Differential RF Circuits and Mixed-Mode S-Parameters

Differential vs Single-Ended RF

A differential (balanced) circuit uses two conductors carrying equal-amplitude, opposite-phase signals (V+, V−). Common-mode noise (e.g., power supply ripple, digital switching) appears equally on both conductors and cancels at the differential input, giving excellent noise rejection (CMRR = 20–40 dB typically).

Even and Odd Mode Analysis

  Even mode (common mode): both conductors driven in phase (V+ = V−)
  Odd mode (differential mode): conductors driven out of phase (V+ = −V−)

  Even-mode impedance Z_even: effective Z₀ seen by each conductor in even excitation
  Odd-mode impedance Z_odd:  effective Z₀ seen in differential excitation

  Coupling coefficient C = (Z_even − Z_odd)/(Z_even + Z_odd)

  For a differential pair: Z_diff = 2 × Z_odd (differential port impedance)
  Standard: Z_diff = 100 Ω (= 2 × 50 Ω single-ended)

Mixed-Mode S-Parameters

  For a differential 4-port, define mixed-mode parameters:
  Sdd: differential-to-differential (wanted signal path)
  Scc: common-mode-to-common-mode (noise rejection path)
  Sdc: differential-to-common (mode conversion)
  Scd: common-to-differential (mode conversion)

  CMRR = Sdd21 / Scc21  [ratio, dB: higher = better noise rejection]
  Mode conversion (Sdc): indicates imperfect balance → signal degradation

Balun for Differential-to-Single-Ended Conversion

A balun connects a single-ended (50 Ω coaxial) source to a differential device (100 Ω dipole, balanced mixer). Performance is characterized by amplitude balance (<0.5 dB), phase balance (<5° from 180°), and CMRR (>20 dB).

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