Why does negative resistance yield error?


by Vinyasi
November 27, 2021

Mathematically, the differential equation leads to an infinity growing current. Indeed, for positive R, we have something proportional to e-t / RC. But change R to -R, the negative sign disappears, and you obtain an exponentially growing behavior as time increases.

Physically, you absorb energy (instead of losing energy in heat), and more current you use, more energy you include in the (closed) system. You create energy out of nothing

by vanderghast
November 28, 2021

Patent it quick

by Foxx
November 28, 2021

Thank you, vanderghast, for the mathematical description. I needed that. So, now I know what it is called...a negative differential resistance (NDR).

But you're not consistent in your statements..."absorb energy" vs "create energy out of nothing"...which is it? It can't be both!

And closed systems don't exist except as a fictional account of oversimplification. The reactive outcome of one reactive component (such as, a capacitor) becomes a contributing parameter for any other similar reactive component located nearby (such as, another capacitor) causing the reactance formula for each (capacitor) to not equal their initial values for each successive period of their frequency in a non-DC system. This makes them parametric and, thus, transcends their physical limitations.

Reactive circuits whose reactive energy escalates, or diminishes, over time tend to absorb, or dissipate, their energy to or from manmade reactive fields since manmade reactive fields tend to be stronger than natural fields of reactive power probably due to the proximity of manmade sources of reactive fields within an urban setting. That's why C. Earl Ammann was charged with stealing energy from the grid after his 1921 demonstration in Denver of a batteryless EV. But if over-reactive circuits can't transfer reactive power from manmade reactive fields, then they will interact with their natural environment. The grounded node, in the negative resistance schematic up-above, qualifies as a connection to the circuit's environment be it a...common ground, or an earth ground, or an aerial, or any combination.

Why are there no spark gaps included in CircuitLab? Maybe because negative resistance is not allowed?

This makes the switches and relays in CircuitLab into virtual switches and virtual relays, rather than realistic switches or realistic relays, since the two contact plates of a realistic switch or a realistic relay act as a variably capacitant, spark gap arcing across its gap as its two contact plates reduce their proximity towards the termination of their closure, or during their initial opening (of any physical switch or relay).

Spark gap behavior is defined as having negative resistance as one of its several characteristics. A negative resistor is included within the macro for a neon bulb in the Micro-Cap version of Berkeley SPICE.

CircuitLab lacks this reality check.

Thank you, again.

by Vinyasi
November 28, 2021

The model assumes that everything of importance is included, so the model, or the simulation if you prefer, acts like an ideal closed system.

You can harness energy, in the real world, and if you want to do it within a model, you have to supply the mechanic of that transfer.

A pure negative (total) resistance makes no sense since with a close loop made of just a battery and that resistor will give, from V = R I, a current where electrons are attracted by electrons. Note that the key word is TOTAL. You can have 5 ohm plus (- 4 ohm) for a total of +1 ohm.

Under simple continuity, the total resistance of any closed loop cannot becomes negative, since from positive to negative, it would have, by continuity, to pass through 0 and thus, creating a short with an infinite current (switching from + infinity to - infinity as resistance pass from + epsilon to - epsilon).

The model does not consider energy, so it does not consider the conservation of energy. It is only by extension that 1 Watt dissipated by a resistor is an energy "lost" that -1 Watt ( the minus due to a negative value for the resistor) could be seen as energy harvested.

You can probably simulate the production of an arc by using a capacitor at the gate of a MOSFET. When the voltage stored at the cap reaches the threshold, the MOSFET starts to conduct (the alternative path provided by the arc is produced).

by vanderghast
November 28, 2021

I guess you’re right! Everything of relevance is included and the simulator is a closed system provided we take a closer look at the equation that you shared with us…

e raised to the power of (-t / RC)

What if we focus on the variable of time.? Because if time should reverse itself, then there is no need to look outside the system for where the energy is coming from, because current has not reversed itself… Only time has!


According to Feynman, positrons are anti-particle electrons attracted to other normal electrons which is what you offered an objection to in your first comment on the presumption that both sets of electrons are of the same persuasion, namely: that both sets of electrons (who are attracted to each other) are of the same time domain. Yet, this is not ridiculous if the two sets of electrons are not of the same time domain.

I have seen this phenomenon in the Berkeley SPICE family of simulators, namely: LTSPICE and Micro-Cap, along with Paul Falstad’s simulator. And I performed a complete analysis of several entire circuits and all of their components in microcap only to conclude that the “a priori” of unidirectional causality is broken whenever the phase of voltage and the phase of current are out of phase by a half cycle of 180° separation. This turns each component (which exhibits negative resistance) into a generator (according to passive sign convention) giving it negative watts. Yet, when I add up all of the subtotals of whatever components are generating negative watts versus all of the components consuming positive watts, it does not always add up to zero! Which leads me to further conclude that cause-and-effect no longer applies and the source of a circuit’s energy is not the cause of that circuit becoming alive with energy. And the load is not the effect of the source providing the load with energy! This simplistic unidirectional relationship only holds true when all of the components of a circuit are consuming positive watts and we exclude the source of energy of the circuit (such as a battery) from any consideration.

In other words… Energy does not move around from one place to another in the format of mass free photons. Instead, information moves around (in the form of voltage gradients of varying dielectric pressures) instructing particles to behave in various ways at every point in time because all particles of matter are dielectrically conscientious of the behavior of neighboring particles and respond, accordingly, as if all particles are alive with consciousness yet without any capacity for disobeying the laws of physics by doing whatever they like provided our laws (or our awareness of such laws and relationships) is complete and leaves nothing out (which I suspect it does because I’ve seen this happen too many times in simulators to assume that our knowledge is complete).

This requirement (that I presume is mandatory on the part of all particles of matter) is analogous to the behavior of a crowd participating in the generation and continuation of a phenomenon (during football games and similar activities) called “the wave” which sends (what looks like) a ripple around the stadium when in fact nothing is moving around the stadium except information and the awareness and the conscientiousness of individuals to participate (in an organized fashion) to create this pattern that we recognize as a ripple but does not exist in reality. Because the only reality is people standing up and sitting down at a certain rate and at a certain point in time representing the rise and fall of energy of the valence electrons of (let’s say) the copper atoms in a copper winding. And should the excitation of the valance electrons of copper wire rise, or rise and fall, more quickly or more extremely (or both) than what the copper atoms can tolerate and still hold themselves together, could cause the disassociation of those copper atoms turning the copper coil into a cloud of micro dust.

But the electricity of the copper coil is behaving according to our laws of electrodynamic behavior only because we have bothered to fashion that copper into a copper coil. Because if it was copper dust, or worse: oxidized copper dust, then none of our electrodynamic laws would apply! Only our laws of chemistry would apply and do nothing to benefit us in the field of electricity. So, the behavior of the valence electrons of copper atoms in a coil of wire is dependent upon us fastening it in such a way that the copper is bound at the atomic level in a manner equivalent to actualizing our electrodynamic laws of behavior for that copper wire.

Notice how simple is this perspective of negative resistance in reversing time for whatever components of a circuit which are willing to do so in order to satisfy the separation of voltage from current by 180° of phase relation. I don’t mean to imply that it’s easy!… But at least it is a simple definition of time reversal.

by Vinyasi
November 29, 2021

In fact, I don’t think the time domain allows for a closed system at all because time is always moving forward and (as far as we know) time will never end! So it’s almost trivial in which direction time proceeds for each component of a circuit… What only matters is whether or not electricity is cohesive. Because if electricity is cohesive, then time is moving forward. But if electricity should break down into its constituent elements of the magnetomotive force versus the electromotive force with 180° of phase relation between each in a non-DC situation, then time is going backwards for that relationship from our standpoint.

Of course, who are we to decide which way is the ultimate reference? Is time moving forward an absolute reference or is time moving backwards the absolute reference? What do we use as an ultimate reference to make such a determination?

by Vinyasi
November 29, 2021

I can't precharge capacitors, here, with "an initial" state of ? volts like it is possible in LTSPICE or Micro-Cap. I do this by appending their initial condition, thusly: "10m ic=1u" to represent 10 milli Farads charged with 1 microvolt. I usually use a microvolt similar to what's available in the atmosphere near ground level and sufficient to run crystal radios in the 1920s, because this does not suppress over-reactance.

Anything higher than one to ten volts and anything less than a femto volt (or thereabouts) tends to not encourage over-reactance among the circuit's caps and coils.

And voltage sources are worse. I try to avoid them since they exercise a heavy hand in their regulation of the circuit's voltage.

If I do use voltage or current sources, I restrict their usage to act as a braking mechanism not unlike the "C" permanent magnets reduced the tendency for the aluminum disks in electromechanical watt-hour meters (from a bygone era) from spinning out-of-control to self-destructive speeds of self-induced rates of escalation.

by Vinyasi
November 29, 2021

I don't see a initial voltage parameter for cap. Maybe you should start a new question for that topic. It seems possible that a Run Time Domain simulation while skipping the "initial" could be the way, but I never used that option.

by vanderghast
November 29, 2021

It is sure that standard algebra is strongly inspired by geometry (thanks to Descartes). Time is not "modelized" nicely, since that algebra does not care about traveling backward.

Other algebras are possible (simply based on basic stuff, such as (-1) times (-1) = -1, instead of +1 for the classical algebra based on geometry) but while they then include a strong dependency toward origine, they require particular care about distribution of multiplication over addition, as example. They may be somehow useful for cases where total-negative values don't exist (absolute temperature, electrical resistance, ... ), the interest in the community is few and restricted. As example, with this time-algebra, square-root of (-1) is -1, no imaginary number required, but we can't divide a positive number by a negative one (or invent an imaginary-time value for that). Note that (-1)/(-1) can be either +1, either -1 (like a square root of a positive number in geometry-algebra). Also note that (-1) to the power of x is defined (which is not the case for geometry-algebra, in the R2 plane), and so on, and so on.

Unfortunately, I doubt that a forum about electronic is the best place to continue on that topic, which can be interesting none the less.

by vanderghast
November 29, 2021



by Vinyasi
November 29, 2021

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