Since I last posted, I've made some considerable revision to the charging and discharging circuit plans based on practical constraints and the ratings of my components. First off, I was unable to find any capacitors in the 1 uF range rated at more than 600 volts, so I settled for a pack of eighteen 0.1 uF 3kV polypropylene caps. In any configuration, a bank comprising all eighteen of these capacitors can safely store a maximum of 8.1 J without risk of breakdown (you can check the math). This is about 20% the energy reported to have been stored in P. Graneau's bank during his experiments. However, Graneau's research shows that cold fog explosions are highly current dependent, so I'm hoping that as long as I can get enough current flowing (i.e. as long as I can get the voltage across my capacitor bank high enough), I can still generate some impressive explosions even with my (relatively) small capacitor bank.
My caps' lower-than-expected voltage rating forced me to downsize some of the components in my charging circuit. Most notably, my 16 kV power supply had to be rebuilt so that its output wouldn't punch big gaping holes through my capacitors. The supply was put together from a 12 VDC wall adapter, a 2000V neon sign inverter, and a five-stage CW multiplier to step up and rectify the inverter's output. I swapped out the 12 volt wall adapter for a 7.5 volt one and chopped three stages off the multiplier to lower the supply's output to around 4.7 kV. The power supply is shown below, along with a couple of the polypropylene caps and a switching relay.
While this should have been suitable for charging any bank made from parallel units of two or more series capacitors, lowering the input voltage made the supply a bit finicky (maybe because inverter was current limited). The supply's output voltage would vary with load resistance; large loads (on the order of a couple megohms)corresponded to normal output voltages (of around 4.7 kV), but smaller loads (down to 500k ohms) would yield lower output voltages (down to around 1 kV). The output would drop to 0 for loads of less than 500k (probably because of the current limiter).
Needless to say, working with such a mercurial supply is undesirable. So, I scrapped it, and ordered a 1.5 kV non-limited inverter (http://www.amazing1.com/hv-dc-power-supplies.htm) to build a new supply from. I'll be able to stick a voltage multiplier on the end of it to step up the output to 3 kV, 6 kV, 9 kV, or whatever is needed. The inverter should be here any day now.
Despite its poor operational characteristics, I was able to use the old power supply to test some other components of the discharging system, namely, my measurement and switching circuits.
Depicted below is a rectifying circuit I threw together to test my measurement system:
On the left, I'm running 120 Vrms @ 60Hz into the transformers, and they're outputting a 60 Vrms sinusoid. On the breadboard, you've got your standard diode bridge rectifier, without voltage regulation. The rectifier produces an 80 VDC signal, with negligible ripple current. I'm using that to charge the shown capacitor (an electrolytic I scrapped from an old HV supply's rectifying circuit). At the far right of the screen, you can see my homemade Rogowski coil (yes, that is a clothespin holding it closed) ready and waiting to capture the discharge current resultant when I flick the switch and short the capacitor's leads to each other.
Wikipedia has a nice article here on the theory behind Rogowski coils. In essence, they're current transformers whose secondary winding produces an voltage proportional to the rate of change of current through the primary winding. My particular coil has a proportionality constant of -1.1785*10^(-8) ohm-seconds. So unfortunately, I wasn't able to get a reading from it when discharging the cap in this configuration; the discharge current was just too small to produce a measurable voltage in the coil.
Switching to the setup shown in the first pic, however, yielded coil outputs that looked something like this:
When I first saw this readout, I grew wary of my coil's accuracy. When looking at the voltage across a discharging a capacitor, one would expect to see a nice RC time constant-esque exponential decay sort of function, not the oscillating wave-packet looking thing shown above. My first thought was that RF noise must be contaminating the signal. Substantial arcing was evident around the relay contacts during discharge; perhaps the coil was picking up the momentary radio noise generated by the sparks, rendering the actual signal indiscernible and accounting for the odd prominence of the sinusoid seen above.
I soon realized that there were several problems with this theory, however. Firstly, the trace shown above was very easy to duplicate, and did not seem to vary heavily with changes in the capacitors' charge time or charging voltage. A transient RF signal should have behaved much more erratically; it seemed unlikely that any such signal would exhibit so much consistency.
Secondly, upon closer inspection of the waveform, it was apparent that the large ≈800 kHz signals were further corrupted by a less obvious, more irregular 20 MHz signal of varying amplitude. This signal would peter out after about 7.5 us, 2.5 us before the end of the discharge event. Due to its higher frequency and lower repeatability, it seemed more likely that this was the radio signal produced by the arcing around the relay. I was then left at a loss for an explanation for the source of my original signal.
After reviewing some literature, I eventually arrived at the conclusion that the signals I was obtaining were actually accurate reflections of the current-flow in my discharge circuit. It turns out that in high voltage, low resistance RC circuits, actual circuit operation tends to deviate significantly from the theoretical. Larger capacitors have a tendency to ring when charged to a high voltage and discharged quickly; when a high-voltage capacitor is discharged through a small resistance, a large current rushes from the more positive plate to the more negative one, which pulls the negative plate below ground and places a negative voltage across the capacitor. Current then rushes back from the more negative plate to the more positive one, which in turn swings the voltage across the cap positive again. The discharge current oscillates back and forth in this manner until the ringing voltage eventually decays to zero and discharge ceases.
The only real way to test the accuracy of this theory was to erect a radio-shield around the relay and see if the Rogowski coil's output was affected. But, before I could do that, I had to devise a way to charge and discharge my capacitors safely.
Ideally, I would switch my charging and discharging circuits a simple SPDT mechanical switch. When the switch was in one state, the charging circuit would be closed and the discharging circuit would be open. When the switch was in the other, the charging circuit would be open and the discharging circuit would be closed (note: this ensures that the charging and discharging circuits can never both be closed simultaneously). Of course, the actual switching mechanism must involve more than just an SPDT switch, as I would want to be able to switch my capacitor bank remotely without having to deal directly with the high-power charging and discharging circuits.
Obviously, no transistor could take on the daunting task of switching a 3 kV signal. So, I resorted to using relays, like the one depicted earlier, to switch the charging and discharging circuits. In the end I had access to three of them, and unfortunately, the three had different default states: the two smaller ones defaulted open, and the bigger one defaulted closed. Neither of the smaller relays could switch a 3 kV signal on their own, so they had to be used together as a single relay with higher inductance and voltage ratings. This made the simple two-state switching circuit (with each state of corresponding to the actuation of one of the two relay groups) impossible, and forced me to employ more creative methods to get the relays to switch when I wanted them to.
Depicted below is one idea I had for such a circuit, employing a simple transistor NOT gate and some small, high-power resistors. The diode across the second inductor is there to protect the transistor from the momentary high voltage produced when the transistor is switched on and the inductor tries to keep a current flowing through it. Also note that the single relay on the left really represents two relays in series.
When the SPDT switch is in its neutral state, the first relay is off, and the second relay is on; both the charging and discharging circuits are open. When the switch is in its low position, the first relay is actuated. Now, both relays are on; the charging circuit is closed, and the discharging circuit is open. When the switch is in it's high position, the transistor is switched on, and current virtually stops flowing through the second relay. Now, the first relay is off, and the second is on; the charging circuit is open, and the discharging circuit is closed.
Another much simpler alternative is shown below.
The symbol immediately downstream of the voltage source is a break-contact switch. In its default position, both relays are on; the charging circuit is closed, and the discharging circuit is open. When the switch is opened, current stops flowing to the relays, and they shut off; now, the charging circuit is open, and the discharging circuit is open.
The video below is a demonstration of the above circuit in action, with a couple of LEDs as replacements for the loads of the charging and discharging circuits.
After additional testing, I found that the circuit also handles HV switching quite well. I should be able to use it when putting together the final discharging circuit.