## 5 Solving Non-Ideal Issues during the Tests
### Analysis of Sum of Integer-Order Integrator and Fractional-Order Differentiator Responses  
This specific case shown in Figure 7 implements the sum of integer-order integrator and fractional-order differentiator. Figures 21 and 22 indicate expected minimum of transfer (magnitude) given by intentional zero frequencies. Figures 23-25 show particular time-domain wave forms at frequencies in area with dominance of integration (800 Hz), differentiation (100 kHz), as well as a frequency of 7 kHz being close to the gain minimum (selected example for \(A_{1}=5\), \(A_{2}=1\)). Figure 21: Frequency response of the system shown in Figure 7 (sum of integer-order integrator and fractional-order differentiator responses) when \(A_{1}\) (integer-order branch) is varying between 0.5 and 5: (**a**) magnitude responses; (**b**) phase responses. Figure 22: Frequency response of the system shown in Figure 7 (sum of integer-order integrator and fractional-order differentiator responses) when \(A_{2}\) (fractional-order branch) is varying between 0.5 and 5: 5: (**a**) magnitude responses; (**b**) phase responses. Figure 23: Time domain response of the system shown in Figure 7 (sum of integer-order integrator and fractional-order differentiator responses) at 800 Hz when sourced by: (**a**) square wave input signal; (**b**) triangular wave input signal. Figure 24: Time domain response of the system shown in Figure 7 (sum of integer-order integrator and fractional-order differentiator responses) at 7 kHz when sourced by: (**a**) square wave input signal; (**b**) triangular wave input signal. Figure 25: Time domain response of the system shown in Figure 7 (sum of integer-order integrator and fractional-order differentiator responses) at 100 kHz when sourced by: (**a**) square wave input signal; (**b**) triangular wave input signal. Results presented in this section (Section 6) indicate quite good correspondence of theoretical expectations and experiments. However, high-frequency limitations of active devices as well as other small-signal parasities influence the high-frequency band significantly. The substantial resonant peak occurs at a frequency around 200-300 kHz. Generally, the frequency limits also depend upon the accuracy of CPE, and therefore, also on used approximation. However, in our case, active devices and real circuitry has significantly higher impact. The resulting operational bandwidth of discussed  
Figure 30: Time domain response of the system in Figure 9 (sum of fractional-order integrator and integer-order differentiator responses) at 50 kHz on: (**a**) square wave input signal; (**b**) triangular wave input signal. Figure 28: Time domain response of the system in Figure 9 (sum of fractional-order integrator and integer-order differentiator responses) at 600 Hz on: (**a**) square wave input signal; (**b**) triangular wave input signal. Figure 29: Time domain response of the system in Figure 9 (sum of fractional-order integrator and integer-order differentiator responses) at 2.15 kHz on: (**a**) square wave input signal; (**b**) triangular wave input signal. systems can be determined between 50 Hz and 100 kHz for both branches, using integrators (fractional and integer-order), between 50 Hz and 10 kHz for both branches, including differentiators, between 50 Hz and 10 kHz for the sum of integer-order integrator and fractional-order differentiator, and finally between 50 Hz and 10 kHz for the sum of fractional-order integrator and integer-order differentiator. The signal dynamics overcomes 40 dB in all presented tests. Therefore, large gain variation occurs, and signals reach very low (tens of mV), as well as very high values (hundreds of mV). It should be considered carefully in the design. We evaluated selected results of magnitude and phase frequency response (Figure 22) for interconnection in Figure 7 (Section 4.3).