# curve

A characteristic curve is the graphical representation of the relationship between two physical quantities , which is characteristic of a component , an assembly or a device. The relationship is given as a line in a plane coordinate system . The characteristic curve is used to illustrate the relationship, but also to reproduce it quantitatively if an algebraic function of the relationship is not known. While a characteristic curve can be obtained directly from measured values , a theoretically unsupported, nevertheless approximately correct function, e.g. B. can be determined from measured values ​​by interpolation and regression .

If another input variable ( parameter ) is to be taken into account, several characteristics are drawn for individual values ​​of the parameter

• in a characteristic field or briefly characteristic field with a common coordinate system or
• in a parallel projection in which the parameter is given its own axis like a variable .
Characteristic curves of voltage sources show their terminal voltage as a function of the current drawn: horizontal: ideal; inclined: real linear; curved: real non-linear, here: solar cell. The three straight lines form a family of characteristics with the source resistance as a parameter.${\ displaystyle U _ {\ mathrm {kl}}}$

Characteristic curves of a semiconductor diode at different temperatures. Voltage drop as a function of the forward current
Characteristic curve of a field effect transistor , which in the upper part can be viewed as linear to such an extent that a transmission with low distortion is possible there. In the lower part of the range, the amplitude of the alternating component of for a small-signal approximation would have to be significantly smaller than shown.${\ displaystyle U _ {\ mathrm {GS}}}$

## Examples

Are simply linear relationships represented as in the basic principles of electrical engineering : The relationship between the electric voltage and electric current at a linear resistance in the form of an inclined, by the coordinate origin continuous straight - or the relationship between and at an ideal voltage source in the form of a horizontal straight line . Linear representations are often idealizations and the real relationships are non-linear . Then characteristics are particularly important. ${\ displaystyle U}$ ${\ displaystyle I}$${\ displaystyle U}$${\ displaystyle I}$

The relationship between and at a diode has an approximately exponentially increasing curve. If the temperature of the diode is added as a parameter , it becomes a family of characteristics with several current-voltage characteristics for selected temperatures. ${\ displaystyle I}$${\ displaystyle U}$

Some electrical components can be changed mechanically by turning or moving. Resistors in particular are available as variable resistors and potentiometers . The characteristic curve describes the resistance value depending on the position (angle of rotation) of a grinder. In addition to the linear characteristic with, there is also the positive-logarithmic (starting from , the resistance changes only slightly at the beginning) and the negative-logarithmic (starting from , the resistance changes very strongly at the beginning). The positive-logarithmic characteristic curve (desired relationship ) of a volume potentiometer results in an adjustment sensitivity that is adapted to the human ear. ${\ displaystyle R}$${\ displaystyle \ alpha}$${\ displaystyle \ alpha \ sim R}$${\ displaystyle \ alpha = 0}$${\ displaystyle \ alpha = 0}$${\ displaystyle \ alpha \ sim \ log (R / R _ {\ mathrm {min}})}$

In control engineering there are characteristic curves that describe the static behavior of a system, as well as those for an individual component. For control valves , for example, there are linear as well as equal-percentage characteristic curves whose curvature is opposite to the curvature of the non-linear characteristic of the controlled system. "Equal percentage" here means that the same changes in stroke correspond to the same relative flow changes (in percentages based on the current flow).

In digital technology, quantization characteristics with a stepped course are used. In addition to the linear quantization characteristic with gradations of the same width over the entire display area, there are also non-linear characteristics with finer gradations for smaller signals within their value range.

## Alternatives

The following are examples of alternatives to the characteristic curve:

Detail enlargement: For components with a non-linear characteristic, a small modulation around an operating point often results in an approximately linear relationship between the input and output variables, for which a linear characteristic can be used for the small-signal behavior .

Table: In electronic controls and microcontrollers , characteristic curves or fields are stored as table values ​​or as analytical functions in order to control complex processes. One application is map control of internal combustion engines , for which the engine map is discretized. Linear interpolation is usually used between the table values.

Function: The voltage-temperature characteristics for thermocouples are specified in the standardization by functions. For applications without computer support, however, these are so difficult to handle that additional tables are provided.

## Parallel projection

Qualitative - - diagram for water${\ displaystyle p}$${\ displaystyle v}$${\ displaystyle T}$

As an example for a parallel projection , the diagram opposite shows the relationship between pressure , specific volume and temperature for water . Characteristic curves for the relationship between and are entered for several values ​​of the parameter . ${\ displaystyle p}$ ${\ displaystyle v}$ ${\ displaystyle T}$${\ displaystyle T}$${\ displaystyle p (v)}$${\ displaystyle p}$${\ displaystyle v}$

A more detailed diagram (and without the anomaly of the water) can be found in, which also contains -characteristic curves at constant as parameters. ${\ displaystyle v (T)}$${\ displaystyle p}$