01 September 2013 29 3K Report

When we see somewhere written "negative resistance", we are never sure what exactly it is, just because it has two varieties - "true" and "differential"... and the former is not a resistance:) We have already started a discussion about the true (absolute) negative resistance

https://www.researchgate.net/post/What_is_negative_impedance_Does_can_it_exist_If_so_how_can_elements_with_negative_impedance_be_implemented_Are_they_passive_or_active

and its op-amp implementation (NIC)

https://www.researchgate.net/post/What_is_the_basic_idea_behind_the_negative_impedance_converter_How_is_it_implemented_How_does_it_operate_What_does_the_op-amp_do_in_this_circuit

Now it remains only to clarify what the negative differential resistance is. To help the discussion, here are my speculations about the amazing phenomenon.

If we increase the voltage across an ordinary ohmic resistor, the current flowing through it increases proportionally according to Ohm's law (Iout = Vin/R). Also, if we increase the current through the resistor, the voltage across it increases as well (Vout = Iin.R). Thus the voltage and the current change in the same directions. But there are mysterious two-terminal electronic components (negative differential resistors, shortly NDR), having just the opposite behavior in the middle part of their IV curves - the voltage across and the current through them change in opposite directions. Some of them - neon lamps, thyristors, have an S-shaped IV curve while other - tunnel, Gunn and lambda diode, have an N-shaped IV curve (see the attached picture).

Although the negative differential resistance seems to be a mystic phenomenon, it is actually based on an extremely simple, clear and intuitive trick - the powerful "dynamizing" idea that is brought here to the utmost degree. IMO a differential negative resistor is nothing more than a kind of "self-varying", dynamic resistor that changes extremely its instant (ohmic, chordal) resistance depending on the current passing through the resistor or on the voltage applied across it... the differential negative resistor is actually an "over-dynamic" resistor.

Negative differential resistors are dynamic but still positive resistors. They have different kinds of resistance in the three parts of their IV curves (located in the 1st or the 3th quadrant) - "positive" in the end parts and negative in the middle part. The three parts form the whole IV curve that, depending on the NDR behavior in the middle part, can be S- or N-shaped. When the input quantity (no matter current or voltage) increases, the S-shaped NDR decreases while the N-shaped NDR increases its instant resistance.

Each of the two NDR can be driven both by voltage and current. To operate in a linear mode, an S-shaped NDR has to be driven by current while an N-shaped NDR - by voltage (the attached picture); v.v., to operate in a bi-stable mode, an S-shaped NDR has to be driven by voltage while an N-shaped NDR - by current. So, in contrast to the widespread but misleading viewpoint, there are no particular current controlled (CCNR) and voltage controlled (VCNR) negative resistors - there are only S-shaped and N-shaped NDR, and each of them can be controlled both by a current and voltage.

In the middle negative resistance region, negative differential resistors behave as two-terminal active elements (such as transistors). They cannot be used independently; they need an additional power supply to be connected. Thus the combination of the negative differential resistor and the power supply can be considered as another kind of a true negative resistor (the other kind of a true negative resistor is a combination of a constant "positive" resistor and a varying voltage source - this is the case in a NIC). From another viewpoint, this combination can be thought as of an electrical source with negative internal resistance. It is a usual practice to think of a negative differential resistor as of a true negative resistor implicitly assuming the existence of a power supply...

As I have told in the question about the true negative impedance, I wasted a few years of my life to struggle with orthodox wikipedians inhabiting the electronics Wikipedia with the idea to tell the truth about the negative (differential) resistance in the respective Wikipedia article... but I could not... All my edits and imagine finally - the whole article about the negative differential resistance, were removed! Here is a short history of this "epic battle" (I was writing under the user names Circuit-fantasist and Circuit dreamer):

https://en.wikipedia.org/wiki/User:Circuit-fantasist/Negative_resistance#Some_history_in_retrospective,

and some my insights shared with wikipedians

https://en.wikibooks.org/wiki/Talk:Circuit_Idea/Negative_Differential_Resistance#How_to_create_negative_resistance

But I did not give up and after a year, I told the truth about the negative differential resistance in Wikibooks:

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

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

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