Error reduction methods

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Error reduction methods
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error reducing strategies

• filtering
• prefiltering
• postfiltering
• correction
• postprocessing
• compensation (balancing)
• feedback
• modulation

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pre-filtering

• pre-filtering (prior to transduction)
• examples
• electrically induced signals (capacitive) ?
  shielding
• magnetically induced signals (inductive)
• ? reducing loop area shielding
• changes in environmental temperature ? isolation
• unwanted optical input ? optical filters
• mechanical disturbances (shocks, vibrations) ?
  dampers
• .....

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electrically induced interference
Vn,i voltage noise source Cs capacitance
between noise source and signal leads Cg
capacitance between signal leads and ground
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shielding
Crest rest capacitance between noise source and
signal leads Cg capacitance between noise source
and ground Csh capacitance between shield and
signal leads
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example thermal isolation (1)

• 3-channel temperature profile measurement system
• restricted height (2 cm)
• max. temperature electronics 80?C
• goal maximizing thermal time constant

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example thermal isolation (2)
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post-filtering

• post-filtering (after transduction)
• in the electrical domain
• low pass, high pass, band pass
• first order, .... higher order
• characteristic (Butterworth, Bessel,...)
• analogue, digital
• Chapter 4.2...

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compensation

• measurement signal interfering signal
• additional sensor
• responding equally to the interference
• not responding to the measurand
• (or) responding to the measurand with opposite
  sign
• result a balanced (differential) pair of sensors

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measurement bridge

• bridge compensator
• bridge indicator

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(1) bridge compensator
accurate absolute measurements of resistances
(impedancies)
?
requires an accurate, adjustable resistor
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(2) bridge indicator
measurement of small changes with respect to the
initial value
in equilibrium all resistances have equal value

• three possibilities
• 1 active element
• 2 active elements (half bridge mode)
• 4 active elements (full bridge mode)

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single element bridge
non linear transfer
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half and full bridge
linear transfer
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advantages of a bridge measurement

• larger dynamic range
• linear transfer (differential sensing)
• stable zero (equilibrium)
• independent of supply voltage
• independent of CM changes (temperature,
  movements, ...)

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feedback

• Prerequisites for an effective error reduction
  are
• high forward path transfer
• stable feedback path transfer

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feedback example (1) accelerometer
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analysis of feedback accelerometer (1)
Hi transfer from acceleration a to inertial
force Fi Hs transfer from force Fs on sensor to
displacement ?x He transfer from displacement to
output voltage Vo Ha transfer of actuator from
output voltage Vo to Fa
independent of system parameters spring, sensor,
interface, gain factor transfer depends only on
mass and actuator
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analysis of feedback accelerometer (2)
mass-spring-damper system m mass (kg) k spring
stiffness (N/m) d damping constant (Ns/m)
higher resonance frequency, less damping
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(auto)correction calibration
S system sensitivity xm measurement
signal xoff offset xref reference input ?s
sensitivity error
three-point measurement
post-processing
full elimination of both additive and
multiplicative (constant or slowly changing)
errors
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End of error reduction methods