13.124. CIRCU124 - Electric Circuit

Matrix or VectorShape Functions Integration Points
Stiffness MatrixNone (lumped) None
Damping MatrixNone (lumped, harmonic analysis only) None
Load VectorNone (lumped)None

13.124.1. Electric Circuit Elements

CIRCU124 contains 10 linear electric circuit element options. These may be classified into two groups:

  1. Independent Circuit Element options, defined by 2 or 3 nodes:

    Resistor (KEYOPT(1) = 0)

    Inductor (KEYOPT(1) = 1)

    Capacitor (KEYOPT(1) = 2)

    Current Source (KEYOPT(1) = 3)

    Voltage Source (KEYOPT(1) = 4)

  2. Dependent Circuit Element options, defined by 3, 4, 5, or 6 nodes:

    Mutual inductor (KEYOPT(1) = 8)

    Voltage-controlled current source (KEYOPT(1) = 9)

    Voltage-controlled voltage source (KEYOPT(1) = 10)

    Current-controlled voltage source (KEYOPT(1) = 11)

    Current-controlled current source (KEYOPT(1) = 12)

13.124.2. Electric Circuit Element Matrices

All circuit options in CIRCU124 are based on Kirchhoff's Current Law. These options use stiffness matrices based on a simple lumped circuit model.

For transient analysis, an inductor with nodes I and J can be presented by:

(13–188)

where:

L = inductance
VI = voltage at node I
VJ = voltage at node J
Δt = time increment
θ = time integration parameter
n = time step n

A capacitor with nodes I and J is represented by:

(13–189)

where:

C = capacitance

Similarly, a mutual inductor with nodes I, J, K and L has the following matrix:

(13–190)

where:

L1 = input side inductance
L2 = output side inductance
M = mutual inductance

For harmonic analysis, the above three circuit element options have only a damping matrix. For an inductor:

(13–191)

for a capacitor:

(13–192)

and for a mutual inductor:

(13–193)


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