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5 Flux-Charge Analysis Method of Memristor Circuits
Fig. 5.8 Equivalent circuit
for an ideal inductor in terms
of the incremental charge
q L (t; t 0 ) and flux ϕ L (t; t 0 )
ϕ L (t; t 0 ) = −ϕ L 0 + L
dq L (t)
dt
.
(5.25)
By observing that
L
dq L (t)
dt
= L
dq L (t; t 0 )
dt
the CR of the ideal inductor L in terms of the incremental variables q L (t; t 0 ) and
ϕ L (t; t 0 ) can be expressed as
ϕ L (t; t 0 ) = −ϕ L 0 + L
dq L (t; t 0 )
dt
(5.26)
that corresponds to the equivalent circuit shown in Fig. 5.8. 5
Again, we stress that the equivalent circuit in the (ϕ, q)-domain has a flux
source ϕ L 0 = i L 0 /L depending on the initial condition i L (t 0 ) = i L 0 for the state
variable i L (t) in the (v, i)-domain. According to (5.26), a natural choice for the state
variable of an inductor in the (ϕ, q)-domain is the incremental charge q L (t; t 0 ).
5.5.2.3 Ideal Resistor
Let us consider an ideal resistor R described by Ohm’s law
v R (t) = Ri R (t).
By integrating between t 0 and t ≥ t 0 , the CR in the (ϕ, q)-domain results to be
ϕ R (t; t 0 ) = Rq R (t; t 0 )
(5.27)
5 The circuit in Fig. 5.8 represents, in the (ϕ, q)-domain, the dual of the initial inductor current
transformation circuit reported in Fig. 2.1 on page 307 in [8].