## 1 Introduction  
The LT1228 is a commercial integrated circuit (IC) using bipolar or complementary metal oxide semiconductor (CMOS) technology. It combines a transconductance amplifier (OTA) and a current feedback amplifier (CFA). LT1228 is one of the attractive components used for realizing voltage-mode (VM) analog circuits. It has wider electronic tunability, higher accuracy, higher frequency applicability and simplicity of implementation, so many topologies based on LT1228 application circuits have been published in the literature [1, 2, 3, 4, 5, 6, 7, 8]. In addition, many active filters and oscillators based on different active components have also been presented in the literature, and they have been widely used in signal generation applications [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. An active VM non-inverting bandpass filter (NBPF) is one of the important filters for analog signal processing, and its transfer function can be expressed as  
\[\frac{\mathrm{V_{NBPF}}}{\mathrm{V_{in}}}=\frac{\mathrm{ds}}{\mathrm{as}^{2}+ \mathrm{bs}+\mathrm{c}} \tag{1}\]where the coefficients \(\mathrm{a}\), \(\mathrm{b}\), \(\mathrm{c}\) and \(\mathrm{d}\) are real numbers, \(\mathrm{V}_{\mathrm{in}}\) is the NBPF input signal and \(\mathrm{V}_{\mathrm{NBPF}}\) is the output response. According to the feedback theory, the VM quadrature sinusoidal oscillator (QSO) can be synthesized by connecting the input voltage of the NBPF to the output response. Therefore, Equation (1) can be rewritten as Equation (2):  
\[[\mathrm{as}^{2}+(\mathrm{b}-\mathrm{d})\mathrm{s}+\mathrm{c}]\mathrm{V}_{ \mathrm{NBPF}}=0 \tag{2}\]  
Based on Equations (1) and (2), the VM QSO can be realized by zeroing the input voltage of the NBPF, and the characteristic equation (CE) of the VM QSO can be expressed as Equation (3):  
\[\mathrm{CE}:\ \mathrm{as}^{2}+(\mathrm{b}-\mathrm{d})\mathrm{s}+\mathrm{c}=0 \tag{3}\]  
The two poles of Equation (3) are obtained as follows:  
\[\mathrm{s}_{1,2}=\frac{-(\mathrm{b}-\mathrm{d})\pm\sqrt{\left(\mathrm{b}- \mathrm{d}\right)^{2}-4\mathrm{ac}}}{2\mathrm{a}}=\frac{(\mathrm{d}-\mathrm{ b})}{2\mathrm{a}}\pm\mathrm{j}\sqrt{\frac{\mathrm{c}}{\mathrm{a}}-(\frac{ \mathrm{d}-\mathrm{b}}{2\mathrm{a}})^{2}} \tag{4}\]  
In Equation (3), the oscillator will oscillate if the condition of oscillation (CO) and the frequency of oscillation (FO) are as given by Equations (5) and (6), respectively:  
\[\mathrm{CO}:\ \mathrm{b}=\mathrm{d} \tag{5}\]  
\[\mathrm{FO}:\ \mathrm{\omega_{O}}^{2}=\frac{\mathrm{c}}{\mathrm{a}} \tag{6}\]  
For a positive feedback system, if the two poles of Equation (4) are located in the right half of the complex plane, the circuit can be built, and the sinusoidal oscillation can be maintained. Therefore, the CO of Equation (5) is modified to become Equation (7):  
\[\mathrm{CO}:\ \mathrm{b}\leq\mathrm{d} \tag{7}\]  
Recently, two interesting VM circuits were proposed in the literature [21; 22]. The circuit proposed in [21] employs five OTAs combined with two grounded capacitors. The circuit proposed in [22] also employs five OTAs combined with two grounded capacitors. However, the passband gain of these two circuits cannot be adjusted independently without affecting the quality factor (Q) and resonance angular frequency (\(\mathrm{\omega_{O}}\)), and it cannot be transformed into an electronically controllable QSO with an independent amplitude control function [21; 22]. An interesting VM QSO with gain controllability of the quadrature voltage output was recently proposed in [23]. The circuit in Figure 5 of [23] employs three LT1228s, two grounded capacitors, two grounded resistors and three floating resistors, but the resistances of the circuit in Figure 5 of [23] are not the smallest. According to the feedback theory, this study proposes isomorphic circuits of the VM NBPFs and VM QSOs with independent amplitude control functionality. Each of the isomorphic circuits contains three LT1228 commercial ICs, two grounded capacitors, two grounded resistors and one floating resistor.