Cap-Offset Block Filter Is Actually Taking a Derivative & Th

[Bret Cahill]

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.


Bret Cahill

 

[John Larkin]

On Fri, 4 Feb 2011 09:31:28 -0800 (PST), Bret Cahill
<BretCahill@peoplepc.com> wrote:

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

And a piece of wire does that, too.

John

 

[John Larkin]

On Fri, 4 Feb 2011 17:10:37 -0800 (PST), Bret Cahill
<BretCahill@aol.com> wrote:

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

And a piece of wire does that, too.

But the offset block or cap filter is _not_ really a one step process.

It's actually a 2 step process that just looks like one step.

It's continuous, no steps.

The voltage transfer function of a capacitor depends on what it's
loaded with.

in----------C-----+-------out
|
|
|
R
|
|
|
gnd

is the standard AC-coupling thing, a single-pole RC highpass.

Gain is 0 at DC, approaching unity at high frequencies. The corner
radian frequency, where the gain is 0.707, is at w=1/(R*C)

Really, you should take an EE101 course if you're interested in this
stuff. Get it right.

John

 

[Bret Cahill]

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

And a piece of wire does that, too.

But the offset block or cap filter is _not_ really a one step process.

It's actually a 2 step process that just looks like one step.


Bret Cahill

 

[Bret Cahill]

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

And a piece of wire does that, too.

But the offset block or cap filter is _not_ really a one step process.

It's actually a 2 step process that just looks like one step.

It's continuous, no steps.

The voltage transfer function of a capacitor depends on what it's
loaded with.

in----------C-----+-------out
                  |
                  |
                  |
                  R
                  |
                  |
                  |
                 gnd

is the standard AC-coupling thing, a single-pole RC highpass.

Gain is 0 at DC, approaching unity at high frequencies. The corner
radian frequency, where the gain is 0.707, is at w=1/(R*C)

But is the derivative then antiderivative POV is valid?


Bret Cahill

 

[Bret Cahill]

This is a philosophical question.

If a lot of large caps are in series the voltages seem to approach the
derivative as you go down the circuit.

If a lot of small caps are in parallel what do the currents indocate?

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

Bret Cahill

 

[John Larkin]

On Fri, 4 Feb 2011 19:25:07 -0800 (PST), Bret Cahill
<BretCahill@aol.com> wrote:

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

And a piece of wire does that, too.

But the offset block or cap filter is _not_ really a one step process.

It's actually a 2 step process that just looks like one step.

It's continuous, no steps.

The voltage transfer function of a capacitor depends on what it's
loaded with.

in----------C-----+-------out
                  |
                  |
                  |
                  R
                  |
                  |
                  |
                 gnd

is the standard AC-coupling thing, a single-pole RC highpass.

Gain is 0 at DC, approaching unity at high frequencies. The corner
radian frequency, where the gain is 0.707, is at w=1/(R*C)

But is the derivative then antiderivative POV is valid?

Not that I can see. The math doesn't work.

John

 

[Bret Cahill]

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

And a piece of wire does that, too.

But the offset block or cap filter is _not_ really a one step process.

It's actually a 2 step process that just looks like one step.

It's continuous, no steps.

The voltage transfer function of a capacitor depends on what it's
loaded with.

in----------C-----+-------out
|
|
|
R
|
|
|
gnd

is the standard AC-coupling thing, a single-pole RC highpass.

Gain is 0 at DC, approaching unity at high frequencies. The corner
radian frequency, where the gain is 0.707, is at w=1/(R*C)

But is the derivative then antiderivative POV is valid?

Not that I can see. The math doesn't work.

A big inductor can integrate. In series after a small cap you recover
the original signal minus offset.


Bret Cahill

 

[Benj]

On Feb 7, 10:14 pm, Bret Cahill <Bret_E_Cah...@yahoo.com> wrote:

Not that I can see. The math doesn't work.

A big inductor can integrate.  In series after a small cap you recover
the original signal minus offset.

An inductor or capacitor does not "integrate" or "differentiate". Only
mathematicians do that!

Those operations approximate the relationship between voltage and
current in those devices which actually are not inductors or
capacitors in reality. "Real" inductors and capacitors only
approximate ideal ones. And even worse, you
don't understand that even these ideal components do not act as you
suggest. The actual setup requires a resistance
that is used to convert current to voltage. You think you are being
cool, but you really don't have a clue.

 

[Bret Cahill]

Not that I can see. The math doesn't work.

A big inductor can integrate.  In series after a small cap you recover
the original signal minus offset.

.. . .

these ideal components do not act as you
suggest. The actual setup requires a resistance
that is used to convert current to voltage.

Everyone can agree than a small enough cap will put out something
proportional to the derivative of the original signal while a large
enough inductor will put out something proportional to the integral.

The question is, can one circuit made up of just capacitors and
resistors take a derivative in one part of the circuit and then
reintegrate back to the original signal minus offset somewhere else?

The derivative and the anti-derivative back to the original signal
should be voltages. Currents or voltages from currents are not
allowed.

If it is possible to get that far it _might_ be possible to argue that
there are actually two processes going on in the single cap offset
block filter.


Bret Cahill

 

In sci.physics Bret Cahill <BretCahill@peoplepc.com> wrote:

Not that I can see. The math doesn't work.

A big inductor can integrate.  In series after a small cap you recover
the original signal minus offset.

. . .

these ideal components do not act as you
suggest. The actual setup requires a resistance
that is used to convert current to voltage.

Everyone can agree than a small enough cap will put out something
proportional to the derivative of the original signal while a large
enough inductor will put out something proportional to the integral.

Nope, it depends on whether it is a series or parallel circuit.

Do you have a clue what the derivative and integral of a sine wave is?

The question is, can one circuit made up of just capacitors and
resistors take a derivative in one part of the circuit and then
reintegrate back to the original signal minus offset somewhere else?

The derivative and the anti-derivative back to the original signal
should be voltages. Currents or voltages from currents are not
allowed.

If it is possible to get that far it _might_ be possible to argue that
there are actually two processes going on in the single cap offset
block filter.


Bret Cahill

You haven't a clue what you are talking about.

Read and understand:

http://en.wikipedia.org/wiki/RC_circuit

This is EE101 stuff and what happens is fully explained in the link.


--
Jim Pennino

Remove .spam.sux to reply.

 

In sci.physics Bret Cahill <BretCahill@peoplepc.com> wrote:

Not that I can see. The math doesn't work.

A big inductor can integrate.  In series after a small cap you recover
the original signal minus offset.

. . .

these ideal components do not act as you
suggest. The actual setup requires a resistance
that is used to convert current to voltage.

Everyone can agree than a small enough cap will put out something
proportional to the derivative of the original signal while a large
enough inductor will put out something proportional to the integral.

The question is, can one circuit made up of just capacitors and
resistors take a derivative in one part of the circuit and then
reintegrate back to the original signal minus offset somewhere else?

The derivative and the anti-derivative back to the original signal
should be voltages.  Currents or voltages from currents are not
allowed.

If it is possible to get that far it _might_ be possible to argue that
there are actually two processes going on in the single cap offset
block filter.

A lot of large caps in series will eventually approach the
derivative. This may be all that is necessary.


Bret Cahill

Gibbering nonsense; see:

http://en.wikipedia.org/wiki/Capacitor

Scroll down to "For capacitors in series".


--
Jim Pennino

Remove .spam.sux to reply.

 

[Bret Cahill]

Not that I can see. The math doesn't work.

A big inductor can integrate.  In series after a small cap you recover
the original signal minus offset.

. . .

these ideal components do not act as you
suggest. The actual setup requires a resistance
that is used to convert current to voltage.

Everyone can agree than a small enough cap will put out something
proportional to the derivative of the original signal while a large
enough inductor will put out something proportional to the integral.

The question is, can one circuit made up of just capacitors and
resistors take a derivative in one part of the circuit and then
reintegrate back to the original signal minus offset somewhere else?

The derivative and the anti-derivative back to the original signal
should be voltages.  Currents or voltages from currents are not
allowed.

If it is possible to get that far it _might_ be possible to argue that
there are actually two processes going on in the single cap offset
block filter.

A lot of large caps in series will eventually approach the
derivative. This may be all that is necessary.


Bret Cahill

 

[Bret Cahill]

But is the derivative then antiderivative POV is valid?

Not that I can see. The math doesn't work.

Consider the reverse as 2 step process -- small inductor integrates
then takes the derivative.

The offset remains just as would be predicted from the above POV.

This isn't a formal proof but it's almost 100% certain someone has
treated the subject before, much more comprehensively as well as
formally.


Bret Cahill

 

[Bret Cahill]

Not that I can see. The math doesn't work.

A big inductor can integrate.  In series after a small cap you recover
the original signal minus offset.

An inductor or capacitor does not "integrate" or "differentiate". Only
mathematicians do that!

A lot of ideal math concepts come from non ideal physical situations.
Newton wouldn't have bothered with calculus w/o an interest in
mechanics.

It might be better to say that the output of a cap is somewhere
between the original function (minus DC offset) and the derivative or
the output of an inductor is always somewhere between the original
function and its integral.

This is juicier fare than what was in the OP.

In math taking a derivative is generally considered a discrete event.
Like getting pregnant either you take a derivative or integral or you
do not.

With capacitors and inductors you have a continuum.

Has this idea ever been approached in math?


Bret Cahill

 

[Bret Cahill]

Not that I can see. The math doesn't work.

A big inductor can integrate.  In series after a small cap you recover
the original signal minus offset.

An inductor or capacitor does not "integrate" or "differentiate". Only
mathematicians do that!

A lot of ideal math concepts come from non ideal physical situations.
Newton wouldn't have bothered with calculus w/o an interest in
mechanics.

It might be better to say that the output of a cap is somewhere
between the original function (minus DC offset) and the derivative or
the output of an inductor is always somewhere between the original
function and its integral.

This is juicier fare than what was in the OP.

In math taking a derivative is generally considered a discrete event.
Like getting pregnant either you take a derivative or integral or you
do not.

With capacitors and inductors you have a continuum.

Has this idea ever been approached in math?

Not long after they got the idea for whole number derivatives and
integrals:

http://www.mathpages.com/home/kmath616/kmath616.htm

 

[John Larkin]

On Mon, 7 Feb 2011 19:14:53 -0800 (PST), Bret Cahill
<Bret_E_Cahill@yahoo.com> wrote:

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

If the cap is small enough and/or if you wait long enough the output
signal will start to approach something proportional to the derivative
of the unfiltered signal.

Increase the size of the cap and it looks like all you did was
eliminate offset when actually the filtering was really a two step
process.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

And a piece of wire does that, too.

But the offset block or cap filter is _not_ really a one step process.

It's actually a 2 step process that just looks like one step.

It's continuous, no steps.

The voltage transfer function of a capacitor depends on what it's
loaded with.

in----------C-----+-------out
|
|
|
R
|
|
|
gnd

is the standard AC-coupling thing, a single-pole RC highpass.

Gain is 0 at DC, approaching unity at high frequencies. The corner
radian frequency, where the gain is 0.707, is at w=1/(R*C)

But is the derivative then antiderivative POV is valid?

Not that I can see. The math doesn't work.

A big inductor can integrate. In series after a small cap you recover
the original signal minus offset.


Bret Cahill

Nonsense. Not even worth discussing.

John

 

[Jasen Betts]

On 2011-02-04, Bret Cahill <BretCahill@peoplepc.com> wrote:

It's easy to eliminate an offset from a fluctuating signal with an
inline capacitor.

The larger cap takes a derivative just like the smaller cap but unlike
the smaller cap the larger cap reintegrates the signal.

this integrating and differentiating with capacitors only works (and
only approximately) when the output voltage is much lower than the
input voltage.

once you're in the pass band of the filter you're getting a different
sort of effect.

--
⚂⚃ 100% natural