Mrthfx

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.

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.

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

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. 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).

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, voltage across the load resistor goes up.

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.

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.

(image source)

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.

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. 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).

^{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.