 # Handling the Heat with Thermal Circuits

When making integrated circuits and thinking about electronics, we want to keep costs low while maintaining performance. We do this by packing higher power into a smaller area. This means things are running incredibly fast, but also incredibly hot. If you haven’t heard of the thermal circuit, it’s a neat model for approximating how hot our electronics can get. This blog introduces the thermal circuit model and heat management solutions in electronics design.

Not all electrical engineers have the chance to study heat transfer and thermodynamics. However, most folks in EE should already know about Ohm’s Law, which states how conventional current flow is directly proportional to the voltage across a resistance. I = ∆V/R is this magical equation.

Fortunately, Fourier’s Law of Thermal Conduction is related to Ohm’s Law—heat flow through a medium is proportional to the temperature across a “thermal” resistance.

Under steady-state thermal conditions, we have heat flow defined as Q = ∆T/RΘ. Fig. 1. Thermal Circuit Analogy

Comparing electrical terminology and thermal terminology reveals several parallels:

 Electrical Terminology Thermal Terminology Voltage, V Temperature, T Current, I Heat Flow, Q Resistance, R Thermal Resistance, RΘ or Θ

Heat flow Q is in units of watts [W] while thermal resistances, referred to as “theta,” are in units of degrees per watt [°C/W].

Consider that the linear circuit conditions will hold for these approximations (e.g. thermal resistances add in series connection like electrical resistances).

## Thermal Data

Thermal data follows the Joint Electron Device Engineering Council (JEDEC) standards for testing and are reported in most datasheets. The temperature in your circuits should never exceed the maximum operating temperature or maximum junction temperature of the device, TJ,MAX (not to be confused with the American department store chain). Exceeding this maximum junction temperature can result in component failure.

Thermal resistance, like the junction-to-ambient and junction-to-case thermal resistances ΘJC and ΘJA, can also be found in the datasheets.

## Modeling Example

In power electronics, linear regulators or low dropout regulators (LDOs) typically convert a higher input voltage to a lower output voltage (i.e. VIN > VOUT). The LT1963A series are LDOs with reported ΘJC = 4°C/W, ΘJA = 50°C/W and TJ,MAX = 125°C.

For an input voltage of 10V, output voltage of 1.5V, and maximum output current of 150mA, the dissipated power (PD) in the linear regulator can be approximated as follows:

P_D=(V_{IN}-V_{OUT})×I_{OUT(MAX)}

P_D=(10V-1.5V)\times(0.150A)=1.275W

We can then approximate TJ for the LT1963A TO-220 package using Fourier’s law as well:

\frac{T_1-T_2}{R_{\Theta}}=Q

T_1=Q\times R_{\Theta}+T_2

When we substitute PD for Q and insert our related variables we find:

T_J=P_D\Theta_{JA}+T_A Fig. 2. Steady-State Thermal Circuit Model

In an environment where the ambient temperature TA is 85° C, we now find TJ:

T_J=(1.275W)(50\degree C/W)+85\degree C=148.75\degree C

Yikes! The approximated TJ would exceed the rated TJ,MAX of 125°—this heat can cause problems in other components in our circuit.

## Modified Thermal Model

Common methods to mitigate this heat involve designs with thermal vias and/or heat sinks. Providing reliable paths for heat dissipation diverts the heat flow and prevents the device from becoming too hot. If we add a heat sink with a sink-to-ambient thermal resistance (ΘSA) of 15°C/W and connect it to the device with some thermal interface material (TIM), such as thermal paste, represented by case-to-sink thermal resistance (ΘCS) with a value of 0.5°C/W, we have the following model: Fig. 3. Heat-Sink Thermal Circuit Model

Recall that we can add these values in series to find the equivalent junction-to-ambient thermal resistance:

\Theta_{JA}=\Theta_{JC}+\Theta_{CS}+\Theta_{SA}

\Theta_{JA}=(4\degree C/W)+(15\degree C/W)+(0.5\degree C/W)=(19.5\degree C/W)

We can approximate TJ again with our junction temperature equation:

T_J=P_D \Theta_{JA}+T_A

T_J=(1.275W)(19.5\degree C/W)+85\degree C=109.9 \degree C

With the added heat sink, we are now operating the device safely and much less below TJ,MAX.

To conclude, thermal management can be pretty straightforward.  Understanding this data is how we start to think about overlooked, but critical aspects of part selection and safe design. Find the next blog post in this series here.