the band
`variation_ps`	Peak-to-peak ripple in ps
`distance_error_cm`	Effective additional path length from group-delay ripple ($c \cdot \tau_{pp}$)

In the GUI¶

VNA scan type → import a 2-port capture with S21(s). The group-delay plot appears alongside S11/S21.

Programmatic / MCP¶

Full UWB analysis (group delay + SFF + transfer function + impulse response):

analyze_uwb_channel("/path/to/cap.s2p", distance_m=1.0)

Just group delay is derived inside analyze_uwb_channel — there isn't a dedicated MCP tool for group delay alone because it's almost always wanted alongside the other UWB metrics. Use the full analysis and pluck result["group_delay"].

Common gotchas¶

Phase unwrapping — compute_group_delay_from_s21 handles this internally, but the sweep needs enough frequency density (≥ 200 points typical) to unwrap cleanly.
Antenna pair vs DUT — measured group delay includes BOTH antennas plus the air gap. Subtract a reference air-only measurement if you only want the DUT contribution.