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Old 1st December 2002, 04:28 PM   #1
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Default Opamp low-pass roll-off question

Can someone help me figure out how to use this formula to calculate a low-pass roll-off for an opamp. This was taken from the datasheet for the National LM3875. I just can't figure out where the "s" variable comes from....

Help!

Thanks
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Old 1st December 2002, 05:49 PM   #2
eLarson is offline eLarson  United States
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I think they are using the "s" in the sense of the
Laplace transform. The impedance of the capacitor
can be expressed

1 / (sC)

The formula is the overall impedance of the parallel
combination of the two branches. There was some
fancy factoring to make the resulting expression
look like that of a couple of parallel resistors:
ab / (a + b).

I'm not sure why they left the s in there like that and
then set the whole thing equal to "f", though.

I would take s itself to mean "j*2pi*f" where j is the
square root of -1.

E.
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Old 1st December 2002, 06:41 PM   #3
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You lost me I can add, subtract and, if I make an effort, multiply and divide...

Can you please look at this schematic and tell me which values I should use to set the low-pass roll-off at 100khz -3b (that should allow for a flat response to 20KHZ?)
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Old 1st December 2002, 07:11 PM   #4
halojoy is offline halojoy  Sweden
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Default Refering to first diagram

first take the values at 1 kHz
at that f the resistance of C (also called reactance Cx) is very large, almost infinite,
it blocks currents with low freq almost totally

so gain is like (20k/1k)+1=21 at 1 kHz
the Cx of C gets smaller the higher f
at 100kHz it is 100 times smaller than at 1 kHz

say it is 10 kohm

resistance of Cf+Rf2= 30kohm
Rf1=20kohm
the resulting resistance is for the signal currents
these 2 resistances in parallell, 20k//30k
gain at 100kHz is (resulting resistance/1k)+1

somebody else will have to fill in here
with more exact info
and formulas
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Old 1st December 2002, 08:11 PM   #5
Optical is offline Optical  New Zealand
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If you use a sallen-key circuit, the values are much easier to calculate... just a thought
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Old 1st December 2002, 08:41 PM   #6
eLarson is offline eLarson  United States
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Quote:
Originally posted by ppereira
You lost me I can add, subtract and, if I make an effort, multiply and divide...

Can you please look at this schematic and tell me which values I should use to set the low-pass roll-off at 100khz -3b (that should allow for a flat response to 20KHZ?)
Sorry, it wasn't my intention to lose you, only to
try to explain where they got the "s" from.

Optical brings up a good point: why not try a
different topology with the same part? If you set
up a Bessel-type of response you can get pretty
much linear phase (constant group delay) and you
won't need to shoot for so much bandwidth.

(More bandwidth is not necessarily better.)

Erik
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Old 1st December 2002, 08:50 PM   #7
eLarson is offline eLarson  United States
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(Ooops... ran out of editting time. )

R3 should go to ground, by the way.

If you set the equation they give in the app note
equal to the value of R3, you will get a value of "s"
that satisfies the condition.

It would make it easier if you set one of C or R to a
value before hand. Pick a value of part that you have
laying around or make the two Rs the same.

E.
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Old 1st December 2002, 10:28 PM   #8
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In the datasheet formula quoted there is a zero (s+1/(Rf2.Cf)) and a pole (s+1/[Cf.(Rf1+Rf2)]

These take the form of (S+a) and the 3dB points will occur when f=a/(2.pi)

The pole or low-pass corner frequency will be f = 1/[2.pi.Cf.(Rf1+Rf2)] and the zero at f = 1/(2.pi.Cf.Rf2)
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Old 1st December 2002, 11:35 PM   #9
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Thanks everybody. It seems that if I apply traderbam's formula - f = 1/[2.pi.Cf.(Rf1+Rf2)] - and use a 1.2K resistor for Rf2, leave Rf1 at 30.1K and a 50pf Cap for Cf I should get around 100KHZ.... Did I get this right?
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Old 1st December 2002, 11:52 PM   #10
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Forgot to ask. What does this do to the high frequency pole? It was set to (almost) exactly 4KHZ by Ri and Ci (20KHZ at -.25db) fc = 1/(2p Ri Ci). Does it stay the same after I add Rf2 and Cf? I should have stated my goal when I started this thread: a high frequency pole at 4KHZ and a low frequency pole at 100KHZ....
Thanks again.

Paul
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