Copper Alloy Inductors
Stabilize Current Sensing
By Donna Schaefer, Applications Engineer, BI Technologies,
Fullerton, Calif., and Bryan Yarborough, Applications
Engineer, IRC, Corpus Christi, Texas
For CPU VRM designs, a copper alloy features a
more constant dc resistance over temperature
than a traditional copper inductor, with little in
the way of performance tradeoffs.
C
urrent sensing is a critical part of microprocessor VR11x computing power as it provides
overcurrent protection, phase-to-phase balancing and load line adherence. The trend is
to lower voltage and improve efficiency in the
power architecture. This requires tighter voltage regulation
during transients with the accuracy of current sensing being critical.
Recommended current-sensing methods vary among
vendors, but sensing through an inductor’s resistance (RDC)
is a popular method because it is considered lossless. Less
than 1% is degraded from the power efficiency, and accuracy
is good because the inductor is sensing the actual output
current to the load. The stability of the inductor’s inductance
and RDC over temperature is critical, and tighter tolerances
can improve the accuracy of the measurement.
Presently, negative temperature coefficient of resistance
Material
Resistivity
r (Ω-m) at 20°C
Copper
1.68 3 10-8
Silver
1.59 3 10-8
Gold
2.44 3 10-8
Aluminum
2.82 3 10-8
Lead
2.2 3 10-7
Tin
1.09 3 10-7
Tungsten
5.28 3 10-8
Iron
1.0 3 10-7
Resistive alloy
1.0 3 10-7
Table. Material resistivity properties.
(NTC) thermistors are used to sense the inductor’s temperature. The thermistor provides correction for the change
in resistance of the inductor’s copper conductor material,
which has a large temperature coefficient of resistance
(TCR), 3900 ppm/°C.
However, a thermistor is an additional component on
the bill of materials; it complicates the board layout and is
not dynamically responsive. By using a copper-alloy material for the inductor conductor, the TCR can be lowered to
700 ppm/°C, and the tolerance at room temperature can
be controlled to ±2%, essentially making for an inductor
with a constant RDC.
Thermal Correction with an NTC Thermistor
A closer examination of how an NTC thermistor is used
in current sensing can show why it has a large error margin
due to nonuniform heat distribution.
Current is sensed across the inducTemperature
tor in each phase of the voltage regulacoefficient
tor by detecting the voltage across the
of resistivity
inductor’s RDC . An R-C network is
(ppm/°C)
connected in parallel to the inductor
3900
where the voltage across the capacitor
is proportional to the inductor output
3800
current. If the time constant of the R-C
3400
network matches the time constant
of the inductor, L/RDC , then accurate
3900
sensing is accomplished.[1]
3900
Compensating for the high TCR
of the copper-inductor conductor
4500
requires a thermal sensor. Thermal
4500
sensing is typically done external to
5000
the PWM control chip, because the
chip is not positioned next to the
700
components that are dissipating high
amounts of heat.
30
Power Electronics Technology April 2008
www.powerelectronics.com
4.98
Fig. 1. The single-turn conductor strip on the left, made of a
resistive alloy material, may be somewhat larger in size than
the one on the right, made of copper, but it offers a much better
temperature coefficient of resistivity. The size comparison is
made at an equivalent
RDC at 125°C.
0408PET23_F1
Fig. 2. Overall impact in an inductor’s size shows a minimal
difference in package size for a plain copper inductor (left)
versus one made using a resistive alloy material (right). This
comparison is made at an equivalent RDC at 125°C.
An NTC thermistor is located close to one of the output inductors along with a biasing resistor. The number
of output inductors depends on the number of voltage
regulator phases. Errors in the compensation method occur because there are differences in board and component
temperature and the thermistor can’t dynamically respond.
This error margin is most critical for output-voltage load
line regulation.
According to STMicroelectronics’ data sheet for the
L6756 multiphase controller for VR11x applications[2], three
factors typically affect the load line regulation tolerance
band: controller tolerance, current-sense circuit tolerance
and time-constant matching error tolerance. The tolerance
band for the current-sense circuit is directly related to the
inductor DCR tolerance, the accuracy of the NTC thermistor and the accuracy of the temperature measurement for
the copper-inductor conductor. The formula for calculating
this tolerance is:
the number of
phases. These two variables are significant
0408PET23_F2
factors in the accuracy of the sensing. If the thermistor is
eliminated and the coefficient of resistance is minimized
by the selection of the conductor material, then the error
associated with the inductor RDC current sensing can be
improved significantly.
Traditionally, copper has been used for the conductor
material in inductors because of its very low resistance,
which provides a small physical conductor size. The dc
resistance is a measure of a material’s resistance to the flow
of electric current and is defined as:
A
(Eq. 2)
ρ = R×
l
where ρ is resistivity (V-m), R is resistance (V), A is
cross-sectional area (m2) and l is length (m).
The table shows a resistivity comparison between several
common materials. Like all things in engineering, tradeoff
is the name of the game. And if we can obtain a material
with a slightly higher resistivity but with a much better TCR,
then there’s a net advantage. As can be seen from the table,
a resistive alloy with a very low TCR is a good choice.
TCR defines the amount of change in a material’s resistance over a change in temperature (°C) expressed in
percent or parts per million. At normal operating circuit
conditions, the electric resistance of metal conductors varies
linearly with temperature. Most metals increase in resistivity
as temperature increases. Copper typically increases 0.39%,
or 3900 ppm. For example, a 1-mΩ part becomes 1.4 mΩ
for a 100°C change in temperature.
Resistive alloys have a much more stable TCR compared
to copper. There are many different alloy materials, but one
with a TCR of 0.07%, or 700 ppm, is an excellent choice for
a lossless inductor. A conductor of this material with an
RDC of 1 mΩ would equate to 1.07 mΩ for the same conditions noted previously. The tradeoff for the resistive alloy
is that, due to a higher resistivity level, the conductor must
TOBCURRENTSENSE =
(
)
 k 2 DCR k 2 Rg
α × ∆T × k NTC
2
V 2 AVP × 
+
+ k 2 NTC 0 +
DCR 
N
N


(Eq. 1)
where VAVP is the output voltage (adaptive voltage
positioning), kDCR is the inductor RDC tolerance, kRg is the
trans-conductance resistor, kNTC0 is the tolerance of the NTC
thermistor at room temperature, α is the copper temperature
coefficient of resistance, kNTC is the temperature accuracy,
ΔT is the change in temperature, DCR is the inductor RDCat
room temperature and N is the number of phases.
The error related to the inductor RDC tolerance can be
divided by the number of phases as can the error for the Rg
resistors. This helps reduce the significance of these variables. However, the tolerance on the NTC thermistor and
the error in temperature measurement are not impacted by
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5.21
31
Power Electronics Technology April 2008
current sensing
DC resistance (m7)
Not Invented Here
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Copper
Alloy
25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Temperature (°C)
Fig. 3. A resistive alloy conductor has higher stability versus one made of copper.
Although the latter type shows a lower dc resistance at 25°C (green line), it increases
at 125°C. The former type’s dc resistance (red line) is more constant over that same
temperature range.
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DC resistance (m7)
Edison didn’t invent the Light Bulb,
0408PET23_F3
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Copper, +8%
Copper, –8%
Alloy, +2%
Alloy, –2%
25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Temperature (°C)
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Fig. 4. The RDC tolerance of a resistive alloy (red lines) over temperature is significantly
tighter than for a traditional copper conductor (green lines). The former varies from
from 0.59 mΩ to 0.66 mΩ, while the latter varies from 0.46 mΩ to 0.79 mΩ.
be physically larger to achieve a low
resistance when compared to copper.
0408PET23_F4
When evaluating
RDC at maximum
operating temperature conditions, the
difference is not as significant.
A comparison of single-turn conductor strips that equate to the same
RDC at 125°C is shown in Fig. 1. The
larger conductor on the left is with
the resistive alloy material and the
smaller conductor on the right is with
copper. To minimize the difference
in the physical size of the conductor,
the alloy width and thickness were
doubled while the length was held
constant.
The overall impact on the physical
size of the inductor is shown to scale
in Fig. 2. The inductor with the copper
conductor is approximately 7 mm 3
10 mm while the inductor with the
32
Power Electronics Technology April 2008
alloy conductor is approximately 10
mm 3 11 mm. The overall height and
length are similar with the main difference being the width of the part.
Even though this size difference
is a negative, the gain in temperature
stability is considerable. Fig. 3 shows
how a copper conductor that starts
at a R DC of 0.50 mΩ at 25°C will
increase to 0.74 mΩ at 125°C while
the alloy material will increase from
0.60 mΩ at 25°C to 0.64 mΩ at 125°C.
In actual circuit conditions, the 125°C
is not unrealistic as part of the normal
operating parameters.
If you take into consideration
that the nominal RDC of the resistive
alloy material will be toleranced at
±2% instead of the inductor industry
standard of ±8% for copper, the tighter
tolerance band over temperature is
www.powerelectronics.com
current sensing
significantly better. Fig. 4 shows again
the 0.5-mΩ copper conductor versus
the 0.6-mΩ alloy conductor, but with
the tolerance band also shown. The
copper conductor, when selected at
the low and high end of the tolerance
band over temperature, can vary from
0.46 mΩ to 0.79 mΩ while the alloy
conductor can vary from 0.59 mΩ to
0.66 mΩ.
There are many challenges an
inductor manufacturer encounters
when controlling the RDC precision
on the production floor. The ability
to accurately measure is easier to accomplish with a resistive alloy than
with copper because of the lower temperature sensitivity of the alloy. If the
temperature of the copper conductor
is just 1°C higher than previous test
conditions, the resistance will change
by 0.39%. With the resistive alloy
material, a 1°C change in temperature
is only a 0.07% change in value, much
less significant in the manufacturing
test environment.
In addition, the low ohmic range
offers a significant engineering challenge with regard to repeatability.
This has two main facets. First, the
mechanical geometry of the part must
be tightly controlled. The conductor
must not have a stack up of greater
than ±1% in any dimension, which
equates to 0.000118 in. (0.003 mm)
in thickness, 0.0068 in. (0.175 mm)
in length or 0.002 in. (0.05 mm) in
width.
The second facet is the low and
precise resistance value that the above
geometry entails. The conductor must
have a very consistent 2% tolerance to
perform the task, which is equivalent
to 20 µΩ of variation from a target
resistance of 1 mΩ with a resistive
alloy. In applications that use copper,
the challenge increases further by
the even lower resistance values. If a
copper conductor is used, then at a
resistance of 0.3 mΩ, a 2% part would
only permit 6 µΩ of variation.
Simple ohm-meters will not accurately measure resistance at these
small levels because of the voltage
drop in the measuring leads; fourterminal sensing is required. Clearly
www.powerelectronics.com
a
b
Four-terminal
probe
Four-terminal
probe
Fig. 5. For accurate measurements of an inductor’s RDC , a four-terminal probe is
necessary. Inductor contact points are shown from side and bottom views.
defined points of measurement must
low ohmic values due to the sensitive
be identified on the conductor (Fig. 5).
nature of these measurements.
A four-terminal connection increases
Additionally, these measurements
the accuracy of the current measuremust be made continuously and fed
ment by removing
the resistance in the
back to the equipment during the
0408PET23_F5
test leads and solder connections.
manufacturing process to assure the
Typically, a solder connection is
precision of the part throughout the
considered to have no appreciable
production. If this feedback method
impact on the overall resistance. But
were not used, the precision would
it plays a larger role in the situation
be entirely dependent on the absolute
of a low-resistance current-detection
consistency of the mechanical dimenshunt at very low values. At high cursions of the conductor material from
rents and low-resistance values, even
the mill.
the smallest amount of differences in
Using a new and innovative inducresistance will affect signal accuracy.
tor conductor material and improved
For example, a solder joint that added
manufacturing process with test
5 µΩ of resistance would introduce an
capabilities can provide a precise
additional 1% of error on a 1% resistor
current-sensing inductor with a tight
at 0.5 mΩ.
tolerance band and temperatureTwo terminal connections would
stable current sensing. This device
introduce an excessive amount of
will aid PWM controller manufacturerror at the solder-joint region meners in their quest for a higher level
tioned previously and the additional
of control accuracy for multiphase
PETech
lead length from the part. This type of
voltage regulators. application requires a four-terminal
References
connection often referred to as a
1. Huang, Wenkang; Clarkin, John;
Kelvin connection, which connects
Cheng, Peter; and Schuellein, George.
two points for a current path and two
“Inductors Allow Loss-Less Current
points to measure the voltage signal.
Sensing in Multiphase DC-DC ConThis results in a higher-precision resisverters,” PCIM magazine, June 2001.
tance measurement by removing the
2. “L6756 2/3/4 Phase Buck Controller
voltage drop that would occur due to
for Processor Applications,” STMicrothe contact resistance. This method for
electronics data sheet, February 2008.
measurement must be used for these
33
Power Electronics Technology April 2008