Calculating Primary Current / Impedance
swordfish, Tue Jul 24 2018, 02:42AMHi All,
I have a quick question I hope someone can help with about primary current, or maybe more correctly, primary impedance calculations.
Calculations I see for primary current use the formula I = V/sqrt(L1/C1). However, literature for series LC circuits seems to state that at the resonant frequency Xl = Xc, and therefore the impedance drops to that provided by pure resistance. Is anyone able to explain why we use the above formula rather than assuming purely resistive losses? I know I'm missing something here!
Many thanks,
Greg
Re: Calculating Primary Current / Impedance
Sulaiman, Tue Jul 24 2018, 03:47AM
the primary capacitor is in parallel with the primary inductance
Sulaiman, Tue Jul 24 2018, 03:47AM
the primary capacitor is in parallel with the primary inductance
Re: Calculating Primary Current / Impedance
swordfish, Tue Jul 24 2018, 04:01AM
Ah yes, I see now. Makes more sense looking at it as a parallel resonant circuit! Thanks!
swordfish, Tue Jul 24 2018, 04:01AM
Ah yes, I see now. Makes more sense looking at it as a parallel resonant circuit! Thanks!
Re: Calculating Primary Current / Impedance
Dr. Slack, Tue Jul 24 2018, 06:25AM
Resistive losses are 'small', therefore the current is controlled by energy considerations, at least initially.
The formula I = V/sqrt(L/C) is just another way of saying I^2L/2 (energy stored in primary due to current) = V^2C/2 (energy stored in capacitor due to voltage).
Dr. Slack, Tue Jul 24 2018, 06:25AM
Resistive losses are 'small', therefore the current is controlled by energy considerations, at least initially.
The formula I = V/sqrt(L/C) is just another way of saying I^2L/2 (energy stored in primary due to current) = V^2C/2 (energy stored in capacitor due to voltage).
Re: Calculating Primary Current / Impedance
Uspring, Tue Jul 24 2018, 09:37AM
Is that a SGTC or a DRSSTC you are asking about? In a SGTC primary inductance and capacitance are in parallel, while in a DRSSTC they are in series.
Uspring, Tue Jul 24 2018, 09:37AM
Is that a SGTC or a DRSSTC you are asking about? In a SGTC primary inductance and capacitance are in parallel, while in a DRSSTC they are in series.
Re: Calculating Primary Current / Impedance
Fumeaux, Tue Jul 24 2018, 03:54PM
I think I have an useful tool for you: http://www.classictesla.com/java/javatc3d/javatc3d.html
There you can look at an array of varius (some are useful) calculations.
Fumeaux, Tue Jul 24 2018, 03:54PM
I think I have an useful tool for you: http://www.classictesla.com/java/javatc3d/javatc3d.html
There you can look at an array of varius (some are useful) calculations.
Re: Calculating Primary Current / Impedance
klugesmith, Tue Jul 24 2018, 08:36PM
The series/parallel question is a good opportunity to discuss duality.
A simple LC tank circuit (figure A) is series, because both components share a current. It's also parallel, because the components share a voltage. As Dr Slack said, the voltage/current magnitude ratio is the tank impedance Z = sqrt(L/C).
If you add an impedance-vs-frequency meter in series (figure B), the reading matches "series circuit" formula. High Z at DC.
If you add an impedance-vs-frequency meter in parallel (figure C), the reading matches "parallel circuit" formula. Low Z at DC.
[edit] Cases B and C are equally disruptive to the original circuit. One has a new voltage element sharing the common current; the other has a new current element sharing the common voltage.
Now back to question in OP. The log |Z| vs log f chart at the bottom of figure B has a wide V shape. Its asympotes are |Z| = 1/wC below resonance and |Z| = wL above resonance. (here using w in place of radian frequency ω = 2 pi f.) The asymptotes cross at the resonant frequency, where 1/w = sqrt(LC), and |Z| for the capacitor and inductor are both sqrt(L/C).
What about that narrow impedance dip at resonance, you asked? It goes down to the circuit's resistance value, far far below sqrt(L/C). Well that means that at resonance, the driver (our Z meter) needs to force only a tiny voltage to see a large current. Or conversely, if the Z meter is forcing a fixed current, it sees a very small voltage between the terminals. The voltages across the capacitor and inductor are still sqrt(L/C) times the current, either way.
In other words, at resonance, the third voltage element in figure B has a very small value with respect to the current and the tank voltage. The third current element in figure C has a very small value with respect to the voltage and the tank current.
Does that help? [\edit]
The tank in a DRSSTC could theoretically be driven either way, though component limitations seem to favor an AC source in series. In SGTC we charge the cap through inductor in series (switch open). Then close the switch (spark gap), so the LC resonates as in figure A. Same as figure B, with the forcing voltage source stepped to 0 volts.
klugesmith, Tue Jul 24 2018, 08:36PM
The series/parallel question is a good opportunity to discuss duality.
A simple LC tank circuit (figure A) is series, because both components share a current. It's also parallel, because the components share a voltage. As Dr Slack said, the voltage/current magnitude ratio is the tank impedance Z = sqrt(L/C).
If you add an impedance-vs-frequency meter in series (figure B), the reading matches "series circuit" formula. High Z at DC.
If you add an impedance-vs-frequency meter in parallel (figure C), the reading matches "parallel circuit" formula. Low Z at DC.
[edit] Cases B and C are equally disruptive to the original circuit. One has a new voltage element sharing the common current; the other has a new current element sharing the common voltage.
Now back to question in OP. The log |Z| vs log f chart at the bottom of figure B has a wide V shape. Its asympotes are |Z| = 1/wC below resonance and |Z| = wL above resonance. (here using w in place of radian frequency ω = 2 pi f.) The asymptotes cross at the resonant frequency, where 1/w = sqrt(LC), and |Z| for the capacitor and inductor are both sqrt(L/C).
What about that narrow impedance dip at resonance, you asked? It goes down to the circuit's resistance value, far far below sqrt(L/C). Well that means that at resonance, the driver (our Z meter) needs to force only a tiny voltage to see a large current. Or conversely, if the Z meter is forcing a fixed current, it sees a very small voltage between the terminals. The voltages across the capacitor and inductor are still sqrt(L/C) times the current, either way.
In other words, at resonance, the third voltage element in figure B has a very small value with respect to the current and the tank voltage. The third current element in figure C has a very small value with respect to the voltage and the tank current.
Does that help? [\edit]
The tank in a DRSSTC could theoretically be driven either way, though component limitations seem to favor an AC source in series. In SGTC we charge the cap through inductor in series (switch open). Then close the switch (spark gap), so the LC resonates as in figure A. Same as figure B, with the forcing voltage source stepped to 0 volts.
Re: Calculating Primary Current / Impedance
swordfish, Tue Jul 24 2018, 10:21PM
Thanks very much everyone for the advice, I think I understand it sufficiently now. Appreciate the effort some of you have gone to to help!
swordfish, Tue Jul 24 2018, 10:21PM
Thanks very much everyone for the advice, I think I understand it sufficiently now. Appreciate the effort some of you have gone to to help!
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