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- 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

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.

- 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 I
^{2}R losses. - DC current (I
_{DC}) is the current value above which operation is not recommended without testing the component in its intended application.

Therefore, the current rating is based on the data sheet 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 data sheet ambient temperature, see the “Ambient Temperature Range” section of this application note.

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.

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.

P

where:

P_{avg} = 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.

P

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.

P

where:

P_{A} = 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.

P

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.

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:

T

where:

T_{c} is the component temperature

T_{a} is the ambient (surrounding environment) temperature

T_{r} 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 + 49.4°C) = 134.4°C at the Irms current

T

T

T

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 + 49.4°C) = 134.4°C at the Irms current

Equation 4 can be used to calculate the approximate DC resistance of a component within the operating temperature range:

DCR

where:

DCR

DCR

T2 is the temperature in °C at which the DC resistance is being calculated

An ideal pulsed waveform is described by the period (T = 1/ frequency), amplitude, pulse width (t_{on}), and duty cycle, as shown in Figure 1. Ideal pulsed waveforms are rectangular. Real pulsed waveforms have rise time, fall-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.

Figure 1

The duty cycle (D) is the ratio of the pulse width (time duration) to the pulse period, as shown in Equation 5.

D = t_{on} / T (5)

where:

D = duty cycle

t_{on} = pulse width in seconds, T = period in seconds

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.

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.

D = duty cycle

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.

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 = P

For one cycle of a continuous (100% duty cycle) waveform, and invoking Equation 1:

Energy = (Irms)

where:

ESR_{c} = 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,

ESR

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 = P_{pulsed} × t_{on} (7)

Energy = (I_{pulsed})^{2} × ESR_{pulsed} × t_{on}

where:

P_{pulsed} = equivalent pulsed power

t_{on} = pulse width in seconds

ESR_{pulsed} = effective series resistance to the pulsed current

While the pulse width (t_{on}) and the pulsed current amplitude (I_{pulsed}) are defined for a specific application, the above logic requires either knowledge of ESR_{pulsed} or the assumption that it is equivalent to ESR_{c}. For the purposes of this discussion, we assume that ESR is frequency-dependent, but not waveform-dependent, therefore ESR_{pulsed} = ESR_{c}. With this assumption, equating the energy terms of Equation 6 and Equation 7, and canceling the ESR terms:

P

t

ESR

While the pulse width (t

(Irms)^{2} × T = (I_{pulsed})^{2} × t_{on} (8)

(Irms)^{2} / (I_{pulsed})^{2} = t_{on} / T (9)

and since D is t_{on} / T,

(Irms)^{2} / (I_{pulsed})^{2} = D

Solving for the equivalent pulsed current,

I_{pulsed} = ((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,

I_{pulsed} = ((0.1 A)^{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.

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.

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 value to obtain all positive values; take the mean value; and then take the square root.

Figure 3

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.

Our current ratings are typically based on a specific temperature rise (T_{r} ) 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 (T_{a}) and 25°C. The increase in resistance depends on the thermal coefficient of resistance (TCR) of the wire (α). For copper wire, α ≈ 0.00393. When full rated current is applied to the component at a higher ambient temperature, the increased wire resistance results in increased I^{2}R 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 (T_{c}) when operating at a higher ambient temperature (T_{a}) follows. We begin with the definition of the temperature coefficient of resistance, using 25°C as our reference temperature.

α = The derivation of the equation for determining the component temperature (T

The increase in temperature due to the increased resistance =

T

T

T

T

For α = 0.00393

T

∆R = Increase in resistance due to higher ambient temperature T

T

R

R

T

T

Use the following equations to convert between average, rms, peak, and peak-to-peak values of various waveforms of current or voltage.

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 (≃1.414 × rms) Peak-to-Peak = 2 × √2 × rms (≃2.828 × rms) |

Given a Peak Value:Average = 0.636 × Peak rms = 1/ √2 × Peak (≃0.707 × 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 (≃0.354 × Peak-to-Peak) Peak = 0.5 × Peak-to-Peak |

Average = rms = Peak | Peak-to-Peak = 2 × Peak |

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 (≃1.73 × rms) Peak-to-Peak = 2 × √3 × rms (≃3.46 × rms) |

Given a Peak Value:Average = 0.5 × Peak rms = 1/√3 × Peak (≃0.578 × 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 (≃0.289 × Peak-to-Peak) Peak = 0.5 × Peak-to-Peak |

- Assistance with Safety Agency Approvals
- Basics of Inductor Selection (from Electronic Design magazine)
- Calibration, Compensation, and Correlation
- Getting Started: An Introduction to Inductor Specifications
- Hipot Testing of Magnetic Components
- How Current and Power Relates to Losses and Temperature Rise
- Measuring Self Resonant Frequency
- Operating Voltage for Inductors
- Selecting Current Sensors and Transformers
- Simulation Model Considerations: Part I
- Simulation Model Considerations: Part II
- S-parameters for High-frequency Circuit Simulations
- Testing Inductors at Application Frequencies
- Working Voltage Ratings Applied to Inductors

- PCB Washing and Coilcraft Parts
- Selecting Flux for Soldering Coilcraft Components
- Soldering Surface Mount Components

- Broadband Chokes for Bias Tee Applications
- Inductors as RF Chokes
- Key Parameters for Selecting RF Inductors

- Beyond the Data Sheet: The Need for Smarter Power Inductor Specification Tools
- Choosing Inductors for Energy Efficient Power Applications
- Current Sense Transformers for Switched-mode Power Supplies
- Determining Inductor Power Losses
- Ferrite Vs Pressed Powder-core Inductors
- Forward or Flyback? Which is Better?
- Notes on Thermal Aging in Inductor Cores
- Selecting Coupled Inductors for SEPIC Applications
- Selecting Inductors to Drive LEDs
- Selecting the Best Inductor for Your DC-DC Converter
- Structured Design of Switching Power Transformers
- Transformers for SiC FETs

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- Common Mode Filter Design Guide
- Common Mode Filter Inductor Analysis
- Data Line Filtering
- Fundamentals of Electromagnetic Compliance
- Passive LC Filter Design and Analysis
- Selecting Common Mode Filter Chokes for High Speed Data Interfaces

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- Coilcraft Conical Inductors
- Designing a 9th Order Elliptical Filter for MoCA® Applications
- Measuring Sensitivity of Transponder Coils
- Power-handling Capabilities of Inductors
- Signal Transformer Application
- Transponder Coils in an RFID System
- Using Baluns and RF Components for Impedance Matching
- Using Standard Transformers in Multiple Applications