130:
20:
700:
electrical analysis. If the algebraic sum of the currents is not zero, such as in example diagram (c), then the energy delivered from an external generator is not equal to the energy entering the pair of circuit poles. The energy transfer at that place is thus more complex than a simple flow from one subsystem to another and does not meet the generalised definition of a port.
657:
502:
553:
683:
are not guided by electrical conductors. They are, instead guided by the walls of the waveguide. Thus, the concept of a circuit conductor pole does not exist in this format. Ports in waveguides consist of an aperture or break in the waveguide through which the electromagnetic waves can pass. The
699:
The concept of ports can be extended into other energy domains. The generalised definition of a port is a place where energy can flow from one element or subsystem to another element or subsystem. This generalised view of the port concept helps to explain why the port condition is so defined in
168:
It cannot be determined if a pair of nodes meets the port condition by analysing the internal properties of the circuit itself. The port condition is dependent entirely on the external connections of the circuit. What are ports under one set of external circumstances may well not be ports under
647:
The one-pole representation of a port will start to fail if there are significant ground plane loop currents. The assumption in the model is that the ground plane is perfectly conducting and that there is no potential difference between two locations on the ground plane. In reality, the ground
643:
and that current is sourced to or sunk into the ground plane that is equal and opposite to that going into the other pole of any port. In this topology a port is treated as being just a single pole. The corresponding balancing pole is imagined to be incorporated into the ground plane.
560:
In general, a circuit can consist of any number of ports—a multiport. Some, but not all, of the two-port parameter representations can be extended to arbitrary multiports. Of the voltage and current based matrices, the ones that can be extended are z-parameters and
719:
it is a two-port. For instance, a mechanical actuator has one port in the electrical domain and one port in the mechanical domain. Transducers can be analysed as two-port networks in the same way as electrical two-ports. That is, by means of a pair of
343:
728:. However, the variables at the two ports will be different and the two-port parameters will be a mixture of two energy domains. For instance, in the actuator example, the z-parameters will include one electrical impedance, one
648:
plane is not perfectly conducting and loop currents in it will cause potential differences. If there is a potential difference between the commoned poles of two ports then the port condition is broken and the model is invalid.
224:−1 poles. For instance, in the figure example (c), if the poles 2 and 4 are each split into two poles each then the circuit can be described as a 3-port. However, it is also possible to connect generators to pole pairs
188:
pair of poles meets the port condition. However, it is possible to deal with such a circuit by splitting one or more poles into a number of separate poles joined to the same node. If only one external
193:
terminal is connected to each pole (whether a split pole or otherwise) then the circuit can again be analysed in terms of ports. The most common arrangement of this type is to designate one pole of an
177:. On the other hand, if generators are connected to pole pairs (1, 4) and (2, 3) then those pairs are ports, the pairs (1, 2) and (3, 4) are no longer ports, and the circuit is a
102:" connected to the outside world through its ports. The ports are points where input signals are applied or output signals taken. Its behavior is completely specified by a
691:
to exist at the same time. In such cases, for each physical port, a separate port must be added to the analysis model for each of the modes present at that physical port.
110:
and current at its ports, so the internal makeup or design of the circuit need not be considered, or even known, in determining the circuit's response to applied signals.
497:{\displaystyle {\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}}
703:
The port concept is particularly useful where multiple energy domains are involved in the same system and a unified, coherent analysis is required such as with
161:
the current flowing into one pole from outside the circuit is equal to the current flowing out of the other pole into the external circuit. Equivalently, the
333:
Linear two port networks have been widely studied and a large number of ways of representing them have been developed. One of these representations is the
525:. Most of the other descriptions of two-ports can likewise be described with a similar matrix but with a different arrangement of the voltage and current
664:, a type of waveguide directional coupler. Directional couplers have four ports. This one has one port permanently terminated internally with a
569:
frequencies because voltages and currents are not convenient to measure in formats using conductors and are not relevant at all in
687:
Waveguides have an additional complication in port analysis in that it is possible (and sometimes desirable) for more than one
75:
961:
704:
715:. A transducer may be a one-port as viewed by the electrical domain, but with the more generalised definition of
940:
925:
910:
895:
880:
865:
850:
304:
157:
if it is a physical object). The port condition is that a pair of poles of a circuit is considered a port
213:
In the most general case, it is possible to have a generator connected to every pair of poles, that is,
27:
has a port connecting it to an external circuit. The port meets the port condition because the current
541:
253:
190:
170:
173:
are connected to the pole pairs (1, 2) and (3, 4) then those two pairs are ports and the circuit is a
956:
308:
725:
537:
153:
Any node of a circuit that is available for connection to an external circuit is called a pole (or
117:, but the definition in terms of current is not appropriate and the possible existence of multiple
679:
devices, but a port can no longer be defined in terms of circuit poles because in waveguides the
635:. In these formats, one pole of each port in a circuit is connected to a common node such as a
154:
44:
577:
are used at these frequencies and these too can be extended to an arbitrary number of ports.
265:
729:
680:
103:
8:
609:
581:
665:
640:
639:. It is assumed in the circuit analysis that all these commoned poles are at the same
257:
203:
52:
48:
936:
921:
906:
891:
876:
873:
Electromagnetics, Microwave
Circuit and Antenna Design for Communications Engineering
861:
846:
668:, so only three ports are visible. The ports are the openings in the centres of the
284:
87:
56:
669:
328:
165:
of the currents flowing into the two poles from the external circuit must be zero.
95:
68:
60:
169:
another. Consider the circuit of four resistors in the figure for example. If
733:
721:
688:
661:
605:
585:
277:
273:
178:
174:
158:
133:
Simple resistive network with three possible port arrangements: (a) Pole pairs
118:
36:
303:) are easier to synthesise than the general case. For a two-element one-port
950:
628:
526:
316:
288:
162:
31:
entering one terminal of the port is equal to the current exiting the other.
684:
bounded plane through which the wave passes is the definition of the port.
636:
601:
574:
562:
334:
252:
Any two-pole circuit is guaranteed to meet the port condition by virtue of
129:
269:
214:
83:
712:
708:
632:
589:
312:
300:
296:
292:
261:
79:
627:
circuit topologies are commonly unbalanced circuit topologies such as
552:
858:
RF and
Microwave Engineering: Fundamentals of Wireless Communications
676:
624:
570:
566:
533:
114:
99:
91:
256:
and they are therefore one-ports unconditionally. All of the basic
597:
593:
244:
generators in all and the circuit has to be treated as a 6-port.
107:
19:
736:
that are ratios of one electrical and one mechanical variable.
315:
are studied since these are lossless and are commonly used in
78:. Many common electronic devices and circuit blocks, such as
16:
Point of entry and exit of electrical energy to/from a circuit
283:
Study of one-ports is an important part of the foundation of
711:
analysis. Connection between energy domains is by means of
63:(terminals) connected to an outside circuit which meets the
773:
Russer, Chapter 10, "Microwave circuits: Linear multiports"
202:−1 poles. This latter form is especially useful for
556:
Coaxial circulators. Circulators have at least three ports
656:
55:
to an external circuit, as a point of entry or exit for
901:
Dean
Karnopp, Donald L. Margolis, Ronald C. Rosenberg,
620:
71:
flowing into the two nodes must be equal and opposite.
580:
Circuit blocks which have more than two ports include
459:
395:
352:
346:
521:are the voltages and currents respectively at port
74:The use of ports helps to reduce the complexity of
532:Common circuit blocks which are two-ports include
496:
184:It is even possible to arrange the inputs so that
948:
220:generators, then every pole must be split into
675:The idea of ports can be (and is) extended to
198:-pole circuit as the common and split it into
781:
779:
565:. Neither of these are suitable for use at
337:which can be described in matrix form by;
886:Herbert J. Carlin, Pier Paolo Civalleri,
776:
751:
749:
206:topologies and the resulting circuit has
149:are ports; (c) no pair of poles are ports
655:
551:
128:
113:The concept of ports can be extended to
18:
933:Acoustics: Sound Fields and Transducers
694:
94:, are analyzed in terms of ports. In
949:
843:Circuit Systems with MATLAB and PSpice
746:
802:
800:
764:Carlin & Civalleri, pp. 213–216
615:
13:
291:. Two-element one-ports (that is
14:
973:
797:
124:
828:Beranek & Mellow, pp. 96–100
98:, the circuit is regarded as a "
931:Leo Leroy Beranek, Tim Mellow,
835:
705:mechanical–electrical analogies
860:, John Wiley & Sons, 2012
845:, John Wiley & Sons, 2008
822:
813:
788:
767:
758:
1:
739:
547:
311:can be used. In particular,
651:
322:
247:
7:
841:Won Y. Yang, Seung C. Lee,
106:of parameters relating the
10:
978:
962:Linear electronic circuits
326:
141:are ports; (b) pole pairs
96:multiport network analysis
59:. A port consists of two
726:transfer function matrix
280:) are one-port devices.
935:, Academic Press, 2012
888:Wideband Circuit Design
305:Foster's canonical form
254:Kirchhoff's current law
121:must be accounted for.
918:Bond Graph Methodology
755:Yang & Lee, p. 401
672:
557:
498:
309:Cauer's canonical form
150:
32:
875:, Artech House, 2003
681:electromagnetic waves
659:
555:
499:
287:, most especially in
132:
22:
730:mechanical impedance
695:Other energy domains
582:directional couplers
344:
916:Wolfgang Borutzky,
794:Russer, pp. 237–238
724:equations or a 2Ă—2
610:directional filters
573:formats. Instead,
258:electrical elements
890:, CRC Press, 1997
673:
558:
494:
488:
448:
381:
204:unbalanced circuit
151:
88:electronic filters
49:electrical network
33:
670:waveguide flanges
285:network synthesis
57:electrical energy
969:
957:Circuit theorems
920:, Springer 2009
829:
826:
820:
819:Borutzsky, p. 20
817:
811:
804:
795:
792:
786:
783:
774:
771:
765:
762:
756:
753:
722:linear algebraic
616:RF and microwave
503:
501:
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471:
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445:
444:
433:
432:
419:
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407:
406:
386:
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378:
377:
364:
363:
329:two-port network
243:
235:
231:
227:
210:−1 ports.
148:
144:
140:
136:
76:circuit analysis
30:
26:
977:
976:
972:
971:
970:
968:
967:
966:
947:
946:
903:System Dynamics
856:Frank Gustrau,
838:
833:
832:
827:
823:
818:
814:
805:
798:
793:
789:
785:Gustrau, p. 162
784:
777:
772:
768:
763:
759:
754:
747:
742:
734:transimpedances
697:
654:
618:
586:power splitters
550:
519:
512:
487:
486:
480:
476:
473:
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466:
462:
455:
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348:
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331:
325:
278:current sources
274:voltage sources
250:
241:
237:
233:
229:
225:
218:
146:
142:
138:
134:
127:
119:waveguide modes
28:
24:
17:
12:
11:
5:
975:
965:
964:
959:
945:
944:
929:
914:
905:, Wiley, 2000
899:
884:
871:Peter Russer,
869:
854:
837:
834:
831:
830:
821:
812:
796:
787:
775:
766:
757:
744:
743:
741:
738:
696:
693:
689:waveguide mode
662:Moreno coupler
653:
650:
617:
614:
549:
546:
527:column vectors
517:
510:
505:
504:
491:
483:
479:
475:
474:
469:
465:
461:
460:
458:
451:
443:
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401:
397:
396:
394:
389:
384:
376:
372:
368:
367:
362:
358:
354:
353:
351:
327:Main article:
324:
321:
249:
246:
239:
216:
179:bridge circuit
175:box attenuator
159:if and only if
126:
125:Port condition
123:
65:port condition
47:connecting an
37:circuit theory
35:In electrical
15:
9:
6:
4:
3:
2:
974:
963:
960:
958:
955:
954:
952:
942:
938:
934:
930:
927:
923:
919:
915:
912:
908:
904:
900:
897:
893:
889:
885:
882:
878:
874:
870:
867:
863:
859:
855:
852:
848:
844:
840:
839:
825:
816:
809:
803:
801:
791:
782:
780:
770:
761:
752:
750:
745:
737:
735:
731:
727:
723:
718:
714:
710:
706:
701:
692:
690:
685:
682:
678:
671:
667:
663:
658:
649:
645:
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634:
630:
626:
622:
613:
611:
607:
603:
599:
595:
591:
587:
583:
578:
576:
572:
568:
564:
554:
545:
543:
539:
535:
530:
528:
524:
520:
513:
489:
481:
477:
467:
463:
456:
449:
441:
437:
429:
425:
415:
411:
403:
399:
392:
387:
382:
374:
370:
360:
356:
349:
340:
339:
338:
336:
330:
320:
318:
317:filter design
314:
310:
306:
302:
298:
294:
290:
289:filter design
286:
281:
279:
275:
271:
267:
263:
259:
255:
245:
223:
219:
211:
209:
205:
201:
197:
192:
187:
182:
180:
176:
172:
166:
164:
163:algebraic sum
160:
156:
131:
122:
120:
116:
111:
109:
105:
101:
97:
93:
89:
85:
81:
77:
72:
70:
66:
62:
58:
54:
50:
46:
43:is a pair of
42:
38:
21:
932:
917:
902:
887:
872:
857:
842:
836:Bibliography
824:
815:
807:
790:
769:
760:
716:
702:
698:
686:
674:
666:matched load
646:
637:ground plane
619:
602:multiplexers
579:
575:s-parameters
563:y-parameters
559:
531:
522:
515:
508:
506:
335:z-parameters
332:
282:
251:
221:
212:
207:
199:
195:
185:
183:
167:
152:
112:
84:transformers
73:
64:
40:
34:
713:transducers
590:circulators
538:attenuators
313:LC circuits
301:LC circuits
80:transistors
951:Categories
941:0123914213
926:1848828829
911:0471333018
896:0849378974
881:1580535321
866:111834958X
851:0470822406
740:References
732:, and two
709:bond graph
633:microstrip
548:Multiports
534:amplifiers
270:capacitors
171:generators
115:waveguides
92:amplifiers
677:waveguide
652:Waveguide
641:potential
625:microwave
598:duplexers
594:diplexers
571:waveguide
567:microwave
323:Two-ports
266:resistors
262:inductors
248:One-ports
191:generator
100:black box
45:terminals
806:Karnopp
155:terminal
69:currents
23:Network
810:, p. 14
629:coaxial
606:hybrids
542:filters
236:making
108:voltage
53:circuit
939:
924:
909:
894:
879:
864:
849:
808:et al.
507:where
234:(3, 2)
232:, and
230:(1, 4)
226:(1, 3)
147:(2, 3)
143:(1, 4)
139:(3, 4)
135:(1, 2)
104:matrix
90:, and
67:– the
61:nodes
937:ISBN
922:ISBN
907:ISBN
892:ISBN
877:ISBN
862:ISBN
847:ISBN
717:port
623:and
608:and
540:and
514:and
299:and
145:and
137:and
41:port
39:, a
707:or
631:or
307:or
242:= 6
51:or
953::
799:^
778:^
748:^
660:A
621:RF
612:.
604:,
600:,
596:,
592:,
588:,
584:,
544:.
536:,
529:.
442:22
430:21
416:12
404:11
319:.
297:RL
295:,
293:RC
276:,
272:,
268:,
264:,
228:,
186:no
181:.
86:,
82:,
943:.
928:.
913:.
898:.
883:.
868:.
853:.
523:n
518:n
516:I
511:n
509:V
490:]
482:2
478:I
468:1
464:I
457:[
450:]
438:z
426:z
412:z
400:z
393:[
388:=
383:]
375:2
371:V
361:1
357:V
350:[
260:(
240:2
238:C
222:n
217:2
215:C
208:n
200:n
196:n
29:I
25:N
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