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I am trying to analyse the following Armstrong oscillator circuit from HF Tesla coil experiments. I am particularly interested in this topology because of the class E operation and the high efficiency mentioned in the original project.

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As the first step, I simulate the circuit and my LTSpice circuit is as follows. MOSFET R6020PNJ is used instead of 2SK2698 (The MOSFET model (STW14NM50) that is available in the same author's post was not giving me the oscillation). Inductance of primary, secondary and tickler coils are calculated from the geometry parameters provided in the project description. A series capacitor is added to the secondary to make the secondary self resonating at 4.76MHz to be same as the original project. A load resistance is added to make the secondary loop.

enter image description here

I understand the objective of original project is to generate an arc inside a Faraday cage, however, here, I am trying to use the secondary as the load.

First, I want to understand the operation of this topology. Particularly, the role of C3 and C4 is not clear to me.

Next, I would like to derive equations for oscillation frequency and the oscillation voltages across L1 and L2. I understand From the simulations that the frequency of the oscillation (~7.8MHz in this simulation) is highly dependent on the secondary resonance, but not equal to the self-resonance of secondary coil, or, L1-C4 resonance. (apparently, I also noticed that the input and output capacitance of the MOSFET are substantially larger than C4 : C_iss=2040p, C_oss=1660pF, C_rss=70pF) How Can I calculate the oscillation frequency?

A supplementary question to this analysis is asked here:

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I want to understand the operation of this topology. Particularly, the role of C3 and C4 is not clear to me.

Lc and C3 form a supply voltage filter - in other words they try to prevent interference getting back onto the 60 volt line. This might be better explained if you gave a link to where the circuit came from. For instance, those components will also prevent noise from the 60 volts getting on to the oscillator but, the bigger picture isn't available so it's guesswork.

C4 (and the parasitic MOSFET drain source capacitance) dictate the resonant frequency of the oscillator along with L1. Loading effects due to RL on the secondary may shift this frequency slightly due to the coupling factor between the coils.

Next, I would like to derive equations for oscillation frequency

Any derivation needs to take into account plenty of minor as well as major factors and this is best served using a simulation tool but, the main factors involve: -

  • L1
  • C4 in parallel with MOSFET capacitance
  • The above form a resonant circuit
  • C5 and the secondary coil form a series tuned circuit that feeds the load
  • That series tuned circuit and the coupling (0.8) will modify the oscillation frequency.

If I were to analyse it I'd probably use a sim and do an AC analysis that involved stimulating L1 and C4 (plus MOSFET capacitance) with a current source and looking where the resonant peaks might occur in the frequency spectrum for different loading values.

From that I'd consider going down the route of making a formula based on what I'd seen in the simulation.

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  • \$\begingroup\$ Thank you @Andy aka, Links to the original references where the circuit is extracted are included in the question. I managed to simulate the AC analysis and got few more issues to clarify; should I look at the frequency response of node Gate, Drain or L2?(phase([VL2])=-360 near oscillation freq) (Not sure if should I edit the same question or should I add a new question to elaborate on this) \$\endgroup\$ – Pojj Mar 15 '18 at 14:37
  • \$\begingroup\$ Look at the output which would drive the gate to estimate where oscillation would occur i.e. 180 degrees phase shift. Or maybe leave the transistor in with the DC bias on the gate and inject a signal between bias and gate with L3 replaced by the signal injection. Now look at the output from L3 to see what frequency makes 360 degrees shift. \$\endgroup\$ – Andy aka Mar 15 '18 at 15:01
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    \$\begingroup\$ Firstly, removing your acceptance of this answer because you have supplementary questions is not always a good thing to do. As far as I'm concerned you should have asked a new question based on your observation that the peaking frequency in the AC response doesn't match the oscillation frequency. That phenomena is well understood and isn't related to this question in its origins. You see it in standard colpitts oscillators and virtually all LC based oscillators including XTAL oscillators. \$\endgroup\$ – Andy aka Apr 24 '18 at 9:23
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    \$\begingroup\$ Regards the phase shift that produces oscillation and the peaking frequency seen in the AC analysis if you go to this website and alter the resistance value to 90 ohms and press "calculate" then use the advance button, you'll see that the red graph (magnitude) does not peak at the natural frequency (15.915 kHz) but at 12.64 kHz. You will also see that the phase angle is -62.7 degrees whereas at Fn it is always 90 degrees. This is demonstarting that peaking frequency doesn't always correspond with oscillation frequency. \$\endgroup\$ – Andy aka Apr 24 '18 at 9:40
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    \$\begingroup\$ The peak you show at 8.69 MHz doesn't seem to correspond to 0 degrees. I think the vast amount of data you are presenting makes this hard to analyse as a 3rd party. I think you should target one capacitance value and show amplitude and phase responses for it then say what it oscillates at and put it in a new question. Adding it to this draws little attention from others and although I will get involved (time permitting) I believe it deserves a new question. \$\endgroup\$ – Andy aka Apr 24 '18 at 10:49

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