194
5 Flux-Charge Analysis Method of Memristor Circuits
f 1 (ϕ M1 (t))
f 2 (ϕ M2 (t))
−
+
v(t)
i(t)
−
+
ϕ(t; t 0 )
q(t; t 0 )
f 1 (ϕ M1 0 )
ϕ M1 0
f 1 (ϕ M1 (t))
q M1 (t; t 0 )
−
+
ϕ M1 (t; t 0 )
f 2 (ϕ M2 0 )
ϕ M2 0
f 2 (ϕ M2 (t))
q M2 (t; t 0 )
−
+
ϕ M2 (t; t 0 )
Fig. 5.20 (a) Parallel connection of two flux-controlled memristors and (b) equivalent circuit in
the (ϕ, q)-domain
Example 5.13 (Parallel Connection of Flux-Controlled Memristors) Consider as in
Fig. 5.20a the parallel connection of two flux-controlled memristors with CRs
q M i (t; t 0 ) = f i (ϕ M i (t; t 0 ) + ϕ M i 0 ) − f i (ϕ M i 0 )
.
= ˜
f i (ϕ M i (t; t 0 ); ϕ M i 0 )
where ϕ M i 0 = ϕ M i (t 0 ) and i = 1, 2.
We have from KqL
q(t; t 0 ) = q M 1 (t; t 0 ) + q M 2 (t; t 0 )
while KϕL yields
ϕ(t; t 0 ) = ϕ M 1 (t; t 0 ) = ϕ M 2 (t; t 0 ).