Re: Why should I (not) use an internal oscillator for 8-bit micros

From: David Brown (david_at_no.westcontrol.spam.com)
Date: 08/19/04 

Date: Thu, 19 Aug 2004 10:27:49 +0200

"Paul Carpenter" <paul$@pcserv.demon.co.uk> wrote in message
news:20040818.2000.302242snz@pcserv.demon.co.uk...
> On Wednesday, in article <cfv4uf$p6p$1@news.netpower.no>
> david@no.westcontrol.spam.com "David Brown" wrote:
> >"Paul Carpenter" <paul$@pcserv.demon.co.uk> wrote in message
> >news:20040817.1842.302217snz@pcserv.demon.co.uk...
> >> No it is a concept block about forgetting the effects of dividing down
a
> >> faster clock to get a more accurate slower clock.
> >>
> >> Consider the problem of cheap digital clocks/watches that use a
32.768KHz
> >> oscillator, using cheap as possible components but still only drift a
few
> >> seconds a month or even year. This is because the second timing is
> >produced
> >> by dividing down the 32.768KHz by 32768 (15bits) to produce the 1
second
> >> pulse, so the error rate is the oscillator drift * 1/32768 !!
> >>
> >I don't know whether to laugh or cry at this post. If a 32.768 KHz
crystal
> >is 1% out, then when the signal is divided by 32768 to get a second
pulse,
> >the second pulse will be 1% out. It's that simple! It doesn't matter a
>
> When the divisor used is an EXACT match with the prefered divisor then
yes.
> When the divisor used is integer rounded it is not an exact match with
> prefered divisor, and does have an effect on what is going to happen.
>

That's certainly true. I must admit I've been assuming that exactly
matching divisors have been used throughout this thread. Being a power of
2, 32768 is convenient to use as a divisor, but it is hardly a requirement -
baud rate divisors are seldom a power of two. But the value still doesn't
matter (unless you think of a crystal specified in Hz as having an inherrent
+/- 0.5 Hz tolerance).

> If expected divisor is 32890 and only 32768 can be achieved the ratio is
> different due to the combination of the effects, what was missed off
> of the above was "* expected divisor" (due to late night)..
>
> i.e. expected divisor 1
> * ---------------- or * -------------- * expected divisor
> actual divisor actual divisor
>
> For EXACT matching ratios (e.g. powers of two) this would reduce to '1'
>

If your hardware can't divide by something other than a power of two, then I
would agree. However, while digital clock manufactorers are looking to save
the smallest fraction of a cent, I don't think a divide by 32890 circuit
would add greatly to the manufacturing costs, so it's not something I
considered relevant. The emphasis of your post seemed to me that the
relevance of 32.678 KHz was that it needed a relatively small divisor to get
a one-second pulse, and that was what I reacted to. Certainly other posters
in this thread have thought the size of the divisor to be relevant - if you
don't, then I appologise for assuming you made the same mistake.

> >**** if the crystal is at 32.768 KHz or 9.192631770 GHz (the oscillation
> >frequency of the most common type of atomic clock) - the percentage error
of
> >the source frequency translates directly to the percentage error in the
> >divided frequency.
>
> Both of those examples are exact powers of two, chosen for that precise
> reason.
>

9.192631770 GHz is not a power of two, and was not "chosen" - it comes from
a particular electron transition in cesium ions. Actually, the ISO
definition of a second is 9192631770 such transition times.

> >The main reason 32.678 kHz crystals are used in watches is because 32.768
> >kHz crystals are used in watches - i.e., the economics of volume make it
> >cheaper to make that particular frequency with high accuracies. A low
> >frequency was picked because a low frequency means low power.
>
> Also the NOMINAL value of the crystal is an exact power of two.
> No rounding of divisors putting errors in the way, and simpler logic
> required, less logic also means less power.

There is no "rounding" of divisors if the nominal value of the crystal were
an exact multiple of a Hz. In fact, there is rounding of divisors in
digital watches with 32kHz crystals, since they routinely show hundreths of
a second. The hundreths are not exact, but the rounding is catered for when
seconds are counted. In the early days of digital watches, when there were
more discrete components, picking a power of two for the divisor was a good
idea, since the circuitry for a divide-by-power-of-two scaler is easier than
a divide-by-arbitrary-integer scaler, but for modern designs, the difference
is negligble.

>
> >But if logic and physics fail those of you who don't understand timing
> >errors, fall back on experience - the most accurate (in terms of how
> >accuractly it measures time, not how accuractly you happen to have set
it)
> >clock in your room is probably your digital watch, running off a crystal
in
> >the kHz range.
>
> Nominal frequency is exact power of two.
>
> > The least accurate will be your PC's clock, running off a
> >crystal in the MHz range.
>
> Using a cheap 4 * NTSC subcarrier 14.3818MHz crystal[1], made in huge
volumes
> with economies of scale to make them cheaply and with high accuracy.
> This frequency is then divided by 12 then divided by 65536, to give an
> approx 18.2Hz interupt rate (actually 18.287..Hz), to achieve 18Hz
interupt
> would require a divisor of 66582.407, more than 16bits of the 8254. This
> feeds interupt and timer software that has loads of kludges in to add part
> seconds every n or x or y seconds, to get nearly right. It was never
designed
> to be a time piece, we all know how deterministic PC software is. The
errors
> come from many parts, so not a valid comparison. Why they did not try to
> achieve 20Hz interupt rates instead still amazes me, as this would have a
> much more accurate timebase clock relative to counters of seconds.
>
> >But the most accurate you have access to will be
> >if you have a GPS receiver, since they get their time from satellites
with
> >atomic clocks running in the GHz range. Perhaps that will make you
realise
> >that the source rate and the divisor do not matter !
>
> GPS is chosen to be an accurate time piece, otherwise GPS will not work.
> This has to be designed to be an extremely accurate time piece first using
> an exact power of two for the purpose of not introducing rounding errors.
>

You are correct the GPS was designed for and requires a very high accuracy
clock. The power of two argument is completly wrong, however. Having an
*integer* divisor is very relevant - part of the (many) inaccuracies in PC
clocks comes from kludges to get non-integer divisors.

> [1] The frequency was chosen for using the clock to drive the output from
a
> CGA card to a TV using NTSC output. Using it as the clock for the
timing
> circuit of the system clock was more an afterthought of reducing
numbers
> of oscillators.
>
> --
> Paul Carpenter | paul@pcserv.demon.co.uk
> <http://www.pcserv.demon.co.uk/> Main Site
> <http://www.gnuh8.org.uk/> GNU H8 & mailing list info.
> <http://www.badweb.org.uk/> For those web sites you hate.
>

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