Three-Winding Transformer

Compute sum of RF signals

Libraries:
RF Blockset / Circuit Envelope / Elements

Description

The Three-Winding Transformer block models three coupled inductors within the circuit envelope simulation environment.

The block implements the relations

$\begin{matrix} v_{1} (t) = L_{1} \frac{d}{d t} [i_{1} (t)] + M_{12} \frac{d}{d t} [i_{2} (t)] + M_{13} \frac{d}{d t} [i_{3} (t)] \\ v_{2} (t) = M_{12} \frac{d}{d t} [i_{1} (t)] + L_{2} \frac{d}{d t} [i_{2} (t)] + M_{23} \frac{d}{d t} [i_{3} (t)] \\ v_{3} (t) = M_{13} \frac{d}{d t} [i_{1} (t)] + M_{23} \frac{d}{d t} [i_{2} (t)] + L_{3} \frac{d}{d t} [i_{3} (t)] \\ M_{p q} = K_{p q} \sqrt{L_{p} L_{q}} \end{matrix}$

where:

L₁, L₂, and L₃ represent inductances.
M_pq represents the mutual inductance between the pth and qth inductors, with coefficient of coupling K_pq.
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.

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:

$\begin{matrix} i (t) = \sum_{{f_{k}}} (i_{I_{k}} (t) + j \cdot i_{Q_{k}} (t)) e^{j (2 π f_{k}) t} \\ v (t) = \sum_{{f_{k}}} (v_{I_{k}} (t) + j \cdot v_{Q_{k}} (t)) e^{j (2 π f_{k}) t} \end{matrix}$

Parameters

expand all

Inductance L1 — Inductance value of first inductor
`1e-6 H` (default) | nonnegative scalar integer

Inductance value of the first inductor, specified as a nonnegative scalar integer in henries. Specify the units of the inductance from the corresponding drop-down menu.

Data Types: double

Inductance L2 — Inductance value of second inductor
`1e-6 H` (default) | nonnegative scalar integer

Inductance value of the second inductor, specified as a nonnegative scalar integer in henries. Specify the units of the inductance from the corresponding drop-down menu.

Data Types: double

Inductance L3 — Inductance value of third inductor
`1e-6 H` (default) | nonnegative scalar integer

Inductance value of the third inductor, specified as a nonnegative scalar integer in henries. Specify the units of the inductance from the corresponding drop-down menu.

Data Types: double

Inductance L3 — Inductance value of third inductor
`1e-6 H` (default) | nonnegative scalar integer

Inductance value of the third inductor, specified as a nonnegative scalar integer in henries. Specify the units of the inductance from the corresponding drop-down menu.

Data Types: double

Coefficient of coupling K12 — Coupling coefficient of first and second inductors
`0.9` (default) | nonnegative scalar integer

Coupling coefficient for the mutual inductance of the first and second inductors, specified as a nonnegative scalar integer between 0 and 1

Data Types: double

Coefficient of coupling K13 — Coupling coefficient of first and third inductors
`0.9` (default) | nonnegative scalar integer

Coupling coefficient for the mutual inductance of the first and third inductors, specified as a nonnegative scalar integer between 0 and 1

Data Types: double

Coefficient of coupling K23 — Coupling coefficient of second and third inductors
`0.9` (default) | nonnegative scalar integer

Coupling coefficient for the mutual inductance of the second and third inductors, specified as a nonnegative scalar integer between 0 and 1

Data Types: double

Note

The minimum nonzero inductance value that the RF Blockset 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.

Version History

Introduced before R2006a

Three-Winding Transformer

Description

Parameters

Inductance L1 — Inductance value of first inductor 1e-6 H (default) | nonnegative scalar integer

Inductance L2 — Inductance value of second inductor 1e-6 H (default) | nonnegative scalar integer

Inductance L3 — Inductance value of third inductor 1e-6 H (default) | nonnegative scalar integer

Inductance L3 — Inductance value of third inductor 1e-6 H (default) | nonnegative scalar integer

Coefficient of coupling K12 — Coupling coefficient of first and second inductors 0.9 (default) | nonnegative scalar integer

Coefficient of coupling K13 — Coupling coefficient of first and third inductors 0.9 (default) | nonnegative scalar integer

Coefficient of coupling K23 — Coupling coefficient of second and third inductors 0.9 (default) | nonnegative scalar integer

Version History

See Also

Inductance L1 — Inductance value of first inductor
`1e-6 H` (default) | nonnegative scalar integer

Inductance L2 — Inductance value of second inductor
`1e-6 H` (default) | nonnegative scalar integer

Inductance L3 — Inductance value of third inductor
`1e-6 H` (default) | nonnegative scalar integer

Inductance L3 — Inductance value of third inductor
`1e-6 H` (default) | nonnegative scalar integer

Coefficient of coupling K12 — Coupling coefficient of first and second inductors
`0.9` (default) | nonnegative scalar integer

Coefficient of coupling K13 — Coupling coefficient of first and third inductors
`0.9` (default) | nonnegative scalar integer

Coefficient of coupling K23 — Coupling coefficient of second and third inductors
`0.9` (default) | nonnegative scalar integer