Series Resistance inside a Capacitor is Negative Resistance

[Vinyasi]

By adding series resistance to capacitors and inductors in Paul Falstad's electronic simulator, I've discovered that to do so effectively makes it into negative resistance for capacitors since the equations for a simple inductor model (not a transformer model) is the reciprocal (hyperbolic inversion) of a capacitor.

Many of my circuits designed over the past year lie dormant with series resistance. Some spring to overunity from their prior state of non-overunity.

Circuit Simulator Applet ported to JavaScript by Iain Sharp, from the original in Java by Paul Falstad, Used Here to Promote the Simulation of Surges Arising from the Judicious Use of Negative Resistance.
vs
Circuit Simulator Applet ported to JavaScript by Iain Sharp, from the original in Java by Paul Falstad, Used Here to Promote the Simulation of Surges Arising from the Judicious Use of Negative Resistance.

Some remain exactly the same as before. A few lose either power gain or else don't behave normally.

A comparison can be made by going here...
Index of /circuitjs1/vinyasi-cts

A list of those circuits which retain overunity is here...
Series Resistance is a Reality Check for Electronic Simulations

Equivalent series resistance, Component models -- Wikipedia

https://www.youtube.com/watch?v=EXYc6uWKBgE -- YT vid

[Vinyasi]

Correction to Capacitor Model

By adding series resistance to capacitors and inductors in Paul Falstad's electronic simulator, I've discovered that to do so effectively makes it into negative resistance for capacitors since the equations for a simple inductor model (not a transformer model) is the reciprocal (hyperbolic inversion) of a capacitor.

Many of my circuits designed over the past year lie dormant with series resistance. Some spring to overunity from their prior state of non-overunity.

Circuit Simulator Applet ported to JavaScript by Iain Sharp, from the original in Java by Paul Falstad, Used Here to Promote the Simulation of Surges Arising from the Judicious Use of Negative Resistance.
vs
Circuit Simulator Applet ported to JavaScript by Iain Sharp, from the original in Java by Paul Falstad, Used Here to Promote the Simulation of Surges Arising from the Judicious Use of Negative Resistance.

Some remain exactly the same as before. A few lose either power gain or else don't behave normally.

A comparison can be made by going here...
Index of /circuitjs1/vinyasi-cts

A list of those circuits which retain overunity is here...
Series Resistance is a Reality Check for Electronic Simulations

Equivalent series resistance, Component models -- Wikipedia

https://www.youtube.com/watch?v=EXYc6uWKBgE -- YT vid

I made an error of not treating the series resistance of capacitors as a fixed amount based -- not on its Farads, but -- on the dielectric material according to the Wikipedia article. Since using 30 ohms for standard aluminum dielectric material killed simple circuits (Paul Falstad's as well as mine), I opted for the minimum for ceramics of 10 milli ohms.

The problem with my prior assumption was that I was assuming that series resistance for capacitors varies directly with capacitance. So, I multiplied a presumed amount of resistance of one thousand ohms against the capacitance. This was wrong. Instead, I added a fixed amount of 10 milli ohms to capacitance before it's divided into the time step of the simulator.

Now, I have to go over the list of circuits that survived the prior version of series resistance to see what has survived this time.

[Vinyasi]

Updated series resistance in Paul Falstad's Electronic Simulator

By hovering the cursor over a cap or coil, its series resistance is displayed in the lower right corner of the canvas. And capacitors' series resistance can be modified per component since the dielectric material determines this. Updated the list of circuits which retain their overunity despite the presence of series resistance.