What is a thermal transfer function ?

In my previous article, I explained the concept of thermal impedance. The point is that when a variable power is dissipated in a device, temperature variations of that device depends on power, of course, but also depends on the power variation frequency.

As shown in this article, EZMod3D can generate complex impedance vs. frequency data and fit these data with a Laplace transfer function.

Now, what about the temperature of another point in the system. Of course, it also changes. Amplitude and phase of temperature at any point in the system depends on dissipating devices temperature change and on a thermal transfer function from dissipating device to point of interest.

In this article, the same dissipating device in the same chip and same package as in the previous article will be used.

Cover image shows temperature amplitude distribution in the chip top plane a frequency 1E-3 hertz for 1°C temperature amplitude in the dissipating device.

And here is the situation at 1 kHz:

Temperature amplitude decreases faster with distance at 1 kHz.

Not only can EZMod3D plot temperature maps but it can also extract data versus frequency at a given point.

For instance, here is what temperature amplitude data look like, at the chip center top:

As expected, low frequency gain is close to 1. This means that when dissipating device temperature changes slowly, chip center temperature changes accordingly.

But when frequency increases, chip center temperature changes less and less while phase lag increases.

Given a fixed temperature amplitude in dissipating device, this plot is directly the transfer function from dissipating device to chip center.

Just as for thermal impedance, EZMod3D complex data can be fitted by a Laplace transfer function and then fed into an electrical simulator like eldo or LTSPICE.

These tools not only can operate in the frequency domain directly from the Laplace data, but by computing impulse response, they can simulate the system in the time domain.

Should the dissipating device be driven at constant power amplitude over frequency, its temperature would be the product of power by thermal impedance and temperature at chip center would be the product of power by thermal impedance and by transfer function.

For instance, here are the temperature change versus time in the dissipating device and at chip center for a 1W 1000 us power pulse. Top curve shows power pulse, center curve shows dissipating device temperature and bottom curve shows chip center temperature

As can be seen, temperature swing at chip center is reduced but it lasts much longer than dissipating device temperature swing.

Again, EZMod3D can analyze temperature at any point in a system as a response to dissipated power, in the frequency domain. Data can be fitted by a Laplace transfer function and used to simulate time domain variations.