A series RLC circuit
A series
RLC
circuit consists of a resistor, a capacitor, and an inductor connected in series, as shown in figure 3.36. If
R
,
L
, and
C
are the resistance, inductance, and capacitance, then the relations between voltage (
v
) and current (
i
) 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
vC
, the voltage across the capacitor, and
iL
, 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
RLC
that takes as arguments the parameters
R
,
L
, and
C
of the circuit and the time increment
dt
. In a manner similar to that of the
RC
procedure of exercise
3.73
,
RLC
should produce a procedure that takes the initial values of the state variables,
vC₀
and
iL₀
, and produces a pair (using
cons
) of the streams of states
vC
and
iL
. Using
RLC
, generate the pair of streams that models the behavior of a series
RLC
circuit with
K = 1
ohm,
C = 0.2
farad,
L = 1
henry,
dt = 0.1
second, and initial values
iL₀ = 0
amps and
vC₀ = 10
volts.