Earlier articles in this series explored measurement of a test inductor with the NanoVNA concentrating on frequencies below the first self resonance of the inductor.
Above is the test inductor, enamelled wire on an acrylic tube.
The inductor is really a resonator with many resonance modes, this article focusses on the first series resonance.
Let’s hook it up to the NanoVNA for an s11 reflection measurement of G, the real part of Y which itself is the reciprocal of Z.
Above, one wire is plugged into the centre pin of the top / Port 1 connector. The other wire is clamped to the external male threads of the Port 2 connector using a plastic clothes peg. Note that this VNA is modified, it has the two coax outers bonded together.
In fact, we have the underlying inductor connected by 35mm of 570Ω two wire transmission line, so there is a small amount of impedance transformation (which could be approximately corrected in this case by setting port extension to 20ps… but that is not done for this article).
Let’s consider the application of the inductor to be the plate DC supply choke in a high power valve amplifier. In this application. Series resonances at intended operating frequencies are a design problem as they effectively shunt the signal path with a low impedance to ground, and the choke component may have dangerously high dissipation.
A common method of modelling inductors is as an inductance in series with some resistance, and a small parallel equivalent capacitance that accounts for the first high impedance resonance. That equivalent circuit will not reveal the series resonances of the inductor (resonator).
The RF voltage impressed upon the choke is approximately the full swing of the plate RF voltage. The reason for focusing on G is that you will recall that \(P=E^2G=\frac{E_p^2G}{2}\), so knowing the expected RF voltage at the plate, we can calculate the power dissipated in the choke at its resonant frequency.
Let’s look at measured conductance from 1-101MHz. Note how G peaks very sharply at 70.75MHz. The inductor (resonator) has a series self resonance at 70.75MHz and G=0.00153S.
Lets assume for this discussion that in a certain 10-100MHz high power valve PA, that Ep=2000V. Power dissipated in the choke would be \(P=\frac{E_p^2G}{2}=\frac{2000^2 \cdot 0.00153}{2}=3060 \text{ W}\).
3kW would destroy this choke in a very short time. Whilst this might be a suitable choke at some frequencies in the declared range, it is certainly not suitable at or near its resonance at 70.75MHz.
Above is a zoomed in view of G. At the marker, power dissipated in the choke would be \(P=\frac{E_p^2G}{2}=\frac{2000^2 \cdot 0.00002}{2}=40 \text{ W}\). This is not a stunning choke for several reasons.
Now this is not an ideal fixture for measuring a plate choke but it does demonstrate the occurrence and problems associated with a series self resonance in the operating frequency range of such a transmitter.
There are techniques for choke design that try to move self resonances outside the desired operating range, or modify the self resonance so that it is not such a problem… but this article is not about that, but demonstrating relevant measurement.