SP3L, Stray Capacitance and the Limits of Y21 Choke Measurements
SP3L, Stray Capacitance and the Limits of Y21 Choke Measurements
A grounded winding is a different network. SP3L’s companion technical note shows why the location of a stray capacitance matters as much as its value.
RF.Guru working definition: Common-mode current is the non-cancelling phasor-sum current in a specified set of conductors, evaluated at a defined cross-section and using a declared current-direction convention. In the intended differential transmission-line mode, the outgoing and return currents are equal and opposite, so their phasor sum is zero. When they do not cancel, the remaining current must close through another reference or return path—such as the outside of a coax shield, a mast, equipment chassis, station wiring, nearby structures, earth, the operator, or distributed coupling through the environment.
This broader working definition is especially useful in practical antenna systems. On transmit, non-cancelling current on the outside of the coax can make the feedline and connected structures part of the radiating antenna system unless that path is intentional, clearly defined and properly controlled—for example by providing the required return path and placing a suitable common-mode choke at the correct boundary.
Jacek Pawlowski, SP3L, raises a question that matters directly to my earlier writing about Y21: what happens when the measurement connects parts of a choke to an RF reference that would otherwise be absent? The July–August 2026 QEX listing prompted this comparison. The detailed source examined here is his separate author-published TN-3, revision 1.0, dated 1 July 2026, together with TN-4 and the public QEX calculation workbook. I have not verified the full magazine text against TN-3; claims about circuits and figures below refer specifically to the technical note.
My conclusion is quite specific: Y21 separates terminal shunts in the appropriate network model. It does not generally reconstruct a choke before distributed capacitance to the measurement reference was introduced. Pawlowski’s transformer method changes the physical measurement boundary as well as the impedance presented to the analyzer. That is a different operation from changing S-parameters into Y-parameters.
What Pawlowski actually models
TN-3 reports different impedance peaks from reflection and series-through measurements of a 13-turn RG174 choke on a 2.4-inch mix-43 core. The discrepancy becomes larger when the NanoVNA is connected to external computing equipment. These are Pawlowski’s observations, not RF.Guru measurements. They motivate a model in which small capacitances connect intermediate points along the winding to the VNA reference.
His starting network is a parallel combination of 8,640 Ω, 175 µH and 0.921 pF. He divides its impedance into ten equal series sections. Each section therefore contains 864 Ω in parallel with 17.5 µH and 9.21 pF. Nine additional capacitors connect the intermediate junctions to ground. The 0.2 pF and 0.5 pF cases refer to each of those nine capacitors, not one capacitor across the complete choke. See TN-3, printed pages 3–6, Figures 3–7.
This is a useful explanatory network. It reproduces the direction of the discrepancies without pretending to be a unique electromagnetic model of every winding. Its segment capacitances are an equivalent-circuit construction; they are not nine independently measured inter-turn capacitances. The peak shifts demonstrated by this network should not be promoted into a universal rule for every possible parasitic topology.
Four capacitances that must remain distinct
| Capacitance path | What it changes | What Y21 can separate |
|---|---|---|
| Physical winding self-capacitance | The choke’s own frequency-dependent impedance and resonances | It remains part of the DUT. Removing it would describe a different component. |
| A DUT terminal to the common port reference | A local shunt branch at the calibrated terminal | An ideal endpoint shunt changes a diagonal Y term without changing Y21. |
| Direct fixture coupling from input terminal to output terminal | A transfer path in parallel with the wanted branch | It remains in Y21. Separate characterization is needed to remove a stable fixture contribution. |
| An intermediate winding point to the reference | Current distribution and voltage division inside the measured network | It generally changes Y21 itself. Endpoint-shunt separation cannot undo that change. |
A nearby grounded plate can create several of these paths at once. Calling all of them “stray capacitance” is convenient language, but insufficient circuit analysis. The distinction is also essential when deciding whether a capacitance is an unwanted bench artifact or a real consequence of the final enclosure, mounting hardware or antenna installation.
Why the minus sign is correct, and what the equation means
Take both port voltages relative to the same RF reference, with both port currents defined into the two-port. For a branch admittance Yb between the terminals and local shunts Ya and Yc, the port equations are:
I1 = (Ya + Yb)V1 − YbV2
I2 = −YbV1 + (Yc + Yb)V2
Y21 = −Yb, hence Zb = −1/Y21.
The minus sign follows from the current convention. For equal real reference impedances Z0, the full matrix conversion is Y = (I − S)(I + S)−1/Z0. It needs the genuine complex two-port data, consistent port orientation and declared calibration planes. A single S21 magnitude trace does not supply that matrix.
This is the extraction described in my Y21 measurement guide. The important qualification is physical: the equivalent π branch extracted from an arbitrary reciprocal network need not equal the original ungrounded component. An exact mathematical equivalent does not identify which parasitic currents existed before the test fixture was attached.
A minimal counterexample to universal cancellation
Split an impedance Z into two equal series halves. Add a shunt admittance y from their midpoint to the common reference. Use the chain-matrix convention [V1, I1]T = M[V2, −I2]T. Cascading the two series halves and the intervening shunt gives:
B = Z + yZ²/4, and Y21 = −1/B.
Therefore −1/Y21 = Z + yZ²/4.
The extra term survives a perfect S-to-Y conversion. With Z = 5,000 Ω, a 0.2 pF midpoint capacitance and 30 MHz, it adds approximately +j236 Ω. This independently calculated example uses a resistor to make the algebra transparent. It is not a measured choke. It proves the limitation without invoking calibration error or analyzer noise.
Moving the same shunt to either endpoint changes the result: B then stays equal to Z. That is precisely why the location of Pawlowski’s intermediate-node capacitances matters.
Recalculating the ten-section example
I independently cascaded TN-3’s ten parallel-RLC sections and nine shunts, using ideal components and a 1–60 MHz sweep in 5 kHz steps. The reflection column uses the ladder input impedance with its far end grounded. The voltage-ratio column uses the expression printed beside TN-3 Figure 6. The Y21 column is my extension of the same circuit, not a result attributed to Pawlowski.
| Each internal shunt | Reflection peak | TN-3 voltage-ratio peak | Full Y21 branch peak |
|---|---|---|---|
| 0 pF | 8.640 kΩ at 12.535 MHz | 8.640 kΩ at 12.535 MHz | 8.640 kΩ at 12.535 MHz |
| 0.2 pF | 8.444 kΩ at 9.585 MHz | 9.061 kΩ at 15.850 MHz | 9.055 kΩ at 15.845 MHz |
| 0.5 pF | 8.048 kΩ at 7.275 MHz | 11.340 kΩ at 20.265 MHz | 11.306 kΩ at 20.260 MHz |
These are rounded numerical model results, not precision claims about the original choke. The model reproduces the opposite peak shifts shown in TN-3. More importantly for this comparison, full Y21 extraction also retains a large shift. At 0.5 pF per internal node, its peak is about 31% higher and occurs about 62% higher in frequency than the ungrounded model’s peak.
There is a small but instructive distinction between the note’s terminal-voltage expression and an ideal S21 conversion. For chain parameters A, B, C and D, its 50 Ω voltage-ratio expression gives B + 50(A − 1). Applying 100(1/S21 − 1) to the complete two-port instead gives B + 50(A + D − 2) + 2,500C. They coincide for a pure series element; internal shunts make them different. In the 0.5 pF case, the latter peaks near 11.376 kΩ at 20.265 MHz. This modest difference does not overturn the note’s physical argument, but I would not describe the two calculations as identical.
Direct coupling produces a different error
Now put a fixture capacitance Cf directly across the DUT terminals. The extracted transfer branch becomes:
Zextracted = 1 / [1/ZDUT + jωCf].
For a hypothetical 5 kΩ resistor at 30 MHz, 0.2 pF produces approximately 4,828 − j910 Ω: a magnitude of 4,913 Ω, only 1.73% below the true magnitude, but a phase error of −10.67°. With 0.5 pF, the magnitude drops to 4,523 Ω and the phase reaches −25.23°. A magnitude-only plot can therefore look reassuring while the extracted reactance is already wrong.
These are sensitivity examples, not Pawlowski’s distributed-capacitance model and not product tests. The dimensionless quantity |ωCfZDUT| indicates when this particular bypass becomes significant. Frequency, capacitance, DUT phase, calibration residuals and transmission noise all matter. There is no universal “Y21 fails above this many kilohms” boundary.
An open-fixture transfer measurement can support subtraction of a stable, additive transfer admittance: Y21,corr = Y21,loaded − Y21,open. It cannot remove the DUT’s physical self-capacitance, and it cannot reconstruct a distributed internal network that changes when the DUT is inserted. Geometry and repeatability decide whether the subtraction represents the experiment.
What the voltage transformer changes
Pawlowski’s TN-3 setup uses ten turns on the DUT side and one on the analyzer side, with separated windings. An ideal 10:1 turns ratio would refer a 5 kΩ load to 50 Ω. The actual transformer also has finite magnetizing impedance, leakage, loss and capacitive coupling, so simply multiplying an input reading by 100 is inadequate.
He characterizes the reciprocal transformer through open, short and known-load input measurements, plus a direct measurement of that load. Calling these O, S, L and ZL, respectively, gives:
z11 = O
z22 = ZL(O − L)/(L − S)
p = z12z21 = z22(O − S)
ZDUT = p/(z11 − Zin) − z22.
For a reciprocal transformer p = z12². This is a complex square, not |z12|². With currents defined into both ports and a passive load connected to port 2, V2 = −ZDUTI2; that convention gives the signs above. The analyzer port and load port must retain their identities throughout calibration and measurement.
I checked this inversion independently and compared calculations from the QEX workbook’s source inputs with its saved results: 401 numeric rows in each of its three input sheets agreed to floating-point precision. That checks the implemented algebra. It does not independently certify the original measurements.
The transformer helps because it reduces the direct grounding constraint on the DUT and presents a more favorable impedance to the analyzer. It does not make interwinding capacitance disappear. A model identified with one physical geometry may cease to describe the fixture after moving a winding or introducing a different nearby conductor.
TN-3 Figure 9 shows close agreement between the two methods after transformer correction. I regard that as useful consistency evidence. Both measurements still share the transformer and its identification model, so their agreement alone is not an absolute uncertainty bound. Additional known loads, geometry checks and repeat measurements would make the case stronger. The inversion also becomes sensitive when Zin approaches z11, or when the loaded and shorted identification measurements become too similar.
How I would apply this to a choke measurement
My earlier discussion of Y21’s strengths and limits remains the starting point. Pawlowski’s note adds a particularly useful challenge: deliberately test whether coupling from intermediate winding points to the measurement environment is changing the component you think you are extracting.
- Define the common-mode terminal connections and preserve them between methods. Record the enclosure, lead dress, mounting and reference planes.
- Validate full complex S-to-Y extraction with known networks over the intended impedance range. A stable reciprocal distributed ladder can pass a port-reversal check and still differ from the ungrounded DUT.
- Measure the open fixture for direct transfer leakage, then test sensitivity to nearby metal and cable routing. Treat repeatable geometry dependence as evidence about the network, not something automatically canceled by the matrix conversion.
- Compare direct Y21 with a characterized transformer method where their uncertainty ranges overlap. Keep the transformer geometry fixed, measure the reference load’s complex impedance and use the same frequency grid.
- Characterize the finished assembly in its intended mounting as a separate condition. Do not de-embed a real installation capacitance merely to recover a more attractive free-space curve.
Keep impedance, transfer, installed suppression and power separate
For an ideal isolated series impedance in a 50 Ω two-port, S21 = 100/(100 + Z). That describes the declared fixture. An antenna’s exterior-feedline current sees a different source and return network. In a fixed-source lumped approximation its current ratio is Iafter/Ibefore = Zpath/(Zpath + Zchoke). A real installation may change the source and current distribution too.
This is why my two-port measurement article separates complex component impedance, fixture transfer, installed current mapping and powered qualification. None of the calculations here supplies a new RF.Guru rating or establishes product superiority. Common-mode dissipation, winding voltage, differential current, temperature and operating duration require their own evidence.
The useful lesson I take from SP3L’s note is that an extraction method has a physical boundary. Y21 is valuable within its boundary, and transformer isolation can address a different source of disturbance. The strongest measurement report shows which paths were present, which were removed, and which belong to the finished choke in service.
Sources and editions
- QEX July–August 2026, issue 357, contents: confirms the title, author and article start on page 4; not the full article.
- SP3L TN-3, revision 1.0, 1 July 2026: the full author-published technical note analyzed here, especially printed pages 3–9.
- SP3L TN-4, revision 1.0, 1 June 2026: calculator instructions. Its sheet names and column positions should not be assumed identical to later workbook editions.
- ARRL QEX voltage-transformer calculator, filename version 1v2: independently checked numerical conversion and transformer inversion.
Mini-FAQ
- Does Y21 remove every capacitance to ground? No. It separates ideal shunts at the port terminals, but capacitance from intermediate winding points to the reference can change Y21 itself.
- Does Y21 remove direct input-to-output capacitance? No. That coupling contributes to transfer admittance. Removing it requires a valid, stable fixture characterization; the DUT’s own capacitance must remain.
- Is SP3L’s voltage-transformer method the same as Y21 extraction? No. It changes isolation and impedance level, then uses a characterized transformer model to infer the load. Y21 is a two-port network extraction.
- Is there a universal kilohm limit for choke measurement? No. Frequency, topology, coupling, calibration residuals, dynamic range and the required uncertainty determine the usable range.
- Do these calculations establish a choke power rating? No. They are small-signal circuit calculations. Power qualification requires separate electrical and thermal measurements under declared operating conditions.