361

```Document 361-1
Current and Temperature Ratings
Coilcraft Inductor Current Ratings
Introduction
This application note describes:
• How to interpret Coilcraft inductor current and temperature ratings
• Our current ratings measurement method and performance limit criteria
• Calculations for estimating power performance limits
based on current ratings
• How to calculate component temperature from the
temperature rating
• How to estimate component DCR at temperatures
other than 25°C.
• How to calculate performance limits in pulsed waveform applications
• Detailed rms calculations – Appendix A
• Derivation of temperature rise equation – Appendix B
• Conversion factors for various waveforms – Appendix C
Electrical ratings are interdependent. The current through
a component depends on the applied voltage (waveform
and duty cycle) and the component impedance. The impedance of a component depends on the DC resistance
(DCR), the applied signal frequency (for AC resistance),
and the component temperature. The temperature of a
component depends on the thermodynamic (heat transfer) characteristics of the component, the circuit board,
the solder connection, the surrounding environment, the
impedance of the component, and the current through the
component. The power dissipation of a component is a
function of all of these variables.
The maximum operating rating of a component must be
given in terms of a specific measurement method and
performance limit. For example, the performance limit
could be defined as exceeding a specified temperature
rise or as a total breakdown of the insulation or wire. Different measurement methods and performance limit criteria
lead to different conclusions. By establishing the method
of measurement and the performance limit criteria, a
baseline is set for evaluating each application.
Ultimately, circuit designers attempt to determine maximum operating limits for temperature, current, voltage,
and power for each component. Each of these is specific
to the application environment.
Depending on the type of inductor (chip inductor, power
inductor) we may specify an Isat, Irms, or IDC current.
• Saturation current (Isat) is the current at which the
inductance value drops a specified amount below its
measured value with no DC current. The inductance
drop is attributed to core saturation.
• rms current (Irms) is the root mean square current
that causes the temperature of the part to rise a specific amount above 25°C ambient. The temperature
rise is attributed to I2R losses.
• DC current (IDC) is the current value above which
operation is not recommended without testing the
component in its intended application.
For some inductors Isat is lower than Irms. The core
saturates before the component temperature reaches
the performance limit. In this case we may specify only
the Isat as it is the limiting factor. For many inductors, Isat
is higher than Irms. In these cases we may specify only
Irms and the temperature rise above ambient. In many
cases, we specify both Irms and Isat current to illustrate
which measurement is more critical. IDC is specified typically when Irms greatly exceeds Isat.
Coilcraft Measurement Method and
Performance Limit Criteria
rms Current – Irms
We determine Irms by measuring the temperature rise
above 25°C ambient caused by the current through a
representative sample inductor. A low DC bias current is
applied to the inductor, and the temperature of the inductor
is allowed to stabilize. This process is repeated until the
temperature rise reaches the rating limit. The measurements are taken with the sample inductor in still air with
no heat sinking. The limit is typically a 15°C rise for chip
inductors and a 40°C rise for power inductors.
Therefore, the current rating is based on the datasheet
Irms current and temperature rise. The temperature rise
of a component due to current depends on the ambient
temperature. To determine the component temperature
due to rated current at ambient temperatures above the
datasheet ambient temperature, see the “Ambient Temperature Range” section of this application note.
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Document 361-1 Revised 10/22/08
This product may not be used in medical or high
risk applications without prior Coilcraft approval.
Specification subject to change without notice.
Please check web site for latest information.
Document 361-2
Saturation Current – Isat
Isat ratings are established by measuring the inductance
of a representative sample at a specific frequency with
no DC current. The DC current level is then gradually
increased and the inductance is measured.
The Isat rating is the current level at which the inductance
value drops a specified amount (in percent) below its
measured value with no DC current.
Power Limit Calculations
Total or “apparent” power (PA) consists of a combination
of the average (real) power (Pavg) and the reactive (imaginary) power (Pvar). While the purely reactive portion of
power does not consume energy, there is some loss associated with its transmission back and forth in the circuit
because transmission lines are not perfect conductors.
Temperature rise due to the heating effect of current
through an inductor is related to the average real power
dissipated by the inductor. The average real power is a
function of the effective series resistance (ESR) of the
inductor and the rms current through the inductor, as
shown in Equation 1.
Pavg = (Irms)2 × ESR(1)
Ambient temperature is described as a range, such as
“– 40°C to +85°C.” The range describes the recommended
ambient (surrounding environment) temperature range
of operation. It does not describe the temperature of the
component (inductor). The component temperature is
given by Equation 3:
Tc = Ta + Tr × 0.00385 × (234.5 + Ta)(3)
where:
Tc is the component temperature
Ta is the ambient (surrounding environment) temperature
Tr is the data sheet temperature rise due to rated current through the inductor
Refer to Appendix B for the derivation of this equation.
Example: The ambient temperature range for a power
inductor is stated as –40°C to +85°C, and the Irms is
rated for a 40°C rise above 25°C ambient.
The worst-case component temperature would be (85°C
+ 49.2°C) = 134.2°C at the Irms current.
DC Resistance vs. Temperature
Equation 4 can be used to calculate the approximate DC
resistance of a component within the operating temperature range:
where:
Pavg = average real power in Watts
Irms = rms current in amps
ESR = effective series resistance in Ohms
Equation 1 can be used to estimate a power limit due to
real losses. The real losses include DC and AC losses,
and are described by the ESR of the inductor. The AC
losses are frequency-dependent, therefore, we recommend using our simulation models to determine the ESR
for calculating the real power dissipation at your specific
application frequency.
The apparent (total) power required by an inductor is a
function of the rms current through the inductor, the rms
voltage across the inductor, and the phase angle difference between the voltage and current. Equation 2 can
be used to estimate the apparent power required for the
inductor.
DCRT2 = DCR25 × ((1 + 0.00385 (T2 − 25))(4)
Where:
DCRT2 is the DC resistance at the temperature T2
DCR25 is the data sheet value of DC resistance at 25°C
T2 is the temperature in °C at which the DC resistance
is being calculated
Pulsed Waveforms
An ideal pulsed waveform is described by the period
(T = 1/ frequency), amplitude, pulse width (ton), and duty
cycle, as shown in Figure 1. Ideal pulsed waveforms are
rectangular. Real pulsed waveforms have rise time, fall
Pulsed waveform
70% duty cycle
(2)
where:
PA = apparent power in Watts
Irms = rms current in amps
Vrms = rms potential across inductor in Volts
θ = phase angle in degrees
Since the AC behavior of an inductor is frequency-dependent, and Vrms is application-specific, we recommend
using our simulation models to determine the apparent
power requirements for your specific application voltage
and frequency.
Amplitude
PA = Irms × Vrms × cos (θ) Ambient Temperature Range
1.2
1.0
0.8
0.6
0.4
0.2
0
ton
0
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T
0.5
1.0
1.5
2.0
Time
Figure 1
Document 361-2 Revised 10/22/08
This product may not be used in medical or high
risk applications without prior Coilcraft approval.
Specification subject to change without notice.
Please check web site for latest information.
Document 361-3
time, overshoot, ringing, sag or droop, jitter, and settling
time characteristics that are not considered in this discussion. We also assume that all pulses in a given application
pulse train have the same amplitude.
The duty cycle (D) is the ratio of the pulse width (time duration) to the pulse period, as shown in Equation 5.
D = ton / T (5)
of this discussion, we assume that ESR is frequencydependent, but not waveform-dependent, therefore ESRpulsed = ESRc. With this assumption, equating the energy
terms of Equation 6 and Equation 7, and canceling the
ESR terms:
(Irms)2 × T = (Ipulsed)2 × ton(8)
(Irms)2 / (Ipulsed)2 = ton / T
where:
D = duty cycle
ton = pulse width in seconds, T = period in seconds
and since D is ton / T,
Duty cycle is typically given as a percent of the period.
For example, continuous waves have a 100% duty cycle,
since they are “on” for the whole cycle. Square waves
have a 50% duty cycle: “on” for a half cycle and “off” for
a half cycle. Duty cycle can also be stated as a ratio. A
50% duty cycle is the same as a 0.50 duty cycle ratio.
Solving for the equivalent pulsed current,
(Irms)2 / (Ipulsed)2 = D
To convert to pulsed power values from the equivalent
continuous (100% D) waveform estimated power, equate
the calculated energy values for a cycle, and solve the
equation for the pulsed power. The calculation uses the
definition: energy = power × time.
Energy = Pavg × T (6)
For one cycle of a continuous (100% duty cycle) waveform, and invoking Equation 1:
Energy = (Irms)2 × ESRc × T
where:
ESRc = effective series resistance to continuous current
The ESR is frequency-dependent, and can be obtained
from our simulation model of the chosen inductor.
For one cycle of a pulsed waveform,
Energy = Ppulsed × ton Energy =
(Ipulsed)2
(9)
(7)
× ESRpulsed × ton
where:
Ppulsed = equivalent pulsed power
ton = pulse width in seconds
ESRpulsed = effective series resistance to the pulsed
current
While the pulse width (ton) and the pulsed current amplitude (Ipulsed) are defined for a specific application, the
above logic requires either knowledge of ESRpulsed or the
assumption that it is equivalent to ESRc. For the purposes
Ipulsed = ((Irms)2 / D)0.5 (10)
Example: A chip inductor has an Irms rating of 100 mA
for a 15°C rise above 25°C ambient. The duty cycle for
a particular application is calculated using Equation 5 to
be 30%.
Using Equation 10,
Ipulsed = ((0.1A)2 / 0.30)0.5
Ipulsed = 0.183 A or 183 mA
This calculation predicts an equivalent 15°C rise above
25°C ambient for the 183 mA current pulse at 30% duty
cycle.
The previous calculations assume that, regardless of the
pulse amplitude, width, and duration, if the same amount
of energy calculated from the power rating is delivered to
the component over a cycle, the component will dissipate
the energy safely. There may be physical conditions that
limit this assumption due to the heat dissipation characteristics of the component, the solder connection, the
circuit board, and the environment.
In the previous example, if the duty cycle is reduced to
10%, the calculated pulsed current would be 316 mA,
which is more than three times the rated rms current, although only applied for 1/10 of a cycle. Our current ratings
are based on steady-state measurements, not on pulsed
current waveforms. While the duty cycle assumption is
valid in many cases, we have not verified our ratings for
pulsed waveforms. Therefore, we recommend testing
your specific application to determine if the calculation
assumptions are valid.
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Document 361-3 Revised 10/22/08
This product may not be used in medical or high
risk applications without prior Coilcraft approval.
Specification subject to change without notice.
Please check web site for latest information.
Document 361-4
Appendix A – rms Calculations
Rectified sinusoidal waveform
Figure 2 shows a typical sinusoidal waveform of alternating
current (AC) illustrating the peak and peak-to-peak values.
The horizontal axis is the phase angle in degrees. The
vertical axis is the amplitude. Note that the average value
of a sinusoidal waveform over one full 360° cycle is zero.
Full sinusoidal waveform
Peak
1.0
Peak-to-peak
1.0
0.5
0
-0.5
-1.0
0.5
0
0
100
200
300
Figure 3
value to obtain all positive values; take the mean value;
and then take the square root.
-0.5
-1.0
rms = 0.707
Average = 0.636
0
100
200
300
Figure 2
Figure 3 shows the same full sinusoidal waveform of
Figure 2, full-wave rectified. The average rectified and
rms values are illustrated for comparison.
Calculate the root-mean-square (rms) value by the following sequence of calculations: square each amplitude
The rms value, sometimes called the “effective” value,
is the value that results in the same power dissipation
(heating) effect as a comparable DC value. This is true of
any rms value, including square, triangular, and sawtooth
waveforms.
Some AC meters read average rectified values, and others read “true” rms values. As seen from the conversion
equation in Appendix B, the rms value is approximately
11% higher than the average value for a sinusoidal waveform.
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Document 361-4 Revised 10/22/08
This product may not be used in medical or high
risk applications without prior Coilcraft approval.
Specification subject to change without notice.
Please check web site for latest information.
Document 361-5
Appendix B – Derivation of Temperature Rise Equation
Our current ratings are typically based on a specific
temperature rise (Tr) above 25°C ambient, resulting from
the rated current. When a component is used in a higher
ambient temperature environment, the resistance of the
component wire is higher in proportion to the temperature
difference between the higher ambient (Ta) and 25°C.
The increase in resistance depends on the thermal coefficient of resistance (TCR) of the wire (α). For copper
wire, α ≈ 0.00385. When full rated current is applied to
the component at a higher ambient temperature, the increased wire resistance results in increased I2R losses.
The increased losses are assumed to be converted to
heat, resulting in a temperature rise that is proportional
to the increase in resistance of the wire.
The derivation of the equation for determining the component temperature (Tc) when operating at a higher ambient
temperature (Ta) follows. We begin with the definition of
the temperature coefficient of resistance, using 25°C as
our reference temperature.
R –R
∆R
α = ∆R / (Ta – 25) = Raa – R25
/ (Ta – 25)
R – R25
∆R
R
α = 25 / (Ta – 25) = R25 25 / (Ta – α
25)
/ (Ta – 25) = a
=
/ (Ta
R
R
25
25
∆R
R25
R25
=
α
(T
–
25)
a
∆R
∆R
R
25 = α(Ta – 25)
= α(Ta – 25)
R25
R25
∆R
Tr
∆R ×increase
The
in temperature
R
∆R
25 × Tr
due
to
the
increased
resistance =
× Tr
R25
R25
∆R
Tc = Ta + Tr + ∆R × Tr
R
∆R
Tc = Ta + Tr + 25 × Tr
Tc = Ta + Tr +
× Tr
R25
∆R
R25
Tc = Ta + Tr (1 + ∆R )
∆R
Tc = Ta + Tr (1 + R25 )
Tc = Ta + Tr (1 +
)
R(T
25 –25))
Tc = Ta + Tr (1 + α
R25
a
Tc = Ta + Tr (1 1
+ α (Ta –25))
Tc = Ta + Tr (1 + α (Ta –25))
Tc = Ta + αTr ( + (Ta –25))
α
1
Tc = Ta + αTr ( + (Ta –25))
Tc = Ta + αTr ( 1 + (Ta –25))
α
For
α = 0.00385
α
For
Tc =αTa=+0.00385
0.00385 × Tr (234.5 + Ta ) For α = 0.00385
Tc = Ta + 0.00385 × Tr (234.5 + Ta ) T = T + 0.00385 × T (234.5 + T
c
a
r
a
Definitions:
∆R = Increase in resistance due to higher ambient
temperature Ta
Ta = Ambient temperature (assumed to be >25°C)
Ra = Resistance of copper wire at ambient temperature
(Ta)
R25 = Resistance of copper wire at 25°C ambient
Tr = Datasheet temperature rise due to rated current
Tc = Component temperature due to rated current at
ambient temperature (Ta)
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Document 361-5 Revised 10/22/08
This product may not be used in medical or high
risk applications without prior Coilcraft approval.
Specification subject to change without notice.
Please check web site for latest information.
Document 361-6
Appendix C – Conversion Factors for Various Waveforms
Use the following equations to convert between average, rms, peak, and peak-to-peak values of various waveforms
of current or voltage.
Sinusoidal Waveforms
Given an Average Value: rms = 1.112 × Average
Peak = 1.572 × Average
Peak-to-Peak = 3.144 × Average
Given an rms Value:
Average = 0.899 × rms
Peak = 2 × rms (Q1.414 × rms)
Peak-to-Peak = 2 × 2 × rms (Q2.828 × rms)
Given a Peak Value:
Average = 0.636 × Peak
rms = 1/ 2 × Peak (Q0.707 × Peak) Peak-to-Peak = 2 × Peak Given a Peak-to-Peak Value:
Average = 0.318 × Peak-to-Peak
rms = 1/ (2 × 2 ) × Peak-to-Peak (Q0.354 × Peak-to-Peak)
Peak = 0.5 × Peak-to-Peak
Squarewave Waveforms
Peak-to-Peak = 2 × Peak
Average = rms = Peak
Triangular or Sawtooth Waveforms
Given an Average Value:
rms = 1.15 × Average
Peak = 2 × Average
Peak-to-Peak = 4 × Average
Given an rms Value:
Average = 0.87 × rms
Peak = 3 × rms (Q1.73 × rms)
Peak-to-Peak = 2 × 3 × rms (Q3.46 × rms)
Given a Peak Value:
Average = 0.5 × Peak
rms = 1/ 3 × Peak (Q0.578 × Peak)
Peak-to-Peak = 2 × Peak Given a Peak-to-Peak Value:
Average = 0.25 × Peak-to-Peak
rms = 1/ (2 × 3 ) × Peak-to-Peak (Q0.289 × Peak-to-Peak)
Peak = 0.5 × Peak-to-Peak
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Document 361-6 Revised 10/22/08