WHAT IS DYNAMIC RESISTANCE?

Some components do not have strictly proportional relationship between current and voltage, and they do not follow the Ohm’s Law. A system may be non-linear by design (e.g. semiconductors), or may go non-linear under extreme conditions like fault or transients, fast varying load like welding, thermal runaway. Resistance across these components keeps varying depending on component V-I characteristics or state of material / component at any given point of time.  This resistance is defined as the ratio of a small change in voltage and corresponding change in current. A change of say, 0.2 V (∆I) may change the current by 1 A (∆V) at a given point on V-I curve, while at some other point, the same 0.2V change (∆V) may alter the current by 2 A (∆I). The ratio (∆V / ∆I) denotes the resistive behaviour of component at that instant. This is defined as Dynamic Resistance describes a component reaction to a minute change in voltage or current.

When resistance is measured using steady state DC current and voltage, the resistance is called Static Resistance. DC resistance follows Ohm’s Law, and V-I characteristics are linear.

1. Electronic Circuits

In practical circuits involving semiconductor components like diodes, transistors etc., small AC voltage / current signals are used to bring about a change in output. The AC signals cover a very small segment on V-I curve. Dynamic resistance varies depending on point of reference on the curve. In electronics, this is often called AC Resistance, (or small-signal resistance) for convenience in terminology. If the span on the curve under consideration is very large, the resultant resistance is termed Average AC Resistance.

Thus, there are three terms in use in electronics:

1. Static Resistance / DC resistance-:Measured from point (0,0)  to current V-I point. This follows Ohm’s Law: R = V/I.
2. AC Resistance: Ratio of incremental voltage and incremental currenF ∆V / ∆I)
3. Average AC resistance-

i) Static resistance, often called DC resistance, is determined using Ohm’s Law: R = V/I. This value is calculated by dividing the total voltage across a device by the total current flowing through it at a specific operating point. Static resistance measures the resistance from the origin (0,0) to that point on the device’s Voltage-Current (V-I) characteristic curve.

Static resistance is useful for determining the power dissipated at a fixed operating condition, while  dynamic resistance gives an understanding response of a device to a superimposed alternating current (AC) signal.

ii) Dynamic resistance: The operational reference point on V-I curve is called Quiescent Point (Q Point). Slope on the non-linear curve is continuously changing, and the dynamic resistance depends of the Q point. In diode, the point may be just above its turn-on voltage (with corresponding low dynamic resistance), ideal for signal processing. Dynamic resistance for a specified function be selected on the curve as per design requirements.

A steep slope on V-I curve means a small change in voltage causes a large change in current (low dynamic resistance). Conversely, a shallow slope a large change in voltage can produce a small change in current (high dynamic resistance). This graphical interpretation is fundamental to understanding behaviour of a device when a small AC signal is imposed on a larger DC voltage.

A diode will have very high static resistance at low voltages, since current is near zero. Once it starts conducting, dynamic resistance to small voltage change becomes very low. Dynamic resistance provides valuable factor for an accurate model of component behaviour around a given operating point.

Interpreting the V-I Curve Slope of semiconductor devices

The most practical way to visualize dynamic resistance is by examining the slope of the component’s Voltage-Current $(V-I)$ characteristic curve. This curve plots the current $(I)$ flowing through a component versus the voltage $(V)$ across it. For any given point on the curve, the dynamic resistance is represented by the reciprocal of the slope of the line tangent to the curve at that location.

2. Resistance Spot Welding:

During resistance spot welding, resistance encountered keeps varying throughout the process due to alterations in temperature, phases of material and contact characteristics. Electrical properties and heat generation are not stable, but keep changing. There is a decrease in resistance due to breakdown of oxide layer, and softening of material, and resistivity of material rises with temperature. Dynamic resistance here is calculated as small from small change in current at a precise point on V-I curve.

3. Dynamic Resistance during Fault:

case of fault on line, fault resistance has two components- (1) resistance of arc, and (2) resistance of earth (in case of earth fault); Earth resistance path is through the tower, its footing resistance and earth return. Resistance of earth is the combine of resistance of fault path through the tower, tower base resistance and earth return. Length and resistance of arc in a fault depends on a number of factors. As the arc expands in length before finally breaking, its resistance keeps varying.

Applications of Dynamic resistance in Electronics

Transistors and semiconductor devices are biased around at specific Q point appropriate for AC signal amplification. Low dynamic resistance at this point allows a small input voltage signal to generate much larger change in current output, thus achieving amplification.

Dynamic resistance plays a central role in voltage regulation and circuit stability. Zener diodes operate below their reverse breakdown region, characterized by very small dynamic resistance. Very small changes / fluctuations in input voltage or load can bring about a large change in current, while terminal voltage of Zener remains near constant. This keeps the voltage across Zener stable, protecting sensitive components and maintains stable power supply.