## 3 Application Examples and Discussion  
To demonstrate the feasibility of the proposed method, we first consider the voltage-mode low active and passive sensitivities band pass filter modified from the filter circuit in Figure 1 of [21], as redrawn in Figure 4a. Its transfer function is given by Equation (7). By using the transformation in Table 1, the obtained circuit with its transfer function given by Equation (8) is shown in Figure 4b. Figure 3: A positive-feedback system with a stable amplifier stage, A, and a frequency-selective network, B. A series nullator-norator pair is added during performing the inverse transformation. By zeroing the input signal source, we obtain the oscillator in Figure 5a. The nullator-norator pair in Figure 5a can be realized by a second generation current conveyor (CCII-) [16], as shown in Figure 5b. Taking into account the non-idealities of a current conveyor, namely \(\mathrm{I}_{\mathrm{Z}}=\pm\alpha\mathrm{I}_{\mathrm{X}}\), \(\mathrm{V}_{\mathrm{X}}=\beta\mathrm{V}_{\mathrm{Y}}\), where \(\alpha=1-\mathrm{e}_{\mathrm{i}}\) and \(\mathrm{e}\) denotes the current tracking error, \(\beta=1-\mathrm{e}_{\mathrm{v}}\) and \(\mathrm{e}_{\mathrm{v}}\) denotes the voltage tracking error of a current conveyor, respectively, the non-ideal characteristic equation of the oscillator is expressed by Equation (9). Its oscillation condition and oscillation frequency \(\omega_{o}\) are given by Equations (10) and (11), respectively. The sensitivities of \(\omega_{o}\) to active and passive components are given in Equation (12). It is clear that the obtained oscillator has identical passive sensitivities and has improved active sensitivities compared to the original band pass filter [21]. In addition, the oscillation frequency and the oscillation condition are independently adjustable through with \(R_{3}\) and \(R_{1}\). In reality, \(R_{1}\) must be slightly greater than \(R_{2}/\alpha_{1}\) for the startup of oscillation [22]. Figure 4: **(a)** A CCII-based band pass filter; **(b)** the obtained filter after applying the transformations in Table 1.  
Figure 5: **(a)** The obtained oscillator; **(b)** realization of the obtained oscillator in **(a)**. \[\frac{V_{out}}{V_{in}}=T(s)=\frac{s\bigg{(}C_{2}\bigg{/}R_{2}\bigg{)}}{s^{2}C_{1}C_{2 }+s\bigg{(}C_{2}\bigg{/}R_{1}\bigg{)}+\bigg{/}R_{2}R_{3}} \tag{7}\]  
\[T^{\prime}\big{(}s\big{)}=-\frac{s\bigg{(}C_{2}\bigg{/}R_{2}\bigg{)}}{s^{2}C_{1}C _{2}+\Bigg{(}\frac{1}{R_{1}}-\frac{1}{R_{2}}\bigg{)}C_{2}s+\frac{1}{R_{2}R_{3}}} \tag{8}\]  
\[s^{2}C_{1}C_{2}+sC_{2}\left(G_{1}-\alpha_{1}G_{2}\right)+\alpha_{1}\alpha_{2} \beta_{1}G_{2}G_{3}=0 \tag{9}\]  
\[G_{1}=\alpha_{1}G_{2} \tag{10}\]  
\[\omega_{0}=\sqrt{\frac{\alpha_{1}\alpha_{2}\beta_{1}G_{2}G_{3}}{C_{1}C_{2}}} \tag{11}\]  
\[S_{\alpha_{1},\alpha_{2},\beta_{1}}^{\mathrm{e_{b}}}=\frac{1}{2};S_{\beta_{2} }^{\mathrm{e_{b}}}=0\]  
Figure 4:0  
The second example considers the single CCII-based voltage-mode band pass filter, which is obtained from [23], as shown in Figure 6a. Using the transformed procedure mentioned in Table 2, the derived circuit with its transfer function shown in Equation (13) is given by Figure 6b. Figure 7a shows the derived oscillator by grounding the input source of the circuit in Figure 6b. The nullator and norator in Figure 7a can be realized by a CCII-, as shown in Figure 7b. The characteristic equation of the obtained oscillator can be expressed by Equation (14). The oscillation condition and the oscillation frequency can be respectively given by Equations (15) and (16) with \(R_{2}=R_{3}=R\) and \(C_{1}=C_{2}=C\). It can be found that the oscillation condition and oscillation frequency are orthogonal adjustable. It must be noted that \(R_{1}\) must be slightly less than \(R/3\) for the startup of oscillation. Figure 4:1  
Figure 4:2  
Figure 4:3  
Figure 4:4
Moreover, it can be found that the oscillator in Figure 7b possesses an electrically controllable function of the oscillation condition by using a controlled current conveyor (CCCII-) to realize the CCII- and \(R_{1}\).