what is a differentiator?
Jim Muehlberg
>
> what is a differentiator circuit supposed to do? I am reading about them but
> don't know their function. Thanks
Differentiation is a mathematical operation that determines the rate of
change of a function.
A differentiator is an electrical circuit that does the same same thing
with a voltage or current. For instance if you applied a sine wave to
an IDEAL differentiator, it's output would be a cosine wave.
the mathematical notation might look like this : d/dx sin(x) = cos(x).
--
Jim Muehlberg
mueh...@plains.nodak.edu
John Nagle
>what is a differentiator circuit supposed to do? I am reading about them but
>don't know their function. Thanks
You get out a voltage proportional to the rate of change of the
input.
Differentiators are generally a pain, because any noise in the
input signal generates big outputs. Don't design a differentiator into
anything if there's another way. And if you do have to use one, you'll
probably have to put a low-pass filter in front of it.
John Nagle
R. Taylor
Jim Muehlberg wrote in message <363B34...@plains.nodak.edu>...
>Differentiation is a mathematical operation that determines the rate of
>change of a function.
>
>A differentiator is an electrical circuit that does the same same thing
>with a voltage or current. For instance if you applied a sine wave to
>an IDEAL differentiator, it's output would be a cosine wave.
>
>the mathematical notation might look like this : d/dx sin(x) = cos(x).
>
>--
>Jim Muehlberg
>mueh...@plains.nodak.edu
>
um.... thanks, but i'm not really big on math. i'm only in tenth grade and
don't take Algebra II yet till next semester. sorry :)
Franco Maddaleno
R. Taylor wrote:
> what is a differentiator circuit supposed to do? I am reading about them but
> don't know their function. Thanks
It is a circuit that indicates (with an output voltage) how fast changes its
input voltage.
To do this function, it has a different gain for each frequency: the higher the
frequency, the higher the gain: you can consider it as an unusual form of
filter, more than a high pass it is a high emphasizer.
Usually the differentiator is a headache for the designer because it amplifies
very well the high frequency noise, and it must be designed with care, because
it is unstable (if not designed correctly, it oscillates).
Franco
Jim Muehlberg
Okay... It pays to know your audience.
Here's another way to think of it. Suppose you are going down the hiway
at 60 miles per hour. If you accelerate, you are changing your speed,
of course. The "speed of the change in speed" is acceleration. Also
known as the differential of your velocity.
--
Jim Muehlberg
mueh...@plains.nodak.edu
Eric
input to the next stage, and resistor across the input of the next stage
A Integrator is the same but configerd the other way round.
The two circuits are commonly used in TV as a Sync separator
the sync signal after going though the thee differentiator is suable for
the line oscillator
the sync signal after going though the thee Integrator is suitable for the
frame oscillator
I would like to say more, but I think a book from the library on how TV's
work will tell you better
Sorry I have not got all day to make little picture diagrams
R. Taylor wrote in message <71f8tf$1fiu$1...@news.gate.net>...
+what is a differentiator circuit supposed to do? I am reading about them
but
+don't know their function. Thanks
+
+
Mark Grindell
them being used in real circuits unless their low frequency response has
been "clobbered" somewhat. This might be a surprise (surely it would be
easier to differentiate slowly changing signals) but the maths shows that
in fact the statistics of gaussian noise (at least, the noise occuring in
real circuits), whiile being bounded at low frequencies, contains unbounded
derivatives.
Its odd. One of the first things they used to do at University (when I was
a wee lad) was to show how very unexpectedly strange differentiation
actually is. Its ever so easy with symbolic maths, and to a large extent,
people judge it from the basis of being "so much easier" than integration.
In fact, as soon as the high school books are replaced with the University
text books, and the curtains slowly draw back, revealing a much larger
landscape, students are suddenly faced with several different definitions
of both integrals and differentials - for example, there is the Riemann
integral, the Lebesgue integral, and even the Wierstrauss Integral! My
favorite integral is the Lesbesgue integral. This is defined in such a way
that the integral is defined as the limit of a series of lower bounded
functions which mathematically can be shown to converge to the required
integral (but only do so after an infinite number of iterations). This is
great, because you can use this idea to integrate, say, something like
sin(x) / (x) in a definite integral. The normal rules don't let you do
this.
As for differentiation, the situation is even more bizzarre. There is the
problem of discontinuity - and how the hell do you define one of those,
anyway? This leads to the concept of convergence ( which is almost a whole
year), various different forms of notions about compact spaces, banach
spaces, continuous mappings, topology, and so forth.
Of course, with integration, you can fairly easily integrate piecewise
continuous functions (they act like smoothers - in fact, they are very
similar to low pass filters), wheras with differentiators, a square wave at
the input... Well, I leave that to your imagination!
In the end, there are about four major classifications of the differential
that survive, all formulated in multiple dimensional space for generality.
The one that I always remember is the "GAUTEUX" derivative (I'm rather
interested in layer cake) and this, oddly came to my attention through an
article on reverse convolution with seismic signals.
Very obscure, and just curious really. As far as electronics goes, even
more so, but there you go, I love this stuff!
Good luck. Keep on reading, and have fun.
Mark Grindell
Perth, Australia
R. Taylor <rex...@gate.net> wrote in article
<71f8tf$1fiu$1...@news.gate.net>...
> what is a differentiator circuit supposed to do? I am reading about them
but
James Phillips
: Differentiators are actually quite unstable. You don't often hear about
: them being used in real circuits unless their low frequency response has
: been "clobbered" somewhat. This might be a surprise (surely it would be
Did any of this post make any sense to anybody? It sounds *all* wrong
to me.
--
James Phillips Harvard-Smithsonian Center for Astrophysics
Opinions mine, not Harvard's or Smithsonian's.
Roy McCammon
>
> Mark Grindell (ma...@xenotech.com.au) wrote:
> : Differentiators are actually quite unstable. You don't often hear about
> : them being used in real circuits unless their low frequency response has
> : been "clobbered" somewhat. This might be a surprise (surely it would be
>
> Did any of this post make any sense to anybody? It sounds *all* wrong
> to me.
Sounds wrong to me too. I use them often, but usually call them
phase lead compensation. Sometimes you may want to roll off
the high freqs.
Opinions expressed herein are my own and may not represent those of my employer.
Frank Miles
James Phillips <jp...@cfa0.harvard.edu> wrote:
>Mark Grindell (ma...@xenotech.com.au) wrote:
>: Differentiators are actually quite unstable. You don't often hear about
>: them being used in real circuits unless their low frequency response has
>: been "clobbered" somewhat. This might be a surprise (surely it would be
>
> Did any of this post make any sense to anybody? It sounds *all* wrong
> to me.
Sounds backwards. The LF gain is already low; it's the HF end that has
to be "clobbered" in order that the open-loop to closed-loop intercept
occur at a shallow angle (e.g. a single pole's difference, thinking in
Bode-plot terms) -- else marginal or complete instability can occur.
Regrettably, you can't do *everything* with a clever use of integrators.
-frank
Andrew Ingraham
>
> Mark Grindell (ma...@xenotech.com.au) wrote:
> : Differentiators are actually quite unstable. You don't often hear about
> : them being used in real circuits unless their low frequency response has
> : been "clobbered" somewhat. This might be a surprise (surely it would be
>
> Did any of this post make any sense to anybody? It sounds *all* wrong
> to me.
Differentiator circuits do tend to be somewhat unstable and difficult
to make ... but it has nothing to do with the low frequency response.
One problem is (HF) noise. The increasing HF gain tends to amplify
a lot of noise, which can sometimes make the output less than usable.
The other problem is closed loop stability. You tend to have two
open-loop poles at or very near the origin (one in the op-amp or
whatever active device you use, one in the feedback loop), and extra
compensation may be required to keep it from being an oscillator.
Slew rate of op-amps can also get in the way in some cases.
Differentiators do work ... but only up to some upper frequency limit.
Andy
Rich Sulin
I believe Mr. Grindell was the victim of a "neural misfire", and
swapped "low" for "high" in the second sentence...otherwise it's
OK to me!
Rich
------------
James Phillips wrote:
>
> Mark Grindell (ma...@xenotech.com.au) wrote:
> : Differentiators are actually quite unstable. You don't often hear about
> : them being used in real circuits unless their low frequency response has
> : been "clobbered" somewhat. This might be a surprise (surely it would be
>
> Did any of this post make any sense to anybody? It sounds *all* wrong
> to me.
>
> --
> James Phillips Harvard-Smithsonian Center for Astrophysics
> Opinions mine, not Harvard's or Smithsonian's.
--
+-----------------------------------------
| Richard Sulin
|
| Please remove the anti-spam stars in
| my e-mail address in order to reply.
|
| thus: richs <at> dcdu <dot> com
+-----------------------------------------
Mark Grindell
I didn't keep in touch... so obviously there were a lot of replies arriving
I wasn't aware of.
Yes, I got that the wrong way round, didn't I! I'm glad there are people
with a good grasp of this stuff at least somewhere... I don't tend to move
in circles as interesting as this, that's a solid fact - I used to, though.
I was digressing a bit because I was quite fascinated with the rather
strange things that happen to the concepts of differentiation in various
vector spaces, and I had a few minutes to spare waiting for a compilation.
About ten years ago, I was reading a Springer Verlag book on symbolic
integration, (hoping to write a program to do this) and a lot of the
references on this were very hard to get copies of (they came mostly from
research groups inside IBM, mostly in their European headquarters), so this
was too hard for me to track down, and at that point I probably stopped
doing that line of work.
Keep up the keen work and the beady eyes,
Best wishes fellas,
Mark Grindell
James Phillips <jp...@cfa0.harvard.edu> wrote in article
<36646...@cfanews.harvard.edu>...
jhutton
A differentiator circuit typically produces an output which decreases
exponentially over time. From an electrical standpoint is a function
between series elements one of which stores electrical energy and one
which consumes it. The differential output is the instantaneous
difference between energy stored to energy consumed at any specific
moment during a specified time period. The mathematical function which
predicts these instantaneous values within a specified elapsed time is
an exponential one as is typical with power considerations.
The differentiator is especially useful in dealing with the "rates" of
change.
An analog method of performing differential calculus. In fact this was
the differentiator's original purpose in analog computers.
John
--
* Define your terms *
Jim Muehlberg
> A differentiator circuit typically produces an output which decreases
> exponentially over time.
Yikes! be careful here. An ideal differentiator differentiates it's
input. If the input is an exponential, then the output is an
exponential. The derivative of e^x is e^x. You can't say it "typically"
produces an output which decreases over time.
>From an electrical standpoint is a function
> between series elements one of which stores electrical energy and one
> which consumes it. The differential output is the instantaneous
> difference between energy stored to energy consumed at any specific
> moment during a specified time period. The mathematical function which
> predicts these instantaneous values within a specified elapsed time is
> an exponential one as is typical with power considerations.
An ideal differentiator performs the mathematical function y(x)=d/dx
f(x) where y(x) is the output and f(x) is the input to the
differentiator.
>
> The differentiator is especially useful in dealing with the "rates" of
> change.
Yes this is the definition of a differential.
>
> An analog method of performing differential calculus. In fact this was
> the differentiator's original purpose in analog computers.
>
> John
> --
> * Define your terms *
Yes indeed.
I hate to nit pick... no disrespect intended. But my professors would
never let me get away with this expalnation!
--
Jim Muehlberg Don't forget the reason for the season!
mueh...@plains.nodak.edu
*****REMOVE "X" TO REPLY*****
Edward H Currie
Jim Muehlberg wrote:
>
>
> An ideal differentiator performs the mathematical function y(x)=d/dx
> f(x) where y(x) is the output and f(x) is the input to the
> differentiator.
>
> >
> > The differentiator is especially useful in dealing with the "rates" of
> > change.
>
> Yes this is the definition of a differential.
>
Well no that isn't the deifintion of a differential. Derivative implies rate
of change.
>
> >
> > An analog method of performing differential calculus. In fact this was
> > the differentiator's original purpose in analog computers.
> >
This sentence doesn;t wevenm make any sense ...
>
>
> I hate to nit pick... no disrespect intended. But my professors would
> never let me get away with this expalnation!
>
>
>
Exactly the point, you picked some of the wrong nit ..