Driving a series resonant network is a little tricky. Both current and voltage in the network can get quite high. If we start with some of our initial requirements, we can come up with a rough idea of the coil specs.
With a good driver design, most of the power sent to the exciter network will be dissipated in the coil. I estimated last time that I will need about 1 amp of current from a 5 volt supply. This says that the load resistance is about 5 ohms. The Q of a series resonant network is defined as the reactance of the coil at the drive frequency, divided by the source impedance. The higher the Q, the higher the efficiency. However, the Q will drop, when there is another coil nearby, which is also tuned to the drive frequency. I think a Q of 30 is a good place to start. If the source impedance is about 5 ohms, then the inductive reactance should be about 5 x 30 or 150 ohms. Using the formula Z = 6.28 x FL, where Z is 150 ohms, F is the 125,000Hz drive frequency and L is the inductance in henries. Solving for L, we come up with a target inductance of about 200uH. After calculating the number of turns needed for a circuit with a 4.5” radius, I come up with about 20 turns needed in the coil. Again, this is a starting place and I can add more turns or take turns off it I need to.
Exciter Coil Voltage
What kind of voltage will be induced across the coil? If we assume an average current of 1 amp, the peak to peak current will be about 3 amps. With an inductive reactance of 150 ohms, the expected peak to peak voltage across the coil will be about 3 x 150 or 450 volts, with a peak voltage of about 225v. The insulation of the wire used in the coil will therefore have to be rated at something greater than 300 volts. I might be able to get by with some standard magnet wire with good enamel insulation. The series resonant capacitor will also have to have a high voltage rating. If I use a small gage wire, such as 24ga or smaller, the resistance of the wire might be high enough to keep the Q within reasonable limits. This would also make it easier to stuff the wire coil into a pocket I make in a mouse pad.
I calculated that the target exciter coil inductance should be something around 200uH. To resonant the coil at 125KHz, the series capacitor will need to be carefully selected. Using the formula: F = 1/[6.28 x (LC)^-2] and solving for C, we come up with a capacitance of 0.008uF. A 8200pF capacitor should be close enough. The capacitor should be rated at about 500v and should be a low loss type. A high voltage polypropylene, polystyrene or mica should do the trick. I’ll see what I have in my inventory. I may have to order some.
Power Receiver Coil
The back of my cell phone is about 1.5 inches by 3 inches. If we want to collect about one watt of power at say 5 volts, the load impedance would then need to be about 25 ohms. The Q of a parallel resonant network is defined as the parallel load resistance divided by the inductive reactance of the receiver coil at the frequency F. We don’t want the Q to be too high, since we will not be able to easily tune that coil. There could be a mismatch between the exciter frequency and the resonant frequency of the receiver coil network. The mismatch could be something like +-10%, so a Q of 5 might be a good place to start. If the target load resistance is about 25 ohms, then with a Q of 5, the inductive reactance should be about 5 ohms. Inserting 5 ohms into the equation Z = 6.28 x FL and solving for L, we come up with a target inductance of 6uH. With radius of about 1.2” the number of turns for a 6uH coil works out to about 7 turns. This will be a place to start. I can add more turns if I need to. With a 6uH coil, the parallel capacitance will need to be about 0.27uF. Unlike the exciter network, this capacitor can be a low voltage type. A polyester type rated at about 50 volts should work fine.
Exciter Coil Driver Circuit
I’d like to try a simple push-pull driver circuit for my first test circuit. One such circuit is shown below. The weakness of this circuit is that there may be some power lost during each edge of the square wave drive. Current can shot through both FETs briefly, as the circuit transitions between sourcing and sinking current to the load. If I keep the square wave edges fast, the losses may be acceptable. For testing purposes, I can quickly wire up this driver circuit and use a good signal generator for the 125KHz source. That way, I can easily change the frequency to hit the resonant point. The idea is get an exciter circuit working, so I can see how much power I can pump into the exciter coil. Then, I can build up a receiver coil and see how much power I can couple between the coils. After that, I can refine the system for maximum power transfer.