Negative resistance

In addition, circuits containing amplifying devices such as transistors and op amps with positive feedback can have negative differential resistance.

[18] Most materials, including the ordinary (positive) resistances encountered in electrical circuits, obey Ohm's law; the current through them is proportional to the voltage over a wide range.

One way in which the different types of resistance can be distinguished is in the directions of current and electric power between a circuit and an electronic component.

The illustrations below, with a rectangle representing the component attached to a circuit, summarize how the different types work: In an electronic device, the differential resistance

[49][74][75] This property means if a large enough external voltage or current of either polarity is applied to it, its static resistance becomes positive and it consumes power[74]

In a device or circuit with negative differential resistance (NDR), in some part of the I–V curve the current decreases as the voltage increases:[21]

The larger this is, the larger the potential AC output for a given DC bias current, and therefore the greater the efficiency A negative differential resistance device can amplify an AC signal applied to it[7][10] if the signal is biased with a DC voltage or current to lie within the negative resistance region of its I–V curve.

adds a constant voltage (bias) across the diode so it operates in its negative resistance range, and provides power to amplify the signal.

The diagrams illustrate how a biased negative differential resistance device can increase the power of a signal applied to it, amplifying it, although it only has two terminals.

Due to the superposition principle the voltage and current at the device's terminals can be divided into a DC bias component (

On the Smith chart, a graphical aide widely used in the design of high frequency circuits, negative differential resistance corresponds to points outside the unit circle

[44] Considered as one-port devices, these circuits function similarly to the passive negative differential resistance components above, and like them can be used to make one-port amplifiers and oscillators[2][7] with the advantages that: The I–V curve can have voltage-controlled ("N" type) or current-controlled ("S" type) negative resistance, depending on whether the feedback loop is connected in "shunt" or "series".

) will not oscillate, but the negative resistance will decrease the damping in the circuit (moving its poles toward the jω axis), increasing its Q factor so it has a narrower bandwidth and more selectivity.

[116][117][118][133] In addition, in modern high frequency oscillators, transistors are increasingly used as one-port negative resistance devices like diodes.

the current oscillates sinusoidally at the resonant frequency ω of the tuned circuit, with amplitude either constant, increasing, or decreasing exponentially, depending on the value of α.

; just small enough to allow the oscillator to start, the voltage swing will be mostly limited to the linear portion of the I–V curve, the output waveform will be nearly sinusoidal and the frequency will be most stable.

, the swing extends further into the nonlinear part of the curve, the clipping distortion of the output sine wave is more severe,[134] and the frequency will be increasingly dependent on the supply voltage.

depends on frequency ω but is also nonlinear, in general declining with the amplitude of the AC oscillation current I; while the resonator part

As above, the equality gives the condition for steady oscillation, while the inequality is required during startup to provide excess negative resistance.

[88][118] Negative differential resistance devices such as Gunn and IMPATT diodes are also used to make amplifiers, particularly at microwave frequencies, but not as commonly as oscillators.

[86] To separate the input and output signals, many negative resistance amplifiers use nonreciprocal devices such as isolators and directional couplers.

[147] George Francis FitzGerald first realized in 1892 that if the damping resistance in a resonant circuit could be made zero or negative, it would produce continuous oscillations.

William Duddell, a student of Ayrton at London Central Technical College, brought Thomson's arc oscillator to public attention.

[105][143] By the early 20th century, although the physical causes of negative resistance were not understood, engineers knew it could generate oscillations and had begun to apply it.

[84] Ernst Ruhmer and Adolf Pieper discovered that mercury vapor lamps could produce oscillations, and by 1912 AT&T had used them to build amplifying repeaters for telephone lines.

[143] In 1918 Albert Hull at GE discovered that vacuum tubes could have negative resistance in parts of their operating ranges, due to a phenomenon called secondary emission.

[125][127] Negative differential resistance in semiconductors was observed around 1909 in the first point-contact junction diodes, called cat's whisker detectors, by researchers such as William Henry Eccles[155][156] and G. W.

[156][157] They noticed that when junctions were biased with a DC voltage to improve their sensitivity as radio detectors, they would sometimes break into spontaneous oscillations.

[161] The first widely used solid-state negative resistance device was the tunnel diode, invented in 1957 by Japanese physicist Leo Esaki.

[67][163] Because they have lower parasitic capacitance than vacuum tubes due to their small junction size, diodes can function at higher frequencies, and tunnel diode oscillators proved able to produce power at microwave frequencies, above the range of ordinary vacuum tube oscillators.

Fluorescent lamp , a device with negative differential resistance. [ 1 ] In operation, an increase in current through the fluorescent tube causes a drop in voltage across it. If the tube were connected directly to the power line, the falling tube voltage would cause more and more current to flow, causing it to arc flash and destroy itself. [ 1 ] [ 2 ] To prevent this, fluorescent tubes are connected to the power line through a ballast . The ballast adds positive impedance (AC resistance) to the circuit to counteract the negative resistance of the tube, limiting the current. [ 1 ]
A Gunn diode , a semiconductor device with negative differential resistance used in electronic oscillators to generate microwaves . [ 1 ] [ 15 ] [ 3 ] [ 16 ] [ 4 ] While a positive resistance consumes power from current passing through it, a negative resistance produces power. [ 17 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 10 ] [ 12 ] [ 13 ] [ 11 ]
An I–V curve, showing the difference between static resistance (inverse slope of line B) and differential resistance (inverse slope of line C) at a point (A) .
The quadrants of the I–V plane, [ 24 ] [ 25 ] showing regions representing passive devices (white) and active devices ( red )
A battery has negative static resistance [ 20 ] [ 23 ] [ 32 ] (red) over its normal operating range, but positive differential resistance.
From KVL , the static resistance of a power source ( R S ), such as a battery, is always equal to the negative of the static resistance of its load ( R L ). [ 27 ] [ 42 ]
General (AC) model of a negative resistance circuit: a negative differential resistance device , connected to an external circuit represented by which has positive resistance, . Both may have reactance ( )
An example of an amplifier with positive feedback that has negative resistance at its input. The input current i is

so the input resistance is

If it will have negative input resistance.
An oscillator consisting of a Gunn diode inside a cavity resonator . The negative resistance of the diode excites microwave oscillations in the cavity, which radiate through the aperture into a waveguide (not shown) .
Gunn diode oscillator load lines .
DCL : DC load line, which sets the Q point.
SSL : negative resistance during startup while amplitude is small. Since poles are in RHP and amplitude of oscillations increases.
LSL : large-signal load line. When the current swing approaches the edges of the negative resistance region (green) , the sine wave peaks are distorted ("clipped") and decreases until it equals .