Right, think I have an answer now, thanks to Stewart and Stewart...
If the total integral = pi watts (Ok, volts squared over an arbitrary
impedance, but call them watts for now :-) this is what my 2.5V peak (5V
p-p) squarewave is generating :
In a 1 Hz bandwidth if the power is said to spread out up to Fclock / 2
Then Power for 1 V peak in 1 ohm = 1Hz / 2.5E6Hz * PI
So in more general terms, normalised power density = 2 * PI / Fclock.
Which also agrees with a figure someone at work gave me, based on the
auto-correlation function (I think) of a random data stream, although, to
quote "he wasn't prepared to justify the answer, particularly the derivation
of equation for the ACF"
So for my 2.5V peak waveform, in 20kHz bandwidth (which is roughly what the
soundcard anti-alias filters to) Vrms^2 = 2.5^2 * 20e3/5e6*2*PI = .15708
volts squared which should result in a real RMS value of very close to
396mV - which is more than enough to just be able to pot down to reasonable
levels.
Andy G4JNT
----- Original Message -----
From: Stewart Bryant <[email protected]>
To: <[email protected]>
Sent: Wednesday, December 10, 2003 7:03 PM
Subject: Re: LF: Related Technical Query - Soundcard calibrator
And just to check it out I did a quick numerical integration
using excel and that gives 3.137 which considering the
errors in the model is probably pi.
Stewart
Stewart Bryant wrote:
> Don't you need the integral of sin^2(x)/x^2
> which according to
>
> http://www.sosmath.com/tables/integral/integ37/integ37.html
>
> is pi/2 from 0 to infinity
>
> so by symetry for -infinity to plus infinity is pi
>
> 73
>
> Stewart G3YSX
>
> Andy talbot wrote:
>
>> Yes, the power spectrum of a SIN(X) / X pattern.
>>
>> To Brian 'GVB, the limits will be (theoretically at least) - infinity
>> to infinity, but in practice a few lobes will be sufficient, say about
>> +/- 5
>>
>> Andy
>>
>> -----Original Message-----
>> From: Alexander S. Yurkov [SMTP:[email protected]]
>> Sent: 2003/12/10 20:51
>> To: Rsgb_Lf_Group (E-mail)
>> Subject: Re: LF: Related Technical Query - Soundcard calibrator
>>
>> On Wed, 10 Dec 2003, Andy talbot wrote:
>>
>>
>>> This TOTAL power is spread out in a SIN(x^2)/x^2 pattern.
>>
>>
>>
>> This seems to be strange... May be You mean SIN^2(x)/x^2 ?
>>
>>
>> 73 de RA9MB/Alex
>> http://www.qsl.net/ra9mb
>>
>>
>>
>>
>
>
>
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