# Current–voltage characteristic

Current–voltage characteristic
Figure 1. I–V curve of a P–N junction diode (not to scale).

A current–voltage characteristic is a relationship, typically represented as a chart or graph, between an electric current and a corresponding voltage, or potential difference.

## In electronics

Figure 2. MOSFET drain current vs. drain-to-source voltage for several values of the overdrive voltage, VGSVth; the boundary between linear (Ohmic) and saturation (active) modes is indicated by the upward curving parabola

In electronics, the relationship between the direct current (DC) through an electronic device and the DC voltage across its terminals is called a current–voltage characteristic of the device. Electronic engineers use these charts to determine basic parameters of a device and to model its behavior in an electrical circuit. These characteristics are also known as I-V curves, referring to the standard symbols for current and voltage.

A more general form of current–voltage characteristic is one that describes the dependence of a terminal current on more than one terminal voltage difference; electronic devices such as vacuum tubes and transistors are described by such characteristics.[1]

Figure 1 shows an I–V curve for a P-N junction diode. Figure 2 shows a family of I–V curves for a MOSFET as a function of drain voltage with overvoltage (VGS-Vth) as a parameter.

The simplest I–V characteristic involves a resistor, which according to Ohm's Law exhibits a linear relationship between the applied voltage and the resulting electric current. However, even in this case environmental factors such as temperature or material characteristics of the resistor can produce a non-linear curve.

The transconductance and Early voltage of a transistor are examples of parameters traditionally measured with the assistance of an I–V chart, or laboratory equipment that traces the charts in real time on an oscilloscope.

## In electrophysiology

Figure 3. An approximation of the potassium and sodium ion components of a so-called "whole cell" I–V curve of a neuron.

While I–V curves are applicable to any electrical system, they find wide use in the field of biological electricity, particularly in the sub-field of electrophysiology. In this case, the voltage refers to the voltage across a biological membrane, a membrane potential, and the current is the flow of charged ions across channels in this membrane. The current is determined by the conductances of these channels.

In the case of ionic current across biological membranes, currents are measured from inside to outside. That is, positive currents, known as "outward current", corresponding to positively charged ions crossing a cell membrane from the inside to the outside, or a negatively charged ion crossing from the outside to the inside. Similarly, currents with a negative value are referred to as "inward current", corresponding to positively charged ions crossing a cell membrane from the outside to the inside, or a negatively charged ion crossing from inside to outside

Figure 3 shows an I-V curve that is more relevant to the currents in excitable biological membranes (such as a neuronal axon). The blue line shows the I–V relationship for the potassium ion. Note that it is linear, indicating no voltage-dependent gating of the potassium ion channel. The yellow line shows the I–V relationship for the sodium ion. Note that it is not linear, indicating that the sodium ion channel is voltage-dependent. The green line indicates the I–V relationship derived from summing the sodium and potassium currents. This approximates the actual membrane potential and current relationship of a cell containing both types of channel.

## References

1. ^ H. J. van der Bijl (1919). "Theory and Operating Characteristics of the Themionic Amplifier". Proceedings of the IRE (Institute of Radio Engineers) 7 (2): 97–126. doi:10.1109/JRPROC.1919.217425.

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