Re: lumped circuits and trasmission lines

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Hi Jtwain80,

For transmission lines has no sense speak of voltages and currents but rather it need speak about waves of voltage and waves of currents.
When you solve a circuit like an audio amplifier or an operational amplifier circuit, applying the kirchoff laws and other electrical laws, implicitly you are assuming that the circuit is working under the
condition of lumped circuits. What does this mean? it means that considering the work frequency, the relative wavelength is very large compared with circuit dimensions. So you can assume that the change of electric signal (voltage and current) propagates instantaneously along the circuit.
Actually when the frequency rises and the wavelength become comparable with the circuit dimension, this approximation is no longer valid, now we are in the domain of distributed circuits and transmission lines. A little piece of coax cable (actually infinitesimal) or microstrip behave
like a little capacitor and a little inductor, that we could write as C*dx e L*dx , where x is the longitudinal lenght of cable. Recalling the constitutive equations of capacitor and inductor easily we get probably the most famous equations for e.m.fields engineers after the Maxwell equations,
known as the telegrapher’s equations:

Combining these equations we get two wave equations.
The solution of this equations is the sum of a forward wave and a backward wave.
If a voltage pulse start from source a voltage pulse and then a current pulse travel along the transmission line, they can be partially or completely absorbed by a load, or partially or completely reflected, etc.
If the source start from the middle of a trasmission line, a wave travel long x and a wave long -x.
The constanto Zo = SQRT(L/C) [Ohm] is called the characteristic impedance of the transmission line an is the ratio of voltage to current for the traveling waves.L [H/m]and C[F/m] depend on the physical characteristics
of line.