Why the Y21 Method Does NOT “Lose” 6 dB — A Model-Based Explanation

A common question in choke-measurement discussions is why the Y₂₁ method often shows higher common-mode attenuation than a simple S₂₁ insertion-loss test. Many assume 6 dB is being “added.” It isn’t — the difference comes from using different circuit models.

Circuit Models → Different dB Values

Real coax common-mode loop (the physical model)

Real common-mode currents flow in a single series loop:

CM source → R_CM → Z_CM → return

I0 = Vs / RCM
I  = Vs / (RCM + ZCM)

Att_loop = 20·log10(1 + ZCM / RCM)

Symmetrical 50-Ω two-port (the VNA insertion-loss model)

50 Ω → Z_CM → 50 Ω

S21 = 2Z0 / (2Z0 + ZCM)

Att_2port = 20·log10(1 + ZCM / (2Z0))

The factor of 2 appears because the VNA model uses two series impedances (source + load), whereas the real CM loop has only one.

Where the “6 dB” comes from

If Z_CM ≫ R_CM:

20·log10(Z/R) − 20·log10(Z/(2R)) = 20·log10(2) ≈ 6 dB

The “6 dB” is not an error — it is simply the result of using different circuit models.

What the Y₂₁ Method Actually Measures

The Y₂₁ method does not interpret S₂₁(dB) as loss. It reconstructs the DUT as a π-network using the full S-parameter set:

Y = [ Y1+Y3   −Y3
      −Y3     Y2+Y3 ]

Y21 = −Y3  ⇒  ZCM = −1 / Y21

The 50-Ω reference appears only during S→Y conversion and then cancels out. Y₂₁ therefore yields the true series common-mode impedance of the choke.

Why Y₂₁ Does NOT “Have” the 6 dB

Example:

• Z_CM = 5000 Ω
• Z₀ = 50 Ω

Two-port S₂₁ insertion test

S21 = 100 / 5100 ≈ 0.0196
Att_2port ≈ 34.2 dB

Y₂₁ extraction

ZCM = −1 / Y21 = 5000 Ω

No 6 dB added — this is the real series impedance of the choke.

Insert Z_CM into the real coax loop

With R_CM = 50 Ω:

Att_loop = 20·log10(1 + 5000/50)
         = 20·log10(101)
         ≈ 40.1 dB

Here is the ≈6 dB difference — but it appears because the model changed:

• Real CM loop → one R_CM → ~40 dB
• 50 Ω two-port → two R_CM → ~34 dB

Y₂₁ itself introduces no 6 dB offset. The difference is entirely model-based.

The Real Source of Confusion

• A VNA two-port assumes 50 Ω → DUT → 50 Ω.
• A real CM current path is a single loop with only one R_CM.
• Y₂₁ bypasses the two-port assumption and retrieves Z_CM directly.

Therefore:

• Y₂₁ gives Z_CM in ohms
• The CM loop formula gives real-world CM current reduction
• The two-port formula gives lab insertion loss

The ≈6 dB difference is normal and only appears when switching between the two models.

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