Computing a transfer function (dispersive tx line)

Hallo,
I'm simulating a transmission line with FD-TD. I have to compute the 
numerical transfer function of the simulated line, which is dispersive, with 
a gaussian pulse stimulus. To do that I compute the fft of gaussian pulse 
before puttin it into line (easy: I exactly know how long it is in time), 
then after some propagation, and then compute H(f)=V(f,out)/V(f,in).
My question is: after propagating a bit, the pulse is wider in time.. how 
can I take into account this when computing fft? is there a sort of 
threshold I can apply?

thanx in advance 

Gianguido wrote:
> Hallo,
> I'm simulating a transmission line with FD-TD. I have to compute the 
> numerical transfer function of the simulated line, which is dispersive, 
> with a gaussian pulse stimulus. To do that I compute the fft of gaussian 
> pulse before puttin it into line (easy: I exactly know how long it is in 
> time), then after some propagation, and then compute H(f)=V(f,out)/V(f,in).
> My question is: after propagating a bit, the pulse is wider in time.. 
> how can I take into account this when computing fft? is there a sort of 
> threshold I can apply?
> 
> thanx in advance

The time dispersal is part of the system behavior, you don't want to 
throw it away.  Why don't you use a sinusoidal input, and look at the 
magnitude and phase of the sinusoidal output?  That will give you H(f) 
directly.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/

> The time dispersal is part of the system behavior, you don't want to throw 
> it away.

yes, that's the point: maybe I'll try a fft of the whole signal vector in 
space at the desired time T. This way I should get the effective H(f)

>  Why don't you use a sinusoidal input, and look at the magnitude and phase 
> of the sinusoidal output?  That will give you H(f) directly.

Such a way is good, but to get a wideband H(f) I should run a lot of 
simulations, one for every frequency of the observation band. That's why I 
wanted to use a wideband pulse such gaussian, to get all information in one 
step

thanx 

Gianguido wrote:

>> The time dispersal is part of the system behavior, you don't want to 
>> throw it away.
> 
> 
> yes, that's the point: maybe I'll try a fft of the whole signal vector 
> in space at the desired time T. This way I should get the effective H(f)

Not if the line is dissipative -- in a non dissipative line you could do 
that, though.
> 
>>  Why don't you use a sinusoidal input, and look at the magnitude and 
>> phase of the sinusoidal output?  That will give you H(f) directly.
> 
> 
> Such a way is good, but to get a wideband H(f) I should run a lot of 
> simulations, one for every frequency of the observation band. That's why 
> I wanted to use a wideband pulse such gaussian, to get all information 
> in one step
> 
If you're determined to do it using an FFT then all I can suggest is 
that you make your simulation long enough to capture a good long bit of 
the tail as the thing settles out, and window the data with something 
that prevents the very end from getting chopped off -- I'd use a 
constant that transitions to a raised cosine at the very end of the time 
sample.

No matter what you do you're going to find inaccuracies at the 
high-frequency end where there's not much signal content from the cable 
and lots of windowing effects from the finite measurement interval.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/

> Not if the line is dissipative -- in a non dissipative line you could do 
> that, though.

sure, I didn't say.. non dissipative is my case.

> If you're determined to do it using an FFT then all I can suggest is 
> that you make your simulation long enough [...]

thanx for your tips, Tim! now implementation time ;)

bye

Gianguido wrote:

>> Not if the line is dissipative -- in a non dissipative line you could 
>> do that, though.
> 
> 
> sure, I didn't say.. non dissipative is my case.

I was seeing "dispersive" and making it into "dissipative".  I think 
that looking at the volts/position relationship is still not valid in a 
dispersive line, however.
> 
>> If you're determined to do it using an FFT then all I can suggest is 
>> that you make your simulation long enough [...]
> 
> 
> thanx for your tips, Tim! now implementation time ;)
> 
> bye

Let us know how it works out.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/