Electronic – the physical meaning of negative resistance

currentresistanceresistorsvoltagevoltage-source

I am a bit confused about the physical meaning of negative resistance.

Mathematically, a component which has negative resistance shows a decreasing voltage across its terminal when the current inside it grows, and vice versa. But how is this physically possible?

Somewhere I have read that an example of component with negative resistance is a voltage source. But I do not understand this statement, since a voltage source is a component which at most shows a (positive) internal resistance.

Best Answer

Although the negative resistance is veiled in mystery, in fact it is a quite simple concept. It can be easily explained by analyzing the voltage drops across resistances.

The positive resistor subtracts its voltage drop from the input voltage thus decreasing the current while the (S-shaped) negative resistor adds its voltage drop to the input voltage thus increasing the current. So the positive resistance impedes while the negative resistance helps the current.

The main question is, "How does the negative resistor add its voltage?" There are two techniques to do it leading to the two kinds of negative resistance - differential and absolute.

Negative differential resistor is, in essence, a positive resistor that subtracts its voltage drop V = I.R from the input voltage. But in contrast to the positive resistor that has constant resistance, it is a dynamic resistor that significantly decreases its resistance when the current slightly increases. As a result, instead to increase, the voltage drop (the product of the increasing I and the more vigorously decreasing R) decreases... and this is equivalent to adding voltage. This is the trick - reducing the loss is actually a profit.

S-shaped NDR - operation

See also: Demystifying the Negative Differential Resistance Phenomenon

Absolute negative resistance is done in a more natural way - by a dynamic voltage source (electronic circuit). It changes its voltage proportionally to the current (like a positive resistor) but adds it to the input voltage (instead to subtract). For the purpose of addition, this voltage has an opposite polarity; hence the name of this circuit - “voltage inversion negative impedance converter” (VNIC).

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See also: Investigating the Linear Mode of Negative Impedance Converters with Voltage Inversion

So, the "physical meaning of negative resistance" is "dynamic resistor" or "dynamic source". But what is the point of all this? What negative resistance can be used for?

Negative resistance can compensate equivalent positive resistance. For example, if we connect an S-shaped negative resistor in series to a positive resistor with the same resistance, the equivalent resistance will be zero. Figuratively speaking, the negative resistance has "destroyed" the positive resistance and the combination of two resistors acts as a piece of wire. Mathematically, it is simply R - R = 0… but we, human beings, need a more "physical" explanation... and there it is:

  • Differential negative resistance. If the input source tries to increase the current, the voltage drop across the positive resistor increases and it should affect the current. But the negative resistor vigorously decreases its resistance to reduce the voltage drop across itself by the same value. The total voltage across the whole network (R and -R in series) does not change; it behaves like a Zener diode with zero differential resistance. So the differential negative resistor compensates the change of the voltage drop across the positive resistor... not the very drop.
  • Absolute negative resistance. It compensates the absolute voltage drop across the positive resistor (not only the change) by inserting the same voltage. For this purpose, it uses an additional voltage source with opposite polarity. The total voltage across the whole network is not only constant but zero. The network really behaves as a "piece of wire" and does not impede the current. Popular examples of this arrangement are the transimpedance amplifier and inverting amplifier in which the op-amp output acts as an absolute negative "resistor". It destroys the feedback resistance by compensating the voltage drop across it with equal voltage.

The ordinary voltage source is not a negative "resistor" since its voltage does not change proportionally to the current... it is not dynamic source... it is a constant voltage source. So, if we connect it in series with a resistor, it will compensate only a part of the voltage drop across the resistor equal to its voltage.

It is likely the related discussion in ResearchGate will be of interest to you:

And why are there two more types of negative resistance?

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