LC measurement of transmission line

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i am trying to calculate RLGC of a transmission line given. i have measured rise and fall time with a square wave signal for different frequencies. can anybody tell me the relation of RLGC and time domain parameters?
 

A very short transmission line may act as a lumped reactance--either a series inductance or a shunt capacitance depending on its characteristic impedance. However, if the frequency of interest means the physical length is longer than 1/8th wavelength, the lumped "model" falls apart and is meaningless.

So, for a short line, just try to curve fit a series L or shunt C to the time domain response. For a long line, the length of the line should have not efffect on rise times, so you have to then use true transmission line theory to explain the behavior.
 

It's not clear, if you mean a four element RLGC circuit, or a chain of multiple RLGC circuits. The latter can fairly approximate characteristic impedance and delay of a transmision line, if using a sufficient element count, but not the frequency dependant attenuation.
 

i am considering a short transmission line with no attenuation and a chain of multiple LC ladder circuits. how can we relate LC of line with rise time and fall time at particular freq.?
 

You can simulate at ADS or Spice or AWR. Just design a LC model and simulate, you will get rise time and fall time, and compare it with the measured results. Maybe you need several stages to simulate, the number of stages is determined by the freq. (i.e. wavelength) and the length of your short transmission line.
 

how can we relate LC of line with rise time and fall time at particular freq.
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In my understanding, they are not directly related. The L and C are basically creating the characteristic impedance of the transmission line (Z = √L/C). In addition, they form a cut-off frequency, depending on the "granularity" of the lumped model. But a real transmission line has no cut-off frequency, only a frequency dependant attenuation. It's dominated by the skin effect over a wide frequency range (R ~ √f) and thus can't be modelled by a simple lumped model. To approximate an empirical transmission line with a given lumped circuit, you can use parameter fitting.

A number of profound papers on the topic of transmission line modelling has been published around the APLAC circuit analyzer, e.g.:
The Implementation and Development of a Time-Domain Model of Dispersive Transmission Line lib.tkk.fi/Books/2001/isbn9512263378/papers/1051.pdf
 

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