Mutual Inductor

Model two coupled inductors for circuit envelope analysis

• 

Libraries:
RF Blockset / Circuit Envelope / Elements

Description

The Mutual Inductor block models an inductor within the RF Blockset™ circuit envelope simulation environment. For an introduction to RF simulation, see the example, Simulate High Frequency Components.

The block implements the relations

$$\begin{array}{c}{v}_1(t)=L_1\frac{d}{dt}\left[i_1(t)\right]+M\frac{d}{dt}\left[i_2(t)\right]\\ v_2(t)=M\frac{d}{dt}\left[i_1(t)\right]+L_2\frac{d}{dt}\left[i_2(t)\right]\\ M=K\sqrt{L_1{L}_2}\end{array}$$

where:

• L₁ and L₂ represent inductances.

• M represents a mutual inductance with coefficient of coupling K.

• v₁(t) and v₂(t) represent the voltage across the terminals of the inductors at time t.

• i₁(t) and i₂(t) represent the current through the inductors at time t. The block uses standard dot notation to indicate the direction of positive current flow relative to a positive voltage.

RF Blockset current and voltage signals consist of in-phase (I_k) and quadrature (Q_k) components at each frequency f_k specified in the Configuration block:

$$\begin{array}{c}i(t)={\displaystyle \sum _{\left\{f_k\right\}}\left(i_{I_k}(t)+j\cdot i_{Q_k}(t)\right)e^{j(2\pi f_k)t}}\\ v(t)={\displaystyle \sum _{\left\{f_k\right\}}\left(v_{I_k}(t)+j\cdot v_{Q_k}(t)\right)e^{j(2\pi f_k)t}}\end{array}$$

Parameters

Inductance L1 — Inductance of first inductor

1e-6 H (default) | positive scalar

Inductance of the first inductor, specified as a positive scalar in H, nH, μH, mH.

Inductance L2 — Inductance of second inductor

1e-6 H (default) | positive scalar

Inductance of the second inductor, specified as a positive scalar in H, nH, μH, mH.

Coefficient of coupling — Coefficient of coupling for mutual inductance

0.9 (default) | scalar

Coefficient of coupling for the mutual inductance of the two inductors, specified as a scalar value from 0 through 1.

Version History

Introduced in R2012a