If a transmission line is modeled as RLGC, how does time varying currents at high frequencies propagate from source to load when:
Regards,
Suhas. D.
Transmission lines only work according to the simple equations if the losses along and across the line are a lot less than the energy stored in the inductors and capacitors. If the losses are low, then when a capacitor shorts current to earth, it pulls a high current through an inductor, which doesn't stop when the capacitor voltage is zero, but continues as the magnetic field in the inductor then dies away until the capacitor is fully charged in the other direction, which then discharges back through the inductor and so on. This means that even with seeming low impedance to ground and high impedance in series a transmission line carries power. This was what Heavyside found and is the basis of him recommending adding series inductors to long transmission lines to reduce their distortion - it made the stored energy higher compared to the losses so the performance was closer to the simple equations.
The answer above is excellent regarding the phenomenon of step-by-step signal transmission across the (electric) long lines.
If you are not convinced, please also compare the numerical values of reactance (per unit length) of inductor and capacitor for a single-wire ground return (with technical values for conductor size and distance to ground): the differences, at the same frequency, are of few orders of magnitude (it is incomparable greater the reactance of capacitor comparing to that of the inductor).
The RLGC equivalent circuit for a transmission line is a simplified single mode model. This simple model is valid at low frequencies but is not accurate at very high frequencies.
Sir Marian Costea: "compare the numerical values of reactance (per unit length) of inductor and capacitor for a single-wire ground return (with technical values for conductor size and distance to ground)"
Can you please refer me to some sources?
Dear Sir,
For the case of a single wire placed horizontally above the earth (which is considered perfect conductor), the inductance (p.u. length) can be determined from the relation:L0=(mu0/2*pi)*ln(2h/r0) [H/m], where mu0 is the permeability of the air (or vacuum), r0 – the radius of conductor (r0
If you want sources I suggest you start by looking up coaxial cable and transmission line in Wikipedia, read the relevant sections and then look up the references.
The standar LRCG model of a transmission line is - in fact - a lowpass circuit. At low frequencies, the model holds well- Once the frequency approaches cut-off, the model gets dramatically different from the transmission line.
On the other hand, one may divide one cell of the circuit into a pair of identical, cascaded subcircuits (L/2, C/2, ...) While the low frequency impedance and propagation constant are left intact, the cutoff frequency is doubled. In this way, one may reach a LRCG model suitable for high frequencies as well.
Remember that standard telegraph equations use differential values, and therefore avoid this problém.
Dear Suhas,
welcome!
What you show above is the the socalled lumped distributed model of a transmission line. The transmission line is completely distributed object and it has been found experimentally and theoretically that the the current and the voltage as well as the electric field and the magnetic field have wave nature along the transmission line. If the transmission line is infinitely long or terminated at its wave impedance called also characteristic impedance Zo the voltage will be in form of travelling wave V= Vm cos (wt - 2 pi x/ lambda), where w is the angular frequency of the applied source and lambda is the wavelength.
So if we apply a sinusoidal voltage at a end of a transmission line and terminate it in Zo the voltage will be in form a travelling wave given above. This assuming the transmission line is lossless and thereby the amplitude of the wave Vm will be constant throughout the whole TL. In case of taking the losses into consideration the amplitude will decay exponentially with x across the transmission line as
V= V(0) (exp -alpha x) cos (wt - 2 pi x/ lambda), with V(0) is the voltage at the source end.
If the transmission line is not matched then there will be an incident wave and a reflected wave.
The wave mode is the transverse electromagnetic wave modeTEM since the electric field and the magnetic field are perpendicular to each other as the magnetic field is caused by the current in the conductors.
The transmission line theory is very useful as basis for the electromagnetic wave propagation.
Best wishes
Try reading 'Transmission Circuits' Appendix B by Everardus Mott Williams and James Beech Woodford. Library of Congress Catalog number 57089. In Appendix B is a complete rigorous solution to Maxwell's equations that may answer your questions about the TEM so called principal mode. This appendix was the work of
the late Dr. Woodford and was unusual because Maxwell's equations were hardly ever solved more than 70 years ago. I helped proof read the book when it was first published! It can be obtained online for a reasonable price and is great for your technical library. It seems that a lot of universities get rid of many really good books because their shelves get full with no thought as to their intrinsic value.
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