## 5 Simulation of the f/N Converter Working in Adaptive Mode
Figure 11: The fragment of the diagram showing the process of comparing the set minimum and maximum states with the current state and depending on the obtained relation of selecting the next frequency division coefficient of the clock generator in the next iteration of the program. Figure 12: The panel of the simulator program presenting the initial simulation results of an exemplary test signal. test signal, a significant influence of the averaging error \(\delta_{a}\) is evident. The values of \(N_{xi}\) represent the test signal ranged from 171 to 6656. The relative error of the information processing was within the range of \(-0.29\%\) to \(0.23\%\). Figure 15 shows the first simulation of the adaptive work of the f/N converter. The threshold values for \(N_{xi\ min}\) = 400 and \(N_{xi\ max}\) = 1400 were set. The waveforms obtained show that the clock generator frequency change in the range of large values is triggered at the wrong level of the \(N_{xi}\) value. The quantization error was reduced only in a part of the range of higher instantaneous \(u(t)\) values. In the range of the low voltage values, the adaptive work increased the changes in the processing error, but the maximum error in the discussed range remained unchanged. The instantaneous values of \(N_{xi}\) varied in the range from 200 to 3328. The information processing error \(\delta_{\Sigma}\) varied from \(-0.245\%\) to \(0.236\%\). Figure 14: Results of the simulation of test signal processing by the f/N converter using the basic processing method. Figure 13: Presentation of the formation of the maximum value of the quantization error. Figure 16 shows the simulation results of the f/N converter with the error threshold for the upper range voltages at 0.05%, which corresponds to \(N_{xi\,min}=1000\). The lower range voltage threshold was set at 0.25 \(\times\)\(10^{-3}\)%, which corresponds to setting the rounded value of \(N_{xi\,max}=1744\) (Table 1). The waveforms show that the threshold values have been chosen significantly better. The quantization error for the upper voltage range was reduced; also, the correction for low instantaneous voltages worked correctly. The values of \(N_{xi}\) were in the range of 342 to 4034, which shows that it is possible to increase the processing range by increasing the measurable maximum period of \(T_{xi}\). Compared to the previous simulation, the information processing error \(\delta_{\Sigma}\) has been significantly reduced. Its value was within the range \(-0.146\%\div 0.143\%\). In summary, it can be stated that increasing\(f_{0}\) for small values of \(T_{xi}\) periods reduces the quantization error \(\delta_{k}\). Increasing \(T_{0}\) for large values of \(T_{xi}\) periods causes an increase in the averaging error \(\delta_{a}\), which forces an increase in the intermediate values of the processing error \(\delta_{\Sigma}\) and a decrease in the numerical values of \(N_{xi}\) representing the consecutive periods \(T_{xi}\). However, the threshold value of \(N_{xi\,max}\) may be chosen such that the maximum processing error for the lower range will not change. Figure 16: The results of the simulation of processing for the thresholds \(N_{xi\,min}=1000\), \(N_{xi\,max}=1744\). Figure 15: Processing simulation results for the thresholds \(N_{xi\,min}=400\), \(N_{xi\,max}=1400\). A question may be posed: is it permissible to set the \(N_{xi}\) thresholds arbitrarily? The answer is given by the next two drawings presenting the results of subsequent simulations. Figure 17 shows the results of the simulation of test signal processing with the threshold \(N_{xi}\) set in the entire processing range of 171, which forced the f/N converter to work with the clock signal of \(f_{0}/2\). As a result, \(N_{xi}\) decreased: it changed in the range of \(85\div 3328\), but the information processing error \(\delta_{\Sigma}\) increased noticeably. Its value was within the range \(-0.586\%\div 0.58\%\). Figure 18 shows the opposite.