This article continues on from NanoVNA-H4 – inductor challenge – part 8, this time with an inductor that might be a candidate for a plate RF choke for a HF valve PA.
Above is the prototype DUT, it is 142t of 0.25mm enamelled copper wire close wound on an 18mm PMMA (acrylic) former, it measures 130µH well below first self resonance.
Let’s sweep it with a NanoVNA.
Above is the test fixture, the inductor has 30mm pigtails and they are connected to the Port 1 inner terminal and ‘ground’ at the threads of the Port 2 connector.
The fixture is not perfect, there will be a quite small shift in measured series resonance, more so for the high impedance resonances.
Let’s try e-delay correction.
Above is a plot of just the coil pigtails (well, equivalent wires 30mm long), with e-delay adjusted for uniform s11 phase less than hundredths of a degree over 1-100MHz, and |s11|is hundredths of a dB, this is quite a good fixture for e-delay correction.
Above is the measurement result. We are measuring some quite extreme impedances here, so expect some measurement noise.
The first resonance, a parallel one, is evident at about 13.8MHz. This is a high impedance resonance and not of primary interest in this discussion.
The next resonance is a series one at about 26.9MHz.
There is another parallel resonance at about 29MHz, and there will be more resonances above this sweep range.
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 relatively 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.
Looking at measured conductance from 1-30MHz. Note how G peaks very sharply at 26.9MHz. The inductor (resonator) has a series self resonance at 26.9MHz and G=0.00164S.
Lets assume for this discussion that in a certain 3-30MHz high power valve PA, that Ep=2000V (a kW class PA.) Power dissipated in the choke would be \(P=\frac{E_p^2G}{2}=\frac{2000^2 \cdot 0.00164}{2}=3280 \text{ W}\).
3.3kW 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 26.9MHz.
Let’s do the same calc at 3.6MHz where G=20µS.
Power dissipated in the choke would be \(P=\frac{E_p^2G}{2}=\frac{2000^2 \cdot 0.000020}{2}=40 \text{ W}\).
In practice, such a choke would be wound on a ceramic former, but this prototype is quite sufficient for learning about the challenges of RF choke self resonances.
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 techniques.
On a practical note…
In 1967 I used a choke quite similar to this in my first home made 80/40m AM/CW transmitter, though wound on a salvaged ceramic former.
Above is a measurement of the prototype choke shown above from 2-10MHz. Note that G is around 20µS over that range.
If my 1967 choke behaved similarly, it had an RF voltage swing of about 300Vpk using a 6DQ6A valve, and power dissipated in the choke would have been \(P=\frac{E_p^2G}{2}=\frac{300^2 \cdot 0.000020}{2}=0.9 \text{ W}\), acceptable for a nominal 25W transmitter.