**4. Discussion**

As already mentioned in the foregoing section, the sensor temperature differs from the CPU value that we are mainly interested in. A correction has been made, see Equation (5), so that the correct CPU temperature is obtained in steady-state conditions. However, we want to find out how much difference is obtained in case of a thermal transient problem.

To find an answer to that problem, one can use the equivalent network shown in Figure 3. If a step input power is applied, the sensor temperature Δ*TS* is given by Equation (2). The CPU temperature is then found to be:

$$
\Delta T\_{CPII}(t) = \Delta P\_0 \frac{R(R+R')}{R'+2R} \left(1 - \frac{R'+2R}{2(R+R')} \varepsilon^{-t/\tau\_1} - \frac{R'}{2(R+R')} \varepsilon^{-t/\tau\_2}\right) \tag{11}
$$

Inserting the numerical values τ1 = 210 s, τ2 = 100 s and *R* = 1.818R in Equation (11), one gets:

$$
\Delta T\_{CPII}(t) = 29 \left( 1 - 0.6774e^{-t/210} - 0.3225e^{-t/100} \right) \tag{12}
$$

Notice that in Equation (12), two minus signs appear, which is physically possible because we are dealing with an impedance function, i.e., the temperature is measured between the same nodes where the power is applied.

However, the curve Δ*TS* was multiplied by the correction factor 2.81 so that both curves have the same steady state value, so that a better comparison can be made. As can be seen from Figure 4, there is delay of about 100 s between the CPU and the temperature recorded by the sensor. As a consequence, a heat pulse lasting for less than 100 s will not be detected properly by the temperature sensor.

**Figure 4.** CPU and sensor temperature versus time.

The curve Δ*TCPU* shows also a sharp rise at *t* = 0, which is typical for the temperature of a heat source. During the transient period, the sensor temperature gives a serious underestimate of the *CPU* temperature and, vice versa, an overestimation of the temperature will occur when the power is suddenly reduced.

It is also remarkable that a lot of information regarding the dynamic thermal properties could be gained from a graph like Figure 1. However, the processor was doing a job that has nothing to do with thermal analysis.
