However, efficiency has its limits and consequently, the more output power required results in more power dissipated within the power supply and the associated external components.

As a result, even with highly effcient devices, proper component selection and PCB design are critical in ensuring the junction temperatures and component temperatures do not exceed their maximum limits.

The focus of this article is to highlight a switch mode power supply and a typical power inductor and their performance during high temperature conditions.

Additionally, methods for measuring thermal resistance and thermal capacitance to ambient are discussed. Examples include an inductive boost with a high-current white LED (WLED) current source and a typical power inductor.

Excessive heat from high ambient temperatures or from internal power dissipation can alter the characteristics of electronic components and cause them to shutdown, operate outside specified operating ranges or even fail. Power management devices (and their associated circuitry) run into this problem quite frequently since any power loss between the input and load results in device heating.

This heat must be dissipated away from the device, either into the PCB and nearby components, or the surrounding air. Even in switching power supplies, with traditionally high efficiency, heat must be accounted for when designing the PCB and choosing external components.

Before investigating thermal considerations when designing power management circuitry, a basic understanding of heat transfer is helpful. First, heat is the energy transferred between two systems due to the temperature difference between them. Heat transfer takes place via three mechanisms: conduction, convection and radiation.

Conduction occurs when a device with a high temperature makes contact with a device of low temperature. The high vibration amplitudes of high temperature atoms collide with atoms of the low temperature material and increase the kinetic energy of the low temperature material.

This increase in kinetic energy results in the increase in temperature of the high temperature material and a decrease in temperature of the low temperature material.

In convection, heat transfer occurs from the air surrounding the device. In natural convection, an object heats the surrounding air, which expands as it is heated, creating a vacuum that causes cool air to replace heated air.

This results in a cyclic air flow that continually transfers the heat of the device to the ambient temperature. On the other hand, forced convection would, for example, be a fan intentionally blowing cool air across the device, forcing the displacement of the warm air.

Radiation occurs when electromagnetic waves (thermal radiation) are emitted from an object to the surrounding environment. Radiated heat does not need a medium (heat can radiate through empty space). In PCBs, the primary method of heat transfer is conduction and to a lesser degree convection.

The mathematical model for conducted heat transfer is given by the equation

**
H = K x A x (T _{H} - T_{L})/d, **

where H is the rate of heat transfer in J/s; K is the thermal conductivity of the material; A is the area; (T_{H} - T_{L}) is the temperature difference; and d is the distance.

Heat conducts faster as contact area between interfaces increases, the temperature difference increases, or the length between interfaces decreases.

Heat transfer can be made analogous to an electrical circuit by equating the power (source of heat or H term in the previous equation) to a current source, the difference in temperature between the high temperature and low temperature devices, a voltage drop and the (K x A) /d term as a thermal conductivity, or the inverse d/ (K x A) as a thermal resistance in °C/W.

Often thermal resistance is given the symbol theta or just RA-B, where A and B are the two devices from which heat transfer takes place. Re-writing the rate of heat transfer equation using the electrical analogy results in P>sub>D = (T_{H} - T_{L}) /R_{H-L}.

This analogy can be carried one step further to describe another thermal attribute of a device called thermal capacitance. As thermal resistance is analogous to electrical resistance, thermal capacitance (CT with units in J/°C) is analogous to electrical capacitance.

The electrical analogy of heat transfer using the thermal capacitance in parallel with the thermal resistance gives a thermal impedance (ZT). The simplified RC model of conducted heat transfer is shown in **Figure 1 below**.

Figure 1: Shown is a simplified thermal impedance model. |

The power source is modeled as a current source and the thermal impedance is CT in parallel with RT. In electrical circuits, every thermal interface has a thermal impedance. The thermal impedance varies with material, geometry, size and orientation.

The thermal impedance of a system (or circuit) has an overall thermal impedance to the ambient temperature, which can be broken up into parallel and series combinations of the thermal impedances for each component in the circuit.

For instance, in a semiconductor device, the total thermal impedance between the die (also commonly called the junction) to the surrounding air (called the thermal impedance), from junction to ambient (ZJ-A), would be the sum of the individual thermal impedances of each separate material in the structure.

Consider a discrete MOSFET mounted on a PCB. The steady state thermal impedance (or thermal resistance RJ-A) is the sum of the thermal resistances from the junction to the device case (RJ-C), the case to the heat sink (RC-S) and the heat sink to the air (R_{S}):

**
R _{J-C} = R_{J-C} + R_{C_S} + R_{S-A}**

Additionally, there can be a parallel heat path from the MOSFET junction through the case and into the PCB, and then from the PCB to ambient temperature.

Normally the junction to case would be given by the semiconductor manufacturer. The RC-S and RS-A, on the other hand, are mainly dependent on the properties of the heat sink and PCB. Many factors influence the thermal resistances R_{C-A} or R_{C-S}, including the number of PCB layers, number of via's to secondary planes, proximity to other devices and rate of air flow.

Often, R_{J-A} is listed in device datasheets, but this number is given under specific test board conditions and would only be applicable for comparison between devices measured under the same conditions.

The thermal resistance (R_{JA}) is an important parameter for electronic components since it is a measure of how much heat a device can dissipate, based on ambient conditions and PCB layout. In other words, R_{J-A} will help us estimate the operating junction temperature, based on ambient conditions and power dissipation.

{pagebreak}**Heat dissipation**

As an example of thermal considerations in power management circuitry, consider the LM3554 circuit . (**Figure 2 below**).

Figure 2: Shown is the LM3554 flash LED driver test circuit from National Semiconductor. |

This device is an inductive boost converter designed for high-power flash LEDs used in cellphone applications. The LM3554 is a good test vehicle because it is a small device (1.6mm x 1.6mm x 0.6mm) and can provide up to 6W of output power (1.2A flash current into 5V LEDs).

Even with efficiencies around 85 percent, the relatively large output power capabilities and the tiny 16-bump SMD package make the device susceptible to high operating temperatures.

The primary effects of heat dissipation in the LM3554 are the increased on-resistance of device switches and change in device thresholds. In extreme cases where the temperature rises too high, the device could hit thermal shutdown and turn off.

Knowing an accurate RJ-A will help determine the device's junction temperature during the intended operating power, and ensure the circuit will reliably and predictably meet the application requirement.

In a likely scenario, the device can have an input voltage of 3.6V, an LED voltage of 3.6V and a LED current of 1.2A. In this situation, the converter boosts the output voltage to 300mV above V_{IN}. This provides the 300mV of headroom across the device's two paralleled current sources that regulate the LED current.

The total power drop across the device will be the sum of the power across the synchronous PFET, NFET and two current sources. The PFET and NFET power drops are across resistive components, so the RMS current must be used to get an accurate power estimation.

This current is just the RMS inductor current multiplied by the percentage of the switching period that the NFET and PFET are conducting. If we know the converter efficiency, the duty is given by 1 " D = (V_{IN} x efficiency) / V_{OUT}.

For our case, V_{OUT} = V_{LED} + 300mV and the efficiency is around 90 percent. This gives a PFET duty cycle (1 - D) of 83 percent and an NFET duty cycle of 17 percent. The RMS inductor current equation is:

Where delta x IL is the peak to peak inductor current that, for our case, is approximately 140mA, and ILDC is the average inductor current which given by I_{LED}/(1-D).

The total power loss in the switches becomes 45mW for the NFET (R_{DS_ON} = 125m-ohms) and 265mW for the PFET (R_{DS_ON}= 152m-ohms). Additionally, the current sources have a drop of 300mV x 1.2A = 360mW, giving a total internal power dissipation of 668mW.

The given R_{J-A } in the datasheet is 60°C/W and is taken from a 4- layer JEDEC test board detailed in JESD51-7. Using this RJ-A, the predicted junction temperature at TA = 50°C is 83.4°C. This would not be a problem for the device since it is below the thermal shutdown threshold of 150°C and below 125°C, the maximum operating junction temperature specified in the LM3554 datasheet.

In another scenario, the LM3554 can be set to output a constant +5V during the same flash pulse. The 300mV current source headroom now becomes 5V - 3.6V = 1.4V, resulting in a current source power dissipation of 1.68W.

Assuming the device is still 90 percent efficient in delivering 5V at 1.2A, the duty cycle is now 35.2 percent, making the DC inductor current 1.85A with delta IL of 288mA. The NFET dissipation is now 151mW and the PFET dissipation is 338mW. The total internal power dissipation of 2.169W gives an estimated die temperature (at TA = 50°C) of 180°C, which is 30°C above the thermal shutdown threshold and 55°C above the maximum operating junction temperature.

In reality, the device will not be mounted on a 4LJEDEC test board, but on a PCB with different routing of planes, other components close by that are dissipating power, and a different number of via's to lower layers. All these application variables, in addition to many other, drastically affect the R_{J-A}, which in turn reduces the accuracy of the junction temperature calculations.

{pagebreak}**Measuring thermal impedance**

What we need is an accurate R_{J-A}, which represents the actual circuit. There are various methods to measure R_{J-A}. One method uses the thermal shutdown threshold, which is set at +150°C.

To measure R_{J-A} using this method, we operate the LM3554 at a known power dissipation (P_{DISS}) and raise ambient slowly until the device shuts down. The device has an internal flag that can be set through the I2C compatible interface and returns a '1' when the thermal shutdown threshold is tripped. R_{JA} using this method will be:

Another method is to use one of the device's ESD protection diodes and measure its V_{F} vs. temperature. This is a bit more complicated, but will give a more accurate result since V_{F} can be characterized over the entire temperature range.

The ESD diodes are present on every pin of most semiconductor devices with their anode connected to GND and cathode at the respective pin.

To test the LM3554, we can look at the LEDI/NTC pin and pull a small current out of the pin (<10mA) while varying the temperature.

The absolute maximum rating of each pin is a min of -0.3V but that is due to the ESD diode's VF at max junction temp of +150°C. If we limit the current to less than 10mA, we can look at the diode's VF without damaging the device and without adding any self heating.

Measurement results on this pin yield a linear response from +25°C to +125°C, with a slope of approximately 1.3mV/°C. Once this is done, we can operate the device at a known power dissipation while measuring the V_{F} of the selected ESD diode. When VF reaches a steady state, RJ-A will be:

where V_{F}@TA is the ESD diode's V_{F} at T_{J} = T_{A}, and VF_{@SS} is the ESD diode's V_{F} after T_{J} has reached a steady state temperature while dissipating (P_{DISS}).

Finally, another method uses the change in on-resistance of a MOSFET with temperature. This method can be done using the internal PFET while the device is operating in pass mode. Pass mode on the LM3554 is when the device stops switching and turns the synchronous PFET on continuously.

This happens if V_{IN} is raised to 150mV higher than V_{OUT}. At that point, the boost converter doesn't need to boost VOUT and the PFET passes VIN straight through to VOUT.

Because there is a slight current dependence for a MOSFET's on-resistance, it is necessary to measure the PFET resistance at a current close to the target flash current.

The problem with large test currents is that they can lead to device heating. This can be overcome by setting the flash timeout duration to the minimum of 32ms and measuring the voltage drop across the PFET on an oscilloscope. The result using a 1.2A flash current shows about a 0.42m-ohms/°C slope from +25°C to +125°C. One thing to note is that the PFET is powered from the VOUT pin, so with VOUT = 5V, the on-resistance is lower when VOUT = 3.9V.

Using the three methods, with P_{DISS} = 1.67W, the results show 45°C/W with the thermal shutdown measurement, 42°C/W with the ESD diode's VF and 48°C/W using the PFET on-resistance. **Figure 3 below** shows the PFET's on-resistance and the VF of the ILED/NTC's ESD diode during a 0.856A flash LED test current pulse.

Figure 3: Shown are the LM3554 PFET on-resistance and ESD diode at LEDI/NETC during flash pulse. |

VIN of the device was set to 5V and the timeout duration was set at 1,024ms. VLED was 3.18V, which forced the LM3554 into pass mode. In this mode, the power dissipation is entirely due to the PFET and current source.

At steady state, the VF of the LEDI/NTC's ESD diode was -622mV corresponding to a junction temperature of 95.2°C in an ambient temperature of 25°C. At steady state, the PFET on-resistance measured 154 m-ohms corresponding to a junction temperature of 105°C.

Figure 3 also illustrates the thermal capacitance of the LM3554. The response of VF and R_{PMOS} show an exponential rise similar to a first order RC, which has the equation:

The resulting thermal capacitances are 0.009J/°C using the ESD diode's forward voltage and 0.0044J/°C using the PFET's onresistance. The discrepancy between the temperature readings can be attributed to temperature gradients across the device.

The PFET, which is directly adjacent to the current sources will expectedly have a faster temperature rise and have a higher temperature than the LEDI/NTC pin's ESD diode, which is located further away from the power devices on the IC.

The temperature dif ference is due to the thermal resistance and capacitance of the device's die area between the two measurement points. Also, the response is approximately that of a single time constant exponential. In reality, the power dissipation changes slightly due to the PFET and current sources heating up. This will cause a slight increase in PDISS with increasing junction temperature.

The thermal impedance model provides more insight when dealing with pulse operated devices such as flash LED drivers than thermal resistance alone. Take for example, a flash pulse at 1.2A with VIN of 5V and VLED of 3.4V. In this situation, the device is in pass mode with PDISS = 2.14W.

With RJ-A of 48°C/W and an ambient temperature of 50°C, the steady state model indicates the die temperature rises to 153°C, which is 28°C above the maximum operating junction temperature. If we account for the thermal capacitance (0.0044°C/ J) and figure in a 200ms flash pulse duration, we get a better estimate of die temperature of approximately 113°C.

{pagebreak}**Inductors, temperature**

The topics discussed thus far regarding the LM3554 and high temperatures can also be applied to the LM3554's power inductor. As with semiconductor devices such as the LM3554, excess heat dissipated in a power inductor will alter the devices characteristics and cause unintended operation in both the inductor and power supply.

The primary effects of excessive temperature in the power inductor typically result in an increase in DC winding resistance and a decrease in the saturation current limit. Inductor DC resistance change with temperature takes place due to the resistivity temperature coefficient of the inductor coil. The coil is usually copper, which has approximately a 3.9m?/°C temperature coefficient, resulting in an equation for resistance of

Or, equivalently, 0.39% per degree Centigrade change.

Looking again at the LM3554, the inductor specified with the evaluation kit is the FDSE0312- 2R2 from Toko. At TA = 25°C, the resistance is measured at 137milli-ohms. At 85°C, the resistance change is 50°C x 0.39% = 19.5% (or 164 milii-ohms). With an RMS inductor current of 2A and a VIN = 3.6V, the inductor resistance change would cause a decrease in efficiency of around 1.5 percent.

**Inductor saturation**

Perhaps the biggest concern for the power inductor at high temperatures is the decrease in rated saturation current. With large RMS currents, the internal power dissipation causes an increased inductor temperature, which lowers the saturation point of the inductor.

In saturation, the inductor core material has reached the point where magnetic flux density (B(t)) no longer increases proportional to the magnetic field strength (H(t)). Instead, in saturation, any increase in magnetic field strength caused by the increasing inductor current results in very little increase in magnetic flux density.

If we were to look at the switching regulators inductor current on an oscilloscope, we would see an increase in the inductor current slope as the device enters saturation. This is equivalent to a decrease in inductance.

The increased ripple current will cause an increase in the RMS current and an increase in the inductor's switching losses, both of which increase the inductors power loss and decrease the efficiency. Inductors can have abrupt saturation responses where saturation is reached at a specific point, or they can have gradual saturation responses as with the FDSE0312-2R2 inductor.

Nevertheless, inductor manufacturers will typically spec the saturation point as a specific percentage drop-off of inductance from its value at a given current and temperature. **Figure 4 below** illustrates an example of an inductor operating in saturation.

Figure 4: This example uses a VLS4010-2R2 (2.2 microHenrys) inductor from TDK, which exhibits a sharp drop into saturation. |

The example uses a VLS4010-2R2 (2.2 micro-Henry) inductor from TDK, which exhibits a sharp drop into saturation. This effect is shown with the LM3554 operating in boost-mode at the minimum flash pulse duration of 32ms. The short pulse width limits the self heating of the inductor, making it possible to control the inductor's temperature by adjusting the ambient temperature.

Figure 4's upper left picture shows the inductor operating below the saturation point with a normal triangular current waveform.

As the peak current is kept the same and the temperature is brought up to 50°C (upper right picture), the inductor current slope begins to increase around the 1.76A mark, indicating the inductor's saturation point has moved down with increased temperature. As the temperature is brought up to 70°C and then to 85°C, the entire current waveform eventually occurs with the inductor saturated.

**Estimating inductor temperature**

Various factors add to the temperature increase of the inductor. These include ambient temperature, inductor's thermal impedance and the inductor's internal power dissipation.

Using the inductor's DC resistance change with temperature, we can get a good estimate for the inductor's operating temperature. This is similar to using the ESD diode or the PFET on-resistance in that the inductor coil acts as an internal thermometer.

Going back to our equation for inductor resistance vs. temperature, a ratio of inductor resistance at two temperatures yields a change in temperature (delta T) given by:

A test example using the VLS4010ST-2R2 in the LM3554's circuit with a 1.65A DC current step is shown in **Figure 5, below**.

Figure 5: Shown is the VLF4010ST-2R2 inductor thermal response to 1.65A DC current step. |

The resistance at room temperature starts out at 65 milli-ohms. After more than 30s, the inductor reaches a steady state resistance of 73 milli-ohms corresponding to a steady state operating temperature of around 56°C. Using the definition of thermal resistance (RT) results in:

that the power dissipation of the inductor is a function of its coil resistance, which changes with temperature.

As a result, calculating the inductor's TF at a given RT needs to be accounted for. Plugging the equation for RT into the inductors resistance vs. temperature equation and solving for TF gives:

Figure 5 also reveals that the equivalent inductor temperature rise vs. time has an approximate first order exponential. Again, this has the equation of:

Knowing the thermal impedance of the inductor in the flash LED driver example provides some beneficial insight.

Since it takes a decent amount of time for the inductor to reach a steady state temperature compared to the flash duration (less then 1s), the estimated inductor operating temperature at the full flash current, using a steady state thermal resistance, most likely overestimates the inductors operating temperature.

This might allow for under sizing an inductor that operates in a pulsed device such as a flash LED driver as opposed to a steady state power supply.

**Conclusion**

Estimating the temperature of power management circuitry is often necessary when dealing with high-power devices that have relatively large power dissipations.

Using a generic thermal resistance can be a good comparison for similar devices in the same package, but will most likely result inaccurate temperature predictions. As such, it often becomes necessary to either use complicated thermal calculations or to measure the thermal resistance directly.

The examples highlighted in this article have demonstrated a few of the many methods available to measure a device's temperature and arrive at the device's thermal resistance. Knowing the accurate device temperature along with the device power dissipation enabled the calculation of thermal resistance.

After thermal resistance was known, it was also shown that using a step change in device power dissipation and monitoring the device temperature made it possible to calculate the device's thermal capacitance.

This enabled a more accurate estimate of device temperature due to transient thermal events. The examples listed in this article were done using a high current WLED flash driver, but are equally applicable to other power management devices, both pulse-operated and those designed to operate over longer periods of time.

**Travis Eichhorn** is an Applications Engineer at National Semiconductor Corp.

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