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Three-Winding Transformer

Model three coupled inductors for circuit envelope analysis

Elements

Description

The Three-Winding Transformer block models three coupled inductors within the SimRF™ circuit envelope simulation environment. For an introduction to RF simulation, see the example, Simulate High Frequency Components.

The block implements the relations

$\begin{array}{c}{v}_{1}\left(t\right)={L}_{1}\frac{d}{dt}\left[{i}_{1}\left(t\right)\right]+{M}_{12}\frac{d}{dt}\left[{i}_{2}\left(t\right)\right]+{M}_{13}\frac{d}{dt}\left[{i}_{3}\left(t\right)\right]\\ {v}_{2}\left(t\right)={M}_{12}\frac{d}{dt}\left[{i}_{1}\left(t\right)\right]+{L}_{2}\frac{d}{dt}\left[{i}_{2}\left(t\right)\right]+{M}_{23}\frac{d}{dt}\left[{i}_{3}\left(t\right)\right]\\ {v}_{3}\left(t\right)={M}_{13}\frac{d}{dt}\left[{i}_{1}\left(t\right)\right]+{M}_{23}\frac{d}{dt}\left[{i}_{2}\left(t\right)\right]+{L}_{3}\frac{d}{dt}\left[{i}_{3}\left(t\right)\right]\\ {M}_{pq}={K}_{pq}\sqrt{{L}_{p}{L}_{q}}\end{array}$

where:

• L1, L2, and L3 represent inductances.

• Mpq represents the mutual inductance between the pth and qth inductors, with coefficient of coupling Kpq.

• v1(t), v2(t), and v3(t) represent the voltage across the terminals of the inductors at time t.

• i1(t), i2(t), and i3(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.

SimRF current and voltage signals consist of in-phase (Ik) and quadrature (Qk) components at each frequency fk specified in the Configuration block:

$\begin{array}{c}i\left(t\right)=\sum _{\left\{{f}_{k}\right\}}\left({i}_{{I}_{k}}\left(t\right)+j\cdot {i}_{{Q}_{k}}\left(t\right)\right){e}^{j\left(2\pi {f}_{k}\right)t}\\ v\left(t\right)=\sum _{\left\{{f}_{k}\right\}}\left({v}_{{I}_{k}}\left(t\right)+j\cdot {v}_{{Q}_{k}}\left(t\right)\right){e}^{j\left(2\pi {f}_{k}\right)t}\end{array}$

Dialog Box and Parameters

Inductance L1

Specify the inductance of the first inductor, L1, as a scalar value greater than or equal to 0. Specify the units of the inductance from the corresponding drop-down list. The default value of this parameter is 1e-6 H.

Inductance L2

Specify the inductance of the second inductor, L2, as a scalar value greater than or equal to 0. Specify the units of the inductance from the corresponding drop-down list. The default value of this parameter is 1e-6 H.

Inductance L3

Specify the inductance of the third inductor, L3, as a scalar value greater than or equal to 0. Specify the units of the inductance from the corresponding drop-down list. The default value of this parameter is 1e-6 H.

Coefficient of coupling K12

Specify the coefficient of coupling for the mutual inductance of the first and second inductors, K12, as a scalar value between 0 and 1, inclusive. The default value of this parameter is 0.9.

Coefficient of coupling K13

Specify the coefficient of coupling for the mutual inductance of the first and third inductors, K13, as a scalar value between 0 and 1, inclusive. The default value of this parameter is 0.9.

Coefficient of coupling K23

Specify the coefficient of coupling for the mutual inductance of the second and third inductors, K23, as a scalar value between 0 and 1, inclusive. The default value of this parameter is 0.9.

 Note:   The minimum nonzero inductance value that the SimRF environment recognizes is 1e-18 H. During simulation, the block uses a value of 1e-18 H for any inductance and mutual inductance values specified between 0 and 1e-18 H.