5.8 Formulation of Memristor Circuits Equations
199
C 1
q C1 0
q C1 (t; t 0 )
+
−
ϕ C1 (t; t 0 )
+
−
ϕ a1 (t; t 0 )
q a1 (t; t 0 )
•
•
•
•
L 1
ϕ L1 0 q L1 (t; t 0 )
−
+
ϕ L1 (t; t 0 )
+
−
ϕ b1 (t; t 0 )
q b1 (t; t 0 )
•
•
•
•
R s
M k
ϕ ew (t; t 0 )
q az (t; t 0 )
N R
Fig. 5.22 Circuit representation to derive the SEs in terms of the incremental fluxes ϕ C (t; t 0 ) and
charges q L (t; t 0 ) in the (ϕ, q)-domain
Any circuit in LM can be represented as shown in Fig. 5.22, where all capacitors
and inductors are connected to a resistive nonlinear (n C + n L )-port N R including
ideal resistors, memristors, and ideal independent flux and charge sources. 7 Each
capacitor and inductor is represented by the equivalent circuit shown in Figs. 5.7
and 5.8, respectively.
The CRs (5.32) describing the n C capacitors and n L inductors can be written in
matrix form as follows:
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
C
d
dt
ϕ C (t; t 0 )
= q C (t; t 0 ) + q C 0
L
d
dt
q L (t; t 0 )
= ϕ L (t; t 0 ) + ϕ L 0
(5.34)
7 Multiport N R is resistive because, as already pointed out, the memristor is described by an
algebraic CR in the (ϕ, q)-domain.