NanoVNA-H4 – a ferrite cored test inductor impedance measurement – s11 reflection vs s21 series vs s21 pi

This article documents estimation of common mode choke impedance by three different measurement techniques.

The test uses a small test inductor, 6t on a BN43-202 binocular core and a small test board, everything designed to minimum parasitics. This inductor has quite similar common mode impedance to good antenna common mode chokes.

Above is the SDR-KITS VNWA testboard.

The nanoVNA-H4 v4.3 was calibrated using the test board and its associated OSL components. The test board is used without any additional attenuators, it is directly connected to the nanoVNA-H using 300mm RG400 fly leads.

Above, the test inductor mounted in the s11 shunt measurement position.

Everything is highly symmetric, so measurements of s11 and s21 are copied to s22 and s12 to avoid the measurement noise of actually reversing the test jig and a second calibration set. This would not be appropriate for test fixtures that used floating clip leads.

The VNA does not support 12 term correction, so errors in Zin of Port 2 are uncorrected, and flow into the results for the methods using s21.

Above is a plot of ReturnLoss of Port 2 over the measurement range.

Above is a plot of the components of Zin of Port 2 measured in through configuration of the test board. It is good, but not perfect. Errors flow into methods that depend on s21 through measurements.

s11 shunt reflection

Connecting the DUT in shunt to Port 1 allows measurement of s11, and from that, calculation of impedance. It is straightforward, and most VNAs and PC client software can display the R and X components of impedance directly.

(Agilent 2001) discusses the use of this method on extreme impedances. Note that observed measurement noise is an indicator of whether the method suits the application at hand.

Above is the impedance plot directly from the PC client software (NanoVNA-App). Notwithstanding the advice that you just cannot measure such high impedances with a VNA in reflection mode, much less a $100 jobbie, the curves show very little measurement noise and behave much as would be predicted from knowledge of core, material and winding.

Above is a chart comparing s11 measurement with estimated (calibrated to SRF). Bearing in mind the wide tolerance of ferrite material, the measurement reconciles well with the estimate.

s21 series

Connection of the DUT between ports 1 and 2 allows measurement of higher impedances with relatively lower measurement noise, and might seem to be the preferred method.

An important issue that is not usually given by supporters is that the calculation of Z from s21 depends on an assumed value for Port 2 input impedance, and error in this flows into s21 unless 12 term correction has been used in the measurement. The VNA used for this experiment does not support 12 term correction, and the measured Port 2 input impedance was given earlier..

The transformation of s21 to series impedance is not native to lots of VNAs and PC clients. Calculation of impedance from s21 is not difficult, but it appears from my correspondents that it is commonly messed up.

s21 pi

The s21 pi method calls for connecting the DUT between Port 1 and Port 2 of the VNA, and taking a full s parameter scan of the DUT as in the s21 series method. The s parameters are converted to y parameters and then a pi equivalent circuit.

This method is also known as the Y21 method of measuring common mode choke impedance.

Above, calculation of a pi equivalent circuit from y parameters is trivial.

The assertion by its supporters is that naturally, the shunt elements (y11+y12 and y22+y21) are parasitics due to the test fixture and separating them from the series element -y12 gives the ‘true’ admittance of the common mode choke, or -1/y12 for the choke impedance. (For a reciprocal device such as this, y21=y12, perhaps the reason for the “y21 method” nomenclature.)

It is not obvious to me that allocation of all of the shunt elements to fixture parasitics is valid.

Above is a plot of the components of common mode impedance.

Above is a plot of the admittance of the shunt elements of the pi equivalent network. If those elements were mainly a fixed equivalent capacitance, we would expect the susceptance curves to dominate, to be +ve, and close to a straight line with a slope that implied the equivalent capacitance. They are not so.

Above is a plot of the equivalent shunt capacitance of the shunt elements of the pi equivalent network. They do not look like a constant capacitance, in fact they are a -ve capacitance at all frequencies… so the explanation of parasitic capacitance does not fit the measurements.

Comparison of methods

The above chart compares the three methods. Both s21 methods are almost coincident in this case… but they are different.

A comparison of a different measurement scenario might give quite different results.


There is great benefit in direct reading of R and X, benefit that should not be overlooked.

Uncertainty in Zin of Port 2 rolls up into uncertainty of s21 series impedance measurement.

An attenuator may be used to better control Port 2 Zin, but at the expense of noise performance. In this case, the VSWR of Port 2 is no worse than affordable attenuators.

There was little difference in the s21 based methods here.

The s21 pi method did not reveal a convincing parasitic equivalent capacitance.

Common mode chokes with high impedance are very sensitive to stray capacitance and distributed inductance of connections, and the measurer must consider the design of a test fixture appropriate to the deployment.

In the case of common mode chokes with high impedance one is less interested in the peak impedance values, or even impedance at some specific frequency (since it may be very sensitive to stray capacitance), but rather the range of frequencies where common mode impedance exceeds some criteria.