Linear inductive transformer

Circuit description

In this example we will examine a circuit with a linear inductive transformer.

Goals

• Solve the circuit for given numerical values
• Calculate primary and secondary currents

Modeling the circuit

First we include Symbolics.jl and CircuitS.

using Symbolics
include("../CircuitS.jl")

The we create the circuit and add all of the elements as shown in the picture above:

circuit = create_circuit()
add_element([Resistor, "R1", 1, 3], circuit)
add_element([Resistor, "R2", 0, 2], circuit)
add_element([Voltage, "Ug", 3, 0], circuit)
add_element([InductiveT, "LIT", [1, 0], [2,0], ["L1", "L2", "L12"], ["I1", "I2"] ], circuit)

Simulation

Unfortunately, due to JuliaSymbolics simplify errors, we cannot symbolically solve MNA system of equations for this circuit. Instead, we will pass in values for each component and apply the phasor transform s=j*w.

We achieve this by passing a third parameter into init_circuit function, a string that represents w, and also a replacement for w inside the second argument with some numerical value (w=>1000 in this case).

We will apply the following replacements:

\[R_1 = 100 \Omega \\ R_2 = 100 \Omega \\ U_g = 5V \\ L_1 = 1\mu H \\ L_2 = 1\mu H \\ L_3 = 0.5\mu H \\ I_1 = 50 mA \\ I_2 = 0 \\ \omega = 1000\]

After we've built everything, we initialise and simulate the circuit.

@variables R1 R2 R L1 L2 L12 L I2 I1 Ug w
init_circuit(circuit, Dict([R1=>100, R2=>100, Ug=>5, L1=>1e-6, L2=>1e-6, L12=>5e-7, I1=>50e-3, I2=>0, w=>1000 ]), "w")
result = simulate(circuit)

println(result)

Dict{Any, Any} with 6 entries:
  "I_LIT_1" => 0.05 - 5.0e-7im
  "V3"      => 5.0
  "V2"      => 5.0e-10 + 2.5e-5im
  "I_Ug"    => 5.0e-7im - 0.05
  "I_LIT_2" => -5.0e-12 - 2.5e-7im
  "V1"      => 6.25e-10 + 5.0e-5im