# Current–voltage characteristic

The current–voltage characteristics of four devices: a resistor with large resistance, a resistor with small resistance, a P–N junction diode, and a battery with nonzero internal resistance. The horizontal axis is voltage drop, the vertical axis is current. All four plots use the passive sign convention.

A current–voltage characteristic or I–V curve (current–voltage curve) is a relationship, typically represented as a chart or graph, between the electric current through a circuit, device, or material, and the corresponding voltage, or potential difference across it.

## In electronics

MOSFET drain current vs. drain-to-source voltage for several values of the overdrive voltage, $V_{GS}-V_{th}$; 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 IV curves, referring to the standard symbols for current and voltage.

In electronic components with more than two terminals, such as vacuum tubes and transistors, the current-voltage relationship at one pair of terminals may depend on the current or voltage on a third terminal. This is usually displayed on a more complex current–voltage graph with multiple curves, each one representing the current-voltage relationship at a different value of current or voltage on the third terminal.[1]

For example the diagram at right shows a family of IV curves for a MOSFET as a function of drain voltage with overvoltage (VGS − Vth) as a parameter.

The simplest IV 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 solar cells

Photovoltaic cells are electronic devices that use P-N junctions to directly convert sunlight into electrical power. Like the electronics covered in the section above, the P-N junction in the solar cell has a complex relationship between voltage and current. As both the voltage and current is a function of the light falling on the cell, the relationship between insolation (sunlight)and output power is complex.

In particular, solar cells have a number of mechanisms that will capture slow-moving electrons of low energy (voltage). Under normal conditions in bright sunlight, these effects are saturated and represent a fixed loss in energy terms. However, at lower insolation levels, say on an overcast day, these mechanisms represent an increasing percentage of the total power being generated. It is also common for cells to be saturated if there is too much insolation, and the number of free electrons or their mobility is too small. For instance, in silicon the holes left by the photoelectrons take some time to be neutralized, and during this time they can absorb a photoelectron from another atom within the cell. This leads to maximum production rates as well as minimum.

If photovoltaic cells were free of these effects, the graph between voltage, current and output power would form a rectangle on a graph of current vs. voltage. In practice, the actual output is non-linear. The fill factor, more commonly known by its abbreviation FF, is a parameter which characterizes the non-linear electrical behavior of the solar cell. Fill factor is defined as the ratio of the maximum power from the solar cell to the product of Voc and Isc, and in tabulated data it is often used to estimate the power that a cell can provide with an optimal load under given conditions, P=FF*Voc*Isc. For most purposes, FF, Voc, and Isc are enough information to give a useful approximate model of the electrical behavior of a photovoltaic cell under typical conditions.

## In electrophysiology

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

While V–I 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 through 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.

The figure to the right shows an V–I curve that is more relevant to the currents in excitable biological membranes (such as a neuronal axon). The blue line shows the V–I 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 V–I 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.