For capacitor selection, I will follow the outline of this paper https://www.avx.com/docs/techinfo/RFMicrowaveThinFilm/energytf.pdf
For capacitors, we have a number of limitations. One is the maximum voltage which needs to be at least 1,000 volts. The other is maximum energy stored. We can calculate the maximum energy stored as (using the data sheet specified maximum DC voltage for the largest value capacitor):
\begin{equation}E=\frac {1}{2}CV ^{2}=\frac {1}{2}(3411 \times 10 ^{-12})(1000 ^{2})=1.7 \times 10 ^{-3}\end{equation}
The voltage across the capacitor is a modulated sinusoidal function. For simplicity, I will just look at the carrier. In each half of the cycle, it stores energy in the capacitor and then removes it. So, we can calculate the energy stored in the capacitor as:
\begin{equation}E=\int _{0} ^{\pi}v(t)i(t)dt\end{equation}
And we have:
\begin{equation}v(t)=V\sin(\omega t)\end{equation}
\begin{equation}i(t)=C \frac{dv}{dt}=\omega CV \cos(\omega t)\end{equation}
\begin{equation}E=\int _{0} ^{\pi}\omega CV ^{2}\sin(\omega t)\cos(\omega t)dt\end{equation}
With change of variables:
\begin{equation}z=\omega t\ \ \ dz=\omega dt\ \ \ dt=\frac {dz}{\omega}\end{equation}
\begin{equation}E=\frac {\omega CV ^{2} }{\omega} \int _{0} ^{\pi \omega} \sin(z)\cos(z)dz=CV ^{2}\left [ \frac {\sin ^{2}(z)}{2} \right ] _{0} ^{\pi \omega}=\frac {CV ^{2}\sin ^{2}(\pi \omega)}{2}\end{equation}
Maximum power stored will be with the value of the sin function set at its maximum of 1 or:
\begin{equation}E=\frac {1}{2}CV ^{2}\end{equation}
So, the energy criteria becomes the same as voltage criteria, at least in this case.
Finally, I need to concern myself with heating effects. The maximum rating of reasonably priced capacitors is 125 degrees C. So, I will design for 100 degrees C. Assuming that the internal temperature of the housing will be around 40 degrees C, the temperature rise that can be permitted is 60 degrees C. Many high quality surface mount RF type capacitors come in 1111 packages. The thermal resistance of this package is 67.7 degrees per watt (see the above mentioned paper) so the power dissipation is limited to 0.88 watts. Since the maximum RMS current through the capacitors is 6.8 amps, the maximum capacitor ESR has to be 19 milli Ohms or less.
Peak Capacitor Current (A)
| Cap Voltage (V) | 3,000 pF | 1,410 pF | 682 pF | 340 pF | 173 pF | 86 pF | 43 pF | 22 pF | 12 pF | |
|---|---|---|---|---|---|---|---|---|---|---|
| 160m L | 427 | 9.27 | 6.38 | 3.30 | 1.64 | 0.84 | 0.42 | 0.21 | 0.11 | 0.06 |
| 160m H | 442 | 9.49 | 6.85 | 3.75 | 1.89 | 0.96 | 0.48 | 0.24 | 0.12 | 0.07 |
| 80m L | 442 | - | 9.02 | 6.10 | 3.29 | 1.68 | 0.84 | 0.42 | 0.21 | 0.12 |
| 80m H | 442 | - | 9.36 | 6.72 | 3.74 | 1.92 | 0.95 | 0.48 | 0.24 | 0.13 |
| 40m L | 441 | - | - | 8.98 | 6.08 | 3.35 | 1.67 | 0.83 | 0.43 | 0.23 |
| 40m H | 441 | - | - | 9.10 | 6.27 | 3.48 | 1.74 | 0.87 | 0.45 | 0.24 |
| 20m L | 441 | - | - | 8.89 | 8.96 | 6.16 | 3.33 | 1.67 | 0.85 | 0.47 |
| 20m H | 441 | - | - | - | 9.00 | 6.27 | 3.41 | 1.71 | 0.88 | 0.48 |
| 17m L | 441 | - | - | - | 9.47 | 7.32 | 4.23 | 2.15 | 1.10 | 0.60 |
| 17m H | 441 | - | - | - | 9.53 | 7.36 | 4.26 | 2.17 | 1.11 | 0.60 |
| 15m L | 441 | - | - | - | 9.71 | 7.95 | 4.84 | 2.50 | 1.28 | 0.70 |
| 15m H | 441 | - | - | - | 9.76 | 8.07 | 4.94 | 2.56 | 1.31 | 0.71 |
| 12m L | 441 | - | - | - | 9.53 | 8.62 | 5.59 | 2.96 | 1.52 | 0.83 |
| 12m H | 441 | - | - | - | 9.57 | 8.65 | 5.62 | 2.98 | 1.52 | 0.83 |
| 10m L | 442 | - | - | - | 8.86 | 9.03 | 6.12 | 3.33 | 1.71 | 0.93 |
| 10m H | 441 | - | - | - | - | 9.10 | 6.39 | 3.52 | 1.81 | 0.99 |
| 6m L | 441 | - | - | - | - | 9.55 | 8.58 | 5.61 | 3.05 | 1.65 |
| 6m H | 439 | - | - | - | - | 9.10 | 8.81 | 5.97 | 3.28 | 1.79 |
| Max | 442 | - | 9.36 | 9.1 | 9.76 | 9.1 | 6.39 | 3.52 | 1.81 | 0.99 |
Searching through the Mouser catalog for bargain prices, most standard line of capacitors did not meet the requirements. By accident, I stumbled across the Vishay HiFreq series of capacitors and after I more carefully checked, these were the same capacitors that Jeff, K6JCA had used. Price and availability were also reasonable. The only parts that I found on Mouser meeting 1,000 or 1,500 volts DC specification were values up to 160 pF (DigiKey had none). These capacitors all come in 1111 surface mount package. Below is the ESR data for this family and package. ESR decreases with capacitance and frequency for values starting at 10 pF. But it is not well specified for capacitance values larger than 47 pF and frequencies lower than 100 MHz. ESR for higher value capacitors at lower frequencies will be lower and for lower value capacitors, the current is much lower (above table).
This is what I found based on availability (first number from the table above, second number or numbers are from the list of available parts with some additional data). Per the above table for capacitor currents, as capacitance and frequency decrease, so does the current handling of the capacitor. Fortunately, the current demand on the capacitor also decreases with the same two factors.
- 11 pF: 12 pF (max current at 10 meters, 0.7 Arms, goes down to 85 mArms at 80 meter)
- 21 pF: 22 pF (max current at 10 meters, 1.3 Arms, goes down to 170 mArms at 80 meter)
- 43 pF: 43 pF (2.5 Arms at 10 meters, goes down to 340 mArms at 80 meters)
- 85 pF: 2 x 43 pF = 86 pF (2.3 Arms per capacitor at 10 meter, 340 mArms per capacitor at 80 meter)
- 171 pF: 180 pF (6.4 A rms)
- 341 pF: 180 pF + 150 pF = 330 pF (3.8 Arms to 180 pF & 3.2 Arms to 150 PF)
- 682 pF: 3 x 180 pF + 150 pF = 690 pF (safe with four capacitors sharing 6.5 Arms)
- 1,364 pF: 7 x 180 pF + 150 pF = 1,410 pF (safe with eight capacitors sharing 6.6 Arms)
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