Definition
The phase of an S-parameter (e.g., S21) is the angle of the complex transmission coefficient — it describes the time delay and phase shift experienced by a signal passing through the device:
S21 = |S21|·e^(jφ) φ = phase in degrees or radians
φ(f) = atan2(Im{S21}, Re{S21})
Phase at a single frequency: tells you the phase shift at that frequency
Phase vs frequency: reveals dispersion (different frequencies delayed differently)
Flat phase: all frequencies shifted equally → no dispersion
Phase Unwrapping
S-parameter phase is typically displayed as the principal value (−180° to +180°). For devices with large electrical length (long cables, SAW filters), the phase wraps repeatedly. Most VNAs and analysis tools (including RF View) perform automatic phase unwrapping to show the continuous phase slope.
Phase Linearity Requirements
| Modulation | Phase Linearity Requirement |
|---|---|
| BPSK/QPSK | Moderate — robust to phase error |
| 16-QAM | <5° group delay ripple across channel BW |
| 64-QAM | <2° group delay ripple |
| 256-QAM (LTE Cat 16) | <1° across 20 MHz channel |
| OFDM (LTE, WiFi) | Group delay ripple must be < CP length/10 |
Relation to Group Delay
Group delay τ_g = −dφ/dω = −(1/360°)·dφ/df [in seconds] Linear phase: φ = −2π·f·τ → flat group delay (τ = constant) Non-linear phase: φ varies non-linearly → varying τ_g → signal distortion
S21 Phase in Practical Measurements
- SAW filter: Phase jumps and large phase excursion near band edges
- Quarter-wave T-line: φ = −90° at design frequency, linear slope
- LC matching network: Phase near 0° in passband (no delay), rapid change at resonance
- LNA: Smooth phase vs frequency, determined by device parasitics
RF View Phase View: Select "Phase" from the parameter display in RF View to plot S21 (or any S-parameter) phase in degrees vs frequency. Automatic phase unwrapping removes artificial 360° jumps.