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hi I'm Phil Keller of metro lab I'd like
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to tell you about a technology for
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measuring magnetic fields called flux
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meters
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oh very well techno in technology these
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have been used to measure magnetic
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magnetic fields since 19th century
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Science Museum's still have lots of
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these beautiful instruments usually
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associated with a flip coil to measure
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the Earth's field quite accurately
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modern flux meters don't look like much
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like these instruments of yesteryear but
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they still hold an important place in
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the panoply of options that we have for
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measuring magnetic fields if we look at
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where they are in this categorization of
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magnetic field measurement techniques
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where we categorize all the techniques
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with the along the horizontal axis the
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range that they cover and on the
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vertical axis the precision that they
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can achieve we see that flux meters have
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a pretty impressive place for being such
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a show we caused a well-respected
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a place in history they achieve
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remarkable precision
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second only to NMR and ESR and cover a
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wide range of fields that is absolutely
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second to none so these are very
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flexible instruments but that
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flexibility comes at a price you really
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have to know what you're doing with with
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a flux meter because it is a relatively
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complex device so we're going to talk
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about some of these complexities we're
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going to talk about some of the
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applications and just to give you a
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short overview of what all you can do
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with these devices so let's start with a
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simple scenario on the Left we have a
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strong field region strong field no
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strong magnetic field that tapers off to
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a zero field region
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the right and our job is to find the
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measure the magnetic field strength the
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flux density on the left hand strong
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field region the various ways to attack
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this problem even with a flux meter but
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let's say we decide to use a moving coil
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so we could start with the moving coil
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in the strong field region and move it
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out to the zero field region measuring
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the voltage as we do that move this
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voltage is induced by the flux changing
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in the coil as we move from a high field
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region to a low field region and we
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integrate that flux to find the total
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change over the whole path now an
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interesting point is it doesn't matter
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which path I could take I could move
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directly or I could take a couple of
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detours I will end up at the same error
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with the same answer which is a pretty
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remarkable statement the last step is
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then to divide that integral by the area
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of the coil to convert the total flux
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change into a total aid to a flux
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density change so we now know what is
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the flux density change as you move from
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the high field region to the low field
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region and if you think you know that
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the low field region is at zero you
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actually have an absolute measurement of
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the flux density in that high field
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region so let's take a quick look at the
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math behind all this because you're not
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going to avoid math when you're using
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flux meters now Faraday said that the
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voltage induced in our coil is simply
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equal to the time rate of change of the
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flux that in our in our coil any through
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n minus sign just for convention now the
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flux by definition is the integral of
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the flux density over the area of the
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coil and if the air if the coil just
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consists of n turns of a
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an area that we're calling small a then
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the total area is simply n times a and
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if the flux is flux density is constant
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across that area then the total flux in
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the coil is simply n times a times the
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perpendicular component of the flux
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density which I call their B
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perpendicular because it's important to
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remember that coils are field sensitive
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are Direction sensitive devices they
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only measure the direction the component
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of the field that is along the axis of
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the coil now the expression for the
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voltage is just the time rate of change
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of all that and since the area of the
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coil a number of turns is a constant we
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hope we can just factor those out and
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what we're left with is just the time
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rate of change of the flux density we do
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some cranking and next couple of lines
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show you we take the integral to get rid
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of that that derivative and what we end
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up with is finally an expression for the
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flux density which very importantly on
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the right hand side of the equation has
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the integral the time integral of the
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voltage and that you divide by the total
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area of the coil okay so that's lots of
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simplifications in through there but
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that is the basic equation that is most
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that is applicable to using flux meters
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okay in my introduction I've talked
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about one scenario for using flux meters
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that's a moving coil but there's lots
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others so the first one is that moving
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coil this is used to measure the flux
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change from one area relative to another
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area okay as we've seen now there's
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another way that we could have measured
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the the flux density at that particular
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point we could have flipped
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Coyle and since the flux changes from
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being positive to being negative we have
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twice the flux when we flip it and by
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measuring that flux change and dividing
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by two we can find the the the flux
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density at that particular point another
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configuration is the moving wire
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configuration this is often used for
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very narrow gaps when you have to fit
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through the north and south pole of a
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magnet that's only separated by a
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millimeter where you can't fit a coil in
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there this is often the only solution so
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the idea here is that the area of the
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coil that we're talking about is
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actually the area swept out by the by
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the wire as it goes through the gap we
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also can use just a plain static oil
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this is useful if we have an alternating
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field an oscillating field that induces
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a voltage in this static oil just
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sitting there now one very important
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feature of flux meters is that you can
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get a field map practically for free for
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example I've shown here is a moving wire
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and as we move the wire we yeah we are
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interested not just in the final result
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when we've gone all the way through the
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magnet we're going to save the partial
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integrals as we move the wire through
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the magnet and what we get then is a
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profile of the field as we move that
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wire through through the gap this slide
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shows an application that is very common
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in particle accelerator labs here we're
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not talking about a field map is in a
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linear dimension we're talking about a
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field map as you rotate a coil in the
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gap of a magnet by taking a fourier
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transform of this of these measurement
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we find a we we calculate a multipole
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model for this particular magnet the
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first order one which is just the sine
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wave is the dipole component how does
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this magnet bend the beam the second
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component is the quadrupole moment which
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tells us how this magnet focuses the
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beam and so forth often the scientists
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measure up to 1718 order to go to to be
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able to conclude all the effects that
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this magnet will have on the beam one
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extension of the rotating coil
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measurement is the the concept of
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bucking coils now the idea here is that
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let's say we're measuring a dipole
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magnet but we okay we know what the
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dipole field is that we can measure with
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with an NMR magnetometer what really
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interested in are all the error
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components the quadrupole hex X the pole
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its octupole etc components so what we
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like to do is beat down the dipole
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component down to a reasonable level so
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that it doesn't drown out all these
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other multipole measurements the way we
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do that is we use this sort of a figure
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8 coil okay and as you rotate that the
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flux is positive in one direction and
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negative in the other direction and it
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turns out that exactly cancels out the
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dipole component and therefore lets you
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to focus the full dynamic range of your
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flux meter on the higher-order
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components on the error components so
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far we've talked a lot about coils but
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coils are just one half of a flux meter
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the other half is the voltage integrator
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so usually a voltage integrator is just
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a classic analog integrator as
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see right here but more and more as the
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performance of a DPS improves we can use
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digital integration where we convert or
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digitize the signal at the front end and
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then the integral just becomes a
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numerical sum both techniques have their
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advantages and their disadvantages the
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analogue the limitations of the analog
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integrators are well known first of all
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the size of the capacitor there the C
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limits the lowest frequencies the lower
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end of the bandwidth of the voltage
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integrator you also have problems with
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noise leakage current temperature
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dependence that all need to be carefully
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carefully managed last but not least
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usually want a digital output at the end
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so in any case you have to put in an ADC
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the limitations of the digital
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integrator are also quite well
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understood first of all the Nyquist
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limit limits the upper limit of the the
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bandwidth so the highest frequency that
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you can pass also you might get
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quantitative quantization problems
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if your dynamic range is insufficient
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and last but not least you are totally
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dependent on the linearity of your ADC
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so that's a very brief overview of the
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flux meter technology this is a complex
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and well established technology with a
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large established body of knowledge so
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it does take quite a while to to to
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become competent in using this as this
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technique and there's no way that my
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little overview here can can do that for
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you but I hope at least I've given you
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enough information to whet your appetite
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and look a little further at this
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so at this outstanding technology thank
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you for listening
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