# [SI-LIST] Re: Impulse vs. Step Response?

• From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
• To: "'David Banas'" <DBanas@xxxxxxxxxx>, "'steve weir'" <weirsi@xxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
• Date: Fri, 2 Sep 2011 12:48:29 -0700

```David,

To have 6 dB/octave roll off, try to measure the voltages from node out to
node 0.
You are measuring voltage at the resistor, that is mostly defined by current
through the capacitor in the transient mode. That is why you have matching
spectral content in both cases.

Best regards,
Yuriy

Yuriy Shlepnev
www.simberian.com

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of David Banas
Sent: Friday, September 02, 2011 10:20 AM
To: 'steve weir'; 'si-list@xxxxxxxxxxxxx'
Subject: [SI-LIST] Re: Impulse vs. Step Response?

Okay, so if we're agreed that, for all intents and purposes, I am driving
this circuit with a unit step, as opposed to a unit impulse, why does the
spectral content of my transient simulation output exactly match the output
of the ac sweep, rather than having an additional 6dB/octave roll-off, as
one would expect?

Thanks,
-db

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of steve weir
Sent: Friday, September 02, 2011 10:04 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Impulse vs. Step Response?

David. I was mistaken. Taht's what I get for not looking closely at the
deck.  However your rise time is only 1/20th of the RC time constant so the
result that you will get from the transient will have little difference than
one with a zero rise time.

Steve.
On 9/2/2011 9:48 AM, David Banas wrote:
> "You are not driving your transient with a step"
>
> Why do you say that?
> -db
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx
> [mailto:si-list-bounce@xxxxxxxxxxxxx] On Behalf Of steve weir
> Sent: Thursday, September 01, 2011 6:40 PM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Impulse vs. Step Response?
>
> As long as the frequency / time domain conversions cover a wide enough
> frequency range the FD response and the FFT of the unit impulse should
> match.  You are not driving your transient with a step so there should
> not be a need to consider
>
>       U(w) = H(w)/jw
>
> Steve.
> On 9/1/2011 5:40 PM, David Banas 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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>
> --
> Steve Weir
> IPBLOX, LLC
> 150 N. Center St. #211
> Reno, NV  89501
> www.ipblox.com
>
> (866) 675-4630 Toll-free
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--
Steve Weir
IPBLOX, LLC
150 N. Center St. #211
Reno, NV  89501
www.ipblox.com

(866) 675-4630 Toll-free
(707) 780-1951 Fax

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```