2.5 Memcapacitors and Meminductors: Properties and Signatures
75
2.5 Memcapacitors and Meminductors: Properties and
Signatures
Memcapacitors and meminductors have been originally introduced by L. O. Chua
in [3] as an extension of the memristor concept to lossless elements. 10 As discussed
in Chap. 1, these circuit elements can be also axiomatically introduced via a blackbox approach based on the periodic table of circuit elements. The approach used in
Sect. 2.4 to construct a hierarchical classification of memristor devices from ideal
to generic and then to extended memristors permits to generalize the definitions of
memcapacitor and meminductor (Chap. 1), as follows:
• voltage-controlled memcapacitor
– ideal memcapacitor
q = ˆ
σ
(ϕ)v = C(ϕ)v
˙
q = i
– generic memcapacitor
q = C(x)v
˙
x = g(x, v)
˙
q = i
where x = (x 1 , x 2 , . . . , x n ) T ∈ R n is a vector of state variables
– extended memcapacitor
q = C(x, v)v
˙
x = g(x, v)
˙
q = i
where C(x, 0) is a bounded differentiable function in a neighbor of (x, 0) for
any x
• current-controlled meminductor
– ideal meminductor
ϕ = ˆ
ρ
(q)v = L(q)i
˙
ϕ = v
10 The first name and equations of a memcapacitor and meminductor were introduced by L. Chua
in the last part of the keynote lecture given at the 1st Symposium on Memristor and Memristive
Systems, University of California, Berkeley, November 2008—available online at https://www.
youtube.com/watch?v=QFdDPzcZwbs.
75
2.5 Memcapacitors and Meminductors: Properties and
Signatures
Memcapacitors and meminductors have been originally introduced by L. O. Chua
in [3] as an extension of the memristor concept to lossless elements. 10 As discussed
in Chap. 1, these circuit elements can be also axiomatically introduced via a blackbox approach based on the periodic table of circuit elements. The approach used in
Sect. 2.4 to construct a hierarchical classification of memristor devices from ideal
to generic and then to extended memristors permits to generalize the definitions of
memcapacitor and meminductor (Chap. 1), as follows:
• voltage-controlled memcapacitor
– ideal memcapacitor
q = ˆ
σ
(ϕ)v = C(ϕ)v
˙
q = i
– generic memcapacitor
q = C(x)v
˙
x = g(x, v)
˙
q = i
where x = (x 1 , x 2 , . . . , x n ) T ∈ R n is a vector of state variables
– extended memcapacitor
q = C(x, v)v
˙
x = g(x, v)
˙
q = i
where C(x, 0) is a bounded differentiable function in a neighbor of (x, 0) for
any x
• current-controlled meminductor
– ideal meminductor
ϕ = ˆ
ρ
(q)v = L(q)i
˙
ϕ = v
10 The first name and equations of a memcapacitor and meminductor were introduced by L. Chua
in the last part of the keynote lecture given at the 1st Symposium on Memristor and Memristive
Systems, University of California, Berkeley, November 2008—available online at https://www.
youtube.com/watch?v=QFdDPzcZwbs.