High-Q switched-capacitor BandPass Filter?

[mikem]

Is there such a thing as a High-Q switched-capacitor BandPass Filter
whose center frequency can be "tuned" +- 20% synchronously with its
switching clock?

I need something that would take in a ~45Hz periodic signal with lots of
higher odd-order harmonics, and spit out only the fundamental minus the
harmonics, with no or predictable phase shift. The Q needs to be high
enough to attenuate the second and subsequent harmonics by more than 40db.

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.

Extra points if the filter could select the secon or third harmonics
on command, relative to the same switching clock.

The clock could be something like 32X to 256X the fundamental.

Is a power of two for the clock preferable? (vs e.g. 50X)

MikeM

 

[Jamie]

hmm,.
well i am not 100% sure what your doing how ever.
i can tell you that i once made an inductive tuned filter
using a secondary field to be shunted which effects the
primary field over all effect on the reasonant point with out
coming into direct contact with the primary signal.
another way is if you want to deal with caps only you can
use a diode switch current path to tailer the cap via some
DC current.
that would be 2 diodes back to back with current flowing in both
directions.
or to really do it rite, take a PIC or Atmel 8051 type mirco with
lots of memory and a ADC converter using a FFT (fast fourier
Transform)! you will have a DSP filter.


mikem wrote:

Is there such a thing as a High-Q switched-capacitor BandPass Filter
whose center frequency can be "tuned" +- 20% synchronously with its
switching clock?

I need something that would take in a ~45Hz periodic signal with lots of
higher odd-order harmonics, and spit out only the fundamental minus the
harmonics, with no or predictable phase shift. The Q needs to be high
enough to attenuate the second and subsequent harmonics by more than 40db.

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.

Extra points if the filter could select the secon or third harmonics
on command, relative to the same switching clock.

The clock could be something like 32X to 256X the fundamental.

Is a power of two for the clock preferable? (vs e.g. 50X)

MikeM

 

[Walter Harley]

"mikem" <mikem@bogus.adr> wrote in message
news:c7dmcu$qv9$1@coward.ks.cc.utah.edu...

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.

Are you suggesting that bandpass filters don't introduce phase shift, or are
you suggesting that switched-capacitor filter don't introduce phase shift?
I'm no expert, but I don't think either suggestion is correct.

 

[MikeM]

Walter Harley wrote:

"mikem" <mikem@bogus.adr> wrote in message
news:c7dmcu$qv9$1@coward.ks.cc.utah.edu...

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.


Are you suggesting that bandpass filters don't introduce phase shift, or are
you suggesting that switched-capacitor filter don't introduce phase shift?
I'm no expert, but I don't think either suggestion is correct.

Say that I'm clocking a 100X 45Hz switched capacitor bandpass filter at 4500Hz.
Is not the frequency at which the magnitude is max and the phase shift is zero
45Hz? (I plan to make the filter clock an exact integer multiple of the freq
that I'm trying to filter....

MikeM

 

[John Larkin]

On Thu, 06 May 2004 09:42:21 -0600, mikem <mikem@bogus.adr> wrote:

Is there such a thing as a High-Q switched-capacitor BandPass Filter
whose center frequency can be "tuned" +- 20% synchronously with its
switching clock?

Yes. This is easily done with an MF10/LMF100-type general-purpose
filter chip and a few resistors... see the National app notes. The
LMF100 is a more modern poly-gate version of the MF10, I think.

I need something that would take in a ~45Hz periodic signal with lots of
higher odd-order harmonics, and spit out only the fundamental minus the
harmonics, with no or predictable phase shift. The Q needs to be high
enough to attenuate the second and subsequent harmonics by more than 40db.

Sounds feasible. Make sure you have a simple RC or Sallen-Key lowpass
ahead of the filter to prevent aliasing, and another after to filter
out clock glitches.

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.

Extra points if the filter could select the secon or third harmonics
on command, relative to the same switching clock.

Just rubber-band the clock.

The clock could be something like 32X to 256X the fundamental.

Is a power of two for the clock preferable? (vs e.g. 50X)

Not really. Doesn't matter much, but higher is better as regards
aliasing. I think the MF10 bandpass design allows arbitrary clock-cf
ratios.

Note that SCFs are a bit noisy, and are *very* sensitive to noise on
the power rails. They will cheerfully alias high-frequency noise back
into the passband.

John

MikeM

 

[MikeM]

John Larkin wrote:

On Thu, 06 May 2004 09:42:21 -0600, mikem <mikem@bogus.adr> wrote:

Extra points if the filter could select the secon or third harmonics
on command, relative to the same switching clock.

Just rubber-band the clock.

You got me on that one???

MikeM

 

[SioL]

"MikeM" <trashcan@yahoo.com> wrote in message news:c7e3hc$637$1@coward.ks.cc.utah.edu...

John Larkin wrote:

On Thu, 06 May 2004 09:42:21 -0600, mikem <mikem@bogus.adr> wrote:

Extra points if the filter could select the secon or third harmonics
on command, relative to the same switching clock.

Just rubber-band the clock.

You got me on that one???

MikeM

Duct tape?

SioL

 

[Walter Harley]

"MikeM" <trashcan@yahoo.com> wrote in message
news:c7e1lu$52b$1@coward.ks.cc.utah.edu...

Walter Harley wrote:
"mikem" <mikem@bogus.adr> wrote in message
news:c7dmcu$qv9$1@coward.ks.cc.utah.edu...

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.


Are you suggesting that bandpass filters don't introduce phase shift, or
are
you suggesting that switched-capacitor filter don't introduce phase
shift?
I'm no expert, but I don't think either suggestion is correct.


Say that I'm clocking a 100X 45Hz switched capacitor bandpass filter at
4500Hz.
Is not the frequency at which the magnitude is max and the phase shift is
zero
45Hz? (I plan to make the filter clock an exact integer multiple of the
freq
that I'm trying to filter....

Here's my understanding; as I said, I'm no filter expert, so perhaps someone
who knows what they're talking about will correct me.

A switched-capacitor filter is just a filter design that uses switched
capacitors to implement the integrators that are part of an active filter
design such as biquad or state-variable or whatever. There are two reasons
to do that: one is that the integrator gain (and thus the filter frequency)
is controlled by the switching frequency; the other is that it's easier to
make precision capacitor ratios on silicon than it is to make precision
capacitors and resistors. And for low frequencies, you don't need
high-value components, you just lower the switching frequency.

But either way, you've still got the same biquad or state-variable or
whatever filter, it's just that it happens to be implemented using switched
capacitors. You still have to decide on a filter characteristic: Bessel,
Chebyshev, whatever. That characteristic, combined with the number of
poles, determines the phase shift. And so far as I know, all filters have
nonzero phase shift; they have to, because it takes finite time to determine
frequency.

 

[Tim Wescott]

Walter Harley wrote:

"MikeM" <trashcan@yahoo.com> wrote in message
news:c7e1lu$52b$1@coward.ks.cc.utah.edu...

Walter Harley wrote:

"mikem" <mikem@bogus.adr> wrote in message
news:c7dmcu$qv9$1@coward.ks.cc.utah.edu...


I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.


Are you suggesting that bandpass filters don't introduce phase shift, or

are

you suggesting that switched-capacitor filter don't introduce phase

shift?

I'm no expert, but I don't think either suggestion is correct.


Say that I'm clocking a 100X 45Hz switched capacitor bandpass filter at

4500Hz.

Is not the frequency at which the magnitude is max and the phase shift is

zero

45Hz? (I plan to make the filter clock an exact integer multiple of the

freq

that I'm trying to filter....


Here's my understanding; as I said, I'm no filter expert, so perhaps someone
who knows what they're talking about will correct me.

A switched-capacitor filter is just a filter design that uses switched
capacitors to implement the integrators that are part of an active filter
design such as biquad or state-variable or whatever. There are two reasons
to do that: one is that the integrator gain (and thus the filter frequency)
is controlled by the switching frequency; the other is that it's easier to
make precision capacitor ratios on silicon than it is to make precision
capacitors and resistors. And for low frequencies, you don't need
high-value components, you just lower the switching frequency.

But either way, you've still got the same biquad or state-variable or
whatever filter, it's just that it happens to be implemented using switched
capacitors. You still have to decide on a filter characteristic: Bessel,
Chebyshev, whatever. That characteristic, combined with the number of
poles, determines the phase shift. And so far as I know, all filters have
nonzero phase shift; they have to, because it takes finite time to determine
frequency.

If you're picking out a carrier a bandpass filter will have zero phase
error at the carrier, because the filter is "anticipating" the carrier
as much as it is "sensing" it.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

 

[John Popelish]

Walter Harley wrote:

"MikeM" <trashcan@yahoo.com> wrote in message
news:c7e1lu$52b$1@coward.ks.cc.utah.edu...
Walter Harley wrote:
"mikem" <mikem@bogus.adr> wrote in message
news:c7dmcu$qv9$1@coward.ks.cc.utah.edu...

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.


Are you suggesting that bandpass filters don't introduce phase shift, or
are
you suggesting that switched-capacitor filter don't introduce phase
shift?
I'm no expert, but I don't think either suggestion is correct.


Say that I'm clocking a 100X 45Hz switched capacitor bandpass filter at
4500Hz.
Is not the frequency at which the magnitude is max and the phase shift is
zero
45Hz? (I plan to make the filter clock an exact integer multiple of the
freq
that I'm trying to filter....

Here's my understanding; as I said, I'm no filter expert, so perhaps someone
who knows what they're talking about will correct me.

A switched-capacitor filter is just a filter design that uses switched
capacitors to implement the integrators that are part of an active filter
design such as biquad or state-variable or whatever. There are two reasons
to do that: one is that the integrator gain (and thus the filter frequency)
is controlled by the switching frequency; the other is that it's easier to
make precision capacitor ratios on silicon than it is to make precision
capacitors and resistors. And for low frequencies, you don't need
high-value components, you just lower the switching frequency.

But either way, you've still got the same biquad or state-variable or
whatever filter, it's just that it happens to be implemented using switched
capacitors. You still have to decide on a filter characteristic: Bessel,
Chebyshev, whatever. That characteristic, combined with the number of
poles, determines the phase shift. And so far as I know, all filters have
nonzero phase shift; they have to, because it takes finite time to determine
frequency.

I believe you are confusing group delay with steady state phase
shift. I think the OP is generally correct that most band pass
filters have nearly zero phase shift (or an inversion) at center band,
and I think this also applies to switched capacitor implementations.

--
John Popelish

 

[Tom Bruhns]

(I was first thinking of a particular type of switched-capacitor
filter which almost does what you want: extremely narrow bandwitdh is
easy, the phase shift is zero at the center frequency, etc...but
unfortunately has response at harmonics too. Better suited to pick
one signal out of a relatively narrow range of frequencies.)

How about a linear-phase low pass filter, perhaps with some zeros to
really knock out the harmonics? Or possibly a linear phase bandpass?
Then you'd have a constant time delay...not a constant phase shift,
but a phase shift which is linearly related to the frequency. You can
make it as an analog active filter, or a digital filter. The digital
one might be easier, especially at such a low frequency. In fact, if
you eventually need to digitize the signal anyway, a delta-sigma ADC
may be just the ticket: it may be able to do the filtering for you,
if you pick the output rate correctly and pick a converter with FIR
filters inside. Of course, if you digitize fast enough to capture the
harmonics, then extracting them digitally should be no great problem.

Can you tell us more about the application, like what you're needing
to do with the filtered signal, and whether a linear-phase filter
would do, and whether you can have a clock which is locked to the
signal frequency? You mentioned "lots of higher odd-order harmonics."
Is the third a problem, or only ones beyond that? Is the second for
sure not a problem? (You also mentioned in your post that being able
to look at second and third would be an advantage...) It makes quite
a difference, because there's a lot bigger ratio between your highest
fundamental and the lowest third than there is between the highest
fundamental and the lowest second, and so forth! Is there a maximum
permissable delay through the filter?

Cheers,
Tom


mikem <mikem@bogus.adr> wrote in message news:<c7dmcu$qv9$1@coward.ks.cc.utah.edu>...

Is there such a thing as a High-Q switched-capacitor BandPass Filter
whose center frequency can be "tuned" +- 20% synchronously with its
switching clock?

I need something that would take in a ~45Hz periodic signal with lots of
higher odd-order harmonics, and spit out only the fundamental minus the
harmonics, with no or predictable phase shift. The Q needs to be high
enough to attenuate the second and subsequent harmonics by more than 40db.

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.

Extra points if the filter could select the secon or third harmonics
on command, relative to the same switching clock.

The clock could be something like 32X to 256X the fundamental.

Is a power of two for the clock preferable? (vs e.g. 50X)

MikeM

 

[Jerry Avins]

Tim Wescott wrote:

...

If you're picking out a carrier a bandpass filter will have zero phase
error at the carrier, because the filter is "anticipating" the carrier
as much as it is "sensing" it.

A bandpass filter behaves enough like a tank circuit to draw conclusions
from one by analogy. A tank (parallel L-C tuned) circuit looks inductive
below resonance and capacitive above it. At resonance, it is resistive,
hence no phase shift. I don't think that has much to do with sensing,
anticipation, or any other activity commonly engaged in by hunters.

Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ

 

[Tim Wescott]

Jerry Avins wrote:

Tim Wescott wrote:

...

If you're picking out a carrier a bandpass filter will have zero phase
error at the carrier, because the filter is "anticipating" the carrier
as much as it is "sensing" it.


A bandpass filter behaves enough like a tank circuit to draw conclusions
from one by analogy. A tank (parallel L-C tuned) circuit looks inductive
below resonance and capacitive above it. At resonance, it is resistive,
hence no phase shift. I don't think that has much to do with sensing,
anticipation, or any other activity commonly engaged in by hunters.

Jerry

You're right, tank circuits also don't normally visit sleazy bars on
their way home, or snap off "sound shots".

I was trying to frame my answer in Walter's language, which was pretty
well anchored in the time domain. In this respect a tank circuit _does_
anticipate the carrier value, in that if you feed it a carrier that
suddenly stops it will continue to oscillate at it's natural frequency
(hopefully close to the carrier frequency), with the amplitude dying off
according to the Q of the tank.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

 

[Ban]

John Popelish wrote:

Here's my understanding; as I said, I'm no filter expert, so perhaps
someone who knows what they're talking about will correct me.

A switched-capacitor filter is just a filter design that uses
switched capacitors to implement the integrators that are part of an
active filter design such as biquad or state-variable or whatever.
There are two reasons to do that: one is that the integrator gain
(and thus the filter frequency) is controlled by the switching
frequency; the other is that it's easier to make precision capacitor
ratios on silicon than it is to make precision capacitors and
resistors. And for low frequencies, you don't need high-value
components, you just lower the switching frequency.

But either way, you've still got the same biquad or state-variable or
whatever filter, it's just that it happens to be implemented using
switched capacitors. You still have to decide on a filter
characteristic: Bessel, Chebyshev, whatever. That characteristic,
combined with the number of poles, determines the phase shift. And
so far as I know, all filters have nonzero phase shift; they have
to, because it takes finite time to determine frequency.

I believe you are confusing group delay with steady state phase
shift. I think the OP is generally correct that most band pass
filters have nearly zero phase shift (or an inversion) at center band,
and I think this also applies to switched capacitor implementations.

Well, if the design is done properly, a bandpass filter will be of minimum
phase. This implies that at the center frequency the phase shift is indeed
0°, but just a little bit up or down it will rise resp. fall to +/-n*45° n
being the order. The effect for a pulse input is a smear in the response
time. whereas a sine input at the resonance will have a slow reaction
because of the rise time. You can calculate these effects by using the
normal transmission equation. No free lunch here either.
--
ciao Ban
Bordighera, Italy

 

[Walter Harley]

"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message
news:109ll7hc0dhlp13@corp.supernews.com...

I was trying to frame my answer in Walter's language, which was pretty
well anchored in the time domain. In this respect a tank circuit _does_
anticipate the carrier value, in that if you feed it a carrier that
suddenly stops it will continue to oscillate at it's natural frequency
(hopefully close to the carrier frequency), with the amplitude dying off
according to the Q of the tank.

In addition to my own ignorance about filters, I was trying to cover for
what I thought might be a confusion on the part of the OP - it wasn't clear
from the posting how much he understood, and the confusion between
implementation and filter characteristic made me wonder. Formally, a pure
sine wave has no beginning and no end, so we can talk about zero
steady-state phase shift. But some people seem to think that "zero phase
shift" means you can hit a switch to turn on the sine wave, and have the
sine wave instantly show up at the output of the filter (zero group delay).
I don't think there are filters with zero group delay, but maybe I'm wrong
about that.

 

[Max Hauser]

"Walter Harley" in message news:c7e9i0$3uj$0@216.39.172.65...

. . .
Here's my understanding; as I said, I'm no filter expert, so perhaps
someone who knows what they're talking about will correct me.

A switched-capacitor filter is just a filter design that uses switched
capacitors to implement the integrators that are part of an active
filter design such as biquad or state-variable or whatever. There
are two reasons to do that: one is that the integrator gain (and thus
the filter frequency) is controlled by the switching frequency; the
other is that it's easier to make precision capacitor ratios on silicon
than it is to make precision capacitors and resistors.

I think that's a good summary (although we did figure out how to make
precise RC time constants also, so there is less motivation to substitute
for them, and less design of sw-cap filters than in the past). It is still
impractical to make very big capacitors on an IC.

And for low frequencies, you don't need high-value
components, you just lower the switching frequency.

But either way, you've still got the same . . . filter, it's just that it
happens to be implemented using switched capacitors. You still
have to decide on a filter characteristic: Bessel, Chebyshev,
whatever. That characteristic, combined with the number of poles,
determines the phase shift. And so far as I know, all filters have
nonzero phase shift; they have to, because it takes finite time to
determine frequency.

Agreed. (By the way S-C filters, being discrete-time, can be analyzed and
designed using all the mathematics of digital filters. The usual topologies
of "switched-capacitor" imply an IIR type of response, although specialized
technologies have built efficient FIR analog filtering for years. MOS
switched-cap integrator circuitry can be configured to do FIR responses too,
if there is a need that fits the technology (which in practice is rare).

Here's a bit of filter trivia for you. General writing on filters tends to
say offhand that analog continuous-time filters always have infinite impulse
response (IIR) and nonlinear phase response. The former is certainly wrong
and long has been (specialized analog technologies implemented FIR filtering
for radar long before digital filtering existed to speak of, and specialized
continuous-time FIR technologies do so today in other applications). Common
lumped RCL or active-RC analog filter implementations do give IIR responses
having nonlinear phase. But they can be configured to approximate truly
linear phase (or finite impulse response) as precisely as you want -- the
same way they approach ideal lowpass or highpass (which they also cannot do
in their native forms). It's all a matter of proper approximation
approach -- Bessel, Thompson, elliptic, etc.

(By the way, in careful usage "biquad" is a transfer function with quadratic
numerator and denominator -- "biquadratic" -- like "bilinear" -- as in one
of the common s-z domain mappings for continuous-discrete time filter
tranformation. It is not a specific topology, although there is some
history of using it for certain second-order topologies. I think that was
in my "old farts' electronics quiz" on sci.electronics.design, from 1986,
re-posted a few months ago.)

Max

 

[Ted Wilson]

mikem <mikem@bogus.adr> wrote in message news:<c7dmcu$qv9$1@coward.ks.cc.utah.edu>...

Is there such a thing as a High-Q switched-capacitor BandPass Filter
whose center frequency can be "tuned" +- 20% synchronously with its
switching clock?

I need something that would take in a ~45Hz periodic signal with lots of
higher odd-order harmonics, and spit out only the fundamental minus the
harmonics, with no or predictable phase shift. The Q needs to be high
enough to attenuate the second and subsequent harmonics by more than 40db.

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.

Extra points if the filter could select the secon or third harmonics
on command, relative to the same switching clock.

The clock could be something like 32X to 256X the fundamental.

Is a power of two for the clock preferable? (vs e.g. 50X)

MikeM

Hi Mike

You can think of switched capacitors as simply a means of generating
frequency-controlled resistive elements:

Charge on a capacitor, q = C*V = I*t

Therefore V/I = t/C and, since R = V/I

R = t/C

Substituting t = 1/f

R = 1/(f*C)

Thus, for a given C, the higher the frequency, the lower the
resistance.

A resistor, (or resistors), generated in this manner can be plugged
into any standard circuit configuration, to provide circuit adjustment
by means of adjusting a frequency, which of course can be generated
and controled with digital precision.

Personally, to implement a band-pass function, I would use a
bridge-tee configuration, which provides very well controlled Q, (not
to be confused with the "q" discussed above), and centre frequency for
given component values.

As discussed by others in the thread, the phase shift is nominally
zero at the centre frequency.

If you are interested, I will post more information.

Regards

Ted Wilson

 

[John Larkin]

On Thu, 6 May 2004 23:37:36 -0700, "Max Hauser"
<maxREMOVE@THIStdl.com> wrote:

I think that's a good summary (although we did figure out how to make
precise RC time constants also, so there is less motivation to substitute
for them, and less design of sw-cap filters than in the past). It is still
impractical to make very big capacitors on an IC.

Then why doesn't somebody make a line of integrated continuous-time
DDS lowpass filters? This is such an obvious need... and we surely
have enough integrated SCSI terminators and white LED charge pumps to
last forever.

John

 

[mikem]

mikem <mikem@bogus.adr> wrote in message news:<c7dmcu$qv9$1@coward.ks.cc.utah.edu>...

Is there such a thing as a High-Q switched-capacitor BandPass Filter
whose center frequency can be "tuned" +- 20% synchronously with its
switching clock?

I need something that would take in a ~45Hz periodic signal with lots of
higher odd-order harmonics, and spit out only the fundamental minus the
harmonics, with no or predictable phase shift. The Q needs to be high
enough to attenuate the second and subsequent harmonics by more than 40db.

I think that this function could also be done by just a low pass, but
I'm worried about the phase shift that a low pass might introduce.

Extra points if the filter could select the secon or third harmonics
on command, relative to the same switching clock.

The clock could be something like 32X to 256X the fundamental.

Is a power of two for the clock preferable? (vs e.g. 50X)

Tom Bruhns wrote:

... suggestions snipped

Can you tell us more about the application, like what you're needing
to do with the filtered signal,

The application is vibration analysis. I want to hang an accelerometer
on the front of an direct-drive 6-cyl 4-cycle aircraft engine. The
accelerometer output will respond (first order) to any mass inbalance
at the propeller end of the engine (propeller is used as the engine
flywheel). The accelerometer output will be periodic. It can be
described as a sinosoid with harmonics.

. . . and whether a linear-phase filter
would do, and whether you can have a clock which is locked to the
signal frequency?

It is hard to lock the clock as an exact multiple of the period. See below.

You mentioned "lots of higher odd-order harmonics."
Is the third a problem, or only ones beyond that? Is the second for
sure not a problem?

I'm guessing that there will be lots of third harmonic because three
of the cylinders fire on each rotation of the engine. Since it is
a two-bladed prop, and the aircraft will be tested by running it up
to cruise RPM on the ground, there may be some second harmonic induced
as each prop blade passes within a few inches of the ground (happens
twice per revolution).

(You also mentioned in your post that being able
to look at second and third would be an advantage...) It makes quite
a difference, because there's a lot bigger ratio between your highest
fundamental and the lowest third than there is between the highest
fundamental and the lowest second, and so forth! Is there a maximum
permissable delay through the filter?

The purpose of the analysis is to resolve the amplitude and phase of
the fundamental. The phase will be relative to engine shaft position.
The phase (+-180deg) tells you where to put a counteracting weight. The
amplitude tells you how much weight to add.

My idea is to sample the accelerometer at a fixed rate, at a rate such
that several hundred samples are taken per each revolution. As the
engine speed varies (and it will vary), there will be
a slightly more or fewer samples per revolution on any given revolution.
The sample number at which the new period begins is not always
the same. (There will be a separate channel to record an index
mark on the engine shaft).

The time-series of samples will contain the funamental (at the
rotational period) and harmonics. Since the period does not
span the same number of samples for each revolution, I'm thinking
that using an FFT to extract the amplitude and phase would not work
very well.

Suppose that I do this using a laptop and an PCMCIA analog data
aquisition card. Sampling the accelerometer at a fixed-sampling rate is
easy. Sampling the output of a photocell looking at a piece of
reflective tape on the engine shaft on channel two of the AD is easy, too.

After I have several revolutions worth of data aquired, I can
analyise the data post facto; it does not have to be done in real
time, rev by rev, although it could be if I built hardware with
an embedded DSP.

I have played around with some data in Excel. I have fitted a
sine to the sampled data by creating a column of data generated
by a sine function based on four parameters, DCoffset, Amplitude,
Omega, and Phase. The next column I created is the square of the
difference between each data point and the sine value.

Using Excel's "Solver", it will diddle the four sine generation
parameters to minimize the sum of the squares of the errors.
Plotting the fitted sine on top of the original data shows that it
does the expected job of threading the sine between the original
data points.

I haven't tried it, but I supposed that using a second pass,
I could fit a sine at twice the freq of the fundamental through
the collection of points minus each fundamental sine value...

The Amplitude and Phase of the fundamental sine fitted to the original
sampled data contain the information about the mass imbalance.

In this context, what methods can be used to quickly find the ampitude
and phase of a sine fitted to a series of points containing higher
harmonics and some uncorrelated noise???

MikeM

 

[Dave VanHorn]

Would you be thinking of a boxcar averager?