Negative resistance Definition
It is a characteristic of some electronic instruments in which an increase in the current (I) gives rise to a voltage (V) drop across the circuit. It is also called negative differential resistance or negative differential conductance. Normally in ohmic resistors, the current through a conductor between two points is directly proportional to the potential difference, according to Ohm’s law. On the other hand, negative resistors exhibit reverse behavior. Although it has only a theoretical existence, certain types of diodes display this property. It is analogous to negative temperature coefficient of resistance that occurs when a physical property of a material lowers with increasing temperature.
Negative resistance Properties
Some electric circuits show a negative current–voltage characteristic, which signifies that current flow is inversely proportional to the potential difference. Tunnel diodes and Gunn diodes usually display a negative current–voltage curve. In simple words, these are nonlinear devices connected to a two terminalcircuit. The property is also exhibited by doublebase diodes in which the emitter current increases until the power supply restricts it. This generally occurs when various active components are used to design a circuit in order to provide a source of energy. In fact, any current passing through a negative resistance adds energy to circuits, unlike a positive resistor that consumes the same energy. In a typical voltage vs. current graph, a true negative resistor has a negative curve that passes through the origin of the coordinate system that makes it act like a currenttovoltage converter. For example, if the same current I flows through a positive resistor as well as an Sshaped negative resistor with the same resistance R, the former subtracts a voltage drop V = R.I from the circuit while the latter adds the same amount of voltage. Negative resistors are usually auxiliary sources that cannot operate independently and rely heavily on the main source of current.
Negative resistance History
In the past, negative differential resistance was observed in arc discharge equipments and few vacuum tubes such as the dynatron. With the advent of solid state technology, it became possible to manufacture devices that could display this characteristic. John G. Linvill and Leo Esaki were the pioneers of negative impedance converter and tunnel diode, respectively.
Negative resistance Equation
An amplifier with a positive feedback will always exhibit the property at its input and is usually given by:
and
If Rin is large,
The above figure represents a negative resistance circuit, which in actual is an opamp implementation of the negative impedance converter. R1 and op amp are two resistors that form a negative feedback noninverting amplifier with a current gain of 2 amperes (A). The input resistance is given by:
Negative differential resistance enables the welldefined input terminal to be connected into another network. In order to produce any value of negative impedance (Z), positive impedance has to be selected.
Negative resistance Applications
The property has the following uses:
Oscillators
Oneport negative resistors like tunnel diodes, Gunn diodes and magnetron tubes are used in a number of electronic oscillator circuits. A DC voltage is applied to a circuit comprising of a resonator like LC circuit, cavity conductor or quartz crystal, connected across a negative resistor. An active negative resistor produces sustained oscillations after counteracting the effective loss resistance of the resonator. The circuits are highly applicable for oscillators at microwave frequencies. Regions of amplifying devices such as vacuum tubes exhibiting negative differential resistance are referred to as “oscillators”.
Amplifiers
At frequencies between 300 MHz (0.3 GHz) and 300 GHz, a negative resistor can function as a signal amplifier. However, these devices do not completely exhibit the property at microwave frequencies and usually demand the use of a filter. A circuit can be subjected to pure resistance if the reactive components of the device’s equivalent circuit are absorbed into the filter design in the presence of a bandpass filter that passes frequencies in a desired range, and attenuates the ones outside the range. The output terminal is attached to one port of a 3port circulator. The reflection coefficients at two ends of the filter for a positive value of R0 are given below:
Г1= Z1 R0/ Z1+R0 and, Г2= Z2R1/ Z2+R1
In the absence of resistive elements, energy dissipation is nil and the two reflection coefficients are equal i.e.│Г1│=│Г2│
The input power that enters the circulator moves towards the matching filter and gets reflected at both of its ports. A small amount of the power enters the load and is represented by:
Pout/Pin=│Г1│2
The following is obtained when R0 is replaced by negative differential resistance:
R0’= R0
Г1= Z1+R0/ Z1R0 and,
│Г1’│=│Г2’│= 1/│Г1│
The resulting reflection coefficients have higher magnitude and enhance the power reaching the load. Amplification between two ports is a consequence of a voltage drop.
Frequency changers and mixers
Nonlinear tunnel diodes are generally used as frequency converters. The electronic equipments having a negative resistance are designed in such a way that they give a conversion gain of more than 20 dB.
Antenna design
An antenna circuit uses negative differential resistance to offset resistance from other elements in the circuit. It includes an antenna for coupling with a near field radiation at a resonant frequency and a capacitance element connected in series with the receive antenna. It is specifically denoted as “negative impedance”. It is also observed in multiple driven elementscontaining antennas. Negative impedance negates the effects of positive impedance. Some of the devices exhibiting this property are:

Deboo integrator

Load cancellers

Howland current source
References
http://en.wikipedia.org/wiki/Negative_resistance
http://www.standrews.ac.uk/~www_pa/Scots_Guide/RadCom/part5/page1.html
http://sciblogs.co.nz/physicsstop/2010/11/16/negativeresistance/
http://www.sparkbangbuzz.com/els/zincoscel.htm