8768:
4912:
5423:
4922:
2301:
194:
8516:
5418:{\displaystyle {\begin{aligned}{\frac {\mathbf {V} _{\mathsf {L}}}{\mathbf {V} _{\mathsf {S}}}}&=\left^{-1}\\&={\frac {\mathbf {Z} _{\mathsf {L}}\mathbf {Z} _{\mathsf {C}}}{\mathbf {Z} _{\mathsf {C}}\left(\mathbf {Z} _{\mathsf {L}}+\mathbf {Z} _{\mathsf {S}}\right)\cosh \left({\boldsymbol {\gamma }}x\right)+\left(\mathbf {Z} _{\mathsf {L}}\mathbf {Z} _{\mathsf {S}}+\mathbf {Z} _{\mathsf {C}}^{2}\right)\sinh \left({\boldsymbol {\gamma }}x\right)}}\end{aligned}}}
1883:
11103:
2598:
11113:
11092:
8216:
11123:
2356:
6243:
8712:
2296:{\displaystyle {\begin{aligned}{\frac {\partial ^{2}}{\partial x^{2}}}V(x,t)-LC\,{\frac {\partial ^{2}}{\partial t^{2}}}V(x,t)&=\left(RC+GL\right){\frac {\partial }{\partial t}}V(x,t)+GR\,V(x,t)\\{\frac {\partial ^{2}}{\partial x^{2}}}I(x,t)-LC\,{\frac {\partial ^{2}}{\partial t^{2}}}I(x,t)&=\left(RC+GL\right){\frac {\partial }{\partial t}}I(x,t)+GR\,I(x,t)\end{aligned}}}
8201:
1834:
3187:
3891:
3579:
9075:
6019:
4172:
8511:{\displaystyle {\begin{aligned}{\frac {\partial ^{2}}{\partial x^{2}}}V&=LC{\frac {\partial ^{2}}{\partial t^{2}}}V+\left(RC+GL\right){\frac {\partial }{\partial t}}V+GRV,\\{\frac {\partial ^{2}}{\partial x^{2}}}I&=LC{\frac {\partial ^{2}}{\partial t^{2}}}I+\left(RC+GL\right){\frac {\partial }{\partial t}}I+GRI.\end{aligned}}}
6511:
7961:
1602:
2987:
2593:{\displaystyle {\begin{aligned}{\frac {\partial }{\partial x}}\mathbf {V} _{\omega }(x)&=-\left(j\omega L_{\omega }+R_{\omega }\right)\mathbf {I} _{\omega }(x),\\{\frac {\partial }{\partial x}}\mathbf {I} _{\omega }(x)&=-\left(j\omega C_{\omega }+G_{\omega }\right)\mathbf {V} _{\omega }(x).\end{aligned}}}
7911:
3307:
3687:
3375:
8863:
6694:
4002:
6315:
9286:
5834:. The first equation shows that the induced voltage is related to the time rate-of-change of the current through the cable inductance, while the second shows, similarly, that the current drawn by the cable capacitance is related to the time rate-of-change of the voltage.
6845:
5642:
9178:
4275:
1279:
can be inferred from Terman: "The power factor ... tends to be independent of frequency, since the fraction of energy lost during each cycle ... is substantially independent of the number of cycles per second over wide frequency ranges." A function of the form
6238:{\displaystyle {\begin{aligned}{\frac {\partial ^{2}V}{\partial t^{2}}}-{\tilde {v}}^{2}{\frac {\partial ^{2}V}{\partial x^{2}}}&=0\\{\frac {\partial ^{2}I}{\partial t^{2}}}-{\tilde {v}}^{2}{\frac {\partial ^{2}I}{\partial x^{2}}}&=0\end{aligned}}}
7139:
3992:
3680:
5560:
8196:{\displaystyle {\begin{aligned}{\frac {\partial }{\partial x}}V(x,t)&=-L{\frac {\partial }{\partial t}}I(x,t)-R\,I(x,t)\,,\\{\frac {\partial }{\partial x}}I(x,t)&=-C{\frac {\partial }{\partial t}}V(x,t)-G\,V(x,t)\,.\end{aligned}}}
1829:{\displaystyle {\begin{aligned}{\frac {\partial }{\partial x}}V(x,t)&=-L\,{\frac {\partial }{\partial t}}I(x,t)-RI(x,t)\\{\frac {\partial }{\partial x}}I(x,t)&=-C\,{\frac {\partial }{\partial t}}V(x,t)-GV(x,t)\end{aligned}}}
55:. In the time domain the independent variables are distance and time. The resulting time domain equations are partial differential equations of both time and distance. In the frequency domain the independent variables are distance
6536:
3182:{\displaystyle {\begin{aligned}{\frac {d^{2}}{dx^{2}}}\mathbf {V} _{\omega }(x)&=\gamma ^{2}\mathbf {V} _{\omega }(x)\\{\frac {d^{2}}{dx^{2}}}\mathbf {I} _{\omega }(x)&=\gamma ^{2}\mathbf {I} _{\omega }(x)\end{aligned}}}
5963:
5898:
1364:
6908:
5821:
3192:
9183:
8696:
6701:
7484:
5469:
9080:
454:
7901:
6706:
5746:
4176:
4007:
8868:
6541:
6320:
6292:
is the propagation speed of waves traveling through the transmission line. For transmission lines made of parallel perfect conductors with vacuum between them, this speed is equal to the speed of light.
6024:
4927:
3380:
2992:
2361:
1888:
1607:
8221:
7966:
3886:{\displaystyle {\begin{aligned}\mathbf {I} _{\omega ,F}(x)=\mathbf {I} _{\omega ,F}(a)\,e^{+\gamma (a-x)}\,;\\\mathbf {I} _{\omega ,R}(x)=\mathbf {I} _{\omega ,R}(b)\,e^{-\gamma (b-x)}\,;\end{aligned}}}
3574:{\displaystyle {\begin{aligned}\mathbf {V} _{\omega ,F}(x)=\mathbf {V} _{\omega ,F}(a)\,e^{+\gamma (a-x)}\,;\\\mathbf {V} _{\omega ,R}(x)=\mathbf {V} _{\omega ,R}(b)\,e^{-\gamma (b-x)}\,;\end{aligned}}}
7598:
6290:
9070:{\displaystyle {\begin{aligned}V_{1}&=V_{2}\cosh(\gamma x)+I_{2}Z_{\mathsf {o}}\sinh(\gamma x)\,,\\I_{1}&={\frac {V_{2}}{Z_{\mathsf {o}}}}\sinh(\gamma x)+I_{2}\cosh(\gamma x)\,.\end{aligned}}}
1582:
so at a high enough frequency, dielectric losses will exceed resistive losses. In practice, before that point is reached, a transmission line with a better dielectric is used. In long distance rigid
795:
at radio frequencies, and for simplicity is treated as if it were zero, with any voltage dissipation or wire heating accounted for as corrections to the "lossless line" calculation, or just ignored.
7238:
5566:
4167:{\displaystyle {\begin{aligned}\mathbf {V} _{\omega ,F}(x)=\mathbf {Z} _{c}\,\mathbf {I} _{\omega ,F}(x),\\\mathbf {V} _{\omega ,R}(x)=\mathbf {Z} _{c}\,\mathbf {I} _{\omega ,R}(x),\end{aligned}}}
7012:
3692:
7017:
6506:{\displaystyle {\begin{aligned}V(x,t)&={\mathcal {R_{e}}}{\bigl \{}V(x)\,e^{j\omega t}{\bigr \}}\,,\\I(x,t)&={\mathcal {R_{e}}}{\bigl \{}I(x)\,e^{j\omega t}{\bigr \}}\,,\end{aligned}}}
670:
728:
The capacitance couples voltage to the energy stored in the electric field. It controls how much the bunched-up electrons within each conductor repel, attract, or divert the electrons in the
4854:
4801:
4748:
4695:
4595:
4542:
4489:
4436:
3895:
3583:
2848:
2783:
2703:
2638:
4642:
4383:
2971:
2933:
1580:
8853:
The solutions of the telegrapher's equations can be inserted directly into a circuit as components. The circuit in the figure implements the solutions of the telegrapher's equations.
1545:
5714:
wire resistance and insulation conductance can be neglected, and the transmission line is considered as an ideal lossless structure. In this case, the model depends only on the
4892:
1393:
7188:
2353:
The telegrapher's equations in the frequency domain are developed in similar forms in the following references: Kraus, Hayt, Marshall, Sadiku, Harrington, Karakash, Metzger.
788:
a little of the voltage along the line as heat deposited into the conductor, leaving the current unchanged. Generally, the line resistance is very low, compared to inductive
7914:
In the presence of losses the solution of the telegrapher's equation has both damping and dispersion, as visible when compared with the solution of a lossless wave equation.
8623:
8588:
8557:
5710:
5680:
2887:
1442:
2741:
517:
5902:
5837:
43:. The equations and their solutions are applicable from 0 Hz (i.e. direct current) to frequencies at which the transmission line structure can support higher order
1283:
5497:
9431:
6531:
3327:
1509:
638:
610:
583:
556:
98:
9561:
3351:
9541:
9514:
9487:
9460:
9402:
9375:
9348:
7686:
7639:
7541:
7514:
7367:
7292:
7265:
1471:
481:
8528:
and their first derivatives. These extra terms cause the signal to decay and spread out with time and distance. If the transmission line is only slightly lossy
7956:
7936:
7749:
7729:
7706:
7659:
7159:
6854:
6013:
5990:
5741:
5489:
4339:
4313:
2806:
2661:
2343:
2323:
1877:
1856:
1262:
1242:
641:
to emphasize that the values are derivatives with respect to length, and that the units of measure combine correctly. These quantities can also be known as the
394:
364:
338:
296:
266:
242:
125:
73:
10367:
732:
conductor. By deflecting some of these bunched up electrons, the speed of the wave and its strength (voltage) are both reduced. With a larger capacitance,
7374:
1586:, to get very low dielectric losses, the solid dielectric may be replaced by air with plastic spacers at intervals to keep the center conductor on axis.
11147:
816:
it between the conductors. Generally, wire insulation (including air) is quite good, and the conductance is almost nothing compared to the capacitive
7754:
3302:{\textstyle \gamma \equiv \alpha +j\beta \equiv {\sqrt {\left(R_{\omega }+j\omega L_{\omega }\right)\left(G_{\omega }+j\omega C_{\omega }\right)}}}
141:. The resulting frequency domain equations are ordinary differential equations of distance. An advantage of the frequency domain approach is that
6248:
867:
are zero, which is the simplest and by far most common form of the telegrapher's equations used, but slightly unrealistic (especially regarding
6689:{\displaystyle {\begin{aligned}{\frac {dV}{dx}}=-j\omega LI=-L{\frac {dI}{dt}}\\{\frac {dI}{dx}}=-j\omega CV=-C{\frac {dV}{dt}}\end{aligned}}}
8628:
7199:
11075:
11047:
11042:
10067:
6922:
10027:
8736:
396:
of the dielectric material separating the two conductors is represented by a shunt resistor between the signal wire and the return wire (
9615:
5428:
404:
7371:
the most general solution of the wave equation for the voltage is the sum of a forward traveling wave and a backward traveling wave:
7688:
represents the amplitude profile of a wave traveling from right to left. It can be seen that the instantaneous voltage at any point
8210:
3996:
The negative sign in the previous equation indicates that the current in the reverse wave is traveling in the opposite direction.
9281:{\displaystyle \gamma \equiv {\sqrt {\left(R_{\omega }+j\omega L_{\omega }\right)\left(G_{\omega }+j\omega C_{\omega }\right)}},}
484:
7556:
804:
Conductance between the lines represents how well current can "leak" from one line to the other. Conductance couples voltage to
11069:
699:
makes the wave move more slowly, just as waves travel more slowly down a heavy rope than a light string. Large inductance also
661:. All these constants are constant with respect to time, voltage and current. They may be non-constant functions of frequency.
9570:, sheath, common, earth, or ground. So every two-wire balanced transmission line has two modes which are nominally called the
6840:{\displaystyle {\begin{aligned}{\frac {d^{2}V}{dx^{2}}}+k^{2}V&=0\\{\frac {d^{2}I}{dx^{2}}}+k^{2}I&=0\\\end{aligned}}}
5637:{\displaystyle {\frac {\mathbf {V} _{\mathsf {L}}}{\mathbf {V} _{\mathsf {S}}}}={\frac {1}{2}}e^{-{\boldsymbol {\gamma }}x}\,}
695:– i.e. with a large inductance, it is difficult to increase or decrease the current flow at any given point. Large inductance
11152:
11064:
11054:
11034:
10836:
7322:
374:
222:
9595:
account for the interaction of the transmission line with the external circuit. This circuit is a useful equivalent for an
10201:
11126:
11059:
10905:
9173:{\displaystyle Z_{\mathsf {o}}\equiv {\sqrt {\frac {R_{\omega }+j\omega L_{\omega }}{G_{\omega }+j\omega C_{\omega }}}},}
1269:
9566:
Every two-wire or balanced transmission line has an implicit (or in some cases explicit) third wire which is called the
10831:
4270:{\displaystyle \mathbf {Z} _{c}={\sqrt {\frac {R_{\omega }+j\omega L_{\omega }}{G_{\omega }+j\omega C_{\omega }}}}\,,}
10925:
9980:
9910:
9885:
9857:
9829:
9801:
9753:
9693:
8754:
3366:
10710:
10258:
10060:
9722:
879:
Representative parameter data for 24-gauge telephone polyethylene insulated cable (PIC) at 70 °F (294 K)
10821:
4815:
4762:
4709:
4656:
4556:
4503:
4450:
4397:
2814:
2749:
2669:
2604:
7309:
are constant at any point on the line, provided that the cross-sectional geometry of the line remains constant.
10816:
9661:
5831:
4609:
4350:
2938:
2900:
1550:
166:
can be reflected on the wire, and that wave patterns can form along the line. Originally developed to describe
1838:
They can be combined to get two partial differential equations, each with only one dependent variable, either
10841:
2981:
691:
The inductance couples current to energy stored in the magnetic field. It makes it look like the current has
11116:
10877:
10774:
10317:
10112:
10084:
9624:
7134:{\displaystyle I(x)={\frac {V_{1}}{Z_{\mathsf {o}}}}\,e^{-jkx}-{\frac {V_{2}}{Z_{\mathsf {o}}}}\,e^{+jkx}}
1514:
859:
tend to drop as the frequency goes up. The figure at right shows a lossless transmission line, where both
11157:
11106:
10613:
10053:
7958:
are too substantial to ignore, the differential equations describing the elementary segment of line are
4911:
10965:
10887:
10826:
10533:
6533:
is the angular frequency of the steady-state wave. In this case, the telegrapher's equations reduce to
528:
of the infinitesimal elements shown in the figure, and that the values of the components are specified
9435:
The voltage and current relations are symmetrical: Both of the equations shown above, when solved for
4868:
1369:
10737:
10698:
10543:
10443:
10372:
10305:
10132:
8727:
7164:
8767:
3987:{\displaystyle \mathbf {I} _{\omega }(x)=\mathbf {I} _{\omega ,F}(x)-\mathbf {I} _{\omega ,R}(x)\,.}
3675:{\displaystyle \mathbf {V} _{\omega }(x)=\mathbf {V} _{\omega ,F}(x)+\mathbf {V} _{\omega ,R}(x)\,.}
11096:
10338:
10273:
10226:
10186:
9714:
8857:
8595:
8564:
8533:
7192:
5686:
5656:
4896:
2859:
1406:
673:
Schematic showing a wave flowing rightward down a lossless transmission line. Black dots represent
646:
201:
The telegrapher's equations, like all other equations describing electrical phenomena, result from
10935:
10920:
10764:
10715:
10638:
10538:
10216:
10102:
10097:
5555:{\displaystyle \mathbf {Z} _{\mathsf {L}}=\mathbf {Z} _{\mathsf {S}}=\mathbf {Z} _{\mathsf {C}},}
2714:
495:
206:
154:
10857:
10643:
10458:
10403:
10398:
10211:
10176:
642:
202:
10006:
10759:
10563:
10528:
10448:
10428:
10350:
10238:
10159:
9408:
6516:
3312:
1479:
163:
142:
83:
10092:
9546:
3336:
843:
depend on the material used to build the cable or feedline. All four change with frequency:
10673:
10633:
10603:
10360:
10295:
10117:
9563:
terms' signs made negative ("1"→"2" direction is reversed "1"←"2", hence the sign change).
9519:
9492:
9465:
9438:
9380:
9353:
9326:
7664:
7617:
7519:
7492:
7340:
7270:
7243:
3330:
2708:
1449:
1395:
close to 1.0 would fit Terman's statement. Chen gives an equation of similar form. Whereas
789:
654:
650:
460:
174:
776:
Resistance corresponds to resistance interior to the two lines, combined. That resistance
8:
10683:
10623:
10382:
10344:
10142:
10127:
5722:
elements. The telegrapher's equations then describe the relationship between the voltage
760:
712:
39:. The equations are important because they allow transmission lines to be analyzed using
7641:
represents the amplitude profile of a wave traveling from left to right – in a positive
681:
The role of the different components can be visualized based on the animation at right.
618:
590:
563:
536:
10910:
10867:
10798:
10668:
10598:
10573:
10508:
10355:
10076:
9543:
yield exactly the same relations, merely with subscripts "1" and "2" reversed, and the
7941:
7921:
7734:
7714:
7691:
7644:
7295:
7144:
6913:
5998:
5975:
5474:
4324:
4298:
2791:
2646:
2328:
2308:
1862:
1841:
1247:
1227:
813:
379:
349:
341:
323:
281:
251:
227:
110:
58:
9651:
740:
line (which always has the opposite charge) partly cancels out these repulsive forces
10950:
10872:
10786:
10769:
10732:
10578:
10408:
10377:
10243:
10137:
9976:
9949:
9906:
9881:
9853:
9825:
9797:
9749:
9739:
9718:
9689:
9657:
8771:
Equivalent circuit of an unbalanced transmission line (such as coaxial cable) where:
8722:
7601:
7548:
532:
so the picture of the component can be misleading. An alternative notation is to use
134:
130:
103:
36:
10618:
9581:
In the top circuit, the voltage doublers, the difference amplifiers, and impedances
645:
to distinguish from the secondary line constants derived from them, these being the
10955:
10915:
10895:
10862:
10791:
10749:
10663:
10518:
10503:
10478:
10453:
10413:
10263:
10122:
10107:
9667:
5958:{\displaystyle {\frac {\partial I}{\partial x}}=-C{\frac {\partial V}{\partial t}}}
5893:{\displaystyle {\frac {\partial V}{\partial x}}=-L{\frac {\partial I}{\partial t}}}
210:
149:
52:
32:
1359:{\displaystyle G(f)=G_{1}\cdot \left({\frac {f}{f_{1}}}\right)^{g_{\mathrm {e} }}}
10583:
10438:
10206:
10181:
10169:
9596:
8701:
6309:
808:
deposited as heat into whatever serves as insulation between the two conductors.
805:
752:
745:
704:
488:
303:
178:
171:
44:
9578:. The circuit shown in the bottom diagram only can model the differential mode.
268:
increases approximately proportional to the square root of frequency due to the
10781:
10653:
10628:
10588:
10558:
10433:
10268:
10221:
10196:
10154:
9972:
9620:
7606:
6312:
have ceased), the voltage and current take the form of single-tone sine waves:
3354:
970:
748:, making the wave move slightly slower, and also gives the transmission line a
669:
658:
397:
299:
182:
40:
11141:
10930:
10703:
10693:
10608:
10498:
10493:
10483:
10468:
10290:
10149:
9793:
9600:
5968:
1583:
781:
214:
197:
Schematic representation of the elementary components of a transmission line
193:
10808:
10648:
10593:
10523:
10488:
10423:
10322:
10312:
10164:
8520:
These equations resemble the homogeneous wave equation with extra terms in
6305:
1272:. The constancy of the capacitance is a consequence of intentional design.
946:
785:
6903:{\displaystyle k\equiv \omega {\sqrt {LC}}={\frac {\omega }{\tilde {v}}}.}
5816:{\displaystyle {\begin{aligned}V&=V(x,t)\\I&=I(x,t)\end{aligned}}}
11008:
10658:
10568:
10553:
10513:
10473:
10332:
9774:
1265:
937:
817:
318:
269:
48:
7294:
are arbitrary constants of integration, which are determined by the two
11013:
10720:
10418:
10327:
10283:
10253:
10231:
10035:
9817:
9745:
8691:{\displaystyle \alpha \approx {\frac {R}{2Z_{0}}}+{\frac {GZ_{0}}{2}}~}
7910:
2853:
276:
10998:
10463:
10278:
10045:
8781:
is the trans-admittance of VCCS (Voltage
Controlled Current Source),
6302:
5730:
along the transmission line, each of which is a function of position
344:
167:
76:
10007:"SPICE Simulation of Transmission Lines by the Telegrapher's Method"
7479:{\displaystyle V(x,t)=f_{1}(x-{\tilde {v}}t)+f_{2}(x+{\tilde {v}}t)}
5830:
The equations themselves consist of a pair of coupled, first-order,
244:
of the conductors is represented by a series resistor (expressed in
145:
in the time domain become algebraic operations in frequency domain.
10993:
10983:
10900:
10725:
10548:
8856:
The solution of the telegrapher's equations can be expressed as an
874:
674:
307:
10032:
SPICE simulation of transmission lines by the telegrapher's method
7301:
This impedance does not change along the length of the line since
6912:
Each of these two equations is in the form of the one-dimensional
248:
per unit length). In practical conductors, at higher frequencies,
16:
Mathematical descriptions of transmission line voltage and current
10988:
10973:
10191:
7196:
of the transmission line, which, for a lossless line is given by
5464:{\displaystyle \mathbf {H} \equiv e^{-{\boldsymbol {\gamma }}x},}
2974:
692:
400:
per unit length). This resistor in the model has a resistance of
311:
138:
28:
9953:
5825:
2980:
These equations may be combined to produce two, single-variable
449:{\displaystyle R_{\text{shunt}}={\frac {1}{G}}\,\mathrm {ohms} }
11018:
10978:
10300:
9606:
These are not unique: Other equivalent circuits are possible.
8702:
Solutions of the telegrapher's equations as circuit components
7896:{\displaystyle I(x,t)={\frac {1}{Z_{\mathsf {o}}}}{\Bigl }\,.}
3365:
Each of the preceding partial differential equations have two
27:) are a set of two coupled, linear equations that predict the
11003:
10940:
10248:
7751:
relations given by the telegrapher's equations, we can write
994:
912:
367:
10945:
7312:
The lossless line and distortionless line are discussed in
7708:
on the line is the sum of the voltages due to both waves.
7593:{\displaystyle {\tilde {v}}\equiv {\frac {1}{\sqrt {LC}}}}
6285:{\displaystyle {\tilde {v}}\equiv {\frac {1}{\sqrt {LC}}}}
4343:
point at which the values of the reverse waves are known
4317:
point at which the values of the forward waves are known
919:
245:
9320:
to emphasize that they could be functions of frequency.
5494:
In the special case where all the impedances are equal,
137:
of the time domain variables or they can be taken to be
9288:
just as in the preceding sections. The line parameters
7233:{\displaystyle Z_{\mathsf {o}}={\sqrt {\frac {L}{C}}}}
4915:
Coaxial transmission line with one source and one load
3195:
181:), low frequency (such as power lines), and pulses of
9679:
9677:
9549:
9522:
9495:
9468:
9441:
9411:
9383:
9356:
9329:
9186:
9083:
8866:
8631:
8598:
8567:
8536:
8219:
7964:
7944:
7924:
7757:
7737:
7717:
7694:
7667:
7647:
7620:
7559:
7522:
7495:
7377:
7343:
7273:
7246:
7202:
7167:
7147:
7020:
6925:
6857:
6704:
6539:
6519:
6318:
6308:(i.e., when a pure sinusoidal voltage is applied and
6251:
6022:
6001:
5978:
5905:
5840:
5744:
5689:
5659:
5569:
5500:
5477:
5431:
4925:
4871:
4818:
4765:
4712:
4659:
4612:
4559:
4506:
4453:
4400:
4353:
4327:
4301:
4179:
4005:
3898:
3690:
3586:
3378:
3339:
3315:
2990:
2941:
2903:
2862:
2852:
the voltage at that point appearing across the shunt
2817:
2794:
2752:
2717:
2707:
the current at that point passing through the series
2672:
2649:
2607:
2359:
2331:
2311:
1886:
1865:
1844:
1605:
1553:
1517:
1482:
1476:
Usually the resistive losses grow proportionately to
1452:
1409:
1372:
1286:
1250:
1230:
621:
593:
566:
539:
498:
463:
407:
382:
352:
326:
284:
254:
230:
205:. In a more practical approach, one assumes that the
113:
86:
61:
7161:
is a real quantity that may depend on frequency and
7007:{\displaystyle V(x)=V_{1}\,e^{-jkx}+V_{2}\,e^{+jkx}}
1599:
The telegrapher's equations in the time domain are:
9960:
9741:
Subscriber Loop
Signaling and Transmission Handbook
7330:
823:, and for simplicity is treated as if it were zero.
129:The frequency domain variables can be taken as the
9674:
9555:
9535:
9508:
9481:
9454:
9425:
9396:
9369:
9342:
9280:
9172:
9069:
8690:
8617:
8582:
8551:
8510:
8205:By differentiating both equations with respect to
8195:
7950:
7930:
7895:
7743:
7723:
7700:
7680:
7653:
7633:
7592:
7535:
7508:
7478:
7361:
7286:
7259:
7232:
7182:
7153:
7133:
7006:
6919:In the lossless case, it is possible to show that
6902:
6839:
6688:
6525:
6505:
6284:
6237:
6007:
5984:
5967:These equations may be combined to form two exact
5957:
5892:
5815:
5704:
5674:
5636:
5554:
5483:
5463:
5417:
4886:
4848:
4795:
4742:
4689:
4636:
4589:
4536:
4483:
4430:
4377:
4333:
4307:
4269:
4166:
3986:
3885:
3674:
3573:
3345:
3321:
3301:
3181:
2965:
2927:
2881:
2842:
2800:
2777:
2735:
2697:
2655:
2632:
2592:
2337:
2317:
2295:
1871:
1850:
1828:
1574:
1539:
1503:
1465:
1436:
1387:
1358:
1256:
1236:
632:
604:
577:
550:
511:
475:
448:
388:
358:
332:
290:
260:
236:
119:
92:
67:
9848:Marshall, Stanley V.; Skitek, Gabriel G. (1987).
7884:
7800:
1224:This data is from Reeve (1995). The variation of
744:each conductor. Larger capacitance equals weaker
11139:
9924:
9922:
875:Values of primary parameters for telephone cable
9948:(1st ed.). Academic Press. pp. 1–10.
9894:
9843:
9841:
9824:(3rd ed.). McGraw-Hill. pp. 380–419.
9656:(5th ed.). McGraw-Hill. pp. 381–392.
664:
340:between the two conductors is represented by a
9847:
1511:and dielectric losses grow proportionately to
10061:
9998:
9966:
9919:
9905:(1st ed.). McGraw-Hill. pp. 61–65.
9880:(1st ed.). Saunders College Publishing.
9871:
9869:
9683:
7321:harvp error: no target: CITEREFMarshall1987 (
7298:(one for each end of the transmission line).
6490:
6454:
6400:
6364:
5826:The equations for lossless transmission lines
4277:where the following symbol definitions hold:
2810:is decreased by the current loss produced by
2665:is decreased by the voltage loss produced by
851:tend to increase for higher frequencies, and
491:. If the dielectric is an ideal vacuum, then
47:. The equations can be expressed in both the
9943:
9937:
9838:
9781:
8592:signal strength will decay over distance as
1402:is conductivity as a function of frequency,
213:elementary components, each representing an
11076:Global telecommunications regulation bodies
9967:Miano, Giovanni; Maffucci, Antonio (2001).
9944:Metzger, Georges; Vabre, Jean-Paul (1969).
9645:
9643:
9641:
4858:value of the reverse current wave at point
4849:{\displaystyle \mathbf {I} _{\omega ,R}(b)}
4805:value of the forward current wave at point
4796:{\displaystyle \mathbf {I} _{\omega ,F}(a)}
4752:value of the reverse current wave at point
4743:{\displaystyle \mathbf {I} _{\omega ,R}(x)}
4699:value of the forward current wave at point
4690:{\displaystyle \mathbf {I} _{\omega ,F}(x)}
4599:value of the reverse voltage wave at point
4590:{\displaystyle \mathbf {V} _{\omega ,R}(b)}
4546:value of the forward voltage wave at point
4537:{\displaystyle \mathbf {V} _{\omega ,F}(a)}
4493:value of the reverse voltage wave at point
4484:{\displaystyle \mathbf {V} _{\omega ,R}(x)}
4440:value of the forward voltage wave at point
4431:{\displaystyle \mathbf {V} _{\omega ,F}(x)}
2843:{\displaystyle \mathbf {V} _{\omega }(x)\,}
2778:{\displaystyle \mathbf {I} _{\omega }(x)\,}
2698:{\displaystyle \mathbf {I} _{\omega }(x)\,}
2633:{\displaystyle \mathbf {V} _{\omega }(x)\,}
11112:
10068:
10054:
9900:
9866:
9762:
9616:Reflections of signals on conducting lines
7905:
6296:
11148:Hyperbolic partial differential equations
9933:(1st ed.). Macmillan. pp. 5–14.
9850:Electromagnetic Concepts and Applications
9810:
9731:
9422:
9059:
8959:
8755:Learn how and when to remove this message
8211:hyperbolic partial differential equations
8185:
8166:
8073:
8054:
7889:
7111:
7062:
6984:
6951:
6495:
6471:
6405:
6381:
5633:
4637:{\displaystyle \mathbf {I} _{\omega }(x)}
4378:{\displaystyle \mathbf {V} _{\omega }(x)}
4263:
4129:
4052:
3980:
3875:
3846:
3781:
3752:
3668:
3563:
3534:
3469:
3440:
2966:{\displaystyle \mathbf {V} _{\omega }(x)}
2928:{\displaystyle \mathbf {I} _{\omega }(x)}
2897:indicates possible frequency dependence.
2878:
2839:
2774:
2694:
2629:
2270:
2148:
2069:
1947:
1764:
1656:
1575:{\displaystyle g_{\mathrm {e} }\approx 1}
1423:
677:, and the arrows show the electric field.
508:
431:
188:
170:wires, the theory can also be applied to
158:starting with an August 1876 paper,
10034:. Microwave & RF design – via
10004:
9946:Transmission Lines with Pulse Excitation
9928:
9702:
9684:Johnson, Howard; Graham, Martin (2003).
9638:
8766:
8209:, and some algebra, we obtain a pair of
7909:
7317:
5648:
5491:is the length of the transmission line.
4910:
3360:
668:
217:short segment of the transmission line:
192:
6698:Likewise, the wave equations reduce to
5624:
5449:
5396:
5309:
736:, there is less repulsion, because the
11140:
10075:
9969:Transmission Lines and Lumped Circuits
9931:Transmission lines and Filter Networks
9875:
9768:
9090:
9002:
8935:
8860:with the following defining equations
7790:
7313:
7209:
7174:
7103:
7054:
5594:
5580:
5543:
5526:
5509:
5368:
5351:
5337:
5286:
5269:
5250:
5234:
5220:
5172:
5158:
5137:
5121:
5050:
5036:
4954:
4940:
4919:Johnson gives the following solution,
209:are composed of an infinite series of
10049:
9816:
9737:
35:distributions on a linear electrical
11122:
9903:Time-Harmonic Electromagnetic Fields
9787:
9708:
9649:
8785:is the length of transmission line,
8705:
4646:value of the total current at point
4387:value of the total voltage at point
1540:{\displaystyle f^{g_{\mathrm {e} }}}
2348:
2305:Except for the dependent variable (
306:, etc.) is represented by a series
13:
8477:
8473:
8424:
8414:
8379:
8369:
8335:
8331:
8282:
8272:
8237:
8227:
8133:
8129:
8087:
8083:
8021:
8017:
7975:
7971:
6445:
6441:
6355:
6351:
6205:
6191:
6149:
6135:
6101:
6087:
6045:
6031:
5946:
5938:
5917:
5909:
5881:
5873:
5852:
5844:
3369:in an infinite transmission line.
2483:
2479:
2370:
2366:
2234:
2230:
2162:
2152:
2105:
2095:
2033:
2029:
1961:
1951:
1904:
1894:
1771:
1767:
1724:
1720:
1663:
1659:
1616:
1612:
1560:
1529:
1379:
1348:
442:
439:
436:
433:
162:. The model demonstrates that the
14:
11169:
9769:Terman, Frederick Emmons (1943).
8807:is the characteristic impedance,
8213:each involving only one unknown:
2787:the propagating current at point
2642:the propagating voltage at point
11121:
11111:
11102:
11101:
11090:
10711:Free-space optical communication
9627:preliminary work on this subject
8710:
7331:Loss-free case, general solution
5588:
5574:
5537:
5520:
5503:
5433:
5362:
5345:
5331:
5280:
5263:
5244:
5228:
5214:
5166:
5152:
5130:
5115:
5092:
5075:
5044:
5030:
5001:
4984:
4948:
4934:
4906:
4887:{\displaystyle \mathbf {Z} _{c}}
4874:
4821:
4768:
4715:
4662:
4615:
4562:
4509:
4456:
4403:
4356:
4182:
4132:
4119:
4089:
4055:
4042:
4012:
3955:
3925:
3901:
3821:
3791:
3727:
3697:
3643:
3613:
3589:
3509:
3479:
3415:
3385:
3156:
3118:
3064:
3026:
2944:
2906:
2820:
2755:
2675:
2610:
2564:
2494:
2451:
2381:
1589:
1388:{\displaystyle g_{\mathrm {e} }}
759:voltage needed to push the same
711:voltage needed to push the same
9852:(2nd ed.). Prentice-Hall.
9688:(1st ed.). Prentice-Hall.
8829:is the propagation "constant",
7183:{\displaystyle Z_{\mathsf {o}}}
2745:The second equation means that
812:reduces propagating current by
9056:
9047:
9025:
9016:
8956:
8947:
8913:
8904:
8182:
8170:
8157:
8145:
8111:
8099:
8070:
8058:
8045:
8033:
7999:
7987:
7879:
7870:
7855:
7839:
7830:
7815:
7773:
7761:
7566:
7473:
7464:
7449:
7433:
7424:
7409:
7393:
7381:
7030:
7024:
6935:
6929:
6890:
6468:
6462:
6428:
6416:
6378:
6372:
6338:
6326:
6258:
6175:
6071:
5832:partial differential equations
5806:
5794:
5774:
5762:
4843:
4837:
4790:
4784:
4737:
4731:
4684:
4678:
4631:
4625:
4584:
4578:
4531:
4525:
4478:
4472:
4425:
4419:
4372:
4366:
4154:
4148:
4111:
4105:
4077:
4071:
4034:
4028:
3977:
3971:
3947:
3941:
3917:
3911:
3870:
3858:
3843:
3837:
3813:
3807:
3776:
3764:
3749:
3743:
3719:
3713:
3665:
3659:
3635:
3629:
3605:
3599:
3558:
3546:
3531:
3525:
3501:
3495:
3464:
3452:
3437:
3431:
3407:
3401:
3172:
3166:
3134:
3128:
3080:
3074:
3042:
3036:
2982:partial differential equations
2960:
2954:
2922:
2916:
2836:
2830:
2771:
2765:
2691:
2685:
2626:
2620:
2600:The first equation means that
2580:
2574:
2510:
2504:
2467:
2461:
2397:
2391:
2345:) the formulas are identical.
2286:
2274:
2258:
2246:
2193:
2181:
2136:
2124:
2085:
2073:
2057:
2045:
1992:
1980:
1935:
1923:
1819:
1807:
1795:
1783:
1748:
1736:
1711:
1699:
1687:
1675:
1640:
1628:
1594:
1296:
1290:
1:
9901:Harrington, Roger F. (1961).
9876:Sadiku, Matthew N.O. (1989).
9686:High Speed Signal Propagation
9631:
9323:The ABCD type two-port gives
8818:is the propagation function,
8618:{\displaystyle e^{-\alpha x}}
8583:{\displaystyle G\ll \omega C}
8552:{\displaystyle R\ll \omega L}
5705:{\displaystyle \omega C\gg G}
5675:{\displaystyle \omega L\gg R}
2882:{\displaystyle G+j\omega C\,}
1437:{\displaystyle G_{1},\,f_{1}}
11153:Distributed element circuits
11097:Telecommunication portal
10878:Telecommunications equipment
9878:Elements of Electromagnetics
9653:Engineering Electromagnetics
9597:unbalanced transmission line
7141:where in this special case,
1191:
1162:
1133:
1104:
1075:
1046:
1017:
665:Role of different components
7:
10614:Alexander Stepanovich Popov
10005:McCammon, Roy (June 2010).
9609:
8730:. The specific problem is:
2736:{\displaystyle R+j\omega L}
1209:
1206:
1197:
1180:
1177:
1168:
1151:
1148:
1139:
1122:
1119:
1110:
1093:
1090:
1081:
1064:
1061:
1052:
1035:
1032:
1023:
512:{\displaystyle G\equiv 0\,}
177:, audio frequency (such as
10:
11174:
10318:Telecommunications history
9929:Karakash, John J. (1950).
9738:Reeve, Whitman D. (1995).
767:current through the line).
719:current through the line).
11085:
11027:
10964:
10926:Public Switched Telephone
10886:
10850:
10807:
10748:
10738:telecommunication circuit
10699:Fiber-optic communication
10682:
10444:Francis Blake (telephone)
10391:
10239:Optical telecommunication
10083:
9987:The book uses the symbol
9771:Radio Engineers' Handbook
9650:Hayt, William H. (1989).
3684:For the current equation
3372:For the voltage equation
904:
899:
894:
889:
524:The model consists of an
10837:Orbital angular-momentum
10274:Satellite communications
10113:Communications satellite
9788:Chen, Walter Y. (2004).
9715:Cornell University Press
7193:characteristic impedance
5562:the solution reduces to
4897:Characteristic impedance
1473:are all real constants.
647:characteristic impedance
148:The equations come from
10716:Molecular communication
10539:Gardiner Greene Hubbard
10368:Undersea telegraph line
10103:Cable protection system
9709:Hunt, Bruce J. (2005).
9426:{\displaystyle I_{2}\,}
7918:When the loss elements
7906:Lossy transmission line
6526:{\displaystyle \omega }
6297:Sinusoidal steady-state
3322:{\displaystyle \alpha }
1504:{\displaystyle f^{1/2}}
483:accounts for both bulk
155:transmission line model
93:{\displaystyle \omega }
21:telegrapher's equations
10858:Communication protocol
10644:Charles Sumner Tainter
10459:Walter Houser Brattain
10404:Edwin Howard Armstrong
10212:Information revolution
9790:Home Networking Basics
9557:
9556:{\displaystyle \sinh }
9537:
9510:
9483:
9456:
9427:
9398:
9371:
9344:
9282:
9174:
9071:
8850:
8692:
8619:
8584:
8553:
8512:
8197:
7952:
7932:
7915:
7897:
7745:
7725:
7702:
7682:
7655:
7635:
7594:
7537:
7510:
7480:
7363:
7335:In the loss-free case
7288:
7261:
7234:
7184:
7155:
7135:
7008:
6904:
6841:
6690:
6527:
6507:
6286:
6239:
6009:
5994:the other for current
5986:
5959:
5894:
5817:
5706:
5676:
5638:
5556:
5485:
5465:
5419:
4916:
4888:
4850:
4797:
4744:
4691:
4638:
4591:
4538:
4485:
4432:
4379:
4335:
4309:
4271:
4168:
3988:
3887:
3676:
3575:
3347:
3346:{\displaystyle \beta }
3323:
3303:
3183:
2967:
2929:
2883:
2844:
2802:
2779:
2737:
2699:
2657:
2634:
2594:
2339:
2319:
2297:
1873:
1852:
1830:
1576:
1541:
1505:
1467:
1438:
1389:
1360:
1258:
1238:
678:
643:primary line constants
634:
606:
579:
552:
513:
487:of the dielectric and
477:
450:
390:
360:
334:
292:
262:
238:
198:
189:Distributed components
143:differential operators
121:
94:
69:
10832:Polarization-division
10564:Narinder Singh Kapany
10529:Erna Schneider Hoover
10449:Jagadish Chandra Bose
10429:Alexander Graham Bell
10160:online video platform
9558:
9538:
9536:{\displaystyle I_{2}}
9511:
9509:{\displaystyle V_{2}}
9484:
9482:{\displaystyle I_{1}}
9457:
9455:{\displaystyle V_{1}}
9428:
9399:
9397:{\displaystyle V_{2}}
9372:
9370:{\displaystyle I_{1}}
9345:
9343:{\displaystyle V_{1}}
9283:
9175:
9072:
8858:ABCD two-port network
8770:
8693:
8620:
8585:
8554:
8513:
8198:
7953:
7933:
7913:
7898:
7746:
7726:
7703:
7683:
7681:{\displaystyle f_{2}}
7656:
7636:
7634:{\displaystyle f_{1}}
7595:
7538:
7536:{\displaystyle f_{2}}
7511:
7509:{\displaystyle f_{1}}
7481:
7364:
7362:{\displaystyle R=G=0}
7289:
7287:{\displaystyle V_{2}}
7262:
7260:{\displaystyle V_{1}}
7235:
7185:
7156:
7136:
7009:
6905:
6842:
6691:
6528:
6508:
6287:
6240:
6010:
5987:
5960:
5895:
5818:
5707:
5677:
5649:Lossless transmission
5639:
5557:
5486:
5466:
5420:
4914:
4889:
4851:
4798:
4745:
4692:
4639:
4592:
4539:
4486:
4433:
4380:
4336:
4310:
4272:
4169:
3989:
3888:
3677:
3576:
3367:homogeneous solutions
3361:Homogeneous solutions
3348:
3324:
3304:
3184:
2968:
2930:
2884:
2845:
2803:
2780:
2738:
2700:
2658:
2635:
2595:
2340:
2320:
2298:
1874:
1853:
1831:
1577:
1542:
1506:
1468:
1466:{\displaystyle g_{e}}
1439:
1390:
1361:
1259:
1239:
672:
635:
607:
580:
553:
514:
478:
476:{\displaystyle \ G\ }
451:
391:
361:
335:
293:
263:
239:
196:
164:electromagnetic waves
122:
95:
70:
10674:Vladimir K. Zworykin
10634:Almon Brown Strowger
10604:Charles Grafton Page
10259:Prepaid mobile phone
10187:Electrical telegraph
9547:
9520:
9493:
9466:
9439:
9409:
9381:
9354:
9327:
9184:
9081:
8864:
8737:improve this section
8726:to meet Knowledge's
8629:
8596:
8565:
8534:
8217:
7962:
7942:
7922:
7755:
7735:
7715:
7692:
7665:
7645:
7618:
7557:
7520:
7493:
7375:
7341:
7271:
7244:
7200:
7165:
7145:
7018:
6923:
6855:
6851:is the wave number:
6702:
6537:
6517:
6316:
6249:
6020:
5999:
5976:
5903:
5838:
5742:
5687:
5657:
5567:
5498:
5475:
5429:
4923:
4869:
4816:
4763:
4710:
4657:
4610:
4557:
4504:
4451:
4398:
4351:
4325:
4299:
4177:
4003:
3896:
3688:
3584:
3376:
3337:
3331:attenuation constant
3313:
3193:
2988:
2939:
2901:
2860:
2815:
2792:
2750:
2715:
2670:
2647:
2605:
2357:
2329:
2309:
1884:
1863:
1842:
1603:
1551:
1515:
1480:
1450:
1407:
1370:
1284:
1248:
1228:
827:All four parameters
655:attenuation constant
651:propagation constant
619:
591:
564:
537:
496:
461:
405:
380:
350:
324:
282:
252:
228:
160:On the Extra Current
111:
84:
59:
10624:Johann Philipp Reis
10383:Wireless revolution
10345:The Telephone Cases
10202:Hydraulic telegraph
9713:. Ithaca, NY, USA:
9316:are subscripted by
7661:direction – whilst
7296:boundary conditions
5378:
4284:
4283:Symbol definitions
780:couples current to
203:Maxwell's equations
25:telegraph equations
11158:Transmission lines
10822:Frequency-division
10799:Telephone exchange
10669:Charles Wheatstone
10599:Jun-ichi Nishizawa
10574:Innocenzo Manzetti
10509:Reginald Fessenden
10244:Optical telegraphy
10077:Telecommunications
9717:. pp. 66–67.
9553:
9533:
9506:
9479:
9452:
9423:
9394:
9367:
9340:
9278:
9170:
9067:
9065:
8851:
8688:
8615:
8580:
8549:
8508:
8506:
8193:
8191:
7948:
7928:
7916:
7893:
7741:
7721:
7711:Using the current
7698:
7678:
7651:
7631:
7600:is the waveform's
7590:
7549:analytic functions
7533:
7506:
7476:
7359:
7284:
7257:
7230:
7180:
7151:
7131:
7004:
6914:Helmholtz equation
6900:
6837:
6835:
6686:
6684:
6523:
6503:
6501:
6282:
6235:
6233:
6005:
5982:
5971:, one for voltage
5955:
5890:
5813:
5811:
5702:
5672:
5634:
5552:
5481:
5461:
5415:
5413:
5360:
4917:
4884:
4846:
4793:
4740:
4687:
4634:
4587:
4534:
4481:
4428:
4375:
4331:
4305:
4282:
4267:
4164:
4162:
3984:
3883:
3881:
3672:
3571:
3569:
3343:
3319:
3299:
3179:
3177:
2963:
2925:
2879:
2840:
2798:
2775:
2733:
2695:
2653:
2630:
2590:
2588:
2335:
2315:
2293:
2291:
1869:
1848:
1826:
1824:
1572:
1537:
1501:
1463:
1434:
1385:
1356:
1254:
1234:
679:
633:{\displaystyle G'}
630:
605:{\displaystyle C'}
602:
578:{\displaystyle L'}
575:
551:{\displaystyle R'}
548:
509:
473:
446:
386:
356:
330:
302:around the wires,
288:
258:
234:
199:
152:who developed the
117:
90:
65:
11135:
11134:
10873:Store and forward
10868:Data transmission
10782:Network switching
10733:Transmission line
10579:Guglielmo Marconi
10544:Internet pioneers
10409:Mohamed M. Atalla
10378:Whistled language
9572:differential mode
9273:
9165:
9164:
9008:
8765:
8764:
8757:
8728:quality standards
8719:This section may
8687:
8683:
8658:
8484:
8438:
8393:
8342:
8296:
8251:
8140:
8094:
8028:
7982:
7951:{\displaystyle G}
7931:{\displaystyle R}
7873:
7833:
7796:
7744:{\displaystyle V}
7724:{\displaystyle I}
7701:{\displaystyle x}
7654:{\displaystyle x}
7602:propagation speed
7588:
7587:
7569:
7467:
7427:
7228:
7227:
7154:{\displaystyle k}
7109:
7060:
6895:
6893:
6875:
6805:
6741:
6680:
6633:
6609:
6562:
6280:
6279:
6261:
6219:
6178:
6163:
6115:
6074:
6059:
6008:{\displaystyle I}
5985:{\displaystyle V}
5953:
5924:
5888:
5859:
5613:
5600:
5484:{\displaystyle x}
5409:
5178:
5143:
5100:
5056:
5009:
4960:
4902:
4901:
4334:{\displaystyle b}
4308:{\displaystyle a}
4261:
4260:
3297:
3114:
3022:
2801:{\displaystyle x}
2656:{\displaystyle x}
2490:
2377:
2338:{\displaystyle I}
2318:{\displaystyle V}
2241:
2176:
2119:
2040:
1975:
1918:
1872:{\displaystyle I}
1851:{\displaystyle V}
1778:
1731:
1670:
1623:
1335:
1275:The variation of
1264:is mainly due to
1257:{\displaystyle L}
1237:{\displaystyle R}
1220:
1219:
472:
466:
429:
415:
389:{\displaystyle G}
370:per unit length).
359:{\displaystyle C}
333:{\displaystyle C}
314:per unit length).
291:{\displaystyle L}
261:{\displaystyle R}
237:{\displaystyle R}
135:Fourier transform
131:Laplace transform
120:{\displaystyle s}
104:complex frequency
68:{\displaystyle x}
37:transmission line
11165:
11125:
11124:
11115:
11114:
11105:
11104:
11095:
11094:
11093:
10966:Notable networks
10956:Wireless network
10896:Cellular network
10888:Types of network
10863:Computer network
10750:Network topology
10664:Thomas A. Watson
10519:Oliver Heaviside
10504:Philo Farnsworth
10479:Daniel Davis Jr.
10454:Charles Bourseul
10414:John Logie Baird
10123:Data compression
10118:Computer network
10070:
10063:
10056:
10047:
10046:
10040:
10039:
10024:
10022:
10021:
10016:. RF Design Line
10011:
10002:
9996:
9994:
9990:
9986:
9964:
9958:
9957:
9941:
9935:
9934:
9926:
9917:
9916:
9898:
9892:
9891:
9873:
9864:
9863:
9845:
9836:
9835:
9822:Electromagnetics
9814:
9808:
9807:
9785:
9779:
9778:
9773:(1st ed.).
9766:
9760:
9759:
9735:
9729:
9728:
9706:
9700:
9699:
9681:
9672:
9671:
9668:Internet Archive
9647:
9594:
9562:
9560:
9559:
9554:
9542:
9540:
9539:
9534:
9532:
9531:
9515:
9513:
9512:
9507:
9505:
9504:
9489:as functions of
9488:
9486:
9485:
9480:
9478:
9477:
9461:
9459:
9458:
9453:
9451:
9450:
9434:
9432:
9430:
9429:
9424:
9421:
9420:
9403:
9401:
9400:
9395:
9393:
9392:
9377:as functions of
9376:
9374:
9373:
9368:
9366:
9365:
9349:
9347:
9346:
9341:
9339:
9338:
9319:
9315:
9308:
9301:
9294:
9287:
9285:
9284:
9279:
9274:
9272:
9268:
9267:
9266:
9248:
9247:
9233:
9229:
9228:
9227:
9209:
9208:
9194:
9179:
9177:
9176:
9171:
9166:
9163:
9162:
9161:
9143:
9142:
9132:
9131:
9130:
9112:
9111:
9101:
9100:
9095:
9094:
9093:
9076:
9074:
9073:
9068:
9066:
9040:
9039:
9009:
9007:
9006:
9005:
8995:
8994:
8985:
8976:
8975:
8940:
8939:
8938:
8928:
8927:
8897:
8896:
8880:
8879:
8848:
8841:
8828:
8817:
8806:
8784:
8780:
8760:
8753:
8749:
8746:
8740:
8714:
8713:
8706:
8697:
8695:
8694:
8689:
8685:
8684:
8679:
8678:
8677:
8664:
8659:
8657:
8656:
8655:
8639:
8624:
8622:
8621:
8616:
8614:
8613:
8591:
8589:
8587:
8586:
8581:
8559:
8558:
8556:
8555:
8550:
8527:
8523:
8517:
8515:
8514:
8509:
8507:
8485:
8483:
8472:
8470:
8466:
8439:
8437:
8436:
8435:
8422:
8421:
8412:
8394:
8392:
8391:
8390:
8377:
8376:
8367:
8343:
8341:
8330:
8328:
8324:
8297:
8295:
8294:
8293:
8280:
8279:
8270:
8252:
8250:
8249:
8248:
8235:
8234:
8225:
8208:
8202:
8200:
8199:
8194:
8192:
8141:
8139:
8128:
8095:
8093:
8082:
8029:
8027:
8016:
7983:
7981:
7970:
7957:
7955:
7954:
7949:
7937:
7935:
7934:
7929:
7902:
7900:
7899:
7894:
7888:
7887:
7875:
7874:
7866:
7854:
7853:
7835:
7834:
7826:
7814:
7813:
7804:
7803:
7797:
7795:
7794:
7793:
7780:
7750:
7748:
7747:
7742:
7730:
7728:
7727:
7722:
7707:
7705:
7704:
7699:
7687:
7685:
7684:
7679:
7677:
7676:
7660:
7658:
7657:
7652:
7640:
7638:
7637:
7632:
7630:
7629:
7599:
7597:
7596:
7591:
7589:
7580:
7576:
7571:
7570:
7562:
7542:
7540:
7539:
7534:
7532:
7531:
7515:
7513:
7512:
7507:
7505:
7504:
7485:
7483:
7482:
7477:
7469:
7468:
7460:
7448:
7447:
7429:
7428:
7420:
7408:
7407:
7370:
7368:
7366:
7365:
7360:
7326:
7308:
7304:
7293:
7291:
7290:
7285:
7283:
7282:
7266:
7264:
7263:
7258:
7256:
7255:
7239:
7237:
7236:
7231:
7229:
7220:
7219:
7214:
7213:
7212:
7189:
7187:
7186:
7181:
7179:
7178:
7177:
7160:
7158:
7157:
7152:
7140:
7138:
7137:
7132:
7130:
7129:
7110:
7108:
7107:
7106:
7096:
7095:
7086:
7081:
7080:
7061:
7059:
7058:
7057:
7047:
7046:
7037:
7013:
7011:
7010:
7005:
7003:
7002:
6983:
6982:
6970:
6969:
6950:
6949:
6909:
6907:
6906:
6901:
6896:
6894:
6886:
6881:
6876:
6868:
6850:
6846:
6844:
6843:
6838:
6836:
6819:
6818:
6806:
6804:
6803:
6802:
6789:
6785:
6784:
6774:
6755:
6754:
6742:
6740:
6739:
6738:
6725:
6721:
6720:
6710:
6695:
6693:
6692:
6687:
6685:
6681:
6679:
6671:
6663:
6634:
6632:
6624:
6616:
6610:
6608:
6600:
6592:
6563:
6561:
6553:
6545:
6532:
6530:
6529:
6524:
6512:
6510:
6509:
6504:
6502:
6494:
6493:
6487:
6486:
6458:
6457:
6451:
6450:
6449:
6448:
6404:
6403:
6397:
6396:
6368:
6367:
6361:
6360:
6359:
6358:
6291:
6289:
6288:
6283:
6281:
6272:
6268:
6263:
6262:
6254:
6244:
6242:
6241:
6236:
6234:
6220:
6218:
6217:
6216:
6203:
6199:
6198:
6188:
6186:
6185:
6180:
6179:
6171:
6164:
6162:
6161:
6160:
6147:
6143:
6142:
6132:
6116:
6114:
6113:
6112:
6099:
6095:
6094:
6084:
6082:
6081:
6076:
6075:
6067:
6060:
6058:
6057:
6056:
6043:
6039:
6038:
6028:
6016:
6014:
6012:
6011:
6006:
5993:
5991:
5989:
5988:
5983:
5964:
5962:
5961:
5956:
5954:
5952:
5944:
5936:
5925:
5923:
5915:
5907:
5899:
5897:
5896:
5891:
5889:
5887:
5879:
5871:
5860:
5858:
5850:
5842:
5822:
5820:
5819:
5814:
5812:
5737:
5733:
5729:
5726:and the current
5725:
5721:
5717:
5713:
5711:
5709:
5708:
5703:
5681:
5679:
5678:
5673:
5645:
5643:
5641:
5640:
5635:
5632:
5631:
5627:
5614:
5606:
5601:
5599:
5598:
5597:
5591:
5585:
5584:
5583:
5577:
5571:
5561:
5559:
5558:
5553:
5548:
5547:
5546:
5540:
5531:
5530:
5529:
5523:
5514:
5513:
5512:
5506:
5490:
5488:
5487:
5482:
5470:
5468:
5467:
5462:
5457:
5456:
5452:
5436:
5424:
5422:
5421:
5416:
5414:
5410:
5408:
5407:
5403:
5399:
5383:
5379:
5377:
5372:
5371:
5365:
5356:
5355:
5354:
5348:
5342:
5341:
5340:
5334:
5320:
5316:
5312:
5296:
5292:
5291:
5290:
5289:
5283:
5274:
5273:
5272:
5266:
5255:
5254:
5253:
5247:
5240:
5239:
5238:
5237:
5231:
5225:
5224:
5223:
5217:
5210:
5202:
5198:
5197:
5189:
5185:
5184:
5180:
5179:
5177:
5176:
5175:
5169:
5163:
5162:
5161:
5155:
5149:
5144:
5142:
5141:
5140:
5134:
5133:
5126:
5125:
5124:
5118:
5112:
5105:
5101:
5096:
5095:
5087:
5086:
5078:
5071:
5062:
5058:
5057:
5055:
5054:
5053:
5047:
5041:
5040:
5039:
5033:
5027:
5014:
5010:
5005:
5004:
4996:
4995:
4987:
4980:
4961:
4959:
4958:
4957:
4951:
4945:
4944:
4943:
4937:
4931:
4893:
4891:
4890:
4885:
4883:
4882:
4877:
4861:
4855:
4853:
4852:
4847:
4836:
4835:
4824:
4808:
4802:
4800:
4799:
4794:
4783:
4782:
4771:
4755:
4749:
4747:
4746:
4741:
4730:
4729:
4718:
4702:
4696:
4694:
4693:
4688:
4677:
4676:
4665:
4649:
4643:
4641:
4640:
4635:
4624:
4623:
4618:
4602:
4596:
4594:
4593:
4588:
4577:
4576:
4565:
4549:
4543:
4541:
4540:
4535:
4524:
4523:
4512:
4496:
4490:
4488:
4487:
4482:
4471:
4470:
4459:
4443:
4437:
4435:
4434:
4429:
4418:
4417:
4406:
4390:
4384:
4382:
4381:
4376:
4365:
4364:
4359:
4340:
4338:
4337:
4332:
4314:
4312:
4311:
4306:
4285:
4281:
4276:
4274:
4273:
4268:
4262:
4259:
4258:
4257:
4239:
4238:
4228:
4227:
4226:
4208:
4207:
4197:
4196:
4191:
4190:
4185:
4173:
4171:
4170:
4165:
4163:
4147:
4146:
4135:
4128:
4127:
4122:
4104:
4103:
4092:
4070:
4069:
4058:
4051:
4050:
4045:
4027:
4026:
4015:
3993:
3991:
3990:
3985:
3970:
3969:
3958:
3940:
3939:
3928:
3910:
3909:
3904:
3892:
3890:
3889:
3884:
3882:
3874:
3873:
3836:
3835:
3824:
3806:
3805:
3794:
3780:
3779:
3742:
3741:
3730:
3712:
3711:
3700:
3681:
3679:
3678:
3673:
3658:
3657:
3646:
3628:
3627:
3616:
3598:
3597:
3592:
3580:
3578:
3577:
3572:
3570:
3562:
3561:
3524:
3523:
3512:
3494:
3493:
3482:
3468:
3467:
3430:
3429:
3418:
3400:
3399:
3388:
3352:
3350:
3349:
3344:
3328:
3326:
3325:
3320:
3308:
3306:
3305:
3300:
3298:
3296:
3292:
3291:
3290:
3272:
3271:
3257:
3253:
3252:
3251:
3233:
3232:
3218:
3188:
3186:
3185:
3180:
3178:
3165:
3164:
3159:
3153:
3152:
3127:
3126:
3121:
3115:
3113:
3112:
3111:
3098:
3097:
3088:
3073:
3072:
3067:
3061:
3060:
3035:
3034:
3029:
3023:
3021:
3020:
3019:
3006:
3005:
2996:
2972:
2970:
2969:
2964:
2953:
2952:
2947:
2934:
2932:
2931:
2926:
2915:
2914:
2909:
2890:
2888:
2886:
2885:
2880:
2851:
2849:
2847:
2846:
2841:
2829:
2828:
2823:
2809:
2807:
2805:
2804:
2799:
2786:
2784:
2782:
2781:
2776:
2764:
2763:
2758:
2744:
2742:
2740:
2739:
2734:
2706:
2704:
2702:
2701:
2696:
2684:
2683:
2678:
2664:
2662:
2660:
2659:
2654:
2641:
2639:
2637:
2636:
2631:
2619:
2618:
2613:
2599:
2597:
2596:
2591:
2589:
2573:
2572:
2567:
2561:
2557:
2556:
2555:
2543:
2542:
2503:
2502:
2497:
2491:
2489:
2478:
2460:
2459:
2454:
2448:
2444:
2443:
2442:
2430:
2429:
2390:
2389:
2384:
2378:
2376:
2365:
2349:Frequency domain
2344:
2342:
2341:
2336:
2324:
2322:
2321:
2316:
2302:
2300:
2299:
2294:
2292:
2242:
2240:
2229:
2227:
2223:
2177:
2175:
2174:
2173:
2160:
2159:
2150:
2120:
2118:
2117:
2116:
2103:
2102:
2093:
2041:
2039:
2028:
2026:
2022:
1976:
1974:
1973:
1972:
1959:
1958:
1949:
1919:
1917:
1916:
1915:
1902:
1901:
1892:
1880:
1878:
1876:
1875:
1870:
1857:
1855:
1854:
1849:
1835:
1833:
1832:
1827:
1825:
1779:
1777:
1766:
1732:
1730:
1719:
1671:
1669:
1658:
1624:
1622:
1611:
1581:
1579:
1578:
1573:
1565:
1564:
1563:
1546:
1544:
1543:
1538:
1536:
1535:
1534:
1533:
1532:
1510:
1508:
1507:
1502:
1500:
1499:
1495:
1472:
1470:
1469:
1464:
1462:
1461:
1445:
1443:
1441:
1440:
1435:
1433:
1432:
1419:
1418:
1401:
1394:
1392:
1391:
1386:
1384:
1383:
1382:
1365:
1363:
1362:
1357:
1355:
1354:
1353:
1352:
1351:
1340:
1336:
1334:
1333:
1321:
1311:
1310:
1278:
1270:proximity effect
1263:
1261:
1260:
1255:
1243:
1241:
1240:
1235:
1013:
1012:
1008:
1002:
1001:
997:
989:
988:
984:
978:
977:
973:
965:
964:
960:
954:
953:
949:
941:
940:
933:
927:
926:
922:
907:
902:
897:
892:
884:
883:
870:
866:
862:
858:
854:
850:
846:
842:
838:
834:
830:
822:
811:
801:
794:
779:
773:
765:
764:
746:restoring forces
735:
725:
717:
716:
698:
688:
640:
639:
637:
636:
631:
629:
613:
611:
609:
608:
603:
601:
586:
584:
582:
581:
576:
574:
559:
557:
555:
554:
549:
547:
520:
518:
516:
515:
510:
482:
480:
479:
474:
470:
464:
457:
455:
453:
452:
447:
445:
430:
422:
417:
416:
413:
395:
393:
392:
387:
365:
363:
362:
357:
339:
337:
336:
331:
297:
295:
294:
289:
275:The distributed
267:
265:
264:
259:
243:
241:
240:
235:
221:The distributed
150:Oliver Heaviside
128:
126:
124:
123:
118:
101:
99:
97:
96:
91:
74:
72:
71:
66:
53:frequency domain
11173:
11172:
11168:
11167:
11166:
11164:
11163:
11162:
11138:
11137:
11136:
11131:
11091:
11089:
11081:
11023:
10960:
10882:
10846:
10803:
10752:
10744:
10685:
10678:
10584:Robert Metcalfe
10439:Tim Berners-Lee
10387:
10207:Information Age
10079:
10074:
10044:
10043:
10026:
10019:
10017:
10009:
10003:
9999:
9992:
9988:
9983:
9975:. p. 130.
9965:
9961:
9942:
9938:
9927:
9920:
9913:
9899:
9895:
9888:
9874:
9867:
9860:
9846:
9839:
9832:
9815:
9811:
9804:
9786:
9782:
9767:
9763:
9756:
9748:. p. 558.
9736:
9732:
9725:
9711:The Maxwellians
9707:
9703:
9696:
9682:
9675:
9664:
9648:
9639:
9634:
9612:
9588:
9582:
9548:
9545:
9544:
9527:
9523:
9521:
9518:
9517:
9500:
9496:
9494:
9491:
9490:
9473:
9469:
9467:
9464:
9463:
9446:
9442:
9440:
9437:
9436:
9416:
9412:
9410:
9407:
9406:
9405:
9388:
9384:
9382:
9379:
9378:
9361:
9357:
9355:
9352:
9351:
9334:
9330:
9328:
9325:
9324:
9317:
9314:
9310:
9307:
9303:
9300:
9296:
9293:
9289:
9262:
9258:
9243:
9239:
9238:
9234:
9223:
9219:
9204:
9200:
9199:
9195:
9193:
9185:
9182:
9181:
9157:
9153:
9138:
9134:
9133:
9126:
9122:
9107:
9103:
9102:
9099:
9089:
9088:
9084:
9082:
9079:
9078:
9064:
9063:
9035:
9031:
9001:
9000:
8996:
8990:
8986:
8984:
8977:
8971:
8967:
8964:
8963:
8934:
8933:
8929:
8923:
8919:
8892:
8888:
8881:
8875:
8871:
8867:
8865:
8862:
8861:
8843:
8830:
8819:
8808:
8800:
8786:
8782:
8779:
8772:
8761:
8750:
8744:
8741:
8734:
8715:
8711:
8704:
8673:
8669:
8665:
8663:
8651:
8647:
8643:
8638:
8630:
8627:
8626:
8603:
8599:
8597:
8594:
8593:
8566:
8563:
8562:
8561:
8535:
8532:
8531:
8529:
8525:
8521:
8505:
8504:
8476:
8471:
8450:
8446:
8431:
8427:
8423:
8417:
8413:
8411:
8398:
8386:
8382:
8378:
8372:
8368:
8366:
8363:
8362:
8334:
8329:
8308:
8304:
8289:
8285:
8281:
8275:
8271:
8269:
8256:
8244:
8240:
8236:
8230:
8226:
8224:
8220:
8218:
8215:
8214:
8206:
8190:
8189:
8132:
8127:
8114:
8086:
8081:
8078:
8077:
8020:
8015:
8002:
7974:
7969:
7965:
7963:
7960:
7959:
7943:
7940:
7939:
7923:
7920:
7919:
7908:
7883:
7882:
7865:
7864:
7849:
7845:
7825:
7824:
7809:
7805:
7799:
7798:
7789:
7788:
7784:
7779:
7756:
7753:
7752:
7736:
7733:
7732:
7716:
7713:
7712:
7693:
7690:
7689:
7672:
7668:
7666:
7663:
7662:
7646:
7643:
7642:
7625:
7621:
7619:
7616:
7615:
7604:(also known as
7575:
7561:
7560:
7558:
7555:
7554:
7527:
7523:
7521:
7518:
7517:
7500:
7496:
7494:
7491:
7490:
7459:
7458:
7443:
7439:
7419:
7418:
7403:
7399:
7376:
7373:
7372:
7342:
7339:
7338:
7336:
7333:
7320:
7318:Marshall (1987)
7306:
7302:
7278:
7274:
7272:
7269:
7268:
7251:
7247:
7245:
7242:
7241:
7218:
7208:
7207:
7203:
7201:
7198:
7197:
7173:
7172:
7168:
7166:
7163:
7162:
7146:
7143:
7142:
7116:
7112:
7102:
7101:
7097:
7091:
7087:
7085:
7067:
7063:
7053:
7052:
7048:
7042:
7038:
7036:
7019:
7016:
7015:
6989:
6985:
6978:
6974:
6956:
6952:
6945:
6941:
6924:
6921:
6920:
6885:
6880:
6867:
6856:
6853:
6852:
6848:
6834:
6833:
6823:
6814:
6810:
6798:
6794:
6790:
6780:
6776:
6775:
6773:
6770:
6769:
6759:
6750:
6746:
6734:
6730:
6726:
6716:
6712:
6711:
6709:
6705:
6703:
6700:
6699:
6683:
6682:
6672:
6664:
6662:
6625:
6617:
6615:
6612:
6611:
6601:
6593:
6591:
6554:
6546:
6544:
6540:
6538:
6535:
6534:
6518:
6515:
6514:
6500:
6499:
6489:
6488:
6476:
6472:
6453:
6452:
6444:
6440:
6439:
6438:
6431:
6410:
6409:
6399:
6398:
6386:
6382:
6363:
6362:
6354:
6350:
6349:
6348:
6341:
6319:
6317:
6314:
6313:
6301:In the case of
6299:
6267:
6253:
6252:
6250:
6247:
6246:
6232:
6231:
6221:
6212:
6208:
6204:
6194:
6190:
6189:
6187:
6181:
6170:
6169:
6168:
6156:
6152:
6148:
6138:
6134:
6133:
6131:
6128:
6127:
6117:
6108:
6104:
6100:
6090:
6086:
6085:
6083:
6077:
6066:
6065:
6064:
6052:
6048:
6044:
6034:
6030:
6029:
6027:
6023:
6021:
6018:
6017:
6000:
5997:
5996:
5995:
5977:
5974:
5973:
5972:
5945:
5937:
5935:
5916:
5908:
5906:
5904:
5901:
5900:
5880:
5872:
5870:
5851:
5843:
5841:
5839:
5836:
5835:
5828:
5810:
5809:
5784:
5778:
5777:
5752:
5745:
5743:
5740:
5739:
5735:
5731:
5727:
5723:
5719:
5715:
5688:
5685:
5684:
5683:
5658:
5655:
5654:
5651:
5623:
5619:
5615:
5605:
5593:
5592:
5587:
5586:
5579:
5578:
5573:
5572:
5570:
5568:
5565:
5564:
5563:
5542:
5541:
5536:
5535:
5525:
5524:
5519:
5518:
5508:
5507:
5502:
5501:
5499:
5496:
5495:
5476:
5473:
5472:
5448:
5444:
5440:
5432:
5430:
5427:
5426:
5412:
5411:
5395:
5394:
5390:
5373:
5367:
5366:
5361:
5350:
5349:
5344:
5343:
5336:
5335:
5330:
5329:
5328:
5324:
5308:
5307:
5303:
5285:
5284:
5279:
5278:
5268:
5267:
5262:
5261:
5260:
5256:
5249:
5248:
5243:
5242:
5241:
5233:
5232:
5227:
5226:
5219:
5218:
5213:
5212:
5211:
5209:
5200:
5199:
5190:
5171:
5170:
5165:
5164:
5157:
5156:
5151:
5150:
5148:
5136:
5135:
5129:
5128:
5127:
5120:
5119:
5114:
5113:
5111:
5110:
5106:
5091:
5079:
5074:
5073:
5072:
5070:
5066:
5049:
5048:
5043:
5042:
5035:
5034:
5029:
5028:
5026:
5019:
5015:
5000:
4988:
4983:
4982:
4981:
4979:
4975:
4974:
4970:
4969:
4962:
4953:
4952:
4947:
4946:
4939:
4938:
4933:
4932:
4930:
4926:
4924:
4921:
4920:
4909:
4878:
4873:
4872:
4870:
4867:
4866:
4859:
4825:
4820:
4819:
4817:
4814:
4813:
4806:
4772:
4767:
4766:
4764:
4761:
4760:
4753:
4719:
4714:
4713:
4711:
4708:
4707:
4700:
4666:
4661:
4660:
4658:
4655:
4654:
4647:
4619:
4614:
4613:
4611:
4608:
4607:
4600:
4566:
4561:
4560:
4558:
4555:
4554:
4547:
4513:
4508:
4507:
4505:
4502:
4501:
4494:
4460:
4455:
4454:
4452:
4449:
4448:
4441:
4407:
4402:
4401:
4399:
4396:
4395:
4388:
4360:
4355:
4354:
4352:
4349:
4348:
4326:
4323:
4322:
4300:
4297:
4296:
4253:
4249:
4234:
4230:
4229:
4222:
4218:
4203:
4199:
4198:
4195:
4186:
4181:
4180:
4178:
4175:
4174:
4161:
4160:
4136:
4131:
4130:
4123:
4118:
4117:
4093:
4088:
4087:
4084:
4083:
4059:
4054:
4053:
4046:
4041:
4040:
4016:
4011:
4010:
4006:
4004:
4001:
4000:
3959:
3954:
3953:
3929:
3924:
3923:
3905:
3900:
3899:
3897:
3894:
3893:
3880:
3879:
3851:
3847:
3825:
3820:
3819:
3795:
3790:
3789:
3786:
3785:
3757:
3753:
3731:
3726:
3725:
3701:
3696:
3695:
3691:
3689:
3686:
3685:
3647:
3642:
3641:
3617:
3612:
3611:
3593:
3588:
3587:
3585:
3582:
3581:
3568:
3567:
3539:
3535:
3513:
3508:
3507:
3483:
3478:
3477:
3474:
3473:
3445:
3441:
3419:
3414:
3413:
3389:
3384:
3383:
3379:
3377:
3374:
3373:
3363:
3338:
3335:
3334:
3314:
3311:
3310:
3309:
3286:
3282:
3267:
3263:
3262:
3258:
3247:
3243:
3228:
3224:
3223:
3219:
3217:
3194:
3191:
3190:
3176:
3175:
3160:
3155:
3154:
3148:
3144:
3137:
3122:
3117:
3116:
3107:
3103:
3099:
3093:
3089:
3087:
3084:
3083:
3068:
3063:
3062:
3056:
3052:
3045:
3030:
3025:
3024:
3015:
3011:
3007:
3001:
2997:
2995:
2991:
2989:
2986:
2985:
2948:
2943:
2942:
2940:
2937:
2936:
2910:
2905:
2904:
2902:
2899:
2898:
2861:
2858:
2857:
2856:
2824:
2819:
2818:
2816:
2813:
2812:
2811:
2793:
2790:
2789:
2788:
2759:
2754:
2753:
2751:
2748:
2747:
2746:
2716:
2713:
2712:
2711:
2679:
2674:
2673:
2671:
2668:
2667:
2666:
2648:
2645:
2644:
2643:
2614:
2609:
2608:
2606:
2603:
2602:
2601:
2587:
2586:
2568:
2563:
2562:
2551:
2547:
2538:
2534:
2527:
2523:
2513:
2498:
2493:
2492:
2482:
2477:
2474:
2473:
2455:
2450:
2449:
2438:
2434:
2425:
2421:
2414:
2410:
2400:
2385:
2380:
2379:
2369:
2364:
2360:
2358:
2355:
2354:
2351:
2330:
2327:
2326:
2310:
2307:
2306:
2290:
2289:
2233:
2228:
2207:
2203:
2196:
2169:
2165:
2161:
2155:
2151:
2149:
2112:
2108:
2104:
2098:
2094:
2092:
2089:
2088:
2032:
2027:
2006:
2002:
1995:
1968:
1964:
1960:
1954:
1950:
1948:
1911:
1907:
1903:
1897:
1893:
1891:
1887:
1885:
1882:
1881:
1864:
1861:
1860:
1859:
1843:
1840:
1839:
1823:
1822:
1770:
1765:
1751:
1723:
1718:
1715:
1714:
1662:
1657:
1643:
1615:
1610:
1606:
1604:
1601:
1600:
1597:
1592:
1559:
1558:
1554:
1552:
1549:
1548:
1528:
1527:
1523:
1522:
1518:
1516:
1513:
1512:
1491:
1487:
1483:
1481:
1478:
1477:
1457:
1453:
1451:
1448:
1447:
1428:
1424:
1414:
1410:
1408:
1405:
1404:
1403:
1396:
1378:
1377:
1373:
1371:
1368:
1367:
1347:
1346:
1342:
1341:
1329:
1325:
1320:
1316:
1315:
1306:
1302:
1285:
1282:
1281:
1276:
1249:
1246:
1245:
1229:
1226:
1225:
1010:
1006:
1005:
999:
993:
992:
986:
982:
981:
975:
969:
968:
962:
958:
957:
951:
945:
944:
935:
931:
930:
924:
918:
917:
905:
900:
895:
890:
877:
868:
864:
860:
856:
852:
848:
844:
840:
836:
832:
828:
820:
809:
806:dielectric loss
799:
792:
777:
771:
762:
761:
753:surge impedance
733:
723:
714:
713:
705:surge impedance
696:
686:
667:
622:
620:
617:
616:
615:
594:
592:
589:
588:
587:
567:
565:
562:
561:
560:
540:
538:
535:
534:
533:
530:per unit length
526:infinite series
497:
494:
493:
492:
489:dielectric loss
462:
459:
458:
432:
421:
412:
408:
406:
403:
402:
401:
381:
378:
377:
351:
348:
347:
325:
322:
321:
304:self-inductance
283:
280:
279:
253:
250:
249:
229:
226:
225:
215:infinitesimally
191:
179:telephone lines
172:radio frequency
112:
109:
108:
107:
85:
82:
81:
80:
60:
57:
56:
17:
12:
11:
5:
11171:
11161:
11160:
11155:
11150:
11133:
11132:
11130:
11129:
11119:
11109:
11099:
11086:
11083:
11082:
11080:
11079:
11072:
11067:
11062:
11057:
11052:
11051:
11050:
11045:
11037:
11031:
11029:
11025:
11024:
11022:
11021:
11016:
11011:
11006:
11001:
10996:
10991:
10986:
10981:
10976:
10970:
10968:
10962:
10961:
10959:
10958:
10953:
10948:
10943:
10938:
10933:
10928:
10923:
10918:
10913:
10908:
10903:
10898:
10892:
10890:
10884:
10883:
10881:
10880:
10875:
10870:
10865:
10860:
10854:
10852:
10848:
10847:
10845:
10844:
10839:
10834:
10829:
10824:
10819:
10817:Space-division
10813:
10811:
10805:
10804:
10802:
10801:
10796:
10795:
10794:
10789:
10779:
10778:
10777:
10767:
10762:
10756:
10754:
10746:
10745:
10743:
10742:
10741:
10740:
10730:
10729:
10728:
10718:
10713:
10708:
10707:
10706:
10696:
10690:
10688:
10680:
10679:
10677:
10676:
10671:
10666:
10661:
10656:
10654:Camille Tissot
10651:
10646:
10641:
10636:
10631:
10629:Claude Shannon
10626:
10621:
10619:Tivadar Puskás
10616:
10611:
10606:
10601:
10596:
10591:
10589:Antonio Meucci
10586:
10581:
10576:
10571:
10566:
10561:
10559:Charles K. Kao
10556:
10551:
10546:
10541:
10536:
10534:Harold Hopkins
10531:
10526:
10521:
10516:
10511:
10506:
10501:
10496:
10491:
10486:
10481:
10476:
10471:
10466:
10461:
10456:
10451:
10446:
10441:
10436:
10434:Emile Berliner
10431:
10426:
10421:
10416:
10411:
10406:
10401:
10395:
10393:
10389:
10388:
10386:
10385:
10380:
10375:
10373:Videotelephony
10370:
10365:
10364:
10363:
10358:
10348:
10341:
10336:
10330:
10325:
10320:
10315:
10310:
10309:
10308:
10303:
10298:
10288:
10287:
10286:
10276:
10271:
10269:Radiotelephone
10266:
10261:
10256:
10251:
10246:
10241:
10236:
10235:
10234:
10224:
10219:
10214:
10209:
10204:
10199:
10194:
10189:
10184:
10179:
10174:
10173:
10172:
10167:
10162:
10157:
10155:Internet video
10147:
10146:
10145:
10140:
10135:
10130:
10120:
10115:
10110:
10105:
10100:
10095:
10089:
10087:
10081:
10080:
10073:
10072:
10065:
10058:
10050:
10042:
10041:
9997:
9981:
9973:Academic Press
9959:
9936:
9918:
9911:
9893:
9886:
9865:
9858:
9837:
9830:
9818:Kraus, John D.
9809:
9802:
9796:. p. 26.
9780:
9777:. p. 112.
9761:
9754:
9730:
9723:
9701:
9694:
9673:
9670:(archive.org).
9662:
9636:
9635:
9633:
9630:
9629:
9628:
9621:Law of squares
9618:
9611:
9608:
9586:
9552:
9530:
9526:
9503:
9499:
9476:
9472:
9449:
9445:
9419:
9415:
9391:
9387:
9364:
9360:
9337:
9333:
9312:
9305:
9298:
9291:
9277:
9271:
9265:
9261:
9257:
9254:
9251:
9246:
9242:
9237:
9232:
9226:
9222:
9218:
9215:
9212:
9207:
9203:
9198:
9192:
9189:
9169:
9160:
9156:
9152:
9149:
9146:
9141:
9137:
9129:
9125:
9121:
9118:
9115:
9110:
9106:
9098:
9092:
9087:
9062:
9058:
9055:
9052:
9049:
9046:
9043:
9038:
9034:
9030:
9027:
9024:
9021:
9018:
9015:
9012:
9004:
8999:
8993:
8989:
8983:
8980:
8978:
8974:
8970:
8966:
8965:
8962:
8958:
8955:
8952:
8949:
8946:
8943:
8937:
8932:
8926:
8922:
8918:
8915:
8912:
8909:
8906:
8903:
8900:
8895:
8891:
8887:
8884:
8882:
8878:
8874:
8870:
8869:
8798:
8777:
8763:
8762:
8718:
8716:
8709:
8703:
8700:
8682:
8676:
8672:
8668:
8662:
8654:
8650:
8646:
8642:
8637:
8634:
8612:
8609:
8606:
8602:
8579:
8576:
8573:
8570:
8548:
8545:
8542:
8539:
8503:
8500:
8497:
8494:
8491:
8488:
8482:
8479:
8475:
8469:
8465:
8462:
8459:
8456:
8453:
8449:
8445:
8442:
8434:
8430:
8426:
8420:
8416:
8410:
8407:
8404:
8401:
8399:
8397:
8389:
8385:
8381:
8375:
8371:
8365:
8364:
8361:
8358:
8355:
8352:
8349:
8346:
8340:
8337:
8333:
8327:
8323:
8320:
8317:
8314:
8311:
8307:
8303:
8300:
8292:
8288:
8284:
8278:
8274:
8268:
8265:
8262:
8259:
8257:
8255:
8247:
8243:
8239:
8233:
8229:
8223:
8222:
8188:
8184:
8181:
8178:
8175:
8172:
8169:
8165:
8162:
8159:
8156:
8153:
8150:
8147:
8144:
8138:
8135:
8131:
8126:
8123:
8120:
8117:
8115:
8113:
8110:
8107:
8104:
8101:
8098:
8092:
8089:
8085:
8080:
8079:
8076:
8072:
8069:
8066:
8063:
8060:
8057:
8053:
8050:
8047:
8044:
8041:
8038:
8035:
8032:
8026:
8023:
8019:
8014:
8011:
8008:
8005:
8003:
8001:
7998:
7995:
7992:
7989:
7986:
7980:
7977:
7973:
7968:
7967:
7947:
7927:
7907:
7904:
7892:
7886:
7881:
7878:
7872:
7869:
7863:
7860:
7857:
7852:
7848:
7844:
7841:
7838:
7832:
7829:
7823:
7820:
7817:
7812:
7808:
7802:
7792:
7787:
7783:
7778:
7775:
7772:
7769:
7766:
7763:
7760:
7740:
7720:
7697:
7675:
7671:
7650:
7628:
7624:
7612:
7611:
7607:phase velocity
7586:
7583:
7579:
7574:
7568:
7565:
7552:
7530:
7526:
7503:
7499:
7475:
7472:
7466:
7463:
7457:
7454:
7451:
7446:
7442:
7438:
7435:
7432:
7426:
7423:
7417:
7414:
7411:
7406:
7402:
7398:
7395:
7392:
7389:
7386:
7383:
7380:
7358:
7355:
7352:
7349:
7346:
7332:
7329:
7281:
7277:
7254:
7250:
7226:
7223:
7217:
7211:
7206:
7176:
7171:
7150:
7128:
7125:
7122:
7119:
7115:
7105:
7100:
7094:
7090:
7084:
7079:
7076:
7073:
7070:
7066:
7056:
7051:
7045:
7041:
7035:
7032:
7029:
7026:
7023:
7001:
6998:
6995:
6992:
6988:
6981:
6977:
6973:
6968:
6965:
6962:
6959:
6955:
6948:
6944:
6940:
6937:
6934:
6931:
6928:
6899:
6892:
6889:
6884:
6879:
6874:
6871:
6866:
6863:
6860:
6832:
6829:
6826:
6824:
6822:
6817:
6813:
6809:
6801:
6797:
6793:
6788:
6783:
6779:
6772:
6771:
6768:
6765:
6762:
6760:
6758:
6753:
6749:
6745:
6737:
6733:
6729:
6724:
6719:
6715:
6708:
6707:
6678:
6675:
6670:
6667:
6661:
6658:
6655:
6652:
6649:
6646:
6643:
6640:
6637:
6631:
6628:
6623:
6620:
6614:
6613:
6607:
6604:
6599:
6596:
6590:
6587:
6584:
6581:
6578:
6575:
6572:
6569:
6566:
6560:
6557:
6552:
6549:
6543:
6542:
6522:
6498:
6492:
6485:
6482:
6479:
6475:
6470:
6467:
6464:
6461:
6456:
6447:
6443:
6437:
6434:
6432:
6430:
6427:
6424:
6421:
6418:
6415:
6412:
6411:
6408:
6402:
6395:
6392:
6389:
6385:
6380:
6377:
6374:
6371:
6366:
6357:
6353:
6347:
6344:
6342:
6340:
6337:
6334:
6331:
6328:
6325:
6322:
6321:
6298:
6295:
6278:
6275:
6271:
6266:
6260:
6257:
6230:
6227:
6224:
6222:
6215:
6211:
6207:
6202:
6197:
6193:
6184:
6177:
6174:
6167:
6159:
6155:
6151:
6146:
6141:
6137:
6130:
6129:
6126:
6123:
6120:
6118:
6111:
6107:
6103:
6098:
6093:
6089:
6080:
6073:
6070:
6063:
6055:
6051:
6047:
6042:
6037:
6033:
6026:
6025:
6004:
5981:
5969:wave equations
5951:
5948:
5943:
5940:
5934:
5931:
5928:
5922:
5919:
5914:
5911:
5886:
5883:
5878:
5875:
5869:
5866:
5863:
5857:
5854:
5849:
5846:
5827:
5824:
5808:
5805:
5802:
5799:
5796:
5793:
5790:
5787:
5785:
5783:
5780:
5779:
5776:
5773:
5770:
5767:
5764:
5761:
5758:
5755:
5753:
5751:
5748:
5747:
5701:
5698:
5695:
5692:
5671:
5668:
5665:
5662:
5650:
5647:
5630:
5626:
5622:
5618:
5612:
5609:
5604:
5596:
5590:
5582:
5576:
5551:
5545:
5539:
5534:
5528:
5522:
5517:
5511:
5505:
5480:
5460:
5455:
5451:
5447:
5443:
5439:
5435:
5406:
5402:
5398:
5393:
5389:
5386:
5382:
5376:
5370:
5364:
5359:
5353:
5347:
5339:
5333:
5327:
5323:
5319:
5315:
5311:
5306:
5302:
5299:
5295:
5288:
5282:
5277:
5271:
5265:
5259:
5252:
5246:
5236:
5230:
5222:
5216:
5208:
5205:
5203:
5201:
5196:
5193:
5188:
5183:
5174:
5168:
5160:
5154:
5147:
5139:
5132:
5123:
5117:
5109:
5104:
5099:
5094:
5090:
5085:
5082:
5077:
5069:
5065:
5061:
5052:
5046:
5038:
5032:
5025:
5022:
5018:
5013:
5008:
5003:
4999:
4994:
4991:
4986:
4978:
4973:
4968:
4965:
4963:
4956:
4950:
4942:
4936:
4929:
4928:
4908:
4905:
4904:
4903:
4900:
4899:
4894:
4881:
4876:
4863:
4862:
4856:
4845:
4842:
4839:
4834:
4831:
4828:
4823:
4810:
4809:
4803:
4792:
4789:
4786:
4781:
4778:
4775:
4770:
4757:
4756:
4750:
4739:
4736:
4733:
4728:
4725:
4722:
4717:
4704:
4703:
4697:
4686:
4683:
4680:
4675:
4672:
4669:
4664:
4651:
4650:
4644:
4633:
4630:
4627:
4622:
4617:
4604:
4603:
4597:
4586:
4583:
4580:
4575:
4572:
4569:
4564:
4551:
4550:
4544:
4533:
4530:
4527:
4522:
4519:
4516:
4511:
4498:
4497:
4491:
4480:
4477:
4474:
4469:
4466:
4463:
4458:
4445:
4444:
4438:
4427:
4424:
4421:
4416:
4413:
4410:
4405:
4392:
4391:
4385:
4374:
4371:
4368:
4363:
4358:
4345:
4344:
4341:
4330:
4319:
4318:
4315:
4304:
4293:
4292:
4289:
4266:
4256:
4252:
4248:
4245:
4242:
4237:
4233:
4225:
4221:
4217:
4214:
4211:
4206:
4202:
4194:
4189:
4184:
4159:
4156:
4153:
4150:
4145:
4142:
4139:
4134:
4126:
4121:
4116:
4113:
4110:
4107:
4102:
4099:
4096:
4091:
4086:
4085:
4082:
4079:
4076:
4073:
4068:
4065:
4062:
4057:
4049:
4044:
4039:
4036:
4033:
4030:
4025:
4022:
4019:
4014:
4009:
4008:
3983:
3979:
3976:
3973:
3968:
3965:
3962:
3957:
3952:
3949:
3946:
3943:
3938:
3935:
3932:
3927:
3922:
3919:
3916:
3913:
3908:
3903:
3878:
3872:
3869:
3866:
3863:
3860:
3857:
3854:
3850:
3845:
3842:
3839:
3834:
3831:
3828:
3823:
3818:
3815:
3812:
3809:
3804:
3801:
3798:
3793:
3788:
3787:
3784:
3778:
3775:
3772:
3769:
3766:
3763:
3760:
3756:
3751:
3748:
3745:
3740:
3737:
3734:
3729:
3724:
3721:
3718:
3715:
3710:
3707:
3704:
3699:
3694:
3693:
3671:
3667:
3664:
3661:
3656:
3653:
3650:
3645:
3640:
3637:
3634:
3631:
3626:
3623:
3620:
3615:
3610:
3607:
3604:
3601:
3596:
3591:
3566:
3560:
3557:
3554:
3551:
3548:
3545:
3542:
3538:
3533:
3530:
3527:
3522:
3519:
3516:
3511:
3506:
3503:
3500:
3497:
3492:
3489:
3486:
3481:
3476:
3475:
3472:
3466:
3463:
3460:
3457:
3454:
3451:
3448:
3444:
3439:
3436:
3433:
3428:
3425:
3422:
3417:
3412:
3409:
3406:
3403:
3398:
3395:
3392:
3387:
3382:
3381:
3362:
3359:
3355:phase constant
3353:is called the
3342:
3329:is called the
3318:
3295:
3289:
3285:
3281:
3278:
3275:
3270:
3266:
3261:
3256:
3250:
3246:
3242:
3239:
3236:
3231:
3227:
3222:
3216:
3213:
3210:
3207:
3204:
3201:
3198:
3174:
3171:
3168:
3163:
3158:
3151:
3147:
3143:
3140:
3138:
3136:
3133:
3130:
3125:
3120:
3110:
3106:
3102:
3096:
3092:
3086:
3085:
3082:
3079:
3076:
3071:
3066:
3059:
3055:
3051:
3048:
3046:
3044:
3041:
3038:
3033:
3028:
3018:
3014:
3010:
3004:
3000:
2994:
2993:
2962:
2959:
2956:
2951:
2946:
2924:
2921:
2918:
2913:
2908:
2893:The subscript
2877:
2874:
2871:
2868:
2865:
2838:
2835:
2832:
2827:
2822:
2797:
2773:
2770:
2767:
2762:
2757:
2732:
2729:
2726:
2723:
2720:
2693:
2690:
2687:
2682:
2677:
2652:
2628:
2625:
2622:
2617:
2612:
2585:
2582:
2579:
2576:
2571:
2566:
2560:
2554:
2550:
2546:
2541:
2537:
2533:
2530:
2526:
2522:
2519:
2516:
2514:
2512:
2509:
2506:
2501:
2496:
2488:
2485:
2481:
2476:
2475:
2472:
2469:
2466:
2463:
2458:
2453:
2447:
2441:
2437:
2433:
2428:
2424:
2420:
2417:
2413:
2409:
2406:
2403:
2401:
2399:
2396:
2393:
2388:
2383:
2375:
2372:
2368:
2363:
2362:
2350:
2347:
2334:
2314:
2288:
2285:
2282:
2279:
2276:
2273:
2269:
2266:
2263:
2260:
2257:
2254:
2251:
2248:
2245:
2239:
2236:
2232:
2226:
2222:
2219:
2216:
2213:
2210:
2206:
2202:
2199:
2197:
2195:
2192:
2189:
2186:
2183:
2180:
2172:
2168:
2164:
2158:
2154:
2147:
2144:
2141:
2138:
2135:
2132:
2129:
2126:
2123:
2115:
2111:
2107:
2101:
2097:
2091:
2090:
2087:
2084:
2081:
2078:
2075:
2072:
2068:
2065:
2062:
2059:
2056:
2053:
2050:
2047:
2044:
2038:
2035:
2031:
2025:
2021:
2018:
2015:
2012:
2009:
2005:
2001:
1998:
1996:
1994:
1991:
1988:
1985:
1982:
1979:
1971:
1967:
1963:
1957:
1953:
1946:
1943:
1940:
1937:
1934:
1931:
1928:
1925:
1922:
1914:
1910:
1906:
1900:
1896:
1890:
1889:
1868:
1847:
1821:
1818:
1815:
1812:
1809:
1806:
1803:
1800:
1797:
1794:
1791:
1788:
1785:
1782:
1776:
1773:
1769:
1763:
1760:
1757:
1754:
1752:
1750:
1747:
1744:
1741:
1738:
1735:
1729:
1726:
1722:
1717:
1716:
1713:
1710:
1707:
1704:
1701:
1698:
1695:
1692:
1689:
1686:
1683:
1680:
1677:
1674:
1668:
1665:
1661:
1655:
1652:
1649:
1646:
1644:
1642:
1639:
1636:
1633:
1630:
1627:
1621:
1618:
1614:
1609:
1608:
1596:
1593:
1591:
1588:
1571:
1568:
1562:
1557:
1531:
1526:
1521:
1498:
1494:
1490:
1486:
1460:
1456:
1431:
1427:
1422:
1417:
1413:
1381:
1376:
1350:
1345:
1339:
1332:
1328:
1324:
1319:
1314:
1309:
1305:
1301:
1298:
1295:
1292:
1289:
1253:
1233:
1222:
1221:
1218:
1217:
1214:
1211:
1208:
1205:
1202:
1199:
1196:
1193:
1189:
1188:
1185:
1182:
1179:
1176:
1173:
1170:
1167:
1164:
1160:
1159:
1156:
1153:
1150:
1147:
1144:
1141:
1138:
1135:
1131:
1130:
1127:
1124:
1121:
1118:
1115:
1112:
1109:
1106:
1102:
1101:
1098:
1095:
1092:
1089:
1086:
1083:
1080:
1077:
1073:
1072:
1069:
1066:
1063:
1060:
1057:
1054:
1051:
1048:
1044:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1015:
1014:
1003:
990:
979:
966:
955:
942:
928:
915:
909:
908:
903:
898:
893:
888:
876:
873:
825:
824:
802:
796:
774:
768:
726:
720:
689:
666:
663:
659:phase constant
628:
625:
600:
597:
573:
570:
546:
543:
522:
521:
507:
504:
501:
469:
444:
441:
438:
435:
428:
425:
420:
411:
385:
371:
355:
329:
315:
300:magnetic field
287:
273:
257:
233:
190:
187:
183:direct current
116:
89:
64:
41:circuit theory
15:
9:
6:
4:
3:
2:
11170:
11159:
11156:
11154:
11151:
11149:
11146:
11145:
11143:
11128:
11120:
11118:
11110:
11108:
11100:
11098:
11088:
11087:
11084:
11077:
11073:
11071:
11068:
11066:
11063:
11061:
11058:
11056:
11053:
11049:
11046:
11044:
11041:
11040:
11038:
11036:
11033:
11032:
11030:
11026:
11020:
11017:
11015:
11012:
11010:
11007:
11005:
11002:
11000:
10997:
10995:
10992:
10990:
10987:
10985:
10982:
10980:
10977:
10975:
10972:
10971:
10969:
10967:
10963:
10957:
10954:
10952:
10949:
10947:
10944:
10942:
10939:
10937:
10934:
10932:
10929:
10927:
10924:
10922:
10919:
10917:
10914:
10912:
10909:
10907:
10904:
10902:
10899:
10897:
10894:
10893:
10891:
10889:
10885:
10879:
10876:
10874:
10871:
10869:
10866:
10864:
10861:
10859:
10856:
10855:
10853:
10849:
10843:
10842:Code-division
10840:
10838:
10835:
10833:
10830:
10828:
10827:Time-division
10825:
10823:
10820:
10818:
10815:
10814:
10812:
10810:
10806:
10800:
10797:
10793:
10790:
10788:
10785:
10784:
10783:
10780:
10776:
10773:
10772:
10771:
10768:
10766:
10763:
10761:
10758:
10757:
10755:
10753:and switching
10751:
10747:
10739:
10736:
10735:
10734:
10731:
10727:
10724:
10723:
10722:
10719:
10717:
10714:
10712:
10709:
10705:
10704:optical fiber
10702:
10701:
10700:
10697:
10695:
10694:Coaxial cable
10692:
10691:
10689:
10687:
10681:
10675:
10672:
10670:
10667:
10665:
10662:
10660:
10657:
10655:
10652:
10650:
10647:
10645:
10642:
10640:
10637:
10635:
10632:
10630:
10627:
10625:
10622:
10620:
10617:
10615:
10612:
10610:
10609:Radia Perlman
10607:
10605:
10602:
10600:
10597:
10595:
10592:
10590:
10587:
10585:
10582:
10580:
10577:
10575:
10572:
10570:
10567:
10565:
10562:
10560:
10557:
10555:
10552:
10550:
10547:
10545:
10542:
10540:
10537:
10535:
10532:
10530:
10527:
10525:
10522:
10520:
10517:
10515:
10512:
10510:
10507:
10505:
10502:
10500:
10499:Lee de Forest
10497:
10495:
10494:Thomas Edison
10492:
10490:
10487:
10485:
10484:Donald Davies
10482:
10480:
10477:
10475:
10472:
10470:
10469:Claude Chappe
10467:
10465:
10462:
10460:
10457:
10455:
10452:
10450:
10447:
10445:
10442:
10440:
10437:
10435:
10432:
10430:
10427:
10425:
10422:
10420:
10417:
10415:
10412:
10410:
10407:
10405:
10402:
10400:
10397:
10396:
10394:
10390:
10384:
10381:
10379:
10376:
10374:
10371:
10369:
10366:
10362:
10359:
10357:
10354:
10353:
10352:
10349:
10347:
10346:
10342:
10340:
10337:
10334:
10331:
10329:
10326:
10324:
10321:
10319:
10316:
10314:
10313:Smoke signals
10311:
10307:
10304:
10302:
10299:
10297:
10294:
10293:
10292:
10291:Semiconductor
10289:
10285:
10282:
10281:
10280:
10277:
10275:
10272:
10270:
10267:
10265:
10262:
10260:
10257:
10255:
10252:
10250:
10247:
10245:
10242:
10240:
10237:
10233:
10230:
10229:
10228:
10225:
10223:
10220:
10218:
10215:
10213:
10210:
10208:
10205:
10203:
10200:
10198:
10195:
10193:
10190:
10188:
10185:
10183:
10180:
10178:
10175:
10171:
10168:
10166:
10163:
10161:
10158:
10156:
10153:
10152:
10151:
10150:Digital media
10148:
10144:
10141:
10139:
10136:
10134:
10131:
10129:
10126:
10125:
10124:
10121:
10119:
10116:
10114:
10111:
10109:
10106:
10104:
10101:
10099:
10096:
10094:
10091:
10090:
10088:
10086:
10082:
10078:
10071:
10066:
10064:
10059:
10057:
10052:
10051:
10048:
10037:
10033:
10029:
10028:"Part 1 of 3"
10015:
10008:
10001:
9984:
9982:0-12-189710-9
9978:
9974:
9970:
9963:
9955:
9951:
9947:
9940:
9932:
9925:
9923:
9914:
9912:0-07-026745-6
9908:
9904:
9897:
9889:
9887:0-03-013484-6
9883:
9879:
9872:
9870:
9861:
9859:0-13-249004-8
9855:
9851:
9844:
9842:
9833:
9831:0-07-035423-5
9827:
9823:
9819:
9813:
9805:
9803:0-13-016511-5
9799:
9795:
9794:Prentice Hall
9791:
9784:
9776:
9772:
9765:
9757:
9755:0-7803-0440-3
9751:
9747:
9743:
9742:
9734:
9726:
9720:
9716:
9712:
9705:
9697:
9695:0-13-084408-X
9691:
9687:
9680:
9678:
9669:
9665:
9659:
9655:
9654:
9646:
9644:
9642:
9637:
9626:
9625:Lord Kelvin's
9622:
9619:
9617:
9614:
9613:
9607:
9604:
9602:
9601:coaxial cable
9598:
9592:
9585:
9579:
9577:
9573:
9569:
9564:
9550:
9528:
9524:
9501:
9497:
9474:
9470:
9447:
9443:
9417:
9413:
9389:
9385:
9362:
9358:
9335:
9331:
9321:
9275:
9269:
9263:
9259:
9255:
9252:
9249:
9244:
9240:
9235:
9230:
9224:
9220:
9216:
9213:
9210:
9205:
9201:
9196:
9190:
9187:
9167:
9158:
9154:
9150:
9147:
9144:
9139:
9135:
9127:
9123:
9119:
9116:
9113:
9108:
9104:
9096:
9085:
9060:
9053:
9050:
9044:
9041:
9036:
9032:
9028:
9022:
9019:
9013:
9010:
8997:
8991:
8987:
8981:
8979:
8972:
8968:
8960:
8953:
8950:
8944:
8941:
8930:
8924:
8920:
8916:
8910:
8907:
8901:
8898:
8893:
8889:
8885:
8883:
8876:
8872:
8859:
8854:
8846:
8840:
8837:
8833:
8826:
8822:
8815:
8811:
8804:
8797:
8793:
8789:
8776:
8769:
8759:
8756:
8748:
8738:
8733:
8729:
8725:
8724:
8717:
8708:
8707:
8699:
8680:
8674:
8670:
8666:
8660:
8652:
8648:
8644:
8640:
8635:
8632:
8610:
8607:
8604:
8600:
8577:
8574:
8571:
8568:
8546:
8543:
8540:
8537:
8518:
8501:
8498:
8495:
8492:
8489:
8486:
8480:
8467:
8463:
8460:
8457:
8454:
8451:
8447:
8443:
8440:
8432:
8428:
8418:
8408:
8405:
8402:
8400:
8395:
8387:
8383:
8373:
8359:
8356:
8353:
8350:
8347:
8344:
8338:
8325:
8321:
8318:
8315:
8312:
8309:
8305:
8301:
8298:
8290:
8286:
8276:
8266:
8263:
8260:
8258:
8253:
8245:
8241:
8231:
8212:
8203:
8186:
8179:
8176:
8173:
8167:
8163:
8160:
8154:
8151:
8148:
8142:
8136:
8124:
8121:
8118:
8116:
8108:
8105:
8102:
8096:
8090:
8074:
8067:
8064:
8061:
8055:
8051:
8048:
8042:
8039:
8036:
8030:
8024:
8012:
8009:
8006:
8004:
7996:
7993:
7990:
7984:
7978:
7945:
7925:
7912:
7903:
7890:
7876:
7867:
7861:
7858:
7850:
7846:
7842:
7836:
7827:
7821:
7818:
7810:
7806:
7785:
7781:
7776:
7770:
7767:
7764:
7758:
7738:
7718:
7709:
7695:
7673:
7669:
7648:
7626:
7622:
7609:
7608:
7603:
7584:
7581:
7577:
7572:
7563:
7553:
7550:
7546:
7528:
7524:
7501:
7497:
7489:
7488:
7487:
7470:
7461:
7455:
7452:
7444:
7440:
7436:
7430:
7421:
7415:
7412:
7404:
7400:
7396:
7390:
7387:
7384:
7378:
7356:
7353:
7350:
7347:
7344:
7328:
7324:
7319:
7315:
7314:Sadiku (1989)
7310:
7299:
7297:
7279:
7275:
7252:
7248:
7224:
7221:
7215:
7204:
7195:
7194:
7169:
7148:
7126:
7123:
7120:
7117:
7113:
7098:
7092:
7088:
7082:
7077:
7074:
7071:
7068:
7064:
7049:
7043:
7039:
7033:
7027:
7021:
6999:
6996:
6993:
6990:
6986:
6979:
6975:
6971:
6966:
6963:
6960:
6957:
6953:
6946:
6942:
6938:
6932:
6926:
6917:
6915:
6910:
6897:
6887:
6882:
6877:
6872:
6869:
6864:
6861:
6858:
6830:
6827:
6825:
6820:
6815:
6811:
6807:
6799:
6795:
6791:
6786:
6781:
6777:
6766:
6763:
6761:
6756:
6751:
6747:
6743:
6735:
6731:
6727:
6722:
6717:
6713:
6696:
6676:
6673:
6668:
6665:
6659:
6656:
6653:
6650:
6647:
6644:
6641:
6638:
6635:
6629:
6626:
6621:
6618:
6605:
6602:
6597:
6594:
6588:
6585:
6582:
6579:
6576:
6573:
6570:
6567:
6564:
6558:
6555:
6550:
6547:
6520:
6496:
6483:
6480:
6477:
6473:
6465:
6459:
6435:
6433:
6425:
6422:
6419:
6413:
6406:
6393:
6390:
6387:
6383:
6375:
6369:
6345:
6343:
6335:
6332:
6329:
6323:
6311:
6307:
6304:
6294:
6276:
6273:
6269:
6264:
6255:
6228:
6225:
6223:
6213:
6209:
6200:
6195:
6182:
6172:
6165:
6157:
6153:
6144:
6139:
6124:
6121:
6119:
6109:
6105:
6096:
6091:
6078:
6068:
6061:
6053:
6049:
6040:
6035:
6002:
5979:
5970:
5965:
5949:
5941:
5932:
5929:
5926:
5920:
5912:
5884:
5876:
5867:
5864:
5861:
5855:
5847:
5833:
5823:
5803:
5800:
5797:
5791:
5788:
5786:
5781:
5771:
5768:
5765:
5759:
5756:
5754:
5749:
5699:
5696:
5693:
5690:
5669:
5666:
5663:
5660:
5646:
5628:
5620:
5616:
5610:
5607:
5602:
5549:
5532:
5515:
5492:
5478:
5458:
5453:
5445:
5441:
5437:
5404:
5400:
5391:
5387:
5384:
5380:
5374:
5357:
5325:
5321:
5317:
5313:
5304:
5300:
5297:
5293:
5275:
5257:
5206:
5204:
5194:
5191:
5186:
5181:
5145:
5107:
5102:
5097:
5088:
5083:
5080:
5067:
5063:
5059:
5023:
5020:
5016:
5011:
5006:
4997:
4992:
4989:
4976:
4971:
4966:
4964:
4913:
4907:Finite length
4898:
4895:
4879:
4865:
4864:
4857:
4840:
4832:
4829:
4826:
4812:
4811:
4804:
4787:
4779:
4776:
4773:
4759:
4758:
4751:
4734:
4726:
4723:
4720:
4706:
4705:
4698:
4681:
4673:
4670:
4667:
4653:
4652:
4645:
4628:
4620:
4606:
4605:
4598:
4581:
4573:
4570:
4567:
4553:
4552:
4545:
4528:
4520:
4517:
4514:
4500:
4499:
4492:
4475:
4467:
4464:
4461:
4447:
4446:
4439:
4422:
4414:
4411:
4408:
4394:
4393:
4386:
4369:
4361:
4347:
4346:
4342:
4328:
4321:
4320:
4316:
4302:
4295:
4294:
4290:
4287:
4286:
4280:
4279:
4278:
4264:
4254:
4250:
4246:
4243:
4240:
4235:
4231:
4223:
4219:
4215:
4212:
4209:
4204:
4200:
4192:
4187:
4157:
4151:
4143:
4140:
4137:
4124:
4114:
4108:
4100:
4097:
4094:
4080:
4074:
4066:
4063:
4060:
4047:
4037:
4031:
4023:
4020:
4017:
3997:
3994:
3981:
3974:
3966:
3963:
3960:
3950:
3944:
3936:
3933:
3930:
3920:
3914:
3906:
3876:
3867:
3864:
3861:
3855:
3852:
3848:
3840:
3832:
3829:
3826:
3816:
3810:
3802:
3799:
3796:
3782:
3773:
3770:
3767:
3761:
3758:
3754:
3746:
3738:
3735:
3732:
3722:
3716:
3708:
3705:
3702:
3682:
3669:
3662:
3654:
3651:
3648:
3638:
3632:
3624:
3621:
3618:
3608:
3602:
3594:
3564:
3555:
3552:
3549:
3543:
3540:
3536:
3528:
3520:
3517:
3514:
3504:
3498:
3490:
3487:
3484:
3470:
3461:
3458:
3455:
3449:
3446:
3442:
3434:
3426:
3423:
3420:
3410:
3404:
3396:
3393:
3390:
3370:
3368:
3358:
3356:
3340:
3332:
3316:
3293:
3287:
3283:
3279:
3276:
3273:
3268:
3264:
3259:
3254:
3248:
3244:
3240:
3237:
3234:
3229:
3225:
3220:
3214:
3211:
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3205:
3202:
3199:
3196:
3169:
3161:
3149:
3145:
3141:
3139:
3131:
3123:
3108:
3104:
3100:
3094:
3090:
3077:
3069:
3057:
3053:
3049:
3047:
3039:
3031:
3016:
3012:
3008:
3002:
2998:
2983:
2978:
2976:
2957:
2949:
2919:
2911:
2896:
2891:
2875:
2872:
2869:
2866:
2863:
2855:
2833:
2825:
2795:
2768:
2760:
2730:
2727:
2724:
2721:
2718:
2710:
2688:
2680:
2650:
2623:
2615:
2583:
2577:
2569:
2558:
2552:
2548:
2544:
2539:
2535:
2531:
2528:
2524:
2520:
2517:
2515:
2507:
2499:
2486:
2470:
2464:
2456:
2445:
2439:
2435:
2431:
2426:
2422:
2418:
2415:
2411:
2407:
2404:
2402:
2394:
2386:
2373:
2346:
2332:
2312:
2303:
2283:
2280:
2277:
2271:
2267:
2264:
2261:
2255:
2252:
2249:
2243:
2237:
2224:
2220:
2217:
2214:
2211:
2208:
2204:
2200:
2198:
2190:
2187:
2184:
2178:
2170:
2166:
2156:
2145:
2142:
2139:
2133:
2130:
2127:
2121:
2113:
2109:
2099:
2082:
2079:
2076:
2070:
2066:
2063:
2060:
2054:
2051:
2048:
2042:
2036:
2023:
2019:
2016:
2013:
2010:
2007:
2003:
1999:
1997:
1989:
1986:
1983:
1977:
1969:
1965:
1955:
1944:
1941:
1938:
1932:
1929:
1926:
1920:
1912:
1908:
1898:
1866:
1845:
1836:
1816:
1813:
1810:
1804:
1801:
1798:
1792:
1789:
1786:
1780:
1774:
1761:
1758:
1755:
1753:
1745:
1742:
1739:
1733:
1727:
1708:
1705:
1702:
1696:
1693:
1690:
1684:
1681:
1678:
1672:
1666:
1653:
1650:
1647:
1645:
1637:
1634:
1631:
1625:
1619:
1590:The equations
1587:
1585:
1584:coaxial cable
1569:
1566:
1555:
1524:
1519:
1496:
1492:
1488:
1484:
1474:
1458:
1454:
1429:
1425:
1420:
1415:
1411:
1399:
1374:
1343:
1337:
1330:
1326:
1322:
1317:
1312:
1307:
1303:
1299:
1293:
1287:
1273:
1271:
1267:
1251:
1231:
1215:
1212:
1203:
1200:
1194:
1190:
1186:
1183:
1174:
1171:
1165:
1161:
1157:
1154:
1145:
1142:
1136:
1132:
1128:
1125:
1116:
1113:
1107:
1103:
1099:
1096:
1087:
1084:
1078:
1074:
1070:
1067:
1058:
1055:
1049:
1045:
1041:
1038:
1029:
1026:
1020:
1016:
1004:
996:
991:
980:
972:
967:
956:
948:
943:
939:
929:
921:
916:
914:
911:
910:
886:
885:
882:
881:
880:
872:
819:
815:
807:
803:
797:
791:
787:
783:
775:
769:
766:
758:
754:
751:
747:
743:
739:
731:
727:
721:
718:
710:
706:
702:
694:
690:
684:
683:
682:
676:
671:
662:
660:
656:
652:
648:
644:
626:
623:
598:
595:
571:
568:
544:
541:
531:
527:
505:
502:
499:
490:
486:
467:
426:
423:
418:
409:
399:
383:
376:
372:
369:
353:
346:
343:
327:
320:
316:
313:
309:
305:
301:
285:
278:
274:
271:
255:
247:
231:
224:
220:
219:
218:
216:
212:
208:
204:
195:
186:
184:
180:
176:
173:
169:
165:
161:
157:
156:
151:
146:
144:
140:
136:
132:
114:
105:
87:
78:
62:
54:
50:
46:
45:non-TEM modes
42:
38:
34:
30:
26:
22:
10809:Multiplexing
10684:Transmission
10649:Nikola Tesla
10639:Henry Sutton
10594:Samuel Morse
10524:Robert Hooke
10489:Amos Dolbear
10424:John Bardeen
10343:
10323:Telautograph
10227:Mobile phone
10182:Edholm's law
10165:social media
10098:Broadcasting
10031:
10018:. Retrieved
10013:
10000:
9968:
9962:
9945:
9939:
9930:
9902:
9896:
9877:
9849:
9821:
9812:
9789:
9783:
9770:
9764:
9740:
9733:
9724:0-80148234-8
9710:
9704:
9685:
9666:– via
9652:
9605:
9590:
9583:
9580:
9575:
9571:
9567:
9565:
9322:
8855:
8852:
8844:
8838:
8835:
8831:
8824:
8820:
8813:
8809:
8802:
8795:
8791:
8787:
8774:
8751:
8742:
8735:Please help
8731:
8720:
8519:
8204:
7917:
7731:and voltage
7710:
7613:
7605:
7544:
7334:
7311:
7300:
7191:
6918:
6911:
6697:
6306:steady-state
6300:
5966:
5829:
5652:
5493:
4918:
3998:
3995:
3683:
3371:
3364:
2979:
2894:
2892:
2352:
2304:
1837:
1598:
1475:
1397:
1274:
1223:
1105:100 kHz
1011:1000 ft
987:1000 ft
963:1000 ft
878:
826:
798:Conductance
782:ohmic losses
756:
749:
741:
737:
729:
722:Capacitance
708:
700:
680:
529:
525:
523:
485:conductivity
298:(due to the
200:
159:
153:
147:
24:
20:
18:
11009:NPL network
10721:Radio waves
10659:Alfred Vail
10569:Hedy Lamarr
10554:Dawon Kahng
10514:Elisha Gray
10474:Yogen Dalal
10399:Nasir Ahmed
10333:Teleprinter
10197:Heliographs
9991:instead of
9775:McGraw-Hill
9576:common mode
8739:if you can.
8732:Poor style.
4291:Definition
1595:Time domain
1266:skin effect
1076:10 kHz
818:susceptance
770:Resistance
703:the line's
685:Inductance
375:conductance
319:capacitance
270:skin effect
75:and either
49:time domain
11142:Categories
11055:Antarctica
11014:Toasternet
10936:Television
10419:Paul Baran
10351:Television
10335:(teletype)
10328:Telegraphy
10306:transistor
10284:Phryctoria
10254:Photophone
10232:Smartphone
10222:Mass media
10036:E.E. Times
10020:2010-10-22
10014:cmpnet.com
9746:IEEE Press
9663:0070274061
9632:References
6310:transients
6303:sinusoidal
2854:admittance
1192:5 MHz
1163:2 MHz
1134:1 MHz
1047:1 kHz
936:1000
887:Frequency
277:inductance
223:resistance
207:conductors
175:conductors
11039:Americas
11028:Locations
10999:Internet2
10760:Bandwidth
10464:Vint Cerf
10361:streaming
10339:Telephone
10279:Semaphore
10170:streaming
9264:ω
9256:ω
9245:ω
9225:ω
9217:ω
9206:ω
9191:≡
9188:γ
9159:ω
9151:ω
9140:ω
9128:ω
9120:ω
9109:ω
9097:≡
9051:γ
9045:
9020:γ
9014:
8951:γ
8945:
8908:γ
8902:
8745:June 2012
8636:≈
8633:α
8608:α
8605:−
8575:ω
8572:≪
8544:ω
8541:≪
8478:∂
8474:∂
8425:∂
8415:∂
8380:∂
8370:∂
8336:∂
8332:∂
8283:∂
8273:∂
8238:∂
8228:∂
8161:−
8134:∂
8130:∂
8122:−
8088:∂
8084:∂
8049:−
8022:∂
8018:∂
8010:−
7976:∂
7972:∂
7871:~
7843:−
7831:~
7822:−
7573:≡
7567:~
7465:~
7425:~
7416:−
7083:−
7069:−
6958:−
6891:~
6883:ω
6865:ω
6862:≡
6657:−
6645:ω
6639:−
6586:−
6574:ω
6568:−
6521:ω
6481:ω
6391:ω
6265:≡
6259:~
6206:∂
6192:∂
6176:~
6166:−
6150:∂
6136:∂
6102:∂
6088:∂
6072:~
6062:−
6046:∂
6032:∂
5947:∂
5939:∂
5930:−
5918:∂
5910:∂
5882:∂
5874:∂
5865:−
5853:∂
5845:∂
5734:and time
5697:≫
5691:ω
5667:≫
5661:ω
5625:γ
5621:−
5450:γ
5446:−
5438:≡
5397:γ
5388:
5310:γ
5301:
5192:−
5089:−
5081:−
4990:−
4827:ω
4774:ω
4721:ω
4668:ω
4621:ω
4568:ω
4515:ω
4462:ω
4409:ω
4362:ω
4255:ω
4247:ω
4236:ω
4224:ω
4216:ω
4205:ω
4138:ω
4095:ω
4061:ω
4018:ω
3961:ω
3951:−
3931:ω
3907:ω
3865:−
3856:γ
3853:−
3827:ω
3797:ω
3771:−
3762:γ
3733:ω
3703:ω
3649:ω
3619:ω
3595:ω
3553:−
3544:γ
3541:−
3515:ω
3485:ω
3459:−
3450:γ
3421:ω
3391:ω
3341:β
3317:α
3288:ω
3280:ω
3269:ω
3249:ω
3241:ω
3230:ω
3215:≡
3212:β
3203:α
3200:≡
3197:γ
3162:ω
3146:γ
3124:ω
3070:ω
3054:γ
3032:ω
2950:ω
2912:ω
2873:ω
2826:ω
2761:ω
2728:ω
2709:impedance
2681:ω
2616:ω
2570:ω
2553:ω
2540:ω
2532:ω
2521:−
2500:ω
2484:∂
2480:∂
2457:ω
2440:ω
2427:ω
2419:ω
2408:−
2387:ω
2371:∂
2367:∂
2235:∂
2231:∂
2163:∂
2153:∂
2140:−
2106:∂
2096:∂
2034:∂
2030:∂
1962:∂
1952:∂
1939:−
1905:∂
1895:∂
1799:−
1772:∂
1768:∂
1759:−
1725:∂
1721:∂
1691:−
1664:∂
1660:∂
1651:−
1617:∂
1613:∂
1567:≈
1313:⋅
1018:1 Hz
790:reactance
701:increases
675:electrons
503:≡
345:capacitor
168:telegraph
88:ω
77:frequency
23:(or just
11107:Category
10994:Internet
10984:CYCLADES
10901:Ethernet
10851:Concepts
10775:terminal
10726:wireless
10549:Bob Kahn
10392:Pioneers
10217:Internet
10108:Cable TV
9954:69-18342
9820:(1984).
9610:See also
8721:require
814:shunting
627:′
599:′
572:′
545:′
308:inductor
211:two-port
51:and the
11127:Commons
11117:Outline
11070:Oceania
10989:FidoNet
10974:ARPANET
10787:circuit
10356:digital
10085:History
9599:like a
8723:cleanup
7543:can be
7190:is the
2975:phasors
1207:118.074
1009:⁄
998:⁄
985:⁄
974:⁄
961:⁄
950:⁄
934:⁄
923:⁄
793:ωL
693:inertia
398:siemens
312:henries
139:phasors
33:current
29:voltage
11065:Europe
11035:Africa
11019:Usenet
10979:BITNET
10916:Mobile
10792:packet
10301:MOSFET
10296:device
10093:Beacon
9979:
9952:
9909:
9884:
9856:
9828:
9800:
9752:
9721:
9692:
9660:
9568:shield
9309:, and
9077:where
8842:, and
8686:
8625:where
7614:Here,
7486:where
6847:where
6513:where
6245:where
5425:where
4288:Symbol
3999:Note:
3189:where
1216:15.72
1210:35.989
1198:304.62
1195:999.41
1187:15.72
1181:16.217
1178:53.205
1169:196.03
1166:643.14
1158:15.72
1149:29.111
1140:141.30
1137:463.59
1129:15.72
1108:191.63
1100:15.72
1079:172.70
1071:15.72
1050:172.28
1042:15.72
1021:172.24
847:, and
839:, and
742:within
649:, the
471:
465:
368:farads
11048:South
11043:North
11004:JANET
10941:Telex
10931:Radio
10770:Nodes
10765:Links
10686:media
10264:Radio
10249:Pager
10177:Drums
10143:video
10138:image
10128:audio
10025:also
10010:(PDF)
7551:, and
5653:When
1547:with
1366:with
1213:51.57
1204:142.5
1201:467.5
1184:51.57
1175:148.2
1172:486.2
1155:51.57
1152:8.873
1146:154.3
1143:506.2
1126:51.57
1123:1.197
1120:3.327
1117:177.0
1114:580.7
1111:58.41
1097:51.57
1094:0.162
1091:0.531
1088:185.9
1085:609.9
1082:52.64
1068:51.57
1065:0.022
1062:0.072
1059:186.7
1056:612.5
1053:52.51
1039:51.57
1036:0.000
1033:0.000
1030:186.8
1027:612.9
1024:52.50
784:that
750:lower
738:other
730:other
414:shunt
342:shunt
11060:Asia
10946:UUCP
10906:ISDN
9977:ISBN
9950:LCCN
9907:ISBN
9882:ISBN
9854:ISBN
9826:ISBN
9798:ISBN
9750:ISBN
9719:ISBN
9690:ISBN
9658:ISBN
9574:and
9551:sinh
9516:and
9462:and
9404:and
9350:and
9180:and
9042:cosh
9011:sinh
8942:sinh
8899:cosh
8847:≡ −1
8794:) ≡
8560:and
8524:and
7938:and
7547:two
7516:and
7323:help
7316:and
7305:and
7267:and
7240:and
7014:and
5718:and
5682:and
5471:and
5385:sinh
5298:cosh
3333:and
2973:are
2935:and
1446:and
1268:and
1244:and
863:and
855:and
786:drop
757:less
709:more
657:and
614:and
373:The
317:The
246:ohms
31:and
19:The
10951:WAN
10921:NGN
10911:LAN
10192:Fax
10133:DCT
7545:any
2325:or
1858:or
1400:(·)
871:).
133:or
102:or
11144::
10030:.
10012:.
9971:.
9921:^
9868:^
9840:^
9792:.
9744:.
9676:^
9640:^
9623:,
9603:.
9302:,
9295:,
8834:≡
8773:2/
8698:.
8590:),
7610:).
7369:),
7327:.
6916:.
5738::
3357:.
2984:.
2977:.
1007:nF
1000:km
995:nF
983:μS
976:km
971:μS
959:μH
952:km
947:μH
938:ft
925:km
913:Hz
835:,
831:,
821:ωC
763:AC
715:AC
653:,
185:.
106:,
79:,
11078:)
11074:(
10069:e
10062:t
10055:v
10038:.
10023:;
9995:.
9993:α
9989:μ
9985:.
9956:.
9915:.
9890:.
9862:.
9834:.
9806:.
9758:.
9727:.
9698:.
9593:)
9591:s
9589:(
9587:o
9584:Z
9529:2
9525:I
9502:2
9498:V
9475:1
9471:I
9448:1
9444:V
9433:.
9418:2
9414:I
9390:2
9386:V
9363:1
9359:I
9336:1
9332:V
9318:ω
9313:ω
9311:C
9306:ω
9304:G
9299:ω
9297:L
9292:ω
9290:R
9276:,
9270:)
9260:C
9253:j
9250:+
9241:G
9236:(
9231:)
9221:L
9214:j
9211:+
9202:R
9197:(
9168:,
9155:C
9148:j
9145:+
9136:G
9124:L
9117:j
9114:+
9105:R
9091:o
9086:Z
9061:.
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9048:(
9037:2
9033:I
9029:+
9026:)
9023:x
9017:(
9003:o
8998:Z
8992:2
8988:V
8982:=
8973:1
8969:I
8961:,
8957:)
8954:x
8948:(
8936:o
8931:Z
8925:2
8921:I
8917:+
8914:)
8911:x
8905:(
8894:2
8890:V
8886:=
8877:1
8873:V
8849:.
8845:j
8839:ω
8836:j
8832:s
8827:)
8825:s
8823:(
8821:γ
8816:)
8814:s
8812:(
8810:T
8805:)
8803:s
8801:(
8799:o
8796:Z
8792:s
8790:(
8788:Z
8783:x
8778:o
8775:Z
8758:)
8752:(
8747:)
8743:(
8681:2
8675:0
8671:Z
8667:G
8661:+
8653:0
8649:Z
8645:2
8641:R
8611:x
8601:e
8578:C
8569:G
8547:L
8538:R
8530:(
8526:I
8522:V
8502:.
8499:I
8496:R
8493:G
8490:+
8487:I
8481:t
8468:)
8464:L
8461:G
8458:+
8455:C
8452:R
8448:(
8444:+
8441:I
8433:2
8429:t
8419:2
8409:C
8406:L
8403:=
8396:I
8388:2
8384:x
8374:2
8360:,
8357:V
8354:R
8351:G
8348:+
8345:V
8339:t
8326:)
8322:L
8319:G
8316:+
8313:C
8310:R
8306:(
8302:+
8299:V
8291:2
8287:t
8277:2
8267:C
8264:L
8261:=
8254:V
8246:2
8242:x
8232:2
8207:x
8187:.
8183:)
8180:t
8177:,
8174:x
8171:(
8168:V
8164:G
8158:)
8155:t
8152:,
8149:x
8146:(
8143:V
8137:t
8125:C
8119:=
8112:)
8109:t
8106:,
8103:x
8100:(
8097:I
8091:x
8075:,
8071:)
8068:t
8065:,
8062:x
8059:(
8056:I
8052:R
8046:)
8043:t
8040:,
8037:x
8034:(
8031:I
8025:t
8013:L
8007:=
8000:)
7997:t
7994:,
7991:x
7988:(
7985:V
7979:x
7946:G
7926:R
7891:.
7885:]
7880:)
7877:t
7868:v
7862:+
7859:x
7856:(
7851:2
7847:f
7840:)
7837:t
7828:v
7819:x
7816:(
7811:1
7807:f
7801:[
7791:o
7786:Z
7782:1
7777:=
7774:)
7771:t
7768:,
7765:x
7762:(
7759:I
7739:V
7719:I
7696:x
7674:2
7670:f
7649:x
7627:1
7623:f
7585:C
7582:L
7578:1
7564:v
7529:2
7525:f
7502:1
7498:f
7474:)
7471:t
7462:v
7456:+
7453:x
7450:(
7445:2
7441:f
7437:+
7434:)
7431:t
7422:v
7413:x
7410:(
7405:1
7401:f
7397:=
7394:)
7391:t
7388:,
7385:x
7382:(
7379:V
7357:0
7354:=
7351:G
7348:=
7345:R
7337:(
7325:)
7307:C
7303:L
7280:2
7276:V
7253:1
7249:V
7225:C
7222:L
7216:=
7210:o
7205:Z
7175:o
7170:Z
7149:k
7127:x
7124:k
7121:j
7118:+
7114:e
7104:o
7099:Z
7093:2
7089:V
7078:x
7075:k
7072:j
7065:e
7055:o
7050:Z
7044:1
7040:V
7034:=
7031:)
7028:x
7025:(
7022:I
7000:x
6997:k
6994:j
6991:+
6987:e
6980:2
6976:V
6972:+
6967:x
6964:k
6961:j
6954:e
6947:1
6943:V
6939:=
6936:)
6933:x
6930:(
6927:V
6898:.
6888:v
6878:=
6873:C
6870:L
6859:k
6849:k
6831:0
6828:=
6821:I
6816:2
6812:k
6808:+
6800:2
6796:x
6792:d
6787:I
6782:2
6778:d
6767:0
6764:=
6757:V
6752:2
6748:k
6744:+
6736:2
6732:x
6728:d
6723:V
6718:2
6714:d
6677:t
6674:d
6669:V
6666:d
6660:C
6654:=
6651:V
6648:C
6642:j
6636:=
6630:x
6627:d
6622:I
6619:d
6606:t
6603:d
6598:I
6595:d
6589:L
6583:=
6580:I
6577:L
6571:j
6565:=
6559:x
6556:d
6551:V
6548:d
6497:,
6491:}
6484:t
6478:j
6474:e
6469:)
6466:x
6463:(
6460:I
6455:{
6446:e
6442:R
6436:=
6429:)
6426:t
6423:,
6420:x
6417:(
6414:I
6407:,
6401:}
6394:t
6388:j
6384:e
6379:)
6376:x
6373:(
6370:V
6365:{
6356:e
6352:R
6346:=
6339:)
6336:t
6333:,
6330:x
6327:(
6324:V
6277:C
6274:L
6270:1
6256:v
6229:0
6226:=
6214:2
6210:x
6201:I
6196:2
6183:2
6173:v
6158:2
6154:t
6145:I
6140:2
6125:0
6122:=
6110:2
6106:x
6097:V
6092:2
6079:2
6069:v
6054:2
6050:t
6041:V
6036:2
6015::
6003:I
5992:,
5980:V
5950:t
5942:V
5933:C
5927:=
5921:x
5913:I
5885:t
5877:I
5868:L
5862:=
5856:x
5848:V
5807:)
5804:t
5801:,
5798:x
5795:(
5792:I
5789:=
5782:I
5775:)
5772:t
5769:,
5766:x
5763:(
5760:V
5757:=
5750:V
5736:t
5732:x
5728:I
5724:V
5720:C
5716:L
5712:,
5700:G
5694:C
5670:R
5664:L
5644:.
5629:x
5617:e
5611:2
5608:1
5603:=
5595:S
5589:V
5581:L
5575:V
5550:,
5544:C
5538:Z
5533:=
5527:S
5521:Z
5516:=
5510:L
5504:Z
5479:x
5459:,
5454:x
5442:e
5434:H
5405:)
5401:x
5392:(
5381:)
5375:2
5369:C
5363:Z
5358:+
5352:S
5346:Z
5338:L
5332:Z
5326:(
5322:+
5318:)
5314:x
5305:(
5294:)
5287:S
5281:Z
5276:+
5270:L
5264:Z
5258:(
5251:C
5245:Z
5235:C
5229:Z
5221:L
5215:Z
5207:=
5195:1
5187:]
5182:)
5173:L
5167:Z
5159:C
5153:Z
5146:+
5138:C
5131:Z
5122:S
5116:Z
5108:(
5103:)
5098:2
5093:H
5084:1
5076:H
5068:(
5064:+
5060:)
5051:L
5045:Z
5037:S
5031:Z
5024:+
5021:1
5017:(
5012:)
5007:2
5002:H
4998:+
4993:1
4985:H
4977:(
4972:[
4967:=
4955:S
4949:V
4941:L
4935:V
4880:c
4875:Z
4860:b
4844:)
4841:b
4838:(
4833:R
4830:,
4822:I
4807:a
4791:)
4788:a
4785:(
4780:F
4777:,
4769:I
4754:x
4738:)
4735:x
4732:(
4727:R
4724:,
4716:I
4701:x
4685:)
4682:x
4679:(
4674:F
4671:,
4663:I
4648:x
4632:)
4629:x
4626:(
4616:I
4601:b
4585:)
4582:b
4579:(
4574:R
4571:,
4563:V
4548:a
4532:)
4529:a
4526:(
4521:F
4518:,
4510:V
4495:x
4479:)
4476:x
4473:(
4468:R
4465:,
4457:V
4442:x
4426:)
4423:x
4420:(
4415:F
4412:,
4404:V
4389:x
4373:)
4370:x
4367:(
4357:V
4329:b
4303:a
4265:,
4251:C
4244:j
4241:+
4232:G
4220:L
4213:j
4210:+
4201:R
4193:=
4188:c
4183:Z
4158:,
4155:)
4152:x
4149:(
4144:R
4141:,
4133:I
4125:c
4120:Z
4115:=
4112:)
4109:x
4106:(
4101:R
4098:,
4090:V
4081:,
4078:)
4075:x
4072:(
4067:F
4064:,
4056:I
4048:c
4043:Z
4038:=
4035:)
4032:x
4029:(
4024:F
4021:,
4013:V
3982:.
3978:)
3975:x
3972:(
3967:R
3964:,
3956:I
3948:)
3945:x
3942:(
3937:F
3934:,
3926:I
3921:=
3918:)
3915:x
3912:(
3902:I
3877:;
3871:)
3868:x
3862:b
3859:(
3849:e
3844:)
3841:b
3838:(
3833:R
3830:,
3822:I
3817:=
3814:)
3811:x
3808:(
3803:R
3800:,
3792:I
3783:;
3777:)
3774:x
3768:a
3765:(
3759:+
3755:e
3750:)
3747:a
3744:(
3739:F
3736:,
3728:I
3723:=
3720:)
3717:x
3714:(
3709:F
3706:,
3698:I
3670:.
3666:)
3663:x
3660:(
3655:R
3652:,
3644:V
3639:+
3636:)
3633:x
3630:(
3625:F
3622:,
3614:V
3609:=
3606:)
3603:x
3600:(
3590:V
3565:;
3559:)
3556:x
3550:b
3547:(
3537:e
3532:)
3529:b
3526:(
3521:R
3518:,
3510:V
3505:=
3502:)
3499:x
3496:(
3491:R
3488:,
3480:V
3471:;
3465:)
3462:x
3456:a
3453:(
3447:+
3443:e
3438:)
3435:a
3432:(
3427:F
3424:,
3416:V
3411:=
3408:)
3405:x
3402:(
3397:F
3394:,
3386:V
3294:)
3284:C
3277:j
3274:+
3265:G
3260:(
3255:)
3245:L
3238:j
3235:+
3226:R
3221:(
3209:j
3206:+
3173:)
3170:x
3167:(
3157:I
3150:2
3142:=
3135:)
3132:x
3129:(
3119:I
3109:2
3105:x
3101:d
3095:2
3091:d
3081:)
3078:x
3075:(
3065:V
3058:2
3050:=
3043:)
3040:x
3037:(
3027:V
3017:2
3013:x
3009:d
3003:2
2999:d
2961:)
2958:x
2955:(
2945:V
2923:)
2920:x
2917:(
2907:I
2895:ω
2889:.
2876:C
2870:j
2867:+
2864:G
2850:,
2837:)
2834:x
2831:(
2821:V
2808:,
2796:x
2785:,
2772:)
2769:x
2766:(
2756:I
2743:.
2731:L
2725:j
2722:+
2719:R
2705:,
2692:)
2689:x
2686:(
2676:I
2663:,
2651:x
2640:,
2627:)
2624:x
2621:(
2611:V
2584:.
2581:)
2578:x
2575:(
2565:V
2559:)
2549:G
2545:+
2536:C
2529:j
2525:(
2518:=
2511:)
2508:x
2505:(
2495:I
2487:x
2471:,
2468:)
2465:x
2462:(
2452:I
2446:)
2436:R
2432:+
2423:L
2416:j
2412:(
2405:=
2398:)
2395:x
2392:(
2382:V
2374:x
2333:I
2313:V
2287:)
2284:t
2281:,
2278:x
2275:(
2272:I
2268:R
2265:G
2262:+
2259:)
2256:t
2253:,
2250:x
2247:(
2244:I
2238:t
2225:)
2221:L
2218:G
2215:+
2212:C
2209:R
2205:(
2201:=
2194:)
2191:t
2188:,
2185:x
2182:(
2179:I
2171:2
2167:t
2157:2
2146:C
2143:L
2137:)
2134:t
2131:,
2128:x
2125:(
2122:I
2114:2
2110:x
2100:2
2086:)
2083:t
2080:,
2077:x
2074:(
2071:V
2067:R
2064:G
2061:+
2058:)
2055:t
2052:,
2049:x
2046:(
2043:V
2037:t
2024:)
2020:L
2017:G
2014:+
2011:C
2008:R
2004:(
2000:=
1993:)
1990:t
1987:,
1984:x
1981:(
1978:V
1970:2
1966:t
1956:2
1945:C
1942:L
1936:)
1933:t
1930:,
1927:x
1924:(
1921:V
1913:2
1909:x
1899:2
1879::
1867:I
1846:V
1820:)
1817:t
1814:,
1811:x
1808:(
1805:V
1802:G
1796:)
1793:t
1790:,
1787:x
1784:(
1781:V
1775:t
1762:C
1756:=
1749:)
1746:t
1743:,
1740:x
1737:(
1734:I
1728:x
1712:)
1709:t
1706:,
1703:x
1700:(
1697:I
1694:R
1688:)
1685:t
1682:,
1679:x
1676:(
1673:I
1667:t
1654:L
1648:=
1641:)
1638:t
1635:,
1632:x
1629:(
1626:V
1620:x
1570:1
1561:e
1556:g
1530:e
1525:g
1520:f
1497:2
1493:/
1489:1
1485:f
1459:e
1455:g
1444:,
1430:1
1426:f
1421:,
1416:1
1412:G
1398:G
1380:e
1375:g
1349:e
1344:g
1338:)
1331:1
1327:f
1323:f
1318:(
1308:1
1304:G
1300:=
1297:)
1294:f
1291:(
1288:G
1277:G
1252:L
1232:R
932:Ω
920:Ω
906:C
901:G
896:L
891:R
869:R
865:G
861:R
857:C
853:L
849:G
845:R
841:G
837:R
833:C
829:L
810:G
800:G
778:R
772:R
755:(
734:C
724:C
707:(
697:L
687:L
624:G
612:,
596:C
585:,
569:L
558:,
542:R
519:.
506:0
500:G
468:G
456:.
443:s
440:m
437:h
434:o
427:G
424:1
419:=
410:R
384:G
366:(
354:C
328:C
310:(
286:L
272:.
256:R
232:R
127:.
115:s
100:,
63:x
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