Equivalent circuit

An equivalent circuit diagram is the graphical representation of an equivalent circuit, which electrically behaves exactly as the original electric circuit. This allows an easy manageable representation and predictability can be achieved.

Examples are:

• The source of electrical energy can often be represented as a linear voltage source or linear current source.
• Electrical cables can be characterized in their behavior by the equivalent circuit diagram with line coatings.
• Speakers can be described in their electrical behavior through a complex resistance.
• A capacitor is described at a higher frequency by an LRC circuit.
• The behavior of electronic circuits is in the vicinity to describe an operating point. For this purpose, the components are shown linearized. Thus, for example, a transistor having a non-linear characteristic curve can be described by a resistor and a current source. This equivalent circuit is then called small-signal equivalent circuit.
• Electrical machines such as the three-phase synchronous machine or transformer can be represented by equivalent circuits. From the equivalent circuit diagrams to their operating characteristics can be derived and mapped into vector diagrams.

Frequently provide equivalent circuits simplification of reality represents a compromise between easy -to-handle and precise description of the system. It is a question of the requirement of accuracy, is gone up to which simplification. In particular, the equivalent circuit is then practicable if the difference between the actual circuit in the order of magnitude of measurement errors, and component tolerances.

Another Example

Not easy to see through a Wheatstone bridge, as shown in the left image. In view of its output voltage, it can be replaced by a linear voltage source. Together with the equivalent circuit for a real voltmeter gives the right image. The governing equations for the open-circuit voltage, the source resistance and ultimately measurable voltage can be found in the reference article.

These equations apply without approximations. Only when it is presented as a function of a change in resistance is used, a linearization around a working point, for which the balanced condition is used.

History

The method of equivalent circuits or the equivalent circle was first introduced by Charles P. Steinmetz end of the 19th century for the calculation of transformers and applied at the beginning of the 20th century three-phase machines. After the First World War, the creation of equivalent circuit diagrams for electron tubes naturalized in order to describe these non-ideal and non-linear components by a circuit of ideal components and calculate. Heinrich Barkhausen taught to distinguish between the high-frequency diagram and the circuit diagrams at low frequency.