[SI-LIST] Re: TEM Approximation
- From: norhan@xxxxxxxxxxxx
- To: si-list@xxxxxxxxxxxxx
- Date: Wed, 24 Sep 2003 22:26:30 -0700
Hello Steve,
I should have known that my post will generate questions :-).
The shape of the distorted Gaussian impulse that you saw is very
typical for microwave substrates. It is all over microwave and
guided wave literature. There are several reasons for the
large dispersion and you correctly pointed out one of them:
1. Large dielectric constant of the microstrip substrate (Alumina).
2. Relatively large dimensions (h=0.635 mm, w=0.5 mm, l=123 mm).
3. Shape and width of the exciting impulse (Gauss, sigma=19 ps).
These three reasons give the Gaussian impulse the characteristic
negative tail with some ripples. In addition to these reasons,
the impulse is also influenced by
4. Point source excitation (multi mode excitation).
5. Material losses.
6. Other reasons that I better not mention.
The last three visibly influence the impulse, but the changes
that they make are not really important here.
The main reason why you do not see the characteristic dispersion
tails in your typical PCB TDR measurements is that you do not
have 1-3: your dielectric constant is significantly lower, your
cross sectional dimensions are smaller and your signal waveform
has different characteristics. The last reason really includes
two effects and it requires more elaboration.
While the signal in this example is not particularly fast, it is
slightly faster than the signal out of your TDR and it is an
impulse (not a step). Therefore we have to take the derivative
of your step waveforms to make a comparison. First, the shape of
the resulting impulses (derivatives) is important. Different
impulse shapes are affected by dispersion differently. The TDR
outputs one impulse and the example uses another (Gaussian).
Second, the response to a Gaussian signal is an impulse with
high frequency ripples after it. Similarly the response to the
TDR's input impulse (derivative of the step) is a step with
accentuated high frequency components (j*w*step_response(w)).
But these high frequency components are attenuated by the TDR
because of the limited bandwidth of the TDR system.
The end result is that the useful resolution of the TDR is
reduced when you look at derivatives so impulses do not have
high frequency tails even when they should.
The world looks smoother through a TDR than it really is
(this is not a bad thing :-)).
I think that the losses in the measurements are a secondary
effect in this type of example.
Best regards,
Neven
---
Neven Orhanovic
Applied Simulation Technology
neven@xxxxxxxxxxxxx
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