Passivity (engineering)

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Passivity is a property of engineering systems, used in a variety of engineering disciplines, but most commonly found in analog electronics and control systems. A passive component, depending on field, may be either a component that consumes but does not produce energy (thermodynamic passivity) or a component that is incapable of power gain (incremental passivity).

Control system system to control other devices using control loops

A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large Industrial control systems which are used for controlling processes or machines.

Gain (electronics) ability of a  circuit to increase the power or amplitude of a signal

In electronics, gain is a measure of the ability of a two-port circuit to increase the power or amplitude of a signal from the input to the output port by adding energy converted from some power supply to the signal. It is usually defined as the mean ratio of the signal amplitude or power at the output port to the amplitude or power at the input port. It is often expressed using the logarithmic decibel (dB) units. A gain greater than one, that is amplification, is the defining property of an active component or circuit, while a passive circuit will have a gain of less than one.

Contents

A component that is not passive is called an active component. An electronic circuit consisting entirely of passive components is called a passive circuit and has the same properties as a passive component. Used out-of-context and without a qualifier, the term passive is ambiguous. Typically, analog designers use this term to refer to incrementally passive components and systems, while control systems engineers will use this to refer to thermodynamically passive ones.

Electronic circuit electrical circuit with active components such as transistors, valves and integrated circuits; electrical network that contains active electronic components, generally nonlinear and require complex design and analysis tools

An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. To be referred to as electronic, rather than electrical, generally at least one active component must be present. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified, computations can be performed, and data can be moved from one place to another.

Systems for which the small signal model is not passive are sometimes called locally active (e.g. transistors and tunnel diodes). Systems that can generate power about a time-variant unperturbed state are often called parametrically active (e.g. certain types of nonlinear capacitors). [1]

Thermodynamic passivity

In control systems and circuit network theory, a passive component or circuit is one that consumes energy, but does not produce energy. Under this methodology, voltage and current sources are considered active, while resistors, capacitors, inductors, transistors, tunnel diodes, metamaterials and other dissipative and energy-neutral components are considered passive. Circuit designers will sometimes refer to this class of components as dissipative, or thermodynamically passive.

Voltage source two terminal device which can maintain a fixed voltage; dual of a current source

A voltage source is a two-terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output current. However, a real-world voltage source cannot supply unlimited current. A voltage source is the dual of a current source. Real-world sources of electrical energy, such as batteries, generators, can be modeled for analysis purposes as a combination of an ideal voltage source and additional combinations of impedance elements.

Current source electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it; dual of a voltage source

A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it.

Resistor Passive electrical component providing electrical resistance

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.

While many books give definitions for passivity, many of these contain subtle errors in how initial conditions are treated and, occasionally, the definitions do not generalize to all types of nonlinear time-varying systems with memory. Below is a correct, formal definition, taken from Wyatt et al. [2] which also explains the problems with many other definitions. Given an n-port R with a state representation S, and initial state x, define available energy EA as:

Port (circuit theory) pair of terminals connecting an electrical network or circuit to an external circuit, a point of entry or exit for electrical energy

In electrical circuit theory, a port is a pair of terminals connecting an electrical network or circuit to an external circuit, a point of entry or exit for electrical energy. A port consists of two nodes (terminals) connected to an outside circuit, that meets the port condition; the currents flowing into the two nodes must be equal and opposite.

where the notation supxT≥0 indicates that the supremum is taken over all T  0 and all admissible pairs {v(·), i(·)} with the fixed initial state x (e.g., all voltage–current trajectories for a given initial condition of the system). A system is considered passive if EA is finite for all initial states x. Otherwise, the system is considered active. Roughly speaking, the inner product is the instantaneous power (e.g., the product of voltage and current), and EA is the upper bound on the integral of the instantaneous power (i.e., energy). This upper bound (taken over all T  0) is the available energy in the system for the particular initial condition x. If, for all possible initial states of the system, the energy available is finite, then the system is called passive.

Incremental passivity

In circuit design, informally, passive components refer to ones that are not capable of power gain; this means they cannot amplify signals. Under this definition, passive components include capacitors, inductors, resistors, diodes, transformers, voltage sources, and current sources. They exclude devices like transistors, vacuum tubes, relays, tunnel diodes, and glow tubes. Formally, for a memoryless two-terminal element, this means that the current–voltage characteristic is monotonically increasing. For this reason, control systems and circuit network theorists refer to these devices as locally passive, incrementally passive, increasing, monotone increasing, or monotonic. It is not clear how this definition would be formalized to multiport devices with memory as a practical matter, circuit designers use this term informally, so it may not be necessary to formalize it. [nb 1]

This term is used colloquially in a number of other contexts:

Other definitions of passivity

In electronic engineering, devices that exhibit gain or a rectifying function (such as diodes) are considered active. Only capacitors, inductors, and resistors are considered passive. [3] [4] In terms of abstract theory, diodes can be considered non-linear resistors, but non-linearity in a resistor would not normally be directional, which is the property that leads to diodes being classified as active. [5] United States Patent and Trademark Office is amongst the organisations classing diodes as active devices. [6]

Stability

Passivity, in most cases, can be used to demonstrate that passive circuits will be stable under specific criteria. Note that this only works if only one of the above definitions of passivity is used if components from the two are mixed, the systems may be unstable under any criteria. In addition, passive circuits will not necessarily be stable under all stability criteria. For instance, a resonant series LC circuit will have unbounded voltage output for a bounded voltage input, but will be stable in the sense of Lyapunov, and given bounded energy input will have bounded energy output.

Passivity is frequently used in control systems to design stable control systems or to show stability in control systems. This is especially important in the design of large, complex control systems (e.g. stability of airplanes). Passivity is also used in some areas of circuit design, especially filter design.

Passive filter

A passive filter is a kind of electronic filter that is made only from passive components in contrast to an active filter, it does not require an external power source (beyond the signal). Since most filters are linear, in most cases, passive filters are composed of just the four basic linear elements resistors, capacitors, inductors, and transformers. More complex passive filters may involve nonlinear elements, or more complex linear elements, such as transmission lines.

Television signal splitter consisting of a passive high-pass filter (left) and a passive low-pass filter (right). The antenna is connected to the screw terminals to the left of center. Hilofilter.agr.jpg
Television signal splitter consisting of a passive high-pass filter (left) and a passive low-pass filter (right). The antenna is connected to the screw terminals to the left of center.

A passive filter has several advantages over an active filter:

They are commonly used in speaker crossover design (due to the moderately large voltages and currents, and the lack of easy access to a power supply), filters in power distribution networks (due to the large voltages and currents), power supply bypassing (due to low cost, and in some cases, power requirements), as well as a variety of discrete and home brew circuits (for low-cost and simplicity). Passive filters are uncommon in monolithic integrated circuit design, where active devices are inexpensive compared to resistors and capacitors, and inductors are prohibitively expensive. Passive filters are still found, however, in hybrid integrated circuits. Indeed, it may be the desire to incorporate a passive filter that leads the designer to use the hybrid format.

Notes

  1. This is probably formalized in one of the extensions to Duffin's Theorem. One of the extensions may state that if the small signal model is thermodynamically passive, under some conditions, the overall system will be incrementally passive, and therefore, stable. This needs to be verified.

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Applications of capacitors Uses Of Capacitors In Daily Life.

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Chuas diode

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The following outline is provided as an overview of and topical guide to electronics:

References

  1. Tellegen's Theorem and Electrical Networks. Penfield, Spence, and Duinker. MIT Press, 1970. pg 24-25.
  2. Wyatt Jr., John L.; Chua, Leon O.; Gannett, Joel W.; Göknar, Izzet C.; Green, Douglas N. (January 1981). "Energy Concepts in the State-Space Theory of Nonlinear n-Ports: Part IPassivity" (PDF). IEEE Transactions on Circuits and Systems. CAS-28 (1): 48–61. doi:10.1109/TCS.1981.1084907.
  3. E C Young, "passive", The New Penguin Dictionary of Electronics, 2nd ed, p. 400, Penguin Books ISBN   0-14-051187-3.
  4. Louis E. Frenzel, Crash Course in Electronics Technology, p. 140, Newnes, 1997 ISBN   9780750697101.
  5. Ian Hickman, Analog Electronics, p. 46, Elsevier, 1999 ISBN   9780080493862.
  6. Class 257: Active Solid-state Devices", U.S. Patent and Trademark Office: Information Products Division, accessed and archived 19 August 2019.

Further reading