835:
32:
757:. 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.
862:
For linear filters, potentially greater linearity depending on components required (it is worth noting that in many cases, active filters allow the use of more linear components; e.g. active components can permit the use of a polypropylene or NP0 ceramic capacitor, while a passive one might require
185:
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.,
817:
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
805:
Passivity, in most cases, can be used to demonstrate that passive circuits will be stable under specific criteria. 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,
830:
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,
677:
that satisfies this inequality, known as a "storage function", is equivalent to passivity. For a given system with a known model, it is often easier to construct a storage function satisfying the differential inequality than directly computing the available energy, as taking the supremum on a
662:
919:
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
795:
Sales/product catalogs will often use different informal definitions of this term, as fitting to a particular hierarchies of products being sold. It is not uncommon, for example, to list all silicon devices under "active devices," even if some of those devices are technically
338:
769:
A passive USB to PS/2 adapter consists of wires, and potentially resistors and similar passive (in both the incremental and thermodynamic sense) components. An active USB to PS/2 adapter consists of logic to translate signals (active in the incremental
903:. When current passes through it, a non-energic passive circuit element converts none of the energy supplied to it into heat. It is non-dissipative. Resistors are energic. Ideal capacitors, inductors, transformers, and gyrators are non-energic.
745:
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).
514:
791:
is amongst the organisations classing diodes as active devices. This definition is somewhat informal, as diodes can be considered non-linear resistors, and virtually all real-world devices exhibit some
895:
Passive circuit elements may be divided into energic and non-energic kinds. When current passes through it, an energic passive circuit element converts some of the energy supplied to it into
182:
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.
220:
879:
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
780:
converter is generally just a transformer along with, of course, the requisite connectors, while an active one typically consists of a differential drive or an instrumentation amplifier.
838:
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.
438:
1001:
883:
design, where active devices are inexpensive compared to resistors and capacitors, and inductors are prohibitively expensive. Passive filters are still found, however, in
498:
831:
inductors, and transformers. More complex passive filters may involve nonlinear elements, or more complex linear elements, such as transmission lines.
500:
gives an integral equal to zero, and the available energy is the supremum over all possible trajectories. Moreover, by definition, for any trajectory {
1289:—A complete exposition of dissipative systems, with emphasis on the celebrated KYP Lemma, and on Willems' dissipativity and its use in Control.
50:
657:{\displaystyle {\frac {\operatorname {d} E_{A}(x)}{\operatorname {d} t}}=\nabla E_{A}(x(t))\cdot {\dot {x}}(t)\leq \langle v(t),i(t)\rangle }
150:
and circuit network theory, a passive component or circuit is one that consumes energy, but does not produce energy. Under this methodology,
1250:—Gives a definition of passivity for multiports (in contrast to the above), but the overall discussion of passivity is quite limited.
1136:
859:
Often less expensive in discrete designs (unless large coils are required). Active filters tend to be less expensive in integrated designs.
773:
A passive mixer consists of just resistors (incrementally passive), whereas an active mixer includes components capable of gain (active).
788:
776:
In audio work one can also find both (incrementally) passive and active converters between balanced and unbalanced lines. A passive
1148:
Nordholt, E.H. (1983). Design of High-Performance
Negative Feedback Amplifiers, Elsevier Scientific Publishing Company, Amsterdam,
1009:
871:
crossover design (due to the moderately large voltages and currents, and the lack of easy access to a power supply), filters in
1282:
900:
1153:
853:
Scale better to large signals (tens of amperes, hundreds of volts), where active devices are often expensive or impractical
374:(e.g., all voltage–current trajectories for a given initial condition of the system). A system is considered passive if
750:
333:{\displaystyle E_{A}(x)=\sup _{x\to T\geq 0}\int _{0}^{T}-\langle v(t),i(t)\rangle \,{\mathord {\operatorname {d} }}t}
1243:
1223:
1203:
1180:
1120:
1099:
1078:
984:
787:) are considered active. Only resistors, capacitors, inductors, transformers, and gyrators are considered passive.
68:
20:
1210:—Good collection of passive stability theorems, but restricted to memoryless one-ports. Readable and formal.
887:. Indeed, it may be the desire to incorporate a passive filter that leads the designer to use the hybrid format.
461:. If, for all possible initial states of the system, the energy available is finite, then the system is called
449:
is the upper bound on the integral of the instantaneous power (i.e., energy). This upper bound (taken over all
393:
806:
passive circuits will not necessarily be stable under all stability criteria. For instance, a resonant series
1303:
880:
941:
Wyatt Jr., John L.; Chua, Leon O.; Gannett, Joel W.; Göknar, Izzet C.; Green, Douglas N. (January 1981).
1030:
Tellegen's
Theorem and Electrical Networks. Penfield, Spence, and Duinker. MIT Press, 1970. pg 24-25.
884:
465:
If the available energy is finite, it is known to be non-negative, since any trajectory with voltage
810:
will have unbounded voltage output for a bounded voltage input, but will be stable in the sense of
112:
ones, which consume, but do not produce, energy. As such, without context or a qualifier, the term
1258:. Memorandum UCB/ERL M78/76, Electronics Research Laboratory, University of California, Berkeley.
46:
1266:. Memorandum UCB/ERL M80/3, Electronics Research Laboratory, University of California, Berkeley.
1132:
679:
942:
1230:—Somewhat less readable than Chua, and more limited in scope and formality of theorems.
742:
191:
468:
1041:
8:
872:
811:
754:
695:
120:
101:
85:
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1278:
1239:
1219:
1199:
1176:
1149:
1116:
1095:
1074:
1002:"What are the Main Differences Between Active and Passive Components in Electronics?"
980:
827:
957:
1135:, U.S. Patent and Trademark Office: Information Products Division, accessed and
691:
155:
151:
147:
89:
1273:
Brogliato, Bernard; Lozano, Rogelio; Maschke, Bernhard; Egeland, Olav (2007).
1297:
1187:—Very readable introductory discussion on passivity in control systems.
961:
843:
388:
1191:
876:
440:
is the instantaneous power (e.g., the product of voltage and current), and
179:
175:
868:
727:
719:
783:
In some books, devices that exhibit gain or a rectifying function (e.g.
807:
723:
694:, informally, passive components refer to ones that are not capable of
186:
which also explains the problems with many other definitions. Given an
171:
1262:
Wyatt, J.L.; Chua, L.O.; Gannett, J.; Göknar, I.C.; Green, D. (1980).
1261:
1254:
Wyatt, J.L.; Chua, L.O.; Gannett, J.; Göknar, I.C.; Green, D. (1978).
1253:
749:
Formally, for a memoryless two-terminal element, this means that the
735:
703:
699:
163:
387:. Otherwise, the system is considered active. Roughly speaking, the
890:
711:
707:
355:
167:
159:
84:
is a property of engineering systems, most commonly encountered in
814:, and given bounded energy input will have bounded energy output.
722:, voltage sources, and current sources. They exclude devices like
834:
1269:— A pair of memos that have good discussions of passivity.
765:
This term is used colloquially in a number of other contexts:
1264:
Foundations of
Nonlinear Network Theory, Part II: Losslessness
1190:
784:
777:
731:
715:
896:
702:
signals. Under this definition, passive components include
1256:
Foundations of
Nonlinear Network Theory, Part I: Passivity
940:
1233:
943:"Energy Concepts in the State-Space Theory of Nonlinear
127:, and has the same properties as a passive component.
19:"Active component" redirects here. For other uses, see
1275:
Dissipative
Systems: Analysis and Control, 2nd edition
1051:. Vol. XIII. Encyclopedia of Life Support Systems
123:
consisting entirely of passive components is called a
517:
471:
396:
223:
678:
collection of trajectories might require the use of
875:networks (due to the large voltages and currents),
457:in the system for the particular initial condition
41:
may be too technical for most readers to understand
656:
492:
432:
332:
104:. In contrast, control systems engineers will use
1213:
760:
741:To give other terminology, systems for which the
1295:
891:Energic and non-energic passive circuit elements
842:A passive filter has several advantages over an
247:
100:components and systems, which are incapable of
16:Systems that do not produce or consume energy
651:
621:
427:
397:
316:
286:
1039:
141:
1234:Cruz, Jose; Van Valkenberg, M.E. (1974).
1071:The New Penguin Dictionary of Electronics
1049:Control Systems, Robotics, and Automation
954:IEEE Transactions on Circuits and Systems
789:United States Patent and Trademark Office
668:The existence of a non-negative function
433:{\displaystyle \langle v(t),i(t)\rangle }
362: ≥ 0 and all admissible pairs {
319:
69:Learn how and when to remove this message
53:, without removing the technical details.
833:
685:
1194:; Desoer, Charles; Kuh, Ernest (1987).
370:(·)} with the fixed initial state
1296:
1170:
1133:Class 257: Active Solid-state Devices"
1092:Crash Course in Electronics Technology
974:
508:(·)}, the following inequality holds:
383:is finite for all initial states
1214:Desoer, Charles; Kuh, Ernest (1969).
51:make it understandable to non-experts
999:
25:
13:
1163:
563:
548:
521:
322:
92:. Typically, analog designers use
14:
1315:
1040:Loría, Antonio; Nijmeijer, Henk.
821:
1073:, 2nd ed, p. 400, Penguin Books
30:
1218:. McGraw–Hill Education.
1198:. McGraw–Hill Companies.
1175:(3rd ed.). Prentice Hall.
1142:
1126:
979:(3rd ed.). Prentice Hall.
947:-Ports: Part I—Passivity"
1105:
1084:
1063:
1033:
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993:
968:
934:
913:
826:A passive filter is a kind of
761:Other definitions of passivity
751:current–voltage characteristic
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1196:Linear and Nonlinear Circuits
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881:monolithic integrated circuit
158:are considered active, while
1000:Rath, Subh (29 April 2022).
800:
197:with a state representation
7:
10:
1320:
1277:. Springer Verlag London.
1236:Signals in Linear Circuits
885:hybrid integrated circuits
867:They are commonly used in
205:, define available energy
18:
1042:"Passivity based control"
1006:Electronic Components CSE
698:; this means they cannot
110:thermodynamically passive
1115:, p. 46, Elsevier, 1999
962:10.1109/TCS.1981.1084907
906:
755:monotonically increasing
1171:Khalil, Hassan (2001).
1094:, p. 140, Newnes, 1997
975:Khalil, Hassan (2001).
453: ≥ 0) is the
142:Thermodynamic passivity
134:passive, then it is an
1069:E C Young, "passive",
856:No power supply needed
839:
680:calculus of variations
658:
494:
493:{\displaystyle v(t)=0}
434:
343:where the notation sup
334:
956:. CAS-28 (1): 48–61.
837:
734:, tunnel diodes, and
686:Incremental passivity
659:
495:
435:
335:
98:incrementally passive
1304:Engineering concepts
1238:. Houghton Mifflin.
1216:Basic Circuit Theory
850:Guaranteed stability
515:
469:
394:
221:
201:, and initial state
354:indicates that the
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1113:Analog Electronics
1090:Louis E. Frenzel,
873:power distribution
840:
743:small signal model
654:
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358:is taken over all
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268:
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130:If a component is
121:electronic circuit
86:analog electronics
1284:978-1-84628-516-5
1173:Nonlinear Systems
977:Nonlinear Systems
863:an electrolytic).
828:electronic filter
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1008:. Archived from
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1139:19 August 2019.
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148:control systems
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125:passive circuit
116:is ambiguous.
90:control systems
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47:help improve it
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1111:Ian Hickman,
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1100:9780750697101
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1079:0-14-051187-3
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1053:. Retrieved
1048:
1035:
1026:
1014:. Retrieved
1010:the original
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944:
936:
915:
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877:power supply
866:
841:
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728:vacuum tubes
720:transformers
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96:to refer to
93:
81:
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65:
56:
40:
901:dissipative
724:transistors
172:transistors
1192:Chua, Leon
928:References
808:LC circuit
736:glow tubes
704:capacitors
696:power gain
504:(·),
366:(·),
164:capacitors
102:power gain
920:verified.
801:Stability
712:resistors
708:inductors
652:⟩
622:⟨
619:≤
604:˙
595:⋅
564:∇
552:
525:
428:⟩
398:⟨
317:⟩
287:⟨
284:−
270:∫
261:≥
255:→
168:inductors
160:resistors
106:passivity
94:passivity
82:Passivity
59:July 2018
1298:Category
1156:, p. 15.
1137:archived
899:. It is
812:Lyapunov
796:passive.
463:passive.
356:supremum
869:speaker
700:amplify
152:voltage
114:passive
45:Please
1281:
1242:
1222:
1202:
1179:
1152:
1119:
1098:
1077:
1055:6 July
1016:6 July
983:
785:diodes
770:sense)
732:relays
716:diodes
1045:(PDF)
950:(PDF)
907:Notes
778:balun
1279:ISBN
1240:ISBN
1220:ISBN
1200:ISBN
1177:ISBN
1150:ISBN
1117:ISBN
1096:ISBN
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