Electrical Resistance and Conductance - Static and Differential Resistance

Static and Differential Resistance

The IV curve of a component with negative differential resistance, an unusual phenomenon where the IV curve is non-monotonic. See also: Small-signal model

Many electrical elements, such as diodes and batteries do not satisfy Ohm's law. These are called non-ohmic or nonlinear, and are characterized by an I–V curve which is not a straight line through the origin.

Resistance and conductance can still be defined for non-ohmic elements. However, unlike ohmic resistance, nonlinear resistance is not constant but varies with the voltage or current through the device; its operating point. There are two types:

  • Static resistance (also called chordal or DC resistance) - This corresponds to the usual definition of resistance; the voltage divided by the current
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It is the slope of the line (chord} from the origin through the point on the curve. Static resistance determines the power dissipation in an electrical component. Points on the IV curve located in the 2nd or 4th quadrants, for which the slope of the chordal line is negative, have negative static resistance. Passive devices, which have no source of energy, cannot have negative static resistance. However active devices such as transistors or op-amps can synthesize negative static resistance with feedback, and it is used in some circuits such as gyrators.
  • Differential resistance (also called dynamic, incremental or small signal resistance) - Differential resistance is the derivative of the voltage with respect to the current; the slope of the IV curve at a point
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If the IV curve is nonmonotonic (with peaks and troughs), the curve will have a negative slope in some regions; so in these regions the device has negative differential resistance. Devices with negative differential resistance can amplify a signal applied to them, and are used to make amplifiers and oscillators. These include tunnel diodes, Gunn diodes, IMPATT diodes, magnetron tubes, and unijunction transistors.

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