Model three coupled inductors for circuit envelope analysis
Elements
The Three-Winding Transformer block models three coupled inductors 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
$$\begin{array}{c}{v}_{1}(t)={L}_{1}\frac{d}{dt}\left[{i}_{1}(t)\right]+{M}_{12}\frac{d}{dt}\left[{i}_{2}(t)\right]+{M}_{13}\frac{d}{dt}\left[{i}_{3}(t)\right]\\ {v}_{2}(t)={M}_{12}\frac{d}{dt}\left[{i}_{1}(t)\right]+{L}_{2}\frac{d}{dt}\left[{i}_{2}(t)\right]+{M}_{23}\frac{d}{dt}\left[{i}_{3}(t)\right]\\ {v}_{3}(t)={M}_{13}\frac{d}{dt}\left[{i}_{1}(t)\right]+{M}_{23}\frac{d}{dt}\left[{i}_{2}(t)\right]+{L}_{3}\frac{d}{dt}\left[{i}_{3}(t)\right]\\ {M}_{pq}={K}_{pq}\sqrt{{L}_{p}{L}_{q}}\end{array}$$
where:
L_{1}, L_{2}, and L_{3} represent inductances.
M_{pq} represents the mutual inductance between the pth and qth inductors, with coefficient of coupling K_{pq}.
v_{1}(t), v_{2}(t), and v_{3}(t) represent the voltage across the terminals of the inductors at time t.
i_{1}(t), i_{2}(t), and i_{3}(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:
$$\begin{array}{c}i(t)={\displaystyle \sum _{\left\{{f}_{k}\right\}}\left({i}_{{I}_{k}}(t)+j\cdot {i}_{{Q}_{k}}(t)\right){e}^{j(2\pi {f}_{k})t}}\\ v(t)={\displaystyle \sum _{\left\{{f}_{k}\right\}}\left({v}_{{I}_{k}}(t)+j\cdot {v}_{{Q}_{k}}(t)\right){e}^{j(2\pi {f}_{k})t}}\end{array}$$
Specify the inductance of the first inductor, L_{1},
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
.
Specify the inductance of the second inductor, L_{2},
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
.
Specify the inductance of the third inductor, L_{3},
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
.
Specify the coefficient of coupling for the mutual inductance
of the first and second inductors, K_{12},
as a scalar value between 0
and 1
,
inclusive. The default value of this parameter is 0.9
.
Specify the coefficient of coupling for the mutual inductance
of the first and third inductors, K_{13},
as a scalar value between 0
and 1
,
inclusive. The default value of this parameter is 0.9
.
Specify the coefficient of coupling for the mutual inductance
of the second and third inductors, K_{23},
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 RF Blockset environment
recognizes is |