The experimental result differs from the assumption. The result shows that the ring oscillator frequencies can be grouped into two groups, where the first group is the high frequency group for the test cases with a frequency at around 247 Mhz, and the second group is the low frequency group for the test cases with a frequency at around 235 Mhz. The difference between the average frequency of these two group is 11.64 MHz, which is about 5% of the average frequency. The standard deviations of the fast and slow group are 0.193 and 0.192 respectively. These results also show that this observation is not only true for a single CLB but all the CLB ring oscillators. When we observe the frequency distribution of these 32 test cases, we can see that actually it is of some pattern, as seen in Figure 6.6. The observation result for the first nine test cases is shown in Table 6.5. The frequency change seems to depend on the parity of the 5-bit test case control signal. When the parity of the test case is even, this test case belonged to the low frequency group. In contrast, the odd parity test cases have a high frequency. This can not be explained by the LUT structure which we assumed, as the change of the test cases is only choosing a different path in the LUTs. The path lengths are the same when the test configuration is not changed. Considering the test cases 0 and 1, the paths are very slightly changed. These kinds of the small difference may not cause such a significant change in ring oscillator frequency up to 5%. The current understanding of the LUT structure seems to be inaccurate. But still, as the LUTs are implemented with the 6-input XOR functions and all the input combinations are 57 6 Results Figure 6.6: Frequency comparison of 32 different test cases for a single CLB ring oscillator in one test configuration Table 6.5: Parity dependence of the frequency Test Case Binary Frequency 0 0000 low 1 0001 high 2 0010 high 3 0011 low 4 0100 high 5 0101 low 6 0110 low 7 0111 high 8 1000 high covered, every path that accesses the SRAM bit entries is tested and characterized. No matter what the hidden LUT structure is, the function and the input pins of the LUTs are identical for all the ring oscillators in a same test configuration and test case. As the ring oscillators in the array are using the same hard macro, it is ensured that they have an identical logic function and routing, so the delays of each CLB in different test cases are compared. Hence, the ring oscillator frequencies reflect the delay variation from CLB to CLB. 58 6.4 Temperature Dependency of Delay 6.4 Temperature Dependency of Delay The following experiments investigate the temperature influence on the ring oscillator frequency and the measurement operations influence on the temperature. Two types of experiments are presented in this section, one is using an external heating equipment to control the temperature, the other is measuring the self-heating in the FPGA caused by the proposed delay characterization method. 6.4.1 External Heating The setup of the external heating experiment is shown in Figure 6.7. The heating equipment is refitted from a hot air gun which is normally used for desolering. The fan of the FPGA board is removed and the muzzle of the hot air gun is attached to the heat sink of the FPGA board. We can adjust the heating speed by controlling the temperature and the air pressure of the hot air gun. Figure 6.7: The experiment setup for external heating In the external heat up experiment using the hot air gun, two rows of the ring oscillators in the array mentioned in Section 6.3 are chosen. In both of these two cases, hot air gun temperature is set to 100 , used the same heating air pressure. After each experiment, the hot air gun is turned off, the FPGA is put in the idle mode until it cools down and reaches the temperature equilibrium and then we start another experiment. The heating experiment lasts for ten minutes and results are sampled every second. As we would expect when the FPGA is heated up, the temperature raises and the ring oscillator frequency drops down, shown in Figure 6.9 (a). From Figure 6.9 (b) we can observe 59 6 Results that the temperature and frequency have an approximately linear correlation. Moreover, as the lines which depict the frequency decline of the ring oscillators are parallel, it shows that the frequency-temperature correlation is not depending on the ring oscillator speed. That means in a reasonable operating temperature range (below 100 ), the frequency differences between every two ring oscillators are constant. Even though the absolute path delay will increase as temperature rise, the delay variation among the CLBs can be well measured by the ring oscillator array. (a) (b) Figure 6.8: Temperature and frequency correlation of CLB row 5 for array at coordinate X48Y94 (a) (b) Figure 6.9: Temperature and frequency correlation of CLB row 9 for array at coordinate X48Y94 Linear regression analysis is run for the two rows of ring oscillators. T