Texas Instruments | Bus Bar Theory of Operation | Application notes | Texas Instruments Bus Bar Theory of Operation Application notes

Texas Instruments Bus Bar Theory of Operation Application notes
Application Report
SLOA237 – November 2016
Bus Bar Theory of Operation
Scott Vestal, Javier Contreras
ABSTRACT
Traditional bus bar current measurement techniques use closed loop current modules to accurately
measure and control current. These modules usually require a large magnetic core that encloses the
entire bus bar. Because the compensation current generated inside the module is proportional to the bus
bar current, the power dissipation can be as high as several watts. An alternative approach is to use two
DRV425 devices connected in a differential configuration and mounted on opposite sides of a printed
circuit board (PCB). This board is then placed into a cutout (hole or slot) located in the center of a bus bar.
Figure 1 shows the alternate approach using two DRV425 devices. When a cutout (hole or slot) is placed
in the center of the bus bar, the current is split in two equal parts. Each side of the cutout will generate
magnetic field gradients that oppose one another inside the cutout. The high sensitivity and linearity of the
two DRV425 devices allow small opposing magnetic fields to be sensed and the current to be measured
with high-accuracy levels. The DRV425 devices are placed equidistant from the center of the cutout and
oriented in opposite directions to provide a differential measurement. This differential measurement also
helps to reject outside stray magnetic fields.
DRV425-1
Hole
Bus Bar
(Top View)
I/2
I
I
I/2
DRV425-2
PCB
Figure 1. DRV425 Bus Bar Current Sensing Hole Configuration
1
2
3
4
5
Contents
Magnetic Field Gradient..................................................................................................... 3
DRV425 Sensor Characteristics ........................................................................................... 5
Bus Bar Design Requirements ............................................................................................. 5
Circuit Analysis Description ............................................................................................... 19
Related Documentation.................................................................................................... 25
List of Figures
1
DRV425 Bus Bar Current Sensing Hole Configuration ................................................................. 1
2
Right Hand Rule ............................................................................................................. 3
3
Magnetic Field Around Rectangular Conductor
4
.........................................................................
Magnetic Field Gradients ...................................................................................................
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
3
4
1
www.ti.com
5
Magnetic Fields Inside of a Cutout in a Rectangular Conductor ...................................................... 4
6
Magnetic Field Gradient Inside Cutout .................................................................................... 4
7
DRV425 Fluxgate Sensor Location
8
Bus Bar Geometry ........................................................................................................... 6
9
Hole Cutout Configuration .................................................................................................. 7
10
Slot Cutout Configuration ................................................................................................... 7
11
Vertical PCB Layout Configuration ........................................................................................ 8
12
Vertical Layout in Bus Bar .................................................................................................. 8
13
Vertical Layout Orientation Magnetic Field Measurement.............................................................. 9
14
Horizontal PCB Layout Configuration
15
Horizontal Layout in Bus Bar ............................................................................................. 10
16
Magnetic Field Seen by DRV425-1 ...................................................................................... 11
17
Magnetic Field Seen by DRV425-2 ...................................................................................... 11
18
Horizontal Layout Magnetic Field Measurement ....................................................................... 12
19
Vertical Layout Sensor Spacing .......................................................................................... 13
20
Horizontal Layout Sensor Spacing ....................................................................................... 13
21
Stray Magnetic Field ....................................................................................................... 14
22
Vertical Layout Stray Magnetic Field Susceptibility .................................................................... 15
23
Possible Vertical Saturation Configuration .............................................................................. 16
24
Horizontal Layout Stray Magnetic Field Susceptibility................................................................. 17
25
Possible Horizontal Saturation Configuration........................................................................... 18
26
DRV425 Bus Bar Schematic .............................................................................................. 19
27
DRV425 Bus Bar Function Block Diagram
28
Combination of BR and BL to Create BBar1 and BBar2 .................................................................... 21
29
Circuit With Magnetic Field
30
Stray Field Due to Neighbor Current
.......................................................................................
...................................................................................
.............................................................................
...............................................................................................
....................................................................................
5
10
20
22
24
List of Tables
......................................................................................
1
Vertical Stray Magnetic Field Error
2
Horizontal Stray Magnetic Field Error ................................................................................... 17
16
Trademarks
All trademarks are the property of their respective owners.
2
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Magnetic Field Gradient
www.ti.com
1
Magnetic Field Gradient
When current flows through a conductor it produces a magnetic field perpendicular to the flow of current.
The direction of the magnetic field is determined by the right hand rule as demonstrated in Figure 2. The
thumb points in the direction of the current (I) and the fingers curl in the direction of the magnetic field (B).
I
B
B=
I
2Πr
o
Figure 2. Right Hand Rule
The magnitude of the magnetic field (B) is proportional to the amount of current (I) flowing through the
conductor and inversely proportional to the distance (r) away from the conductor. The magnetic field
gradients are affected by the geometry of the conductor. For a rectangular conductor (bus bar), the
corners of the conductor impact the magnetic field. At distances close to the bus bar, the magnetic fields
resemble more of an ellipse as shown in Figure 3.
B
(Top)
B
I
I
I
B
B
(Side)
(End)
I
I
I
Figure 3. Magnetic Field Around Rectangular Conductor
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
3
Magnetic Field Gradient
www.ti.com
Figure 4 shows the magnetic field gradients around a bus bar.
B
I
Figure 4. Magnetic Field Gradients
When a cutout (hole or slot) is placed in the center of the bus bar, the current is split in two equal parts.
The magnetic fields generated by the current create opposite gradients inside the cutout as shown in
Figure 5 and Figure 6. The opposing fields cancel each other out in the center of the cutout.
BL
(Top)
I/2
I
BL
I
I
I
BR
I/2
BR
BR
BR
BL
(End)
I
(Side)
I
I
Figure 5. Magnetic Fields Inside of a Cutout in a Rectangular Conductor
BL
BR
I/2
I/2
Figure 6. Magnetic Field Gradient Inside Cutout
4
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
DRV425 Sensor Characteristics
www.ti.com
2
DRV425 Sensor Characteristics
The internal fluxgate sensor in the DRV425 is a single-axis sensor. The DRV425 will measure magnetic
fields only in its axis of sensitivity. The DRV425’s axis of sensitivity is in the x-axis when looking at a top
view with pin 1 in the upper left corner. The location of the fluxgate sensor in the package is shown in
Figure 7.
Axis of Sensitivity
y
4mm (typ)
x
1.74 mm
(typ)
4 mm (typ)
DRV425
(Top View)
2 mm (typ)
Fluxgate
Sensor
z
Top
x
0.4 mm (typ)
0.75 mm (typ)
Bottom
Figure 7. DRV425 Fluxgate Sensor Location
3
Bus Bar Design Requirements
In order to accurately measure the magnetic field gradient in a bus bar, two DRV425 devices are placed
inside the cutout at a well-defined distance. The measurement range and resolution depends on the
following factors:
• Bus bar geometry (width and height)
• Cutout configuration and size
• DRV425 PCB orientation (vertical or horizontal)
• DRV425 sensor spacing
Each of these factors can be optimized to create the desired measurement range for a specific
application.
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
5
Bus Bar Design Requirements
3.1
www.ti.com
Bus Bar Geometry
The width (x) and height (y) of the bus bar are needed to accurately measure the magnetic field gradient.
Figure 8 shows the bus bar geometry. A wider (larger x-dimension) and/or thicker bus bar (larger ydimension) produces a smaller magnetic field gradient.
y
x
I
z
y
x
Figure 8. Bus Bar Geometry
3.2
Cutout Configuration and Size
The configuration and size of the cutout have an impact on the magnetic field located inside the cutout.
The cutout in the bus bar has the largest impact on the magnetic field strength measurement. This
document will describe two possible configurations: hole and slot. A smaller cutout cross section will
produce a larger magnetic field strength inside the cutout. The noise level generated by stray magnetic
fields is not affected by the cutout size. Therefore, a larger magnetic field strength from a smaller cutout
cross section will increase the signal-to-noise ratio (SNR).
6
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Bus Bar Design Requirements
www.ti.com
3.2.1
Hole
When a hole is placed in the center of a bus bar, the current is split as shown in Figure 9. Because the
magnetic field is perpendicular to the current flow, the magnetic field concentrates towards the center of
the hole causing the magnetic field to have a 3-dimensional aspect. This is an advantage for this
configuration because it amplifies the desired signal to be measured and increases the SNR. The smaller
the hole diameter (D in Figure 9), the larger the magnetic field gradient inside the hole. The minimum hole
diameter is dictated by the width of the PCB holding the two DRV425 devices (D > ~6 mm).
Bus Bar
(Top View)
I/2
I
I
D
I/2
Figure 9. Hole Cutout Configuration
3.2.2
Slot
Figure 10 shows a slot cutout configuration and dimensions (L and W). When a slot is placed in the center
of a bus bar, the current is split evenly on both sides. The corresponding magnetic field gradients are
symmetric and have a two-dimensional aspect. For maximum magnetic field inside the slot, the width (W)
should be kept as small as possible. When the length (L) is less than 25.4 mm (1 in), the magnetic field
gradients will be influenced by the ends of the cutout and no longer have a two-dimensional aspect.
Bus Bar
(Top View)
I/2
I
L
W
I
I/2
Figure 10. Slot Cutout Configuration
3.3
DRV425 PCB Layout Orientation
The dual DRV425 bus bar implementation has two PCB layout orientations (vertical and horizontal). Both
layout orientations have similar noise rejection. Additionally, each layout orientation has a reduced
susceptibility to saturation by stray magnetic fields.
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
7
Bus Bar Design Requirements
3.3.1
www.ti.com
Vertical PCB Layout Orientation
In the vertical PCB layout orientation each DRV425 device has its axis of sensitivity parallel to the PCB
length as shown in Figure 11. Each device‘s axis of sensitivity is oriented in the opposite directions to
provide a differential measurement.
DRV425-1
Axis of Sensitivity
(Side View)
(Top View)
DRV425-2
Figure 11. Vertical PCB Layout Configuration
In this orientation the PCB is placed in the center of the cutout in parallel with the current flow as shown in
Figure 12. Note: Using the vertical PCB layout orientation allows for a smaller slot width because the width
of the PCB is ~6 mm while the thickness of the PCB + two DRV425 devices is ~3.5 mm. Each DRV425
device will measure the difference in the magnetic fields generated from each side of the cutout.
(Top)
I/2
I
BL
I
I
I
I/2
BR
BR
BL
BL
BR
(End)
I
(Side)
I
I
Figure 12. Vertical Layout in Bus Bar
8
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Bus Bar Design Requirements
www.ti.com
Figure 13 shows the magnetic field gradients measurement for the vertical layout orientation. The
magnetic field strength is larger and closer on the side of the cutout, and the strength decays the farther
away from the side of the cutout. The axis of sensitivity for each DRV425 device needs to be oriented to
match the magnetic field direction closest to its side of the cutout to generate a positive value.
BR2
BL2
BL1
BR1
DRV425-1
Axis of Sensitivity
Z
DRV425-2
BDRV425-1 = BL1 - BR2
BDRV425-2 = BR1 - BL2
B = BDRV425-1 + BDRV425-2 = BL1 - BR2 + BR1 - BL2
Figure 13. Vertical Layout Orientation Magnetic Field Measurement
•
•
•
•
BR1: Magnetic field strength at DRV425-2 from the right side of the cutout
BR2: Magnetic field strength at DRV425-1 from the right side of the cutout
BL1: Magnetic field strength at DRV425-1 from the left side of the cutout
BL2: Magnetic field strength at DRV425-2 from the left side of the cutout
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
9
Bus Bar Design Requirements
3.3.2
www.ti.com
Horizontal PCB Layout Orientation
In the horizontal PCB layout orientation each DRV425 device has its axis of sensitivity perpendicular to
the PCB length as shown in Figure 14. Each device‘s axis of sensitivity is oriented in the opposite
direction to provide a differential measurement.
DRV425-1
Axis of Sensitivity
(Side View)
(Top View)
DRV425-2
Figure 14. Horizontal PCB Layout Configuration
In this configuration the PCB is placed in the center of the cutout perpendicular with the current flow as
shown in Figure 15. Each DRV425 device in this orientation measures the sum of the x-axis component of
the magnetic field strength from each side of the cutout.
(Top)
I/2
I
I
I
I
I/2
(End)
I
(Side)
I
I
Figure 15. Horizontal Layout in Bus Bar
10
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Bus Bar Design Requirements
www.ti.com
Because the DRV425 device’s axis of sensitivity is horizontal for this orientation, each device will only
measure the x-axis component of the magnetic fields. Figure 16 and Figure 17 show the magnetic fields
seen by each DRV425 device Note: Each DRV425 is drawn two times to show how each magnetic field is
measured by the fluxgate sensor.
BL1
BR1
Axis of Sensitivity
y
y
x
x
Magnetic field strength
from left side of cutout
Magnetic field strength
from right side of cutout
BDRV425-1 = BL1x + BR1x
Figure 16. Magnetic Field Seen by DRV425-1
BL1
Magnetic field strength
from left side of cutout
BR1
Magnetic field strength from
right side of cutout
Axis of Sensitivity
x
x
y
y
BDRV425-2 = BR1x + BL1x
Figure 17. Magnetic Field Seen by DRV425-2
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
11
Bus Bar Design Requirements
www.ti.com
Figure 18 shows the combined DRV425 devices and the magnetic fields measured for this orientation.
The axis of sensitivity for each DRV425 device needs to be oriented to match the magnetic field direction.
BL1
BR1
DRV425-1
Axis of Sensitivity
DRV425-2
B = BDRV425-1 + BDRV425-2 = BL1x + BR1x + BR1x + BL1x
Figure 18. Horizontal Layout Magnetic Field Measurement
•
•
3.4
BR1x: Magnetic field strength at each DRV425 from the right side of the cutout in the x-axis
BL1x: Magnetic field strength at each DRV425 from the left side of the cutout in the x-axis
DRV425 Sensor Spacing
The final factor that influences the magnetic field strength in the dual DRV425 bus bar implementation is
the spacing between DRV425 device sensors. The SNR of the desired measured magnetic field to
unwanted stray measured magnetic field does not change with sensor spacing.
12
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Bus Bar Design Requirements
www.ti.com
3.4.1
Vertical PCB Layout Orientation Sensor Spacing
In the vertical PCB layout orientation, the spacing of the DRV425 sensors is shown in Figure 19. A larger
sensor spacing distance will produce a larger measured magnetic field differential in this orientation. For a
slot configuration, smaller sensor spacing enables a thinner slot width.
DRV425-1
DRV425-2
Sensor Spacing
(mm)
Figure 19. Vertical Layout Sensor Spacing
3.4.2
Horizontal PCB Layout Orientation Sensor Spacing
Figure 20 shows the DRV425 sensor spacing for the horizontal PCB layout orientation. A larger sensor
spacing distance produces a larger measured magnetic field sum in this orientation.
DRV425-1
Sensor Spacing
(mm)
DRV425-2
Figure 20. Horizontal Layout Sensor Spacing
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
13
Bus Bar Design Requirements
3.5
www.ti.com
Stray Field Impact
Due to the sensitivity of the DRV425, stray fields affect the measurement accuracy of the desired
magnetic field. A stray field is an unwanted magnetic field that is measured by the DRV425. This
measured stray magnetic field will result in an offset or error. The advantage of having a dual DRV425
orientation with each device’s axis of sensitivity in an opposite direction is the effects from the stray
magnetic fields will be reduced or cancelled. Figure 21 shows how the stray magnetic fields are measured
by the two DRV425 devices.
BStray2
BStray1
DRV425-1
Axis of
Sensitivity
y
x
DRV425-2
BDRV425-1 = ± BStray2
BDRV425-2 = BStray1
B = BDRV425-1 + BDRV425-2 = BStray1 ± BStray2
Figure 21. Stray Magnetic Field
•
•
BStray1: Stray magnetic field strength at DRV425-2
BStray2: Stray magnetic field strength at DRV425-1
When the magnitude of a stray magnetic field is seen by both DRV425 devices and has equal strength
(BStray1 = BStray2), the result will be an offset or error of zero. An example of this type of stray magnetic field
is the Earth’s magnetic field.
14
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Bus Bar Design Requirements
www.ti.com
3.5.1
Vertical PCB Layout Orientation Stray Magnetic Field Susceptibility
The vertical PCB layout orientation is susceptible to stray magnetic fields in the vertical path (y-axis). An
example of this is when two or more bus bars are placed in parallel in the x-axis as shown in Figure 22.
BStray
d
y
I
x
BStray2
BStray1
DRV425-1
Axis of
Sensitivity
DRV425-2
BDRV425-1 = ± BStray2
BDRV425-2 = BStray1
B = BDRV425-1 + BDRV425-2 = BStray1 ± BStray2
Figure 22. Vertical Layout Stray Magnetic Field Susceptibility
•
•
BStray1: Stray magnetic field strength at DRV425-2
BStray2: Stray magnetic field strength at DRV425-1
In this configuration, the distance (d) between the bus bars determines the strength difference of the stray
magnetic field seen as an offset or error. Table 1 provides some example errors illustrating the impact of
stray magnetic fields or crosstalk in this orientation.
Conditions:
• 2 bus bars: 1.5 in (38.1 mm) x 0.09 in (2.286 mm)
• 0.5-in (12.7-mm) hole
• 0.07874-in (2-mm) sensor spacing
• 100A of current
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
15
Bus Bar Design Requirements
www.ti.com
Table 1. Vertical Stray Magnetic Field Error
d (in)
ERROR
0.25
5.18%
0.5
3.77%
1
2.28%
2
1.11%
4
0.44%
6
0.23%
This offset or error can either be left in the system or calibrated out.
Another potential issue with using the vertical PCB layout orientation when two or more bus bars are
placed in parallel in the x-axis is the possibility of saturation. As discussed earlier, each DRV425 device
measures the difference in the magnetic fields generated from each side of the cutout plus the stray fields
from the adjacent bus bar as shown in Figure 23. If the total magnetic field of either DRV425 device is
larger than 2 mT, the DRV425 will saturate and all measurements will be incorrect.
BStray2
BR2
BL2
BStray1
BL1
BR1
DRV425-1
Axis of
Sensitivity
DRV425-2
BDRV425-2 = BR1 - BL2 + BStray1 < 2mT
BDRV425-1 = BL1 - BR2 - BStray2 < 2mT
Figure 23. Possible Vertical Saturation Configuration
16
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Bus Bar Design Requirements
www.ti.com
3.5.2
Horizontal PCB Layout Orientation Stray Magnetic Field Susceptibility
The horizontal PCB layout orientation is susceptible to stray magnetic fields in the horizontal path. An
example of this is when two or more bus bars are placed in parallel in the y-axis as shown in Figure 24.
y
DRV425-1
x
BStray1
BDRV425-1 = ± BStray1
BStray
Axis of
Sensitivity
I
BStray2
d
BDRV425-2 = BStray2
DRV425-2
B = BDRV425-1 + BDRV425-2 = BStray2 ± BStray1
Figure 24. Horizontal Layout Stray Magnetic Field Susceptibility
•
•
BStray1: Stray magnetic field strength at DRV425-2
BStray2: Stray magnetic field strength at DRV425-1
In this configuration, the distance (d) between the bus bars determines the strength difference of the stray
magnetic field seen as an offset or error. Table 2 provides some example errors illustrating the impact of
stray magnetic fields or crosstalk in this orientation.
Conditions:
• 2 bus bars: 1.5 in (38.1 mm) x 0.09 in (2.286 mm)
• 0.5-in (12.7-mm) hole
• 0.07874-in (2-mm) sensor spacing
• 100A of current
Table 2. Horizontal Stray Magnetic Field Error
d (in)
ERROR
1
3.50%
2
1.58%
4
0.56%
6
0.28%
8
0.17%
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
17
Bus Bar Design Requirements
www.ti.com
This offset or error can either be left in the system or calibrated out.
Another potential issue with using the horizontal PCB layout orientation when two or more bus bars are
placed in parallel in the y-axis is the possibility of saturation. As discussed earlier, each DRV425 device
will measure the sum in the magnetic fields generated from each side of the cutout plus the stray fields
from the adjacent bus bar as shown in Figure 23. If the total magnetic field of either DRV425 device is
larger than 2 mT, the DRV425 will be in saturation and all measurements will be incorrect.
BL1
BR1
DRV425-1
BStray1
Axis of
Sensitivity
BStray2
DRV425-2
BDRV425-1 = BL1x + BR1x - BStray1 < 2mT
BDRV425-2 = BR1x + BL1x + BStray2 < 2mT
Figure 25. Possible Horizontal Saturation Configuration
3.6
Bus Bar Design Requirements Summary
The mechanical dimensions of the bus bar and PCB layout configuration all impact the magnetic field
strength generated by the current flow. Of the four factors described above, the size of the cutout has the
largest impact on the magnetic field strength and SNR. When choosing a PCB layout orientation,
knowledge of the overall system and location of potential stray magnetic fields affects the optimal
orientation.
18
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Circuit Analysis Description
www.ti.com
4
Circuit Analysis Description
The circuit for the dual DRV425 bus bar implementation is orientation independent. The layout is different
for each orientation due to the axis of sensitivity, but the circuit is the same, as shown in Figure 26.
BSEL
RSEL0
RSEL1
BSEL
RSEL0
RSEL1
VDD
DRV2
VOUT
DRV1
DRV2
VCM
AINP
AINN
U1
DRV425
OR
U1
DRV425
REFOUT
OR
COMP1
ERROR
COMP2
VDIFF
REFIN
AINP
AINN
REFOUT
COMP1
VOUT
DRV1
REFIN
ERROR
1 µf
1 µf
1 µf
VDD
R1
5.1 Ÿ
GND
VDD
VDD
GND
GND
VDD
VDD
GND
COMP2
1 µf
VDD
R2
5.1 Ÿ
VDD
R3
10 NŸ
10 NŸ
1 µf
+
U3
OPA320
VREF
10 NŸ
Copyright © 2016, Texas Instruments Incorporated
Figure 26. DRV425 Bus Bar Schematic
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
19
Circuit Analysis Description
www.ti.com
Figure 27 shows a functional block diagram for the dual DRV425 bus bar schematic.
Axis of
Sensitivity
Axis of
Sensitivity
Sensor /
Integrator
Differential
Driver
DRV2
DRV2
DRV1
DRV1
Sensor /
Integrator
COMP1
COMP1
I1
Differential
Driver
R1
COMP2
R2
5.1 Ÿ
AINP
I2
5.1 Ÿ
I3
VCM
COMP2
AINP
VDIFF
AINN
AINN
U1
U2
VREF
R3 10 Ÿ
Figure 27. DRV425 Bus Bar Function Block Diagram
20
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Circuit Analysis Description
www.ti.com
4.1
Circuit Analysis of the Dual DRV425 Bus Bar Application
The setup for the configuration described below will be as shown in Figure 12. The current (I) that is
measured creates the magnetic fields BR and BL. BR is the magnetic field created from the right side of the
bus bar, and BL is created from the left side. As previously described, BR has a stronger influence on U1,
and BL has a stronger influence on U2. It is important to note the dominate direction of the magnetic field
at each sensor location. Superposition principle can be used on magnetic fields at the location of each
sensor due to the current on the bar. Figure 28 shows the combination of the field to create BBar1 and BBar2.
The bus bar is symmetrical; therefore, the magnitude of BBar1 and BBar2 are equal – only facing in opposite
directions.
BR2
BL2
BL1
BR1
DRV425-1
Axis of
Sensitivity
BBar1
BBar2
DRV425-1
Axis of
Sensitivity
DRV425-2
BDRV425-1 = BL1 - BR2
BDRV425-2 = BR1 - BL2
DRV425-2
BDRV425-1 = BL1 - BR2 = BBar1
BDRV425-2 = BR1 - BL2 = BBar2
Figure 28. Combination of BR and BL to Create BBar1 and BBar2
The DRV425 has a current output that drives the compensation coil, which is proportional to the magnetic
field sensed by each DRV425 device. There is a detailed description of this in the DRV425 Fluxgate
Magnetic-Field Sensor data sheet. For magnetic field strength calculation, see the DRV425 Bus Bar
Application Magnetic Field Calculator.
Figure 29 zooms in on the bus bar with magnetic fields and the circuit schematic. U1 on the left drives the
compensation current I1, and U2 drives the compensation current I2. These currents combine though R1,
R2 and then flow through R3. The shunt-sense amplifiers are then connected across the resistors to give
either the common mode magnetic field or the difference of the two DRV425 magnetic fields. The circuit
gives two outputs VDiff and VCM. VDiff is the differential magnetic field of the two DRV425 devices while
VCM is the common field seen by both DRV425. The following subsections describe four examples to
show how the circuit behaves.
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
21
Circuit Analysis Description
www.ti.com
I
BL
BL
I
BR
BR
I
BStray
BStray
BStray
BStray
Axis of
Sensitivity
Axis of
Sensitivity
BBar2
Sensor /
Integrator
Differential
Driver
DRV2
DRV2
DRV1
DRV1
COMP1
BBar1
Sensor /
Integrator
COMP1
R1
I1
Differential
Driver
R2
COMP2
COMP2
5.1 Ÿ
AINP
5.1 Ÿ
I3
VCM
I2
AINN
AINP
VDIFF
AINN
U1
U2
VREF
R3
10 Ÿ
Figure 29. Circuit With Magnetic Field
I Out
B
G Flux
(1)
I1 I 2 I 3
(2)
V Diff
I 3 R 3 G amp
V CM
( I1 I 2 ) ( R 1 R 2 ) G amp
(3)
(4)
where:
• Iout: Current out of DRV425 going into Comp1 and out of Comp2
• B: Magnetic field measured at DRV425
• GFlux: Gain of flux gate sensor, 12.2 mA/mT
• Gamp: Gain of the sense amplifier, 4 V/V
• VDiff: Difference in magnetic field detected by both DRV425s
• VCM: Common magnetic field detected by both DRV425s
Conditions:
• 1 bus bar: 1.5 in (38.1 mm) × 0.09 in (2.286 mm)
• 0.5-in (12.7-mm) hole
• 0.07874-in (2-mm) sensor spacing
22
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Circuit Analysis Description
www.ti.com
4.1.1
Example One: No Current Flow, 50-µT Stray Field
IBar = 0
BStray = 50 µT
With the stray field of BStray = 50 µT and the current through the bus bar of I = 0 A, the DRV425s only
detect magnetic fields generated by the stray field, which are the same with both devices. As shown in
Figure 29, BStray is in the opposite direction of U1 sensitivity, which produces a negative current. Using
Equation 1 with B = -50 µT yields the result of I1 = -610 µA. U2 measures the same magnetic field but is in
the same direction of its sensitivity, so it produces a positive I2 = 610 µA. Through Kirchhoff’s current law,
Equation 2 is obtained. In this condition, the calculation results yields the result of I3 = 0. The output
voltages can be calculated with Equation 3 and Equation 4. This calculation produces an output voltage of
VDiff = 0 V and VCM = -49.775 mV. All output voltages are referenced to the Vref voltage and are bipolar.
4.1.2
Example Two: 100-A Current Flow, No Stray Field
IBar = 100 A
BStray =0 µT
With the stray field of BStray = 0 µT and the current through the bus bar of I = 100 A, the DRV425s only
detect magnetic fields generated by the current in the bus bar. The bus bar current creates a magnetic
field of BBar1 = BBar2 = 239.66 µT at each DRV425. As shown in Figure 29, the magnetic field generated
from the bus bar on U1 is in the same direction, which produces a positive current. Using Equation 1 with
B = 239.66 µT yields the result of I1 = 2.924 mA. U2 measures the same magnetic magnitude field and is
in the same direction of its sensitivity so it also produces a positive I2 = 2.924 mA. Through Equation 2, I3
= 5.848 mA. The output voltages can be calculated with Equation 3 and Equation 4. This calculation
produces an output voltage of VDiff = 233.9 mV and VCM = 0 V.
4.1.3
Example Three: 100-A Current Flow, 50-µT Stray Field
IBar = 100 A
BStray =50 µT
With the stray field of BStray = 0 µT and the current through the bus bar of I = 100 A, the DRV425s detect
both magnetic fields generated by the current in the bus bar and the stray field. The bus bar current
creates a magnetic field of 239.66 µT at each DRV425, and the stray field is 50 µT. Using the
superposition principle, the magnetic field will sum at the location of the sensor. The direction and axis of
sensitivity is important to determine if they should add or subtract. So U1 will detect 239.66 µT + (-50 µT) =
189.66 µT, and U2 will detect 239.66 µT + 50 µT = 289.66 µT. Using Equation 1 for each DRV425, the
results are I1 = 2.314 mA and I2 = 3.534 mA. Through Equation 2, I3 = 5.848 mA. Notice the I3 value did
not change from example two (see Section 4.1.2) by adding an ambient field that is constant on both
DRV425. The output voltages can be calculated with Equation 3 and Equation 4. This calculation
produces an output voltage VDiff = 233.9 mV and VCM = -49.776 mV.
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
23
Circuit Analysis Description
4.1.4
www.ti.com
Example Four: 100-A Current Flow, Neighbor Current Stray Field
IBar = 100 A
BStray1 = 143.02 µT
BStray2 = 145.11 µT
Neighbor current = 100 A
Neighbor distance (d) = 4 in (101.6 mm)
The previous examples dealt with a magnetic field constant at both DRV425 devices. A neighbor current,
as seen in Figure 30, will not produce the same magnetic field at each DRV425 device due to the fact
each DRV425 is a different distance from the neighboring current. The distance away from the current
source determines the magnetic field strength; therefore, BStray2 > BStray1. This difference generates an error
that will be detected at the output VDiff. This error is highly influenced by the distance (d) as explained in
Section 3.5. In this example, the distance used is: (d) = 4 in (101.6 mm).
BStray1
y
BStray2
x
d
I
BStray1
BStray2
DRV425-1
Axis of
Sensitivity
DRV425-2
Figure 30. Stray Field Due to Neighbor Current
24
Bus Bar Theory of Operation
SLOA237 – November 2016
Submit Documentation Feedback
Copyright © 2016, Texas Instruments Incorporated
Related Documentation
www.ti.com
The stray fields are now different for each sensor. The bus bar is I = 100 A. The DRV425s detect both
magnetic fields generated by the current in the bus bar and the stray fields generated by neighboring
current. The bus bar current creates a magnetic field of 239.66 µT at each DRV425, and the neighboring
current creates the fields of BStray1 = 143.02 µT and BStray2= 145.11 µT. The superposition principle and
direction of the field is used again to calculate the magnetic field at the location of the sensor. So U1 will
detect 239.66 µT + (-143.02 µT) = 96.64 µT, and U2 will see 239.66 µT + 145.11 µT = 387.77 µT. Using
Equation 1 for each DRV425, the results are I1 = 1.179 mA and I2 = 4.694 mA. Through Equation 2, I3 =
5.873 mA. Notice the I3 value changed from example two (see Section 4.1.2) and example three (see
Section 4.1.3). The output voltages can be calculated with Equation 3 and Equation 4. This calculation
produces an output voltage VDiff = 234.9 mV and VCM = -143.34 mV. The stray fields from the neighbor
current give a 0.428% error.
4.1.5
Circuit Design Considerations
The analysis done in examples one, two, and three were completed with a stray field constant on both
devices. This constant would be something like the earth’s magnetic field, which will vary insignificantly
between both devices. As described in the stray field susceptibility sections of this application report, the
stray fields from other sources will not be completely cancelled, and the error is shown in example four.
The circuit has some tradeoff for making the differential measurement an output. The DRV425 DRV pins
are limited to driving voltages to the supply rails of VDD and GND. Depending on the resistors chosen (R1,
R2, R3) and the value of the compensation coil resistance (see the DRV425 System Parameter Calculator)
the sensing range will be limited. Equation 5 is the limitation. Assumptions made are Vref = VDD/2 and R1
= R2.
MAG diff
G Flux R 3
§
¨¨ MAG Stray G Flux
©
G Flux ·
¸¸ (R 1
2
¹
MAG diff
R coil )
VDD
2
(5)
where:
• MAGdiff: Differential magnetic field
• MAGStray: Common stray magnetic field
• GFlux: Gain of flux gate sensor, 12.2 mA/mT
• Rcoil: Compensation coil resistance
To avoid this limitation and get a higher range, connect each DRV425 individually to measure its own
magnetic field. After the measurements are complete, apply some post processing to calculate the
difference in the magnetic field.
5
Related Documentation
1. Texas Instruments, DRV425 Bus Bar Application Magnetic Field Calculator, Software (SBOC480)
SLOA237 – November 2016
Submit Documentation Feedback
Bus Bar Theory of Operation
Copyright © 2016, Texas Instruments Incorporated
25
IMPORTANT NOTICE FOR TI DESIGN INFORMATION AND RESOURCES
Texas Instruments Incorporated (‘TI”) technical, application or other design advice, services or information, including, but not limited to,
reference designs and materials relating to evaluation modules, (collectively, “TI Resources”) are intended to assist designers who are
developing applications that incorporate TI products; by downloading, accessing or using any particular TI Resource in any way, you
(individually or, if you are acting on behalf of a company, your company) agree to use it solely for this purpose and subject to the terms of
this Notice.
TI’s provision of TI Resources does not expand or otherwise alter TI’s applicable published warranties or warranty disclaimers for TI
products, and no additional obligations or liabilities arise from TI providing such TI Resources. TI reserves the right to make corrections,
enhancements, improvements and other changes to its TI Resources.
You understand and agree that you remain responsible for using your independent analysis, evaluation and judgment in designing your
applications and that you have full and exclusive responsibility to assure the safety of your applications and compliance of your applications
(and of all TI products used in or for your applications) with all applicable regulations, laws and other applicable requirements. You
represent that, with respect to your applications, you have all the necessary expertise to create and implement safeguards that (1)
anticipate dangerous consequences of failures, (2) monitor failures and their consequences, and (3) lessen the likelihood of failures that
might cause harm and take appropriate actions. You agree that prior to using or distributing any applications that include TI products, you
will thoroughly test such applications and the functionality of such TI products as used in such applications. TI has not conducted any
testing other than that specifically described in the published documentation for a particular TI Resource.
You are authorized to use, copy and modify any individual TI Resource only in connection with the development of applications that include
the TI product(s) identified in such TI Resource. NO OTHER LICENSE, EXPRESS OR IMPLIED, BY ESTOPPEL OR OTHERWISE TO
ANY OTHER TI INTELLECTUAL PROPERTY RIGHT, AND NO LICENSE TO ANY TECHNOLOGY OR INTELLECTUAL PROPERTY
RIGHT OF TI OR ANY THIRD PARTY IS GRANTED HEREIN, including but not limited to any patent right, copyright, mask work right, or
other intellectual property right relating to any combination, machine, or process in which TI products or services are used. Information
regarding or referencing third-party products or services does not constitute a license to use such products or services, or a warranty or
endorsement thereof. Use of TI Resources may require a license from a third party under the patents or other intellectual property of the
third party, or a license from TI under the patents or other intellectual property of TI.
TI RESOURCES ARE PROVIDED “AS IS” AND WITH ALL FAULTS. TI DISCLAIMS ALL OTHER WARRANTIES OR
REPRESENTATIONS, EXPRESS OR IMPLIED, REGARDING TI RESOURCES OR USE THEREOF, INCLUDING BUT NOT LIMITED TO
ACCURACY OR COMPLETENESS, TITLE, ANY EPIDEMIC FAILURE WARRANTY AND ANY IMPLIED WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, AND NON-INFRINGEMENT OF ANY THIRD PARTY INTELLECTUAL
PROPERTY RIGHTS.
TI SHALL NOT BE LIABLE FOR AND SHALL NOT DEFEND OR INDEMNIFY YOU AGAINST ANY CLAIM, INCLUDING BUT NOT
LIMITED TO ANY INFRINGEMENT CLAIM THAT RELATES TO OR IS BASED ON ANY COMBINATION OF PRODUCTS EVEN IF
DESCRIBED IN TI RESOURCES OR OTHERWISE. IN NO EVENT SHALL TI BE LIABLE FOR ANY ACTUAL, DIRECT, SPECIAL,
COLLATERAL, INDIRECT, PUNITIVE, INCIDENTAL, CONSEQUENTIAL OR EXEMPLARY DAMAGES IN CONNECTION WITH OR
ARISING OUT OF TI RESOURCES OR USE THEREOF, AND REGARDLESS OF WHETHER TI HAS BEEN ADVISED OF THE
POSSIBILITY OF SUCH DAMAGES.
You agree to fully indemnify TI and its representatives against any damages, costs, losses, and/or liabilities arising out of your noncompliance with the terms and provisions of this Notice.
This Notice applies to TI Resources. Additional terms apply to the use and purchase of certain types of materials, TI products and services.
These include; without limitation, TI’s standard terms for semiconductor products http://www.ti.com/sc/docs/stdterms.htm), evaluation
modules, and samples (http://www.ti.com/sc/docs/sampterms.htm).
Mailing Address: Texas Instruments, Post Office Box 655303, Dallas, Texas 75265
Copyright © 2017, Texas Instruments Incorporated
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Related manuals

Download PDF

advertising