2.5 Memcapacitors and Meminductors: Properties and Signatures
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2.5.2 Volatile and Nonvolatile Memory Properties
Volatile and nonvolatile memory properties of memcapacitors and meminductors
can be derived, mutatis mutandis, as shown for memristors. In particular, the
following attributes are easily obtained:
• ideal memcapacitors (resp., meminductors) present a continuum of nonvolatile
memory states associated with the memcapacitance (resp., meminductance)
values.
For a flux-controlled ideal memcapacitor (resp., charge-controlled ideal
meminductor) a nonvolatile memory state can be programmed by suitable voltage
(resp., current) pulses (similar to Example 2.11 for memristors)
• a generic and extended memcapacitor (resp., meminductor) can act as:
– nonvolatile memory memcapacitor (resp., meminductor) having both a discrete number or a continuum of memory states
– volatile memory memcapacitor (resp., meminductor) having a unique memory
state.
Volatile and nonvolatile features can be investigated by means of the POP in
voltage-controlled memcapacitors (resp., current-controlled meminductors) with
just a scalar state variable x (similar to the Example 2.14 for memristors).
2.5.3 Zero-Crossing Property and Pinched Hysteresis Loops
The comparison between the hierarchical definition of ideal, generic, and extended
(voltage-controlled) memcapacitor given at the beginning of this section and the
corresponding ideal, generic, and extended memristors (respectively in (2.31)–
(2.32), (2.42)–(2.43), and (2.46)–(2.47)) makes it clear that the pair (v, q) in
memcapacitors plays the role of (v, i) in memristors. Hence, it is apparent that the
zero-crossing property between voltage v and current i in memristors turns into the
zero-crossing property between voltage v and charge q in memcapacitors.
Thus, the charge q = 0 at any instant in which the voltage v = 0. However,
since i = 0 does not imply v = 0, a memcapacitor can store energy and deliver the
previously absorbed energy back to a circuit.
By duality, zero-crossing property holds for the flux ϕ and the current i in
meminductors as well.
A direct consequence of the coincidence between the zeros of v (resp., i) and
those of q (resp., ϕ) is that the Lissajoux figure of a memcapacitor (meminductor)
in the (v, q) plane (resp., (i, ϕ) plane) gives a pinched hysteresis loop.
In conclusion, we can summarize the signatures of memcapacitors and meminductors as done at the end of the previous section:
77
2.5.2 Volatile and Nonvolatile Memory Properties
Volatile and nonvolatile memory properties of memcapacitors and meminductors
can be derived, mutatis mutandis, as shown for memristors. In particular, the
following attributes are easily obtained:
• ideal memcapacitors (resp., meminductors) present a continuum of nonvolatile
memory states associated with the memcapacitance (resp., meminductance)
values.
For a flux-controlled ideal memcapacitor (resp., charge-controlled ideal
meminductor) a nonvolatile memory state can be programmed by suitable voltage
(resp., current) pulses (similar to Example 2.11 for memristors)
• a generic and extended memcapacitor (resp., meminductor) can act as:
– nonvolatile memory memcapacitor (resp., meminductor) having both a discrete number or a continuum of memory states
– volatile memory memcapacitor (resp., meminductor) having a unique memory
state.
Volatile and nonvolatile features can be investigated by means of the POP in
voltage-controlled memcapacitors (resp., current-controlled meminductors) with
just a scalar state variable x (similar to the Example 2.14 for memristors).
2.5.3 Zero-Crossing Property and Pinched Hysteresis Loops
The comparison between the hierarchical definition of ideal, generic, and extended
(voltage-controlled) memcapacitor given at the beginning of this section and the
corresponding ideal, generic, and extended memristors (respectively in (2.31)–
(2.32), (2.42)–(2.43), and (2.46)–(2.47)) makes it clear that the pair (v, q) in
memcapacitors plays the role of (v, i) in memristors. Hence, it is apparent that the
zero-crossing property between voltage v and current i in memristors turns into the
zero-crossing property between voltage v and charge q in memcapacitors.
Thus, the charge q = 0 at any instant in which the voltage v = 0. However,
since i = 0 does not imply v = 0, a memcapacitor can store energy and deliver the
previously absorbed energy back to a circuit.
By duality, zero-crossing property holds for the flux ϕ and the current i in
meminductors as well.
A direct consequence of the coincidence between the zeros of v (resp., i) and
those of q (resp., ϕ) is that the Lissajoux figure of a memcapacitor (meminductor)
in the (v, q) plane (resp., (i, ϕ) plane) gives a pinched hysteresis loop.
In conclusion, we can summarize the signatures of memcapacitors and meminductors as done at the end of the previous section: