Why the Y21 Method Does NOT “Lose” 6 dB

A VNA series fixture may show about 34 dB for a 5 kΩ choke, while a calculation for that choke in a 50 Ω common-mode loop gives about 40 dB. Nothing has been added or lost. The two numbers answer different questions. More importantly, the 40 dB result is only an example—not a universal prediction for an antenna installation.

Start with the Quantity Y21 Actually Produces

A full complex two-port S-parameter matrix can be converted to an admittance matrix. For a π-equivalent network with a series branch admittance Y₃ between the ports:

The result is Z in ohms, normally written R + jX. It is not an attenuation figure and therefore cannot contain a 6 dB gain or loss. A dB value appears only when someone chooses a source, load or common-mode path and calculates a ratio.

The VNA reference impedance—normally 50 Ω—is still required in the S-to-Y conversion. It does not literally vanish from the mathematics. What disappears from the extracted DUT model is the mistaken idea that the two 50 Ω matched terminations must remain part of every later installation calculation.

Model 1: A Series Element Between Two 50 Ω VNA Ports

For an ideal series impedance Z_CM between two equal matched VNA ports of reference impedance Z₀:

The factor 2Z₀ is not an error. The measurement model has a 50 Ω source environment and a matched 50 Ω receiving environment. Keysight gives the equivalent series-through conversion as:

This simple conversion is valid when the fixture is well represented by the series-element model. The Y21 π extraction is often preferred when separate shunt admittances at the ports would spoil that approximation.

Model 2: A Reduced Installed Common-Mode Loop

A practical antenna installation may be reduced, at one frequency, to a Thevenin common-mode source V_CM driving an existing path impedance Z_path. That impedance represents the external shield path, antenna coupling, mast, station wiring, ground/environment return and any other elements absorbed into the model.

The magnitude bars are essential. Both impedances can be complex. The simplified expression 20 log₁₀(1 + Z_CM/R) is valid only when the quantities are compatible real positive resistances. Using it blindly for reactive antenna paths can give the wrong answer.

The Famous 5 kΩ Example

Let the extracted choke impedance be a purely resistive 5,000 Ω and let Z₀ = 50 Ω.

In the ideal 50 Ω two-port series fixture

In an assumed 50 Ω installed path

The difference is 5.94 dB in this finite example and tends toward 6.02 dB as |Z_CM| becomes much larger than 50 Ω. That limiting difference follows from comparing denominators of Z₀ and 2Z₀:

Y21 did not create the difference. The analyst first extracted 5 kΩ, then calculated two ratios using two different external circuits.

Why 6 dB Is Not a Universal Correction

The approximate 6 dB relationship requires all of the following:

• the two-port fixture behaves as an ideal series element between equal Z₀ ports;
• the installed pre-choke path is assumed to be Z_path = Z₀;
• the choke impedance dominates both denominators;
• the comparison uses the same voltage/current amplitude convention; and
• complex phase relationships do not invalidate the simple real-resistance approximation.

Change Z_path and the relationship changes. With the same 5 kΩ resistive choke but a 200 Ω resistive path, the installed current reduction is only:

That is about 5.85 dB less than the 34.15 dB two-port insertion-loss figure, not 6 dB more. With reactive Z_path, vector addition can create a peak, a null or a new resonance. A real installation may also have several coupled return paths, so a single-loop equivalent is itself only a local model.

Why Raw S21 and Y21 Are Easy to Confuse

Both quantities originate from a VNA sweep, but they serve different roles:

A chart labelled “Y21 attenuation” has usually performed an additional calculation after extracting Z. That chart must disclose the chosen source and path impedances. Otherwise it is no more universal than a bare S21 dB trace.

The π Model Still Has Limits

In an ideal π representation, local shunts at ports 1 and 2 appear in Y11 and Y22 while the transfer branch appears in Y21. This is why Y21 can outperform the simple series-through equation when terminal-to-reference capacitance matters.

But −1/Y21 is not automatically the choke alone. Direct port-to-port capacitance, electric or magnetic fixture coupling, radiation, cable common mode, calibration error and distributed behaviour also contribute to transfer admittance. At high extracted impedance, even very small leakage paths matter.

Useful checks include fixture open/short/through measurements, reversing the DUT, changing fixture spacing, choking the test leads, measuring known standards and comparing S21 and Y21 in the region where both should agree.

A Better Way to Report the Result

Publish the measurement and the application model separately:

1. Component result: Z_CM(f) = R(f) + jX(f), with fixture, calibration planes and extraction method.
2. Two-port result: measured S21 or insertion loss in the stated Z₀ environment.
3. Application estimate: calculated current reduction for an explicitly stated complex Z_path.
4. Installation evidence: current-probe measurements before and after fitting the choke, taken at several feedline positions.

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