[SI-LIST] Re: Impulse vs. Step Response?
- From: Ihsan Erdin <erdinih@xxxxxxxxx>
- To: David Banas <DBanas@xxxxxxxxxx>
- Date: Fri, 2 Sep 2011 10:38:48 -0400
David,
Your circuit is simple enough to have a closed form solution. With a step
input, the time domain voltage on the capacitor will exponentially rise to
the value of the input according to (1-exp(-t/tau)) relation with
tau=Rin//RL*CL. For an impulse input, however, the time domain response of
the cap will exponentially decay to zero following exp(-t/tau) relation.
Thus, the two time domain responses contrast starkly and looking at the
output of the .tran command you can tell what type of input hspice is
assuming in the time domain analysis. In this case it seems like the input
voltage is an impulse despite the dc definition in Vin. That could all be a
matter of convention and interpretation.
Regards.
Ihsan
On Thu, Sep 1, 2011 at 8:40 PM, David Banas <DBanas@xxxxxxxxxx> wrote:
> Hi all,
>
> I've got a puzzler. I'm using this HSpice deck:
>
> .TITLE AC Sweep vs. Transient Correlation
>
> .OPTION
> + POST
> + PROBE
> + RUNLVL = 5
>
> Rin in out r=1K
> Cout out 0 c=1pF
> Rout out 0 10MEG
>
> Vin in 0 DC 1 AC 1
>
> .IC V(out) = 0
>
> .AC DEC 10 1 1G
> .TRAN 0.05n 1u 0 0.05n UIC
>
> .PROBE AC V(in) V(out)
> .PROBE TRAN V(in) V(out)
>
> .END
>
> to get both the transfer function, H(w), (.AC command) and the unit step
> response, u(t), (.TRAN command) of a simple RC LPF.
>
> Then, I take the FFT of the .TRAN output and compare it to the .AC output.
> And they match!
>
> I wasn't expecting a match, since all my textbooks say there's a `jw'
> factor relating the impulse response and the step response. That is:
>
> U(w) = H(w)/jw
>
> So, when I compared the 2 spectra, I was expecting the FFT of my .TRAN
> output to have an extra 6dB/octave roll-off, as compared to the .AC output,
> due to the `w' in the denominator, above.
>
> Can anyone shed some light on this?
>
> Thanks,
>
> David Banas
> Sr. Member Technical Staff
> Altera
> +1-408-544-7667 - desk
>
> Did you know Altera offers over 150 free online technical training courses?
> Take one today!
>
>
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--
Ihsan Erdin
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