A little more detail, please?

Hi Cyril,

as the names of your jpg-files imply, one difference is that in the first case, the current is not a (mathematical) function of the voltage because for values in the range VNE there is not a unique current value. But the voltage is a function of the current.

In the second case, the dependence of the voltage from the current cannot be described by a mathematical function.

One might suspect, that the physical conduction process depends indeed on the current in the first case (e. g. gas discharge: density of electrons and ions depends on current) and on the voltage in the second case (e. g. tunnel diode: alignment of band states depends on voltage), in the respective critical regions.

Interesting question ,to be used in electrical circuits for improved performance

Honestly, this is one of the few my questions I don't know in advance the answer to:) The Joerg's answer and other comments motivated me to start thinking ... and here is what I came up with today...

In its essence, the negative (differential) resistance NDR is "positive" like the ordinary ohmic resistance. The only difference between them is that the negative resistance vigorously changes when the voltage across or current through it change... so it is a kind of over-dynamic resistance.

If we supply such a negative resistor with a real voltage source with moderate internal resistance, when increase the input voltage in the so-called negative resistance region, the negative resistor has two options - to decrease or to increase its static resistance. In the first case, it will increase the current through and decrease the voltage across it; in the second case, it will decrease the current through and increase the voltage across it. If it does this in the same way, it will have the same differential resistance represented by the same negative slope of its IV curve in the negative resistance region. The other parts of the current-voltage characteristic will remain positive slope thus forming the S- and N-shaped curves.

Note the NDR cannot occupy the whole IV curve as in the case of the "positive" resistance. It can have a negative slope only in some limited middle part of the whole IV curve of a positive resistor. In the end parts, the NDR saturates and the resistance becomes positive; hence the odd "S" or "N" shape. For this purpose, it has somehow to change the monotonous motion of the operating point that draws the IV curve when the input voltage changes; it has to fold up the curve. So there are two ways of folding - bottom up and top down that lead to both types of characteristics.

Maybe I should illustrate this on a piece of paper?

An S-shaped example - a neon lamp. You have only to draw the load (generator) line:)

An N-shaped example - a tunnel diode amplifier.

"Because a two-terminal 'S-shaped' impedance device would

represent a hidden source of energy" -

is my knee-jerk reaction.

Nice to see you again in our discussions, dear Barrie Gilbert!

If I was a fan of the free energy, I would be very pleased with your statement... but I am just a fan of great circuit ideas... and I feel the subtle irony in your words:)

Since the time of my college years, I know that elements and circuits (including both S- and N-shaped negative resistance devices) do not contain their own sources of energy... they only control the energy of external sources. The only difference between these odd devices and conventional "amplifying" devices is they are 2-terminal.

I hope Dorian is far from you...

One state that the device either have

several possible currents for the same voltage (S-type)

or

several possible voltages corresponding to the same currents. (N-type)

Those points might stable/unstable depending on the external impedance attached.

Actually, there are three types of positive resistance:

1) the positive sections of the N-shaped curve.

2) the positive sections of the S-shaped curve.

3) the entire "normal" resistance (shall we call it a "/" shaped curve?)

Very interesting thoughts, Darren... especially the third point about the "linearly-shaped IV curve" of the omic resistance...

Would you look at my considerations below about the philosophy of creating the negative differential resistance?

https://en.wikibooks.org/wiki/Circuit_Idea/Negative_Differential_Resistance#General_considerations_about_creating_the_NDR

Here are some of my thoughts in this direction, initiated by your comment. They are intended for S-shaped negative resistance.

If we have constant ohmic resistance with a moderate value, and we begin increasing the voltage across it (through a high enough resistance), the current through it will increase also moderately since it is a function of only one variable - the voltage. Thus both the voltage and current increase.

If we want to make the current to increase more vigorously in a specific region, we can begin decreasing (within this region) the resistance simultaneously with the voltage variation. The trick is that we change (in opposite directions) both the voltage and resistance in the numerator and denominator of the Ohm's equation. Thus the current becomes a function of two variables and vigorously changes. And what is more interesting, the voltage decreases when the current increases (a favorite statement of textbooks). But why?

As I said above, we supply the S-shaped negative resistor by a voltage source but through a resistor… i.e. we supply it by current. According to the dual form of Ohm’s law, the voltage drop across the negative resistor is V = I.R… and is a function of two variables - the current I and the static resistance R. We gradually increase the current but the resistor more vigorously decreases its resistance. So their product V decreases...

A wonderful trick... but its abilities are limited because we will quickly exhaust the initial reserve of resistance and will reach the minimum of resistance. That is why, in this case, we start from the maximum positive resistance (the bottom section of the S-shaped curve) and finish with the minimum resistance (the top section of the S-shaped curve)...

I assumed we were discussing a symmetrical S-graph on the current axis.

It would be interesting to explain in a simple way why the symmetrical S-graph implies a hidden source of energy. Here are some of my thoughts in this direction:

https://en.wikibooks.org/wiki/Circuit_Idea/Linear_Mode_of_Voltage_Inversion_NIC

A simple explanation could be the following:

In the case of negative differential resistance, we can do whatever the hell is (such as dynamically changing the current resistance like a cat that never falls on its back:) ... but we always remain in the first quadrant.

This means that by injecting current into this super-dynamic resistor, the voltage at its input terminal always remains positive... and its IV curve of whatever form it has (S, N, O, P, Q:) stays in the first quadrant.

We can move it to 2-nd and 4-th quadrant only by connecting a dynamic voltage source so that to inject the current into its negative terminal.

I cannot understand what makes me, all my life, constantly try to comprehend the essence of circuit phenomena...

Here again I thought deeply about the way in which the two types of negative resistance - differential (DNR) and absolute (ANR) solve the same basic task for which they were created - to compensate equivalent positive resistances.

DNR is an element (tunnel diode, Gunn diode...) while ANR is a circuit (VNIC, INIC). Both they add energy to the load with the help of a an additional voltage source (power supply)... but they control it in a different way.

DNR controls the supplying voltage source like an electronic "rheostat" that changes its static resistance in series to the load. ANR controls the supplying voltage source like an "electronic potentiometer" that includes a part of the supplying voltage in series to the load...

What about beautiful circuits in the attachment :-)

I've been impressed once by a circuit using a 4-input TLL gate SN7460 as a S-type negative resistance. Here is it

Article Negative Resistance in Multiemitter Transistors

Other exotic circuits with a mirror-S (omega) and mirror-N-type characteristics are in the attachment.