Wouldn't the gate still rise to +15v when the NPN transistor is turned off?
Resonance is defined as the frequency where XL and XC are equal, at that point they cancel out and the resultant is just the resistance of the circuit. The formula are somewhat difficult for one not familiar with the concept. In your description of combined reactances, inductive and capacitive the values for XL and XC are opposite in sign relative to each other and add algebraically. If for example if the XC was -180 ohms and XL was 90 ohms them the resultant would be -90 ohms. -reactances are capacitive and +reactances are inductive, so if XC =1/(2 X 6.28 X F X C) then 1/C = XC/6.28/F or if positive (inductive) L = XL/6.28/F (C=Farads and L = Henry's). Frequently small value reactances are used to negate other reactance's... one example is power factor correction where typically the load might be inductive in nature (lots of big motors) and provide a mismatched load. Remember that max power transfer occurs where Xload = Xsource (for ac circuits) a capacitor equal to XL (load) is placed in parallel with the load to cancel out the inductive part of the load.
The technique used in driving capacitive mosfet gates is to just 'swamp' them out i.e. provide a drive impedance so low as to force them into a minor consideration.
We can say that (1/Rpar) = (1/Rreq) - (1/Rcir)... `(1/2200) = .0004545... and 1/10000 = .0001... therefore .0004545... - .0001 - .0003545... = .0003545...Rreq = 1/.0003454... = 2K82 ohms and the proof is 1/Rt = 1/10000 + 1/2820 = 2K2 ohms.
The only difference between DC and AC is the sign of the reactance.
Long and complicated until you have done it a few times but trivial with a little experience.
In Closing capacitive reactances I.E. Mosfet Gates are usually driven with a generator that is at least 1/10 the impedance of the gate being driven.
The math and descriptions would occupy several pages and would need to come from 3 different books, Much too long
, I think that if you were able to follow my reasoning so far you have some third year electronics theory education.
I also think that If you are reading this sentence you are either glassy eyed or seriously interested in the topic of impedance matching.
This subject is very complicated as the available gate drive current is a function of the Rise Time of The Driving Pulse not it's Amplitude since we are driving a capacitor. Remember that Rise time is piece-wise equivalent to frequency and that XC (Gate impedance) is an inverse function of frequency.
My hardest subject was Fourier analysis or at least the frequency/time relationships...
The Math is easy... and remember that reciprocal idea, it is applicable to a great deal of electronics especially for deriving solutions to network matching or network solutions.
Finally thank you for a thoughtful review of what I wrote.
That subject tends confuses me as well. which in a nutshell say that if a pulse has 0 rise time it has infinite current