76
2 Fundamental Properties of Mem-Elements
– generic meminductor
ϕ = L(x)i
˙
x = f(x, i)
˙
ϕ = v
where once more x = (x 1 , x 2 , . . . , x n ) T ∈ R n is a vector of state variables
– extended meminductor
ϕ = L(x, i)i
˙
x = f(x, i)
˙
ϕ = v
where L(x, 0) is a bounded differentiable function in a neighbor of (x, 0) for any
x. By duality, both charge-controlled memcapacitors and flux-controlled meminductors can be classified as ideal, generic, and extended. 11 Recall that the ideal
memcapacitor (resp., ideal meminductor) corresponds to the (−1, −2)-element
(resp., (−2, −1)-element) in the Periodic Table of Circuit Elements (Fig. 1.12 in
Chap. 1).
Next, we briefly discuss some main properties and signatures that characterize
memcapacitors and meminductors.
2.5.1 Passivity and Losslessness
Addressing passivity and losslessness of memcapacitors and meminductors is a
nontrivial task that is still the subject of investigation. A specific condition that
guarantees passivity and losslessness in ideal memcapacitors and ideal meminductors can be derived when they are subject to a sinusoidal input [38, Sect. 2]. We
remark that the losslessness property is of special practical interest since it means
that, differently from a memristor, in principle memcapacitors and meminductors
could store data without dissipating energy.
11 Ideal generic memcapacitors and meminductors are not introduced because they can be obtained
by the corresponding ideal elements via a one-to-one transformation as shown for memristors in
the Example 2.20.
2 Fundamental Properties of Mem-Elements
– generic meminductor
ϕ = L(x)i
˙
x = f(x, i)
˙
ϕ = v
where once more x = (x 1 , x 2 , . . . , x n ) T ∈ R n is a vector of state variables
– extended meminductor
ϕ = L(x, i)i
˙
x = f(x, i)
˙
ϕ = v
where L(x, 0) is a bounded differentiable function in a neighbor of (x, 0) for any
x. By duality, both charge-controlled memcapacitors and flux-controlled meminductors can be classified as ideal, generic, and extended. 11 Recall that the ideal
memcapacitor (resp., ideal meminductor) corresponds to the (−1, −2)-element
(resp., (−2, −1)-element) in the Periodic Table of Circuit Elements (Fig. 1.12 in
Chap. 1).
Next, we briefly discuss some main properties and signatures that characterize
memcapacitors and meminductors.
2.5.1 Passivity and Losslessness
Addressing passivity and losslessness of memcapacitors and meminductors is a
nontrivial task that is still the subject of investigation. A specific condition that
guarantees passivity and losslessness in ideal memcapacitors and ideal meminductors can be derived when they are subject to a sinusoidal input [38, Sect. 2]. We
remark that the losslessness property is of special practical interest since it means
that, differently from a memristor, in principle memcapacitors and meminductors
could store data without dissipating energy.
11 Ideal generic memcapacitors and meminductors are not introduced because they can be obtained
by the corresponding ideal elements via a one-to-one transformation as shown for memristors in
the Example 2.20.