4. Practicable circuits
The simulated pulse-width-modulated circuit runs with a 200kHz clock driving a four stage divide-by-12 counter. The Philips 74HCT4046 includes a VCO that is guaranteed to run at least 11MHz with 2.5V at the control input.
A nine-stage divider would allow this clock to run at a nominal 6.14MHz. The $1.70 Xilinix XCR3032XL will accommodate a counter of this length, running at this frequency, while drawing about 1mA.
The faster clock could be exploited to set up a low distortion sine-wave source for lightly loaded tank circuits, by using one of Don Lancaster’s “magic sine wave” binary sequences to match the voltage at the driven end of L3 to the repeating half-sine wave at the centre tap.
Granting the relatively coarse clock, this would presumably approximate the sine wave with three progressively wider pulses along the rising edge, an even wider pulse around the peak and three progressively narrower pulses along the falling edge.
This should reduce the AC current through the inductor to quite low levels, and very nearly eliminate the low order harmonic content of the output waveform.
As the load on the tank circuit increases, the inductor has to deliver a half-sine current, in-phase with the voltage at the centre-tap, to provide the current being absorbed by the resistive component of the load.
In the simulated circuit, this can be effected – to some extent - by moving the drive wave-form to the left as the load increases. We’d have 32 discrete steps available if we did it digitally.
In fact, the desired voltage waveform across the inductor is the integral of desired current waveform through the inductor, which is just the cosine wave; the amplitude of this cosine wave has to be adjusted to match the load on the tank circuit. With the 3.5 pulse approximation to the sine wave we’d initially add a minimum width positive pulse at the 0° end of the sequence, and shave one clock pulse width off the last pulse in the sequence (at around 163°), then progressively shift more of the “on” time from the right hand end of the sequence to the left. There wouldn’t be that many pulses to play with, so we’d be unlikely to be able to contrive even 32 discrete steps.
5. Practical circuit – Analog phase-sensitive detection and frequency control
The pulse width modulated circuit needs a phase-sensitive detector to adjust the clock frequency to the resonant frequency of the tank circuit.
In fact what we want to do is to adjust the clock frequency such that the switching transistors M1 and M2 switch at the zero-crossing point where the voltage at free ends of L2 and L1 are respectively zero. This doesn’t necessarily coincide with the resonant frequency of the tank circuit.
The simplest way to do this would be to integrate the 0° to 90° voltage at the centre-tap and compare it with the integral of the 90° to 180° voltage, which could be done with a 4066 switch and a differential amplifier wired up as an integrator. The output of the integrator would control the voltage applied to the voltage-controlled oscillator (VCO) in the 4046 to keep these two integrals as nearly equal as possible
This has the disadvantage that the peak voltage at the centre tap starts peaking earlier than 90° as the load on the tank circuit increases, which would duplicate the effect of the clock running too slowly. We could reduce the effect of this particular distortion by making the phase-sensitive detector into a box-car integrator and integrate only from 0° to 45° and from 135° to 180°.
We could further reduce the effect by adding a second control loop using a second phase-sensitive detector looking specifically at the position of the peak by integrating from 45° to 90° and comparing this sum with the integral from 90° to 135°. This detector would be more sensitive to the position of the peak than the position of the zero-crossing point, and could be used to centre the peak by adjusting the phase of the drive waveform at L3 with respect to the switching points of M1 and M2.
The first control loop – to force switching at the zero-crossing points of the tank circuit – would have to be slow enough to avoid exciting the 5kHz resonance of L3 with the tank circuit. Because the VCO is a phase integrator, the integrator in the phase sensitive detector would have to have the usual phase advance resistor to prevent the loop from oscillating.
The second control loop would have to be even slower, which ought not to be a problem.
6. Practical circuit – digital control.
It is a truism that most control tasks in low-frequency electronics can be handled by a single-chip microprocessor. This appears to be true here.
A single chip microprocessor with a roughly 20MHz clock, a built-in A/D converter and a 16-bit counter-timer or two – the Microchip 18F6620 looks as if it might do the work – should be able to do the whole job.
The disadvantages are that the output period would have to be adjusted in discrete steps of 100nsec, (0.16%) and any attempt to use the “magic sinewave” technique to minimize higher harmonics would require a lot of program to adjust the pulse widths for every change in frequency. The A/D converter would be used to sample the voltage at the centre tap at the 22.5°, 67.5°, 112.5° and 157.5° points and the processor would adjust the drive frequency and the drive phase accordingly.