Message-ID: <003d01c3bf18$9d03d420$88e486d4@bryan2>
From: "captbrian" <captbrian@ukonline.co.uk>
To: rsgb_lf_group@blacksheep.org
References: <01C3BEFA.E3D319B0.g4jnt@thersgb.net>
Date: Wed, 10 Dec 2003 12:24:16 -0000
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Subject: LF: Re: Related Technical Query - Soundcard calibrator
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What a delight it is to be on this list.  LF could well stand for Literate
and Febrile

I am digital-techniques ill informed and not sure if you are using ^  to
mean "to the power of "

but is your question : "what is the integral of sin(y)/y  where y=x squared
?"  ?

between what values of x?

Bryan - g3gvb


----- Original Message -----
From: "Andy talbot" <g4jnt@thersgb.net>
To: "Rsgb_Lf_Group (E-mail)" <rsgb_lf_group@blacksheep.org>
Sent: 10 December 2003 08:51
Subject: LF: Related Technical Query - Soundcard calibrator


> Is there anyone who can answer this...
>
> I want to make a calibrator to enable accurate (better than 0.5%) absolute
> audio measurements using a soundcard - ie. at audio frequencies to 20kHz.
>   Generating a square wave from CMOS logic with a precisely 5V p-p (2.5v
peak)
> waveform is trivial and can be measured accurately to doubl;e check.  The
> levels of the odd harmonic tones are all precisely defined by :
>
> RMS Amplitude = 2.5V * 4 / PI / SQRT(2) / N
>
> Where N is the (odd) harmonic number, so the fundamental has an amplitude
of
> 2.251 Vrms which can be potted down with an accurate potential divider -
> straightforward, all harmonics can be used at known levels...
>
> Now, here is the complicated bit, I also want to include a calibrated
noise
> source for accurate S/N measurements and evaluation of various decoding
> techniques.  To remove the need for accurate true RMS measurement to set
up
> this unit, I am going to use Pseudo Random Sequence generated from a shift
> register clocked very much faster than the frequencies of interest.  It is
> straightforward to make a 2^32-1 bit long sequence clocked at, say, 5MHz
which
> will have a repeat cycle of  14 minutes, suitable for most purposes - even
Argo
> calibration !   By filtering to a bandwidth significantly less than the
clock
> rate (20kHz max vs. 5MHz) the result will be sufficiently Gaussian to act
as if
> it were true noise.  In practice,  any real hardware filtering won't be
> necessary as the soundcard itself will do the job; but there will be some
basic
> filtering to keep out the nasty birdies likely to be generated.
>
> Now, here is the bit I'm less sure how to work out. How do I calculate the
> noise density of the PN sequence in the area of interest?   Assumimg the
PRN
> Sequence has 1:1 mark/space ratio (with 2^32 bits it will be certainly
near
> enough) and assuming a perfect square edged waveform up to several 5MHz
clocks
> away (guaranteed by using HC series logic) the TOTAL power over the
(almost)
> infinite spectrum from DC to several clock multiples is defined exactly by
the
> RMS value of the waveform; and for a squarewave this is equal to the peak
value
> - here 2.5V.
>
> This TOTAL power is spread out in a SIN(x^2)/x^2 pattern.   Since it will
be
> filtered to, essentially, just a small part of the first spectral lobe,
the
> calculation really comes down to calculating the height of this lobe which
will
> can be assumed to be sufficiently flat over the small bandwidth of
interest.
>  Once that is done, the noise power, and hence the RMS value can be
defined in
>  Volts / SQRT(Hz) which can be added to the signal / test tone of interest
in
> variouis proportions, with the S/N then known exactly.
>
> I'm quite incapable of integrating SIN(x^2)/x^2 from first principles (or
any
> other way for that matter :-) to calculate the level of the main lobe.
Can
> anyone point out the best way to do this calculation ?    Instinct says
that
> for a small bandwidth segment, BW,  close to zero frequency, the power
will be
> proportional to  BW / Fclock,  but I haven't a clue what scaling factors
will
> be included in this, and they are what matter for an absolute level
calibrator.
>
> Andy  G4JNT
>
>
>
>
>
>