Inductor
Purpose
Ideal inductor
Library
Electrical / Passive Components
Description
This component provides one or multiple ideal inductors between its two electrical terminals. If the component is vectorized, a magnetic coupling can be specified between the internal inductors. Inductors may be switched in series only if their momentary currents are equal.
Note
An inductor may not be connected in series with a current source. Doing so would create a dependency between an input variable (the source current) and a state variable (the inductor current) in the underlying state-space equations.
Parameters
- Inductance
The inductance in henries \((\mathrm{H})\). All finite positive and negative values are accepted, including
0. The default is0.001.In a vectorized component, all internal inductors have the same inductance if the parameter is a scalar. To specify the inductances individually use a vector \([ L_1\; L_2 \ldots L_n]\). The length \(n\) of the vector determines the component’s width:
\[\begin{split}\begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix} = \begin{bmatrix} L_{1} & 0 & \cdots & 0 \\ 0 & L_{2} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & L_{n} \end{bmatrix} \begin{bmatrix} \frac{d}{dt} i_1\\ \frac{d}{dt} i_2\\ \vdots \\ \frac{d}{dt} i_n \end{bmatrix}\end{split}\]In order to model a magnetic coupling between the internal inductors enter a square matrix. The size \(n\) of the matrix corresponds to the width of the component. \(L_{i}\) is the self inductance of the internal inductor and \(M_{i,j}\) the mutual inductance:
\[\begin{split}\begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix} = \begin{bmatrix} L_{1} & M_{1,2} & \cdots & M_{1,n} \\ M_{2,1} & L_{2} & \cdots & M_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ M_{n,1} & M_{n,2} & \cdots & L_{n} \end{bmatrix} \begin{bmatrix} \frac{d}{dt} i_1\\ \frac{d}{dt} i_2\\ \vdots \\ \frac{d}{dt} i_n \end{bmatrix}\end{split}\]The inductance matrix must be invertible, i.e. it may not be singular. A singular inductance matrix results for example when two or more inductors are ideally coupled. To model this, use an inductor in parallel with an Ideal Transformer.
The relationship between the coupling factor \(k_{i,j}\) and the mutual inductance \(M_{i,j}\) is
\[M_{i,j} = M_{j,i} = k_{i,j} \sqrt{L_i \cdot L_j}\]- Initial current
The initial current through the inductor at simulation start, in amperes \((\mathrm{A})\). This parameter may either be a scalar or a vector corresponding to the width of the component. The direction of a positive initial current is indicated by a small arrow in the component symbol. The default of the initial current is
0.
Probe Signals
- Inductor current
The current flowing through the inductor, in amperes \((\mathrm{A})\). The direction of a positive current is indicated with a small arrow in the component symbol.
- Inductor voltage
The voltage measured across the inductor, in volts \((\mathrm{V})\).