Unplanned Resonance In CFA Tests

Over the last month I have tried a number of different circuits and, along the way, learned how to make the PSpice software produce more even useful curves. Most significant, however, is my discovery that the D plate, made as a disc with a hole in it, exhibits a strong series resonance that includes a surprisingly large 1.4uH self inductance! If this phenomenon is present in all D plates, it can cause unexpected phase shifts and frequency sensitivities, and prevent otherwise good circuits from meeting all the phase and amplitude requirements for radiating successfully.

My Design Objective

My design objective is to make a broader band CFA that tunes the whole 40-meter band without retuning. (It is usually too wet here to climb up and tune it outside). PSpice shows the required bandwidth, sometimes as much as 7 or 800 kHz, but I have not found this bandwidth in practice.

It seems to me that all the current that flows into the D plate matching tuned circuit should be available for radiation, therefore I set out to increase the capacitance of my D plate to make it the only capacitance in the circuit. But, the 12-inch (30cm) diameter is the widest piece of sheet metal in the shop. So, the capacitance must be increased from the 62pF value at a spacing of .4 inches (1cm) to a much higher value at a reduced spacing, I set the new spacing at 0.1 inch, the thickness of a sheet of lucite that was drilled and assembled to become the dielectric. I expected a 10x increase in capacitance – (.4 inch to .1 inch spacing à 4x; * (lucite dielectric constant approximately 2.5) = 10x).

I measured the capacitance of the new D plate with the MFJ analyzer set to capacitance. At 7 MHz it indicated 2512 pF!!?? Further looking showed a capacitance that varied with frequency all over the place, and was out of the analyzer’s range between 6.09 and 7.04 MHz! At first I thought it was some idiosyncracy of the MFJ analyzer, but when the circuits didn’t behave as I expected, I looked further at the D plate, using the old method of driving it with the signal generator (HP606) and measuring the input voltage with the RF voltmeter (HP400D). It showed a deep null at about 5 MHz with no series inductance!

Null Frequency (MHz)	External Inductance (L2 uH)	Assumed Capacitance (C11 pF)	Computed Inductance (L3 uH)	Diff. from Average Lx (Deviation ^2)
5.62	0	535	1.4990447	0.012630
3.96	1.5	535	1.51923448	0.017575708
3.61	2.5	535	1.13306201	0.064312484
2.85	4.58	535	1.24904617	0.018937864
2.58	5.58	535	1.53291802	0.21391092

Average L3	1.38666108
Sum Deviation ^2	0.13484723

The next step was to find the L and C that formed the evident series tuned circuit. A series of tests with different values of inductors in series with the D plate gave the resonant frequency of each configuration. Figure 1 gives the test circuit and Table 1 gives the results. Five nulls were found by tuning the signal generator and monitoring the circuit input. Each null gives a resonant frequency with an associated assumed D plate capacitance and the combination of the internal and external inductances. Each null can be solved for the sum of the inductances, using the formula:

and then the known L2 subtracted from that value. The average internal inductance value is then found for the 5 test nulls. There is a certain amount of error in each value of frequency, and the sizes of the test inductors. Assuming that they are random, the average is probably better than any single test computation. The exact value of the D plate capacitance is also unknown. To deal with this unknown value, I could have tried to solve the equations for C11, but that was more work than it was worth. An easier way was to find the deviation of each computed internal inductance from the average L3, then square that difference (to remove the sign of the deviation) and add up the results. C11 was then adjusted to minimize the sum of the (deviations)^2. The result (535 pF) is consistent with the expected value, 10x the 62pF old D plate configuration.

The dc resistive losses were found by looking at the null voltage and assuming that it is the result of a voltage divider made up of the dc losses and the cable impedance, 50 ohms. The MFJ impedance measurement of the D plate impedance confirmed this value.

This circuit model for the D plate was then used in the PSpice computation for a promising matching network shown in Figures 2 to 5. I had to decide whether to beat the D plate resonance problem by disassembling everything and cutting current stopping slits in the D plate and ground plane, or joining it by trying everything at 80 meters by tuning the D plate even lower in frequency. I chose the latter, and found the required external L to tune it to a series resonance at 3.5 MHz. At the high C indicated, the computed ratio of E plate voltage to D plate voltage is greater than 1, so I used the current in this external L to couple to a parallel resonant tank circuit to drive the E plate. The “transformer” TX1 in Figures 2-5 is really a tapped air core inductor wound of 2” vinyl pipe. The inductances are shown.

I still do not know enough about which plate radiates in the CFA, so I modeled this circuit 4 ways. I covered all the combinations of space loss from none to loss in both plates. The resulting curves were then compared with the behavior of the circuit to see which model is the best. In these figures, V(5,0) is the voltage from node 5 (the D plate connection) to node 0 (the cable ground). Vp(5,0) is the phase of this voltage relative to the signal generator input. Similarly, V(3,0) is the E plate, and v(2,0) is the input to the network. C2 tunes the E plate, and C6 is the coupling between D and E plate (a guess as to size, but the E plate had this capacitance to the ground plane and D plate and there is considerable interaction between the two).

The circuit was assembled, and the curves compared. The drive voltage and the D plate voltage compared quite closely to the curves of no space loss, Figure 5. I added curves in figures 5b and 5c to show the range of changes possible with the E plate tuning capacitor.

I must conclude that, since there is no visible radiation loss, this system will not radiate! I shall continue to experiment until I find a tuner that shows significant reduction in Q due to radiation losses and an associated wide bandwidth. These characteristics are present in Figure 2.

Originally posted on the AntennaX Online Magazine by Joel C. Hungerford, KB1EGI

Last Updated : 16th May 2024