A series RLC circuit
circuit consists of a resistor, a capacitor, and an inductor connected in series, as shown in figure 3.36. If
are the resistance, inductance, and capacitance, then the relations between voltage (
) and current (
) for the three components are described by the equations
and the circuit connections dictate the relations
Combining these equations shows that the state of the circuit (summarized by
, the voltage across the capacitor, and
, the current in the inductor) is described by the pair of differential equations
The signal-flow diagram representing this system of differential equations is shown in figure 3.37.
Figure 3.36: A series RLC circuit.
Figure 3.37: A signal-flow diagram for the solution to a series RLC circuit.
Write a procedure
that takes as arguments the parameters
of the circuit and the time increment
. In a manner similar to that of the
procedure of exercise
should produce a procedure that takes the initial values of the state variables,
, and produces a pair (using
) of the streams of states
, generate the pair of streams that models the behavior of a series
K = 1
C = 0.2
L = 1
dt = 0.1
second, and initial values
iL₀ = 0
vC₀ = 10
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