# What is the physical meaning of negative resistance?

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.

• Maybe if you see a circuit with two resistors in series (voltage divider), having in the middle 2.5V, a component with negative resistance can be said to 'add voltage' instead of removing voltage... but I leave a real answer to the experts here ;-) – Michel Keijzers Apr 25 '19 at 16:11
• Minus R will provide power, not dissipate power. – analogsystemsrf Apr 25 '19 at 16:41
• There are two types 'S' & 'N'. en.wikibooks.org/wiki/Circuit_Idea/… – Optionparty Apr 26 '19 at 3:10
• A voltage source does not have negative resistance, it has ZERO resistance. If you have such a device, take care not to short it out with a zero ohm resistor. I cannot compute the power dissipated in such a circuit. – richard1941 Apr 26 '19 at 5:43
• Arc discharge is modelled as a negative resistance. – KalleMP Apr 26 '19 at 19:25

There are a number of mechanisms that result in a region where locally increasing voltage results in locally decreasing current. For example, an Esaki (tunnel) diode.

A common example would be a switching power supply with a steady load. Assuming the efficiency is more-or-less constant, increasing the input voltage results in less current being drawn. It is always consuming energy though.

A stand-alone component that exhibits negative resistance (rather than negative differential resistance) is not possible without some kind of energy source within the component, otherwise it would violate conservation of energy ($$\P = E^2/R\$$) and negative P would indicate it is acting as a power source.

If you want to play with a negative resistance effect, one way (assuming you don't mind one end being grounded) is to use a negative impedance converter:

simulate this circuit – Schematic created using CircuitLab

The above circuit acts like a -10K resistor with one end grounded (within its linear range), and works down to about zero volts. Any power it produces comes from the op-amp supplies.

• That is really a fine choice of an example device you picked. – The Photon Apr 25 '19 at 16:23
• @ThePhoton LOL, great minds and all that. – Spehro Pefhany Apr 25 '19 at 16:45
• @J... No, it really is negative differential resistance. You put a stiff voltage across it and keep it from oscillating the current will follow that curve. See, for example, DC Characterization of Tunnel Diodes Under Stable Non-Oscillatory Circuit Conditions by Wang et al. – Spehro Pefhany Apr 25 '19 at 18:31
• This is an example of a "type N" device. There are also "type S" devices. – richard1941 Apr 26 '19 at 5:46

In this context, we have to discriminate between (1) pure differential (dynamic) neg. resistances (as shown in the examples of the other answers) and (b) a static negative resistance.

For a differential neg. resistance (rdiff) the current CHANGES are negativ, for a static neg. resistance the CURRENT itself has a negative sign.

My following answer concerns only the static negative resistor:

Such an element does not "consume" a current - driven by a voltage source, but - the other way round - it drives a current (prop. to the voltage) in an opposite direction into the voltage source.

Hence. it is a voltage-controlled current source. For such circuits only active realisations are possible (using transistors or - in most cases - opamps). The most popular circuit is the NIC (Negative-Impedance Converter).

Shown here is a "Typ-A" NIC block. The grounded resistor (impedance) R3 is converted into a negative resistor (impedance) with a conversion factor (-R1/R2). This typ is short-circuit.stable. (An open-circuit stable NIC results for interchanged opamp inputs).

simulate this circuit – Schematic created using CircuitLab

Comments: The shown NIC is stable as long as the source resistance of the voltage source (not shown in the figure) is smaller than R1. These NIC blocks are use for undamping filters, oscillators and other systems with unwanted positive (parasitic) resistances. Mathematically, they can be treated as "normal" resistors in series and parallel combinations - however, with a negative sign, of course.

A very popular application is the "NIC integrator" (or "Deboo integrator"), where an NIC block is connected to the common node of a simple R-C lowpass. In this case, the NIC can compensate the pos. resistor R - thus resembling a current source which loads the intergating capacitor.

• Why did you answer twice? – pipe Apr 25 '19 at 17:58
• It was by accident.....I have tried to include the figure (later) - and suddenly there were two answers... – LvW Apr 25 '19 at 18:32

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.

Perhaps a voltage source is mentioned, because we all know that an ideal voltage source should have zero internal resistance: a good one will have a small positive resistance, to which is added any wire resistance going to the load.

For an electronically regulated supply, it is possible to force output resistance past zero into negative resistance region. This is done by routing some of the load current so that regulating voltage node is adjusted in such a direction that output voltage is forced up. An example of the common LM317 regulator having negative output resistance is shown below - beware, some loads produce wild results:

simulate this circuit – Schematic created using CircuitLab
Using the built-in circuit simulator, $$\ R_{load} \$$ was swept from 5 ohms up to 15 ohms:

• at 5 ohms, voltage drop across Rload is 4.322V

• at 15 ohms, voltage drop across Rload is 3.993V

The result of that 1-ohm resistor, (and the direction of Rload's current going through it) forces this voltage supply to have negative resistance: at heavier loads, the output voltage goes up. This voltage increase can compensate the voltage drop across the wire resistance.

Anything that drops in voltage with a rise in current has a negative resistance.

Power sources have this property. The passive components with incremental negative resistance include; any gas discharge bulb or arc, Avalanche effect diodes, Tunnel Diodes, SCR's during trigger phase.

https://en.wikipedia.org/wiki/Negative_resistance

But how is this physically possible?

Some components, like Esaki diodes and glow tubes, have an I-V curve that is entirely in the I and III quadrants, but has a negative slope region over a limited range. In this region, a small-signal model of the device will have negative resistance.

In the Esaki diode, this behavior is caused by tunneling current that is possible at low bias but not at higher bias voltage.

It's also possible to make an op-amp circuit with negative input resistance over a limited range. There the I-V curve can even pass through the II and IV quadrants since power can be supplied from the op-amp's power terminals.

Somewhere I have read that an example of component with negative resistance is a voltage source.

Looking at the input side of a regulated switching supply with a fixed load, it will often appear as a negative resistance.

This is because it is a constant power load. If the input voltage drops, the regulator circuit will increase the current drawn in order to continue supplying the load with the desired output voltage.

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.

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).

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 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 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 entire 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 where 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... it is constant. Rather we can think of it as a kind of "Zener diode".

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

And why are there two more types of negative resistance?

A perfect negative resistor is impossible, but a device can have negative resistance characteristics over a limited range.

The resistance of a non-linear device varies and at a given voltage the equivalent resistance is equal to the slope of the line. If the slope is negative in a range, that range has negative resistance.

• Mattmann944...I think it is important to add that your example concerns a DIFFERENTIAL (dynamic) negative resistance only!! Each working point on your "neg. Resistance" curve resembles a POSITIVE static resistance. More than that, a "perfect" negative resistor is possible, indeed (however, as perfect as each electronic part can be....). No ohmic resistor is "perfect". – LvW Apr 25 '19 at 19:25
• Yes, your answer is technically more correct than mine. The OP doesn't appear to be a college student, so I tried to keep it simple. I have only seen negative resistance used in the differential sense. Most of the Wikipedia article is devoted to differential. I did say slope, which implies differential. – Mattman944 Apr 25 '19 at 22:40

Concerning the sentence :

Somewhere I have read that an example of component with negative resistance is a voltage source.

I guess that the "voltage source with a negative resistance" is a crucial missundertanding.

The error is probably the following :

A normal source delivers U = U0 - R I.

If U0 is set to 0 Volts, then the expression becomes U = -R I.

One is tempted to think that the resistor is negative.

In fact, the minus sign comes from the conventions used to describe the sign of the U and I. These conventions are different for sources and passive components

Mostly, and above all in everyday life, this convention is the "Active sign convention" for sources and "passive sign convention" for resistors ( Wiki link )

A lot of people are not aware that they don' t use the same convention when they write U = U0 - RI for a source and U = R I for a resistor

DC-DC Converter inputs are a good example of a negative resistance. As voltage goes down, current increases to provide the same power output. Also a negative resistance can be created by an op amp circuit.

In a simple way, resistance is the ratio between voltage and current, if you plot the voltage versus the current present in a certain component, the resistance will appear as the slope between these variables. In a physic way, a positive resistance means that if the voltage of a component rises, the current that flows by also rises, otherwise, a negative resistance means that when the voltage of a component rises, the current declines.