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Radiant Technologies, Inc.Magneto-Electric Test Procedure
A Charge-Based Magneto-Electric Test Procedure
Scott P. Chapman & Joseph T. Evans, Jr.
Radiant Technologies, Inc.
Aug 9, 2011
IWPMA 2011
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Summary
The goal is to describe an experiment to characterize the charge response of a piezoelectric or multiferroic sample in the presence of a magnetic (B) field by:
P = H
B = H
P = /B
For a multiferroic, H induces P directly. For our piezoelectric sample, P results from direct force (dc) or torque (d) applied to the sample ferroelectric.
Radiant Technologies, Inc.Magneto-Electric Test Procedure
SummaryI will present:
• Mathematics and theory relating predictive and measured polarization response to the magnetic field and magnetic field geometry.
• Experimental considerations.• Experimental design and configuration.• Measured results.• Measured comparison to predictive.
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Magnetic ForceThese three statements apply to understanding Magnetic Force:
• Magnetic force is generated only by moving electric charges.
• For two objects to exert magnetic force both must contain moving charges.
• Magnetic force calculation proceeds as follows:
• Calculate a mathematical field, H, that sums the motion of all charge particles at the point of interest in the field.
• Multiply H by the magnetic permeability factor, , to convert it to a force field, B.
• Use B to calculate magnetic force on the target. This requires the calculation of both the HH coil force and the target force, and their multiplication.
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Geometry
Bsingle coil = 0NIR2 x 0.5(R2+x2)-3/2 (1)
BHHC = 0.5 0NIR2 / [(R2+(x+K/2)2)3/2+[(R2+(x-K/2)2) 3/2] (2)
N = Number of Coils R = Coil Radius (m)I = Current Through Loop (Amps) K = Coil Separation (m)
B = 0.716 0NI/R (3)
For: K = R and x = 0 (Centered Between Coils)
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Basic Test Configuration - Orientation 1
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Basic Test Configuration - Orientation 2
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Basic Test Configuration - Orientation 3
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Plot Measured Charge Vs Field
H
P
P is Measured but H may be inferred
Arbitrary Data
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Independent Field Values
The independent (Field) axis in the data presentation can be determined by:
• Assumed Field by DRIVE Volts into the Current Amplifier. This experiment presented here uses this approach.
• Assumed Field by Measured Current into the Helmholtz Coil. This reduces the number of error sources in the first option by half.
• Field Measured Field by magnetic sensor. Most accurate.
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Some Field Profiles
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Improved Test Configuration - Measure HH Coil Input Current
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Improved Test Configuration - Direct Field Measurement at Sample
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Advanced Test Configuration - Introduce a DC Bias Field
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Program Entry Parameters
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Measurement Configuration
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Data Presentation Configuration
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Direct Force (dc) Measurement
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Direct Force (dc) Response
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Torque (d) Measurement
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Torque (d) Response
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Measured Piezo ConstantsThe constants we measured:
• Parallel to the magnetic axis:
* 61.2 pC/N (10 g = 0.98 N)
* 71.4 pC/N (20 g = 1.96 N)
* 71.4 pC/N (50 g = 4.9 N)
* 68.0 pC/N (Average)
• Torque: 765.0 pC/N
When applying magnetic torque, the force must be calculated from the lever arm length and then multiplied by the equivalent torque piezo constant
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Primary Error Sources
There are three primary sources of error:
• Frequency response of the current amplifier with the attached HH coil. Slow the measurement to ensure the amplifier can provide the requested HH coil input power.
• Parasitic charge resulting from magnetic induction in the RETURN cable. This effect is reduced by slowing the measurement. Measure the effect and subtract from the final measurement.
• Charge measurement accuracy reduced by charge deterioration over long tests. This effect is reduced by speeding the test.
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Pre-Measurement Steps
To prepare for the Magneto-Electric Response Task measurement, perform these steps:
• Calculate the magnetic field at the point where the sample is located.
• Measure the induced current in the cable, under measurement test conditions, and retain to subtract from the measured data.
• Reduce the test speed to reduce inductive current, but no slower than 1000.0 ms.
• Determine through experimentation the maximum frequency and ensure 1/Test Period does not exceed this value.
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Predictive Modelm || B - Centered in HH Coil
Define, for our force inducing magnet:
m = MV
M = Magnetization of Magnet V = Volume
For B || m
F = [m B] (1)
For constant m, as with our magnets:
F = m B/ x (2)
For constant B, as in the center of the Helmholtz coil:
F = 0 => Q = 0
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Predictive Modelm B - Centered in HH Coil
Piezo Constant:
d = 0.75 V x 100 pC/10g (Sense Capacitor) =
75 pC/0.098 N = 765 pC/N
Ftorque ():
m = 4 x 1.08 T/4x10-7 x (0.00252 x 0.006) = 0.4 A/m
Estimated Charge (Q) at 45.0 Gauss:
Q = d x 0.4 A/m x B / Height
= 765 pC/N x 0.4 A/m x 45 e-4 T / 0.006 m
= 229.5 pC
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Predictive Model m || B - At 1 K From Closest Coil
x = 1.5 K = 1.5 R
B = -0.319 0NI/R2
Q = dc x 0.4 A/m x B = d33 x 0.037 x I
What is d33, is 0.037 the Amps/Gauss and How do I use this to predict Q?
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Predictive Modelm B - At 1 K From Closest Coil
At x = 0:
B = 0.716 0NI/R
=> 0NI/R = B/0.716 = 45.0/0.716 = 62.85 G
At x = 1.5 K = 1.5 R:
BHHC = 0.5 0NIR2/(R2+(x+K/2)2)3/2+ 0.5 0NIR2/(R2+(x-K/2)2) 3/2 G
= 0.5 0NIR2/(R2+(1.5R + R/2)2)3/2+ 0.5 0NIR2/(R2+(1.5R-K/2)2)3/2
= 0.1727 0NI/R G = 10.855 G
Q = d x 0.4 A/m x B / Height
= 765 pC/N x 0.4 A/m x 10.855 e-4 T / 0.006 m
= 55.36 pC/m3
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Experiment
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Measured Data - Centered || BAverag ed C harg e
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-60 -40 -20 0 20 40 60
Averag ed Induc tive C urrent
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-60 -40 -20 0 20 40 60
C orrec ted C harg e
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-60 -40 -20 0 20 40 60
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Measured Data - Centered B
Averag ed Induc tive C urrent
-0.00015
-0.0001
-0.00005
0
0.00005
0.0001
0.00015
-60 -40 -20 0 20 40 60
C orrec ted C harg e
-0.00015
-0.0001
-0.00005
0
0.00005
0.0001
0.00015
-60 -40 -20 0 20 40 60
Averag ed C harg e
-0.00015
-0.0001
-0.00005
0
0.00005
0.0001
0.00015
-60 -40 -20 0 20 40 60
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Measured Data - x = R || BAverag ed C harg e
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-60 -40 -20 0 20 40 60
Averag ed Induc tive C urrent
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-60 -40 -20 0 20 40 60
C orrec ted C harg e
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-60 -40 -20 0 20 40 60
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Measured Data - x = R BAverag ed C harg e
-0.00004
-0.00003
-0.00002
-0.00001
0
0.00001
0.00002
0.00003
0.00004
-60 -40 -20 0 20 40 60
Averag ed Induc tive C urrent
-0.00004
-0.00003
-0.00002
-0.00001
0
0.00001
0.00002
0.00003
0.00004
-60 -40 -20 0 20 40 60
C orrec ted C harg e
-0.00004
-0.00003
-0.00002
-0.00001
0
0.00001
0.00002
0.00003
0.00004
-60 -40 -20 0 20 40 60
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Summarize ResultsExperiment Predicted
ResultsMeasuredResults
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Error Sources• Amps/DRIVE Volts conversion for the KEPCO 36-6M
current amplifier. -1.75 Volts/Amp used. Expected current = 45.0 G X 0.0373 Amps/Gauss = 1.68 Amps. Post-data measurement showed 1.799 Amps. Generated 48.15 G.
• Current/Gauss conversion for the Lakeshore MH-6 Helmholtz coil. Used the Lakeshore published conversion of 26.76 G/A => 0.0373 A/G. Did not measure the actual ratio.
• Manual dc and d measurements.
• Unstable measurement surface.
• Unfixed sample subject to bending an shear.
• Joe, please add.
Radiant Technologies, Inc.Magneto-Electric Test Procedure
Conclusion
• Radiant successfully tested the magneto-electric response of a piezoelectric force sensor coupled to a magnet using Radiant’s Magnetoelectric Response Task
• The system was able to cleanly capture the measurements that generated 100 pC of Response
• The sample response differed from our predictions but there were several possible error sources in the test fixture and predictive models.