 Impedance matching for this circuit
is not what would expect. If you attempt to match impedance with the
measured values if capacitance, and inductance as shown in the schematic, the
circuit will never reach the resonant state with the peak voltages found, or current
values shown in the diagram above. The impedance shown is the result of
a LC phase variation that as a result of resonance, and impedance matching
wound up 180 degrees out of phase. When the tank circuit was cold it acted
as a short, or a near short circuit as a load on the oscillator. When the
impedance of the oscillator is lower than the tank circuits starting impedance the
phast shift produced a high impedance load in the parallel tank circuit. The
starting impedance equivalent reqired to produce the output shown involves only
the values of inductive reactance, and capactive reactance as if they were only DC
resistance values in parallel. For example, I could have 1 kilo-ohm of AC
resistance as a result of a starting impedance of 5 ohms, and until the circuit sees
5 or 10 cycles at the right frequency, and starting impedance it will not approach
resonance at the peak voltage, and current values shown here. At about 100
cycles resonance will be achieved. At 100 KHz, that's only a millisecond
but, if the oscillator doesn't have an output impedance that is less than 5 ohms
resonance will not have a peak voltage, or current that is equal the input voltage,
or the current traped in the tank circuit as shown in the diagram.
In order to properly tune the circuit, a
signal must be injected at a matched impedance value stage per stage at each
stages resonant frequency, even if it's a chaotic resonant circuit. Starting at
the final transformer output stage you find the resulting current, and then divide the
volts by the amperes to find the resistive equivalant of that tank circuit when it's
operating with the planned resitive load on the output. A load resistor is
used for the secondary that is equal to the value of the acutal load for the sake of
tuning the primary circuit. The next step is using the value of impedance on
the primary that results from resonance for the next stage, and this includes using
another load resistor that is equal to the value of resistance that is found based
upon the measured values, and impedance equivalence calculation. At this
point the process is repeated working towards the input one stage at a time until
the oscillators input stage has been tuned. Finally, since this is a power
supply circuit, the oscillators frequency is fine tuned to the minor difference that
component values may make impractical as operating frequencies.
Although, anywhere around 100 KHz as a target frequency is ideal.
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