Equivalent circuit diagram

An equivalent circuit diagram is the graphic representation of an equivalent circuit that behaves in the same way electrically as the original electrical circuit . Instead of a confusing, possibly unknown original circuit, the equivalent circuit diagram should be used with an easily comprehensible representation that enables predictability.

Reality and model

Different parts of an entire circuit often influence each other. The behavior of electrical components is often dependent on several influencing variables (e.g. current strength, frequency, temperature) and must be described by several parameters. Nonlinear relationships make mathematical treatment more difficult. This can make a circuit difficult to see through.

Equivalent circuit diagrams often represent a simplification compared to reality in a compromise between an easy-to-use and exact description of the system. It is a question of the accuracy requirement as to what level of simplification is used. In particular, the equivalent circuit is suitable in practice when the difference to the real circuit is in the order of magnitude of measurement errors and component tolerances.

For the equivalent circuit, models of ideal components are defined in circuit theory, which do not exist in their perfection, but which facilitate the description of the real behavior and the mathematical treatment. The simulation of the real behavior requires the equivalent circuit from several idealized elements. These include the voltage source , the current source and the linear resistors .

Equivalent circuit diagram of a real voltage source (with consumer)

It may well be that a component of the equivalent circuit diagram does not even exist as a single component. For example in the first picture the resistor is usually not as discreet as a resistor that could be soldered in. ${\displaystyle R_{\text{i}}}$

Series equivalent circuit diagram of a capacitor

Modeling

Examples of components

• The source of electrical energy can often not be represented as an ideal, but as a linear voltage source or linear current source.
• In many cases, electrical lines cannot be characterized as ideally lossless, but their behavior can be characterized by the equivalent circuit diagram with line coatings.
• Loudspeakers can be described in their electrical behavior by a complex resistance .
• A capacitor can be written to by an LRC circuit at a higher frequency .
• Electrical machines such as the three-phase synchronous machine or transformers can be represented with equivalent circuit diagrams. Their operating behavior can be derived from the equivalent circuit diagrams and displayed in vector diagrams.

Examples of circuits

• For electronic circuits , their behavior is often only in the vicinity to describe an operating point . An associated equivalent circuit is then called a small-signal equivalent circuit . For this purpose, the components are shown linearized. So z. B. a transistor , which has a non-linear characteristic , can be described by an ohmic resistor and a current source.

• A Wheatstone measuring bridge , as shown in the picture on the left, is not easy to see through.

Wheatstone measuring bridge

Equivalent circuit diagram of the bridge as voltage source with equivalent circuit diagram of the voltmeter (framed)

In terms of its output voltage , it can be replaced by a linear voltage source. Together with the equivalent circuit diagram for a real voltage measuring device, the right picture results. The equations for determining the open circuit voltage , the source resistance and the voltage that can ultimately be measured can be found in the reference article. ${\displaystyle U_{5}}$ ${\displaystyle U_{5}}$ ${\displaystyle R_{q}}$ ${\displaystyle U_{\mathrm {5,M} }}$

These equations hold without approximations. Linearization in the vicinity of an operating point for which the calibrated state is used is only used if a change in resistance is shown as a function . ${\displaystyle U_{5}}$

history

The method of equivalent circuit diagrams or the equivalent circuit was first introduced by Charles P. Steinmetz at the end of the 19th century to calculate transformers and applied to three-phase machines at the beginning of the 20th century. After the First World War, it became common practice to create equivalent circuit diagrams for electron tubes in order to describe and calculate these non-ideal and non-linear components using a circuit made up of ideal components. Heinrich Barkhausen taught to differentiate between the high-frequency circuit diagram and the circuit diagrams at low frequency.

literature

• Manfred Seifart: Analog circuits . 6th edition. Verlag Technik, Berlin 2003, ISBN 978-3-341-01298-7 .

Individual evidence

1. ^ Heinrich Frohne, Karl-Heinz Locher, Hans Müller, Thomas Harriehausen, Dieter Schwarzenau: Moeller Fundamentals of Electrical Engineering. Vieweg + Teubner, 22nd edition 2011, p. 20
2. ↑ Heiner Herberg: Electronics: Introduction for all courses. Vieweg, 2002, p. 88