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'How to calculate RC freq?'
1997\02\13@150756 by Gavin Jackson

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I would like to know what formulae is used to
calculate the frequency of an RC oscillator.

I have tried a few formulae that I have come
across in my books on electronics but none of
them come close to the values calculated by
Microchip.

I would really appreciate any help.

Thanks in advance

Gavin
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1997\02\13@212854 by Steve Hardy

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> From: Gavin Jackson <.....vulcanKILLspamspam@spam@MAIL.DIAL-UP.NET>
>
> I would like to know what formulae is used to
> calculate the frequency of an RC oscillator.
>
> I have tried a few formulae that I have come
> across in my books on electronics but none of
> them come close to the values calculated by
> Microchip.

There's no one formula since it depends on the external circuit.  If a
cap is discharging through a res (and nothing else is topping the cap
up or sucking it dry) then the voltage across the cap decays at an
exponential rate.  In fact, the voltage decays to 1/e, about 37%, of
its starting value (whatever that may be) in the time interval of RC
(seconds = ohms times farads).  In an active circuit where the
capacitor is periodically recharged, then the formula for frequency of
oscillation will almost always involve the RC product in the
denominator e.g. 2.2/RC.  However as I said before, the factor (e.g.
2.2) can vary widely depending on the driver circuitry.

Trust Microchip, the formula they give will be correct within its
stated accuracy limitations.

Regards,
SJH
Canberra, Australia

1997\02\13@223911 by John Payson

picon face
> > I would like to know what formulae is used to
> > calculate the frequency of an RC oscillator.
> >
> > I have tried a few formulae that I have come
> > across in my books on electronics but none of
> > them come close to the values calculated by
> > Microchip.
>
>                                 In an active circuit where the
> capacitor is periodically recharged, then the formula for frequency of
> oscillation will almost always involve the RC product in the
> denominator e.g. 2.2/RC.  However as I said before, the factor (e.g.
> 2.2) can vary widely depending on the driver circuitry.
>
> Trust Microchip, the formula they give will be correct within its
> stated accuracy limitations.

The reason Microchip's PIC16Cxx devices don't match what you'd expect from the
RC mode is that when the device is discharging the capacitor it does not do so
through a zero-resistance junction but instead through a finite current sink.
As a result, the resistor you use in the RC oscillator affects not only the
time it takes to charge the capacitor but also the time it takes to discharge.
If the resistor is relatively large (e.g. 47K) then very few electrons will
flow through it while the PIC is trying to discharge the capacitor.  In this
case, reducing the resistor by half will approximately double the frequency.
As the resistor gets below 10K, however, its effects on the discharge rate
become significant and as it falls below about 4.7K they can start to dominate.
For this reason, reducing the resistance below about 4.7K may cause the oscil-
lator to slow down, and reducing it below about 2.7K may stop it all together
(since it can't take electrons out of the cap as fast as the resistor wants to
let them in).

The behavior of the device with different capacitors is fortunately somewhat
more predictable than its behavior with different resistors.  With a pretty
good degree of accuracy, doubling the "net" capacitance will halve the freq-
uency.  So long as you take into account about 2-10pf of lead capacitance,
this formula will hold pretty well.  For example, assume the lead capacitance
is 3pf.  If you attach a 22pf cap to the net, its "net" capacitance would
be about 25pf.  If you use a 47pf cap its net capacitance will be about 50pf,
a twofold increase.

Generally, the larger the R and the larger the C, the more closely the PIC's
speed will mirror the product RC.  Unfortunately, making R and C large will
result in a device that runs rather slowly, but if you are more interested in
accuracy than speed that might not be a problem.

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