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Negative differential resistance (NDR) or differential negative resistance (DNR) is a property of electrical circuit elements composed of certain materials in which, over certain voltage ranges, current is a decreasing function of voltage. This range of voltages is known as a negative resistance region.

The IV curve of an ohmic (static) resistor is sloped from left to right. The only way to slope it from right to left in a limited region is to "dynamize" sufficiently the ohmic resistor in this region. In this way, the problem of obtaining a negative resistance is reduced to the problem of creating a dynamic resistance .

In electrical circuits, static resistance is the ratio of the voltage across a circuit element to the current through it. However, the ratio of the voltage to the current may vary with either voltage or current. The ratio of the change in voltage to the change in current is known as dynamic resistance.

It is more correct to say that a circuit element has a negative differential resistance region than to say that it exhibits negative resistance because even in this region the static resistance of the circuit element is positive, while it is the slope of the resistance curve which is negative.

There are two techniques for obtaining dynamic (negative) resistance - by varying the resistance and by varying the voltage . The first produces negative differential resistance, while the second gives absolute negative resistance.

Resistance variation

This is historically the first and more natural way of creating negative resistance. In electronics, there are a few two-terminal electronic components having negative differential resistance. Some of them have an S-shaped IV curve while other components have an N-shaped IV curve. Electronically-active conductive polymers such as Melanin can also show marked negative differential resistance.

S-shaped constant-voltage dynamic resistance

By dynamically decreasing the resistance of an ordinary ohmic resistor , three degrees of dynamic resistance may be obtained (Fig. 3a): decreased (section 1-2), zeroed (section 2-3) and S-negative differential resistance (section 3-4). As the section 2-3 represents a voltage-stable dynamic resistor (for example, a zener diode), a conclusion may be derived:

An S-shaped negative differential resistor is actually an "over-acting" voltage-stable dynamic resistor.

An example of an electronic component exhibiting a negative differential resistance region is the medium within a gas discharge lamp which, as current increases, ionizes to a greater extent, thereby carrying more current. If such a lamp were allowed to draw power without limit, it would instantly burn itself out. Limiting the possible current is one of the roles of the ballast in a fluorescent lamp.

N-shaped constant-current dynamic resistance

Dually, by dynamically increasing the resistance of an ordinary ohmic resistor (fig. 3b), three other degrees of dynamic resistance may be obtained: increased (section 1-2), infinite (section 2-3) and N-negative differential resistance (section 3-4). As the section 2-3 represents a current-stable dynamic resistor (for example, a barreter or the collector-emitter part of a transistor), another conclusion may be derived:

An N-shaped negative differential resistor is actually an "over-acting" current-stable dynamic resistor.

An example of an electronic component exhibiting an N-shaped negative differential resistance region is the tunnel diode. Such a device, when biased into its negative differential resistance region, acts as an amplifier. See also Gunn diode.

Negative differential resistor is an "over-acting" dynamic resistor (a dynamic resistor with extremely varying resistance).

In compliance with the law of conservation of energy, a plot of the negative differential resistance region of a passive component cannot pass through the origin.

Absolute negative resistance

The negative differential resistor is not a true negative resistor as it does not contain a source; it is just a part of a true negative resistor. In order to get an absolute negative resistor, an additional constant voltage source has to be connected in series:

Actually, the combination of the two components constitutes the varying voltage source needed. By applying this approach, a tunnel diode amplifier is built (see applications).

Applications

Amplification

Basic idea. An amplification is nothing else than controlled attenuation. According to this paradoxical idea, an amplifier consists of two components: a controlled regulating element and a power source. In electronics, the classic 3-terminal regulating element (tube, transistor etc.) acts as an electrically controlled resistor with separate input and output ports. The voltage (current) applied across (through) the input port controls the resistance between the two terminals of the output port.

The odd 2-terminal regulating element (for example, a tunnel diode) acts as an electrically controlled resistor, which input and output are the same. The voltage (current) applied across (through) the two terminals of the element controls the resistance between the same two terminals. In order to do that, the 2-terminal regulating element is actually an "over-acting" dynamic resistor (that is, a negative resistor).

Tunnel diode amplifier. In order to build such a 1-port amplifier, four components have to be connected in series (Fig. 10): a constant-voltage power supply V, an input voltage source V_IN, a "positive" resistor R and a negative differential resistor NDR (for example, a tunnel diode). Actually, the two resistors constitute a "dynamic" voltage divider supplied by a varying composed voltage source (V + V_IN). When the input voltage varies slightly, the negative differential resistor reacts vigorously to this "intervention"; it changes considerably its resistance according to the input voltage, which makes the voltage divider change noticeably its ratio. As a result, the voltage drops across the "positive" and negative resistors vary considerably; therefore, some of them may be used as an output voltage. In this arrangement, the differential negative resistor is not an amplifier; it is just a part of an amplifier (the differential negative resistor is just a 2-terminal regulating element). The combination of the differential negative resistor acting as a regulating element and the power supply constitutes true amplifier:

Non-electrical examples

There are many mechanical systems that exhibit ranges of negative differential resistance. In fact, this is a common design element in systems that are designed to have "detents" or a "positive action" or a "click." A popular example is the well-known pen clicker. Good examples are also the keys on a computer keyboard and on a computer mouse, taking the key position and upward force to be analogous to voltage and current, respectively. As a key is pressed downward, it initially presents a firm and increasing upward force. Beyond a critical point, a zone is entered in which the upward force decreases, which feels like a "sudden" yielding. This is often referred to as a "collapse action" mechanism. There are several keyboard technology that give such collapse action, such as buckling spring switches. A general characteristic of negative resistance systems is that by driving them "firmly" it is possible to traverse the negative resistance region continuously (linear applications), but bistable switching action occurs if the system is driven "loosely" (bi-stable applications).

Components with negative differential resistance

• plasma (plasma channel)
• electric arc*
• fluorescent lamp
• tunnel diode
• IMPATT diode
• Gunn diode
• unijunction transistor
• resonant tunnelling diode
• resonant tunneling transistor
• vacuum tube with significant secondary emission operated in the dynatron mode

Circuits with negative differential resistance

• Lambda diode
• negative impedance converter
• generalized impedance converter
• frequency-dependent negative resistor.

External links

• Peter D. Hooper, G. McHale, and M. I. Newton, "Negative differential resistance in MIM devices from vacuum to atmospheric pressure", Proc. SPIE Int. Soc. Opt. Eng., 2780, 38 (1996)

• Electrical circuits