Versatile Voltage-Mode Biquadratic Filter and Quadrature Oscillator Using Four OTAs and Two Grounded Capacitors

: This article presents a versatile voltage-mode (VM) biquad ﬁlter with independently electronic tunability. The proposed structure using one dual-output operational transconductance ampliﬁer, three single-output operational transconductance ampliﬁers (OTAs) and two grounded capacitors was explored to derive a new VM quadrature oscillator with the independent control of the oscillation frequency and the oscillation condition. The proposed versatile VM biquad ﬁlter achieves nearly all of the main advantages: (i) simultaneous realizations of band-reject, band-pass, and low-pass from the same architecture, (ii) multiple-input and multiple-output functions, (iii) independent electronic adjustability of quality factor and resonant angular frequency, (iv) no resistor needed, (v) all input terminals with cascade functions, (vi) no additional inverting ampliﬁer for input signals, (vii) using only grounded capacitors, and (viii) easy to implement a VM quadrature oscillator with independent electronically controlled oscillation frequency and oscillation condition. The proposed versatile VM biquad ﬁlter employs only four OTAs and two grounded capacitors. The active components of the proposed VM biquad ﬁlter are one less than that of recent reports. The proposed circuit also brings versatility and simplicity to the design of VM biquad ﬁlters and VM quadrature oscillators. Filters and oscillators with less active and passive components have the advantages of low cost, low power dissipation, low circuit complexity, and low noise. Commercially available integrated circuit LT1228 and discrete components can be used to implement the proposed OTA-based circuits. The simulation and experiment results validated the theoretical analysis.

On the basis of the input signals, the VM universal biquads with different filtering functions are obtained, which provide the low-pass (LP), high-pass (HP), band-pass (BP), band-reject (BR), and allpass (AP) filtering functions in one circuit architecture. The advantage of the VM multifunction biquad filter is that it can simultaneously form BP, LP, HP and/or BR outputs in the same architecture, which can improve the flexibility and versatility of practical applications. Although three electronically tunable VM biquads based on OTAs have been recently proposed [45][46][47], these proposed circuits cannot realize BR, BP and LP filtering responses simultaneously. In [48,49], two circuit topologies were proposed in 2019 that operated in a versatile VM biquad filter with five OTAs and two grounded capacitors. Both circuits in [48,49] can achieve five standard filter responses, and can independently control the parameters quality factor (Q) and resonance angular frequency (ωo). The circuits have two more important advantages, that is, they can simultaneously realize BR, BP and LP biquad filters in the same architecture, and they can implement a VM quadrature oscillator with independently electronically controlled condition of oscillation (CO) and frequency of oscillation (FO). Basic block diagram of the three-way high-fidelity loudspeaker crossover network and phase sensitive detection (PSD) system. (a) Triple-section crossover network for high-fidelity loudspeakers [4]; and (b) the PSD system [5]. Table 1. Comparisons of the proposed versatile voltage-mode (VM) biquad filter with previous report circuits.

Proposed Versatile VM Biquad Filter
OTA is an active component available on the market, and is frequently utilized in the application and design of electronic controllable circuits. The symbol of OTA is shown in Figure 2a, which is a single current output OTA. Figure 2b shows the symbol for a DO-OTA, which is a dual current output OTA. The dual current outputs of the OTA can be characterized by I O = ±g m (V + − V − ) [34]. The symbol ± shows the polarity of the current output.

Proposed Versatile VM Biquad Filter
OTA is an active component available on the market, and is frequently utilized in the application and design of electronic controllable circuits. The symbol of OTA is shown in Figure 2a, which is a single current output OTA. Figure 2b shows the symbol for a DO-OTA, which is a dual current output OTA. The dual current outputs of the OTA can be characterized by IO = ±gm (V+ − V−) [34]. The symbol ± shows the polarity of the current output.  Figure 3 shows the proposed versatile VM OTA-C biquad. It employs one DO-OTA, three OTAs and two grounded capacitors with four input signals and three output signals. The routine analysis of the circuit in Figure 3 can derive the following three output voltage signals: From Equations (1)-(3), there are two different possibilities to realize the VM multifunction biquad according to input and output conditions as follows.

Proposed Versatile VM Biquad Filter
OTA is an active component available on the market, and is frequently utilized in the application and design of electronic controllable circuits. The symbol of OTA is shown in Figure 2a, which is a single current output OTA. Figure 2b shows the symbol for a DO-OTA, which is a dual current output OTA. The dual current outputs of the OTA can be characterized by IO = ±gm (V+ − V−) [34]. The symbol ± shows the polarity of the current output.    m3  m2  m1  m4  m1  1  m3  2  1   2   i4  i3  m4  m3  m1  i2  m3  m2  m1  i1  m3  m1  2   Case I: If V i1 = V i2 = V i4 = 0 (grounded) and V i3 = input voltage signal (V in ), then three biquadratic filtering functions can be obtained as shown in Equations (4)-(6): V o1 V in = g m1 g m3 g m4 s 2 C 1 C 2 g m3 + sC 1 g m1 g m4 + g m1 g m2 g m3 (4) V o2 V in = −sC 1 g m3 g m4 s 2 C 1 C 2 g m3 + sC 1 g m1 g m4 + g m1 g m2 g m3 (5) V o3 V in = s 2 C 1 C 2 g m3 + g m1 g m2 g m3 s 2 C 1 C 2 g m3 + sC 1 g m1 g m4 + g m1 g m2 g m3 (6) As indicated in Equations (4)-(6), a non-inverting LP filtering function is obtained from V o1 , an inverting BP (IBP) filtering function is obtained from V o2 , and a non-inverting BR filtering function is obtained from V o3 .
With the inspection of Equations (1)-(3), the filter parameters ω o and Q are obtained as From Equation (7), the filter parameter ω o can be tuned through the g m1 and g m2 first and the filter parameter Q can be adjusted independently through g m3 and/or g m4 without disturbing ω o . Moreover, by selecting g m1 = g m2 = g m and C 1 = C 2 = C, the parameters of ω o and Q in Equation (7) are expressed as Equation (8) shows that the filter parameters of ω o and Q can be non-interactively electronically tuned by varying g m , g m3 and/or g m4 . This means that the parameters ω o and Q of the VM biquad filter can be independently controlled.
Case II: According to Equation (3), with g m1 = g m3 and g m2 = g m4 = kg m1 , the voltage transfer function is as where k is a scaling factor, τ 1 = C 1 g m2 and τ 2 = C 2 g m1 are the realized time-constants. The specializations of the numerator in Equation (9) results in the VM universal biquad standard filtering functions: Obviously, the proposed versatile VM biquad can be used as a multifunction filter with single input and three outputs, as well as a universal filter with four inputs and a single output. Therefore, the proposed VM biquad has more versatility than a single-input-three-output multifunction VM biquad or a multiple-input-single-output universal VM biquad.

Modification of Proposed Filter as VM Quadrature Oscillator
By connecting node V o2 to V i4 and leaving the other voltage inputs as zero in the circuit in Figure 3, the VM quadrature oscillator can be obtained as illustrated in Figure 4. The characteristic equation of the VM quadrature oscillator is obtained in Figure 4: Based on Equation (10), the CO and the FO are: FO: m3 m1 g g ≤ (12) From Equations (11) and (12), the CO can be set by gm2 without affecting the FO. The FO can also be set by gm3 without affecting the CO. Thus, the proposed VM quadrature oscillator supplies the independent control of CO and FO. The relationship between the voltage outputs Vo1 and Vo2 of Figure 4 is represented by the following expression: From Equation (13), the output voltages Vo1 and Vo2 have a phase difference of 90° and are called quadrature signals. The phase of output Vo1 leads the phase of output voltage Vo2 by 90°.

Effect of the Parasitic Impedances in OTA
An ideal DO-OTA is a voltage-controlled current source, with unlimited bandwidth, and unlimited input and output impedance. The non-ideal dual-output currents of DO-OTA are characterized as IO+ = αgm(V+ − V−) and IO− = −βgm(V+ − V−), where α = 1 − εαi and β = 1 − εβi. Here, εαi (|εαi| « 1) and εβi (|εβi| « 1) represent non-ideal DO-OTA current tracking errors. Practically, the performances of the proposed circuits are affected by the internal current tracking errors and the parasitic terminal impedances of the DO-OTA. Figure 5 shows the non-ideal DO-OTA model. The effect of current tracking error and parasitic impedance on the parameters of ωo and Q has been investigated to indicate the performance of the filter. For example, if the parasitic effect is considered, and the parasitic capacitance and parasitic resistance are added to Figure 3, the new topology is shown in Figure 6. The influences of the parasitic impedances of V+1, V−2, V+3 and V+4 terminals will be negligible because they are connected to input voltage source. Taking into account the current tracking errors and parasitic elements shown in Figure 6 and reanalyzing the versatile VM biquadratic filter, the following characteristic equation D(s) is obtained: Based on Equation (10), the CO and the FO are: FO : g m1 ≤ g m3 (12) From Equations (11) and (12), the CO can be set by g m2 without affecting the FO. The FO can also be set by g m3 without affecting the CO. Thus, the proposed VM quadrature oscillator supplies the independent control of CO and FO. The relationship between the voltage outputs V o1 and V o2 of Figure 4 is represented by the following expression: From Equation (13), the output voltages V o1 and V o2 have a phase difference of 90 • and are called quadrature signals. The phase of output V o1 leads the phase of output voltage V o2 by 90 • .

Effect of the Parasitic Impedances in OTA
An ideal DO-OTA is a voltage-controlled current source, with unlimited bandwidth, and unlimited input and output impedance. The non-ideal dual-output currents of DO-OTA are characterized as Here, ε αi (|ε αi | « 1) and ε βi (|ε βi | « 1) represent non-ideal DO-OTA current tracking errors. Practically, the performances of the proposed circuits are affected by the internal current tracking errors and the parasitic terminal impedances of the DO-OTA. Figure 5 shows the non-ideal DO-OTA model. The effect of current tracking error and parasitic impedance on the parameters of ω o and Q has been investigated to indicate the performance of the filter. For example, if the parasitic effect is considered, and the parasitic capacitance and parasitic resistance are added to Figure 3, the new topology is shown in Figure 6. The influences of the parasitic impedances of V +1 , V −2 , V +3 and V +4 terminals will be negligible The following conditions should be satisfied for a biquad filter: The following conditions should be satisfied for a biquad filter: where The following conditions should be satisfied for a biquad filter: Electronics 2020, 9, 1493 9 of 27 sC 3p + G 3p << g m3 (17) Under these conditions in Equations (15)- (17), the modified characteristic equation D 1 (s) is determined as D 1 (s) = α 3 s 2 C 1 C 2 g m3 + β 1 α 4 sC 1 g m1 g m4 + α 1 α 2 α 3 g m1 g m2 g m3 (18) From (18), the modified biquadratic filter parameters of ω o and Q are obtained by The active and passive sensitivities of the biquadratic filter parameters ω o and Q in Equation (19) remain less than or equal to one in magnitude. Hence, the proposed filter has a good sensitivity performance.

Simulation and Experimental Results
Simulation and measurement are essential to verify the theoretical analysis. The theoretical analysis of the proposed filter in Figure 3 and the oscillator in Figure 4 is verified by using PSpice for simulation and commercial LT1228 OTA for implementation. The experimental power supply voltages were ±15 V. According to the LT1228 datasheet [50], the transconductance gain is given by g m = 10 I SET , where I SET is the bias current of LT1228. This feature makes it useful for the electronic control of transconductance gain.

Versatile VM Biquad Filter Simulation and Experimental Results
The proposed filter is verified by simulation and experimental results. The filter was designed to obtain the natural frequency of f o = 144.7 kHz and Q = 1. In this case, the passive component values of Figure 3 were chosen as C 1 = C 2 = 2.2 nF and g m1 = g m2 = g m3 = g m4 = 2 mS (i.e., I b = 200 uA). Figures 7-9 show the gain and phase of simulation and measurement responses of LP (V o1 ), IBP (V o2 ), and BR (V o3 ) filters, respectively, as depicted in Equations (4)- (6). Figures 10-14 show the gain and phase responses of the simulation and measurement of LP, BP, IBP, IHP, and AP filters, respectively. The simulation and measurement results are in accordance with the theoretical value of Equation (9). The power consumption of simulation and measurement are approximately 0.92 W and 1.23 W, respectively. To verify the tunable electronic property of parameter f o without affecting the parameter Q, the tuning transconductance gains, g m1 = g m2 , were simultaneously changed to 1.5 mS, 2 mS and 3 mS, while keeping C 1 = C 2 = 2.2 nF, and g m3 = g m4 = 2 mS for constant Q = 1. Figure 15 shows the simulated and measured gain responses of the BP responses on the V o3 output terminal when V i4 = V in and V i1 = V i2 = V i3 = 0. This illustrates the tunable property of parameter f o without affecting parameter Q. However" to verify the tunable electronic property of parameter Q without affecting parameter f o , the transconductance gain g m4 was given as 2 mS, 1.5 mS and 1 mS, while keeping C 1 = C 2 = 2.2 nF and g m1 = g m2 = g m3 = 2 mS for constant f o = 144.7 kHz. Figure 16 shows the simulated and measured frequency gain responses of the BP responses on the V o3 output terminal when V i4 = V in and V i1 = V i2 = V i3 = 0. This illustrates the tunable property of parameter Q without affecting the parameter f o . These results show that by using various values of g m4 , the parameter Q can be easily adjusted without affecting the parameter f o , as explained in Equation (7).                                  To verify the input dynamic range of the proposed filter, the simulation was repeated for a sinusoidal input signal with fo = 144.69 kHz. Figure 17 shows the input signal and output signal transient waveforms of the BP response on the Vo3 output terminal when Vi4 = Vin and Vi1 = Vi2 = Vi3 = 0. The expansion amplitude is 120 mVpp (peak to peak) without signification distortion. The dependence of the Vo3 output harmonic distortion of the BP responses on input voltage amplitude is illustrated in Figure 18. Figure 18 shows that the total harmonic distortion (THD) is about 3.83% when the input signal increases to 170 mVpp. For the experimental testing, Figure 19 shows the measured input and output voltage waveforms for the BP response, which can be extended to an amplitude of 120 mVpp without signification distortion. Figure 20 shows the spectrum of the BP response of Figure  19. The measured angular frequency is about 144 kHz, which is close to the theoretical value of 144.69 kHz and the error rate is 0.48%. The THD, including the first harmonic to the fifth harmonic components of Figure 20, is about 2.13%. To verify the linear performance of the proposed filter, the 1 dB compression point of the circuit characteristics must be evaluated. Figure 21 shows the measured P1dB of the BP filter output voltage Vo3 by applying input power at an angular frequency of 144.69 kHz, when Vi4 = Vin, and Vi1 = Vi2 = Vi3 = 0. As shown in Figure 21, relative to the output power, the measured P1dB of BP filter is about −5.9 dBm. Furthermore, to represent the nonlinearity of the filter proposed in Figure 3, a two-tone test of intermodulation distortion (IMD) was used to characterize the nonlinearity of the BP response. Figure 22 shows the frequency spectrum of the BP response at the Vo3 output terminal, where Vi4 = Vin, and Vi1 = Vi2 = Vi3 = 0. The BP filter has inter-modulation characteristics by applying two-tone signals around 144.69 kHz. In Figure 22  To verify the input dynamic range of the proposed filter, the simulation was repeated for a sinusoidal input signal with f o = 144.69 kHz. Figure 17 shows the input signal and output signal transient waveforms of the BP response on the V o3 output terminal when V i4 = V in and V i1 = V i2 = V i3 = 0. The expansion amplitude is 120 mV pp (peak to peak) without signification distortion. The dependence of the V o3 output harmonic distortion of the BP responses on input voltage amplitude is illustrated in Figure 18. Figure 18 shows that the total harmonic distortion (THD) is about 3.83% when the input signal increases to 170 mV pp . For the experimental testing, Figure 19 shows the measured input and output voltage waveforms for the BP response, which can be extended to an amplitude of 120 mV pp without signification distortion. Figure 20 shows the spectrum of the BP response of Figure 19. The measured angular frequency is about 144 kHz, which is close to the theoretical value of 144.69 kHz and the error rate is 0.48%. The THD, including the first harmonic to the fifth harmonic components of Figure 20, is about 2.13%. To verify the linear performance of the proposed filter, the 1 dB compression point of the circuit characteristics must be evaluated. Figure 21 shows the measured P1dB of the BP filter output voltage V o3 by applying input power at an angular frequency of 144.69 kHz, when V i4 = V in , and V i1 = V i2 = V i3 = 0. As shown in Figure 21, relative to the output power, the measured P1dB of BP filter is about −5.9 dBm. Furthermore, to represent the nonlinearity of the filter proposed in Figure 3, a two-tone test of intermodulation distortion (IMD) was used to characterize the nonlinearity of the BP response. Figure 22 shows the frequency spectrum of the BP response at the V o3 output terminal, where V i4 = V in , and V i1 = V i2 = V i3 = 0. The BP filter has inter-modulation characteristics by applying two-tone signals around 144.69 kHz. In Figure 22                To collect statistics on the effects of mismatch and change in Figure 3, Monte-Carlo simulations were performed by choosing a 5% tolerance for the capacitor values in Figure 3 and running 100 times in each case. The results when the two capacitor values are 5% Gaussian deviation are shown in Figure 23. In Figure 23, the center frequency of the nominal design was f o = 144.7 kHz by choosing C 1 = C 2 = 2.2 nF and g mi = 2 mS (i = 1 to 4), and the Monte-Carlo analysis shows the median value of 141.8 kHz. The results show that the center frequency achieved by the mismatch of two capacitor values in the proposed circuit has little effect and is completely within the acceptable range. According the Monte-Carlo simulation, as the center frequency varies between 125 and 162.7 kHz, the f o -value of the BP response on the V o3 output terminal was affected in the range of −13.8-12.2%. To collect statistics on the effects of mismatch and change in Figure 3, Monte-Carlo simulations were performed by choosing a 5% tolerance for the capacitor values in Figure 3 and running 100 times in each case. The results when the two capacitor values are 5% Gaussian deviation are shown in Figure 23. In Figure 23, the center frequency of the nominal design was fo = 144.7 kHz by choosing C1 = C2 = 2.2 nF and gmi = 2 mS (i = 1 to 4), and the Monte-Carlo analysis shows the median value of 141.8 kHz. The results show that the center frequency achieved by the mismatch of two capacitor values in the proposed circuit has little effect and is completely within the acceptable range. According the Monte-Carlo simulation, as the center frequency varies between 125 and 162.7 kHz, the fo-value of the BP response on the Vo3 output terminal was affected in the range of −13.8-12.2%.

VM Quadrature Oscillator Simulation and Experimental Results
To confirm the theoretical analysis, the oscillator in Figure 4 is designed as C1 = C2 = 3 nF and gm1 = gm2 = gm4 = 1 mS. In practice, to ensure that the oscillation starts, consider that the value of gm3 = 1.013 mS is greater than gm1. Figure 24 shows the simulated waveforms of the quadrature voltage outputs Vo1 and Vo2 at steady state. The simulated oscillation frequency in Figure 24 is 52.18 kHz, which is close to the theoretical value of 53 kHz. The error percentage between the theoretical and simulated oscillation frequency is −1.5%. In the experimental test, the measured oscillation frequency is 53.28 kHz, which is close to the theoretical value of 53 kHz and the error rate is 0.53%, as shown in Figure  25. The frequency spectrum of the oscillator output voltage, Vo2, is shown in Figure 26. The measured oscillation frequency is 53.56 kHz, which is closed to theoretical value of 53 kHz, and the error rate is 1.06%. The THD in Figure 26 is about 2.8%. Figure 27 shows the simulation and experimental results   126.92 130.67 134.42138.17 141.92 145.67149.42 153.17

VM Quadrature Oscillator Simulation and Experimental Results
To confirm the theoretical analysis, the oscillator in Figure 4 is designed as C 1 = C 2 = 3 nF and g m1 = g m2 = g m4 = 1 mS. In practice, to ensure that the oscillation starts, consider that the value of g m3 = 1.013 mS is greater than g m1 . Figure 24 shows the simulated waveforms of the quadrature voltage outputs V o1 and V o2 at steady state. The simulated oscillation frequency in Figure 24 is 52.18 kHz, which is close to the theoretical value of 53 kHz. The error percentage between the theoretical and simulated oscillation frequency is −1.5%. In the experimental test, the measured oscillation frequency is 53.28 kHz, which is close to the theoretical value of 53 kHz and the error rate is 0.53%, as shown in Figure 25. The frequency spectrum of the oscillator output voltage, V o2 , is shown in Figure 26. The measured oscillation frequency is 53.56 kHz, which is closed to theoretical value of 53 kHz, and the error rate is 1.06%. The THD in Figure 26 is about 2.8%. Figure 27 shows the simulation and experimental results of the oscillation frequency obtained by varying the values of g m2 with C 1 = C 2 = 1nF (or 3 nF), g m1 = g m4 = 1 mS and g m3 = 1.013 mS. When the tuning transconductance gain, g m2 is in the range of 0.5-5 mS, to start and maintain the sine wave oscillation under the same oscillation condition, the electronic tuning oscillation frequency range of the oscillator will be between 37.95 kHz and 355.88 kHz. The simulation and experimental results are consistent with the theoretical values. For wideband frequency adjustment and amplitude stabilization, the automatic gain control (AGC) system is required. Therefore, an additional auxiliary AGC circuit and technology are necessary. The AGC circuit can improve the unbalance of the voltage amplitude generated and can reduce the THD to achieve better performance. This technique has been presented in the literature [31]. Figures 28  and 29 show how to calculate phase noise using the Agilent's phase noise measurement solution. In Figures 28 and 29, the phase noise of the proposed oscillator is lower than −75.42 dBc/Hz (at 1 kHz offset) and −96.71 dBc/Hz (at 10 kHz offset), respectively.              Finally, the experimental test bench for the versatile VM biquadratic filter and quadrature oscillator is shown in Figure 30. In Figure 30, the experimental test bench includes a printed circuit board, a power supply, an oscilloscope, a network analyzer, and a signal analyzer. An oscilloscope is used to measure the time-domain of filter and oscillator waveforms. A network analyzer is used to measure the frequency-domain of the filter gain and phase responses. A signal analyzer is used to measure the frequency spectrum and analyze phase noise. Figures 31-40 show the filter measurement results of the network analyzer. In Figures 31-40, the authors have exported measurement data and added them as additional traces to  in order to compare the theoretical analysis.
board, a power supply, an oscilloscope, a network analyzer, and a signal analyzer. An oscilloscope is used to measure the time-domain of filter and oscillator waveforms. A network analyzer is used to measure the frequency-domain of the filter gain and phase responses. A signal analyzer is used to measure the frequency spectrum and analyze phase noise. Figures 31-40 show the filter measurement results of the network analyzer. In Figures 31-40

Conclusions
In this paper, a configuration for realizing a versatile VM biquad filter with independent electronic tunability and a VM quadrature oscillator with the independent control of CO and FO using OTAs was presented. The proposed versatile VM biquad filter simultaneously exhibits BR, BP and LP filters by using one DO-OTA, three OTAs and two grounded capacitors. The proposed versatile VM biquad filter enjoys the following advantages: (i) four active components and two grounded capacitors are used, (ii) three basic filter responses with a single input and three outputs can be realized, (iii) LP, BP, IBP, HP, BR and AP filter responses can be realized by selecting different four input voltage signals, (iv) have multiple-input and multiple-output functions, (v) have independently and electronically controllable characteristic parameters ωo and Q, (vi) all input terminals have cascade function, and (vii) there is no extra inverting amplifiers for special input signals. The proposed VM quadrature sinusoidal oscillator is based on the proposed VM biquad filter structure. The proposed VM quadrature oscillator provides two sinusoidal output voltages with a phase difference of 90° and only uses grounded capacitors. CO and FO can be independently and electronically controlled. To the best knowledge of the authors, all these properties cannot be obtained simultaneously by any previously known OTA-based VM biquad filters. It must be

Conclusions
In this paper, a configuration for realizing a versatile VM biquad filter with independent electronic tunability and a VM quadrature oscillator with the independent control of CO and FO using OTAs was presented. The proposed versatile VM biquad filter simultaneously exhibits BR, BP and LP filters by using one DO-OTA, three OTAs and two grounded capacitors. The proposed versatile VM biquad filter enjoys the following advantages: (i) four active components and two grounded capacitors are used, (ii) three basic filter responses with a single input and three outputs can be realized, (iii) LP, BP, IBP, HP, BR and AP filter responses can be realized by selecting different four input voltage signals, (iv) have multiple-input and multiple-output functions, (v) have independently and electronically controllable characteristic parameters ωo and Q, (vi) all input terminals have cascade function, and (vii) there is no extra inverting amplifiers for special input signals. The proposed VM quadrature sinusoidal oscillator is based on the proposed VM biquad filter structure. The proposed VM quadrature oscillator provides two sinusoidal output voltages with a phase difference of 90° and only uses grounded capacitors. CO and FO can be independently and electronically controlled. To the best knowledge of the authors, all these properties cannot be obtained simultaneously by any previously known OTA-based VM biquad filters. It must be

Conclusions
In this paper, a configuration for realizing a versatile VM biquad filter with independent electronic tunability and a VM quadrature oscillator with the independent control of CO and FO using OTAs was presented. The proposed versatile VM biquad filter simultaneously exhibits BR, BP and LP filters by using one DO-OTA, three OTAs and two grounded capacitors. The proposed versatile VM biquad filter enjoys the following advantages: (i) four active components and two grounded capacitors are used, (ii) three basic filter responses with a single input and three outputs can be realized, (iii) LP, BP, IBP, HP, BR and AP filter responses can be realized by selecting different four input voltage signals, (iv) have multiple-input and multiple-output functions, (v) have independently and electronically controllable characteristic parameters ω o and Q, (vi) all input terminals have cascade function, and (vii) there is no extra inverting amplifiers for special input signals. The proposed VM quadrature sinusoidal oscillator is based on the proposed VM biquad filter structure. The proposed VM quadrature oscillator provides two sinusoidal output voltages with a phase difference of 90 • and only uses grounded capacitors. CO and FO can be independently and electronically controlled. To the best knowledge of the authors, all these properties cannot be obtained simultaneously by any previously known OTA-based VM biquad filters. It must be emphasized that the proposed versatile VM biquad filter employs only four OTAs and two grounded capacitors, and its active component is one less than that of the recently proposed VM biquad filter in the open literature [47][48][49]. It also brings versatility and simplicity to the design of the VM biquad filter and VM quadrature oscillator. VM biquad filters and VM quadrature oscillators using less active and passive components have the advantages of low cost, low power dissipation, low circuit complexity, and low noise. The simulation and experimental results also confirm the theoretical analysis.