Single VDGA-Based Mixed-Mode Universal Filter and Dual-Mode Quadrature Oscillator

This article presents the circuit designs for a mixed-mode universal biquadratic filter and a dual-mode quadrature oscillator, both of which use a single voltage differencing gain amplifier (VDGA), one resistor, and two capacitors. The proposed circuit has the following performance characteristics: (i) simultaneous implementation of standard biquadratic filter functions with three inputs and two outputs in all four possible modes, namely, voltage-mode (VM), current-mode (CM), trans-admittance-mode (TAM), and trans-impedance-mode (TIM); (ii) electronic adjustment of the natural angular frequency and independently single-resistance controllable high-quality factor; (iii) performing a dual-mode quadrature oscillator with simultaneous voltage and current output responses; (iv) orthogonal resistive and/or electronic control of the oscillation condition and frequency; (v) employing all grounded passive components in the quadrature oscillator function; and (vi) simpler topology due to the use of a single VDGA. VDGA non-idealities and parasitic elements are also investigated and analyzed in terms of their influence on circuit performance. To prove the study hypotheses, computer simulations with TSMC 0.18 μm CMOS technology and experimental confirmatory testing with off-the-shelf integrated circuits LM13600 have been performed.


Introduction
Universal filters are useful active filters that permit all the five typical biquadratic filter functions simultaneously, namely low-pass (LP), band-pass (BP), high-pass (HP), band-stop (BS), and all-pass (AP) responses with the same topology. These circuits are frequently used in the design of a wide variety of electronic instruments, data communications, and control systems since they enable the implementation of various filtering functions based on port selections. In many analog signal processing applications, an active mixed-mode universal biquadratic filter (MUBF) with input voltages and/or currents, and output voltages and/or currents, is necessarily required. Over the last decade, numerous universal biquad filter realizations in mixed-mode operations based on different active components have already been developed in .
Two periodic waveforms having a 90 • phase difference, known as a quadrature oscillator (QO), are frequently required in the design of electronic communication systems. QOs have applications in communication systems to operate quadrature mixers, in instrumentation and measurement systems to test and diagnose electronic devices and circuits, as well as in single-sideband generators. Interesting QO circuits have been reported in the literature, which includes realizations using various active building blocks [32][33][34][35][36][37][38][39][40].
Note that the above-mentioned realizations only work with the mixed-mode universal biquad filter or the QO circuit. Interestingly, [41][42][43][44][45][46][47][48][49][50] suggest circuit realizations that can perform both universal biquad filter and QO with the same circuit design. A comparison of available     Notes: Y = Yes, N = No, N/A = not available, "-" = not realized, R = resistor, C = capacitor, Rmos = MOS-based electronic resistor, OTA = operational transconductance amplifier, DO-OTA = dual-output OTA, MO-OTA = multiple-output OTA, MI-OTA = multiple-input OTA, CCII = second-generation current conveyor, MO-CCII = multiple-output CCII, DP-CCII = digitally programmable current conveyor, DO-CCCII = dual-output second-generation current-controlled conveyor, MO-CCCII = multiple-outputs current-controlled conveyor, FDCCII = fully differential current conveyor, CFOA = current feedback operational amplifier, SCFOA = specific CFOA, UGC = unity-gain cell, DVCC = differential voltage current conveyor, DDCC = differential difference current conveyor, DVCCTA = differential voltage current conveyor transconductance amplifier, DVCCCTA = differential voltage current-controlled conveyor transconductance amplifier, CCCCTA = current controlled current conveyor transconductance amplifier, VDTA = voltage differencing transconductance amplifier, VDGA = voltage differencing gain amplifier, DPCF = digitally programmable current follower, VF = voltage follower, DXCCDITA = dual X current conveyor differential input transconductance amplifier, VCII = second-generation voltage conveyor, I-CB = inverting current buffer, VD-DXCC = voltage differencing dual X current conveyor, EXCCTA = extra X current conveyor transconductance amplifier, VD-EXCCII = voltage differencing extra X CCII, EX-CCCII = extra X CCCII, VDBA = voltage differencing buffered amplifier, CDTA = current differencing transconductance amplifier, CCFTA = current-controlled current follower transconductance amplifier, VDDDA = voltage differencing differential difference amplifier. A voltage differencing gain amplifier (VDGA), a recently introduced active element, was introduced in 2013 [51], and has since been used in a variety of analog signal processing applications [52][53][54][55][56]. As previously stated, we found that no attempts have been made to use a single VDGA to implement both MUBF and DMQO with the same configuration. Considering the growing interest in multiple-mode signal processing, this work therefore proposes a MUBF and DMQO circuit designed using a single VDGA. The circuit makes use of only one resistor and two capacitors as passive components. By significantly modifying the design, the proposed circuit can be categorized as either a MUBF or a DMQO. For the proposed mixed-mode filter, it can perform VM, CM, TAM, and TIM biquadratic filters with an orthogonally controlled the natural angular frequency and the quality factor. Furthermore, the high-Q filter may be easily implemented with a single resistor. For the proposed DMQO, the oscillation condition and the oscillation frequency are separately programmable. The performance of the proposed MUBF and DMQO circuit is illustrated by PSPICE simulation results. To further demonstrate the practicability of the circuit, the experimental test results using commercially available ICs are also conducted.

Overview of VDGA
The VDGA device, which was recently described in [51], is a versatile active element. A wide range of VDGA-based analog signal processing solutions, including active universal filters [52,53], quadrature oscillators [54,55], and tunable capacitance multiplier [56], have been developed in the technical literature. Its schematic representation is illustrated in Figure 1, with p and n representing high-impedance voltage input terminals, z+, z−, x, and o representing high-impedance current output terminals, and w representing a lowimpedance voltage output terminal. The ideal terminal property of the VDGA element is represented by the matrix expression [51]: where g mk (k = A, B, C) is the transconductance gain and β is the transfer voltage gain of the VDGA.

Overview of VDGA
The VDGA device, which was recently described in [51], is a versatile active element. A wide range of VDGA-based analog signal processing solutions, including active universal filters [52,53], quadrature oscillators [54,55], and tunable capacitance multiplier [56], have been developed in the technical literature. Its schematic representation is illustrated in Figure 1, with p and n representing high-impedance voltage input terminals, z+, z−, x, and o representing high-impedance current output terminals, and w representing a low-impedance voltage output terminal. The ideal terminal property of the VDGA element is represented by the matrix expression [51]: where gmk (k = A, B, C) is the transconductance gain and β is the transfer voltage gain of the VDGA.  Figure 2 shows the probable CMOS-built VDGA internal circuit implementation, which comprises three voltage-controlled floating current sources M1k-M9k. Each M1k-M9k implements the corresponding independent adjustable transconductance gmk, as written below [57]: where ik ox Bk μ is the effective channel electronic mobility, Cox is the gate-oxide capacitance per unit  Figure 2 shows the probable CMOS-built VDGA internal circuit implementation, which comprises three voltage-controlled floating current sources M 1k -M 9k . Each M 1k -M 9k implements the corresponding independent adjustable transconductance g mk , as written below [57]: where µ is the effective channel electronic mobility, C ox is the gate-oxide capacitance per unit area, and W and L are the respective channel width and length of M 1k -M 4k . Because each transconductance g ik is proportional to the square root of the bias current I Bk , the value of g mk may be electronically scaled using Equations (2) and (3). A current-controlled voltage amplifier is also accomplished in Figure 2 Figure 3 depicts the proposed universal filter configuration, which consists of a single VDGA, one resistor, and two capacitors. This configuration can be used to implement the mixed-mode universal biquad filter, which includes VM, CM, TAM, and TIM, by selecting appropriate input and output signals, as detailed below.  VM universal biquadratic filter: With iin = 0, all the five general voltage-mode biquadratic filter functions for this three-input two-output universal filter can be achieved as follows.

Proposed Mixed-Mode Universal Biquadratic Filter
• With vin = vi3 (input voltage) and vi1 = vi2 = 0 (grounded), the following LP and BP filter responses are obtained from vo1 and vo2, respectively: and • With vin = vi2 and vi1 = vi3 = 0, the HP response is obtained from vo2, as given by:  Figure 3 depicts the proposed universal filter configuration, which consists of a single VDGA, one resistor, and two capacitors. This configuration can be used to implement the mixed-mode universal biquad filter, which includes VM, CM, TAM, and TIM, by selecting appropriate input and output signals, as detailed below.  Figure 3 depicts the proposed universal filter configuration, which consists of a single VDGA, one resistor, and two capacitors. This configuration can be used to implement the mixed-mode universal biquad filter, which includes VM, CM, TAM, and TIM, by selecting appropriate input and output signals, as detailed below.  VM universal biquadratic filter: With iin = 0, all the five general voltage-mode biquadratic filter functions for this three-input two-output universal filter can be achieved as follows.

Proposed Mixed-Mode Universal Biquadratic Filter
• With vin = vi3 (input voltage) and vi1 = vi2 = 0 (grounded), the following LP and BP filter responses are obtained from vo1 and vo2, respectively: and • With vin = vi2 and vi1 = vi3 = 0, the HP response is obtained from vo2, as given by: VM universal biquadratic filter: With i in = 0, all the five general voltage-mode biquadratic filter functions for this three-input two-output universal filter can be achieved as follows.

•
With v in = v i3 (input voltage) and v i1 = v i2 = 0 (grounded), the following LP and BP filter responses are obtained from v o1 and v o2 , respectively: and and v i1 = v i3 = 0, the HP response is obtained from v o2 , as given by: , and v i3 = 0, the BS response is obtained from v o2 , as given by: , the AP response is also obtained from v o2 , as given by: In Equations (4)-(8), the transfer functions T LP (s), T BP (s), T HP (s), T BS (s), and T AP (s), are as follows. and Equation (4) reveals that the circuit implements the inverted LP filter function with a passband gain of 1/g mC R, whereas the others, represented by Equations (5)-(8), have a passband gain of unity. For the VM operation, no element-matching requirements are needed.
CM universal biquadratic filter: The proposed circuit in Figure 3 can be changed into a CM universal biquad with v i1 = v i2 = v i3 = 0. The five generic current-mode biquad transfer functions realized by this configuration are expressed as follows. and where the passband gain of the BP response is equal to g mA R. Furthermore, the BS response may be realized by simply adding the currents i o1 and i o3 to realize the following current transfer function: Similarly, by retaining g mA R = 1, the AP current response may be obtained by connecting the three currents i o1 , i o2 , and i o3 to obtain the following transfer function: TAM universal biquadratic filter: With v in = v i3 , v i1 = v i2 = 0, and i in = 0, the TAM filter functions are: and Equation (21) represents the TAM filter function of the BP response with an electronically controlled passband gain of g mA . The passband gains for the LP, HP, BS, and AP filter responses are equal to 1/R. It should be noticed from Equation (24) that, in the case of AP filter realization, a simple element condition, g mA R = 1, is necessary.
TIM universal biquadratic filter: According to Figure 3, if v i1 = v i2 = v i3 = 0, the configuration is now operating in TIM universal filter. In this case, the two following TIM responses at voltage outputs v o1 and v o2 can simultaneously be obtained as: and Equations (25) and (26) express the TIM filter functions of the LP and BP filters with passband gains of (−1/g mC ) and R, respectively.
As a consequence, the proposed circuit shown in Figure 3 can be considered as a universal mixed-mode biquadratic filter. The natural angular frequency and the quality factor of this filter are given by [53]. and It is important to note from Equation (27) that the ω o can be electronically tuned by changing the transconductances g mA and g mB . In addition to Equation (28), the high-Q universal filter can be easily realized by tuning the resistor R without affecting the characteristic frequency ω o .

Proposed Dual-Mode Quadrature Oscillator
In Figure 3, by taking v i1 = v i2 = v i3 = i in = 0, and connecting terminal z− to x of the VDGA, the proposed mixed-mode universal biquadratic filter can be worked as a quadrature sinusoidal oscillator. Figure 4 shows the proposed dual-mode quadrature oscillator based on the proposed mixed-mode universal filter in Figure 3. It is worth noting that in this design, all of the passive components are grounded. The characteristic equation of the proposed dual-mode quadrature oscillator in Figure 4 is found as [54]: It is important to note from Equation (27) that the ωo can be electronically tuned by changing the transconductances gmA and gmB. In addition to Equation (28), the high-Q universal filter can be easily realized by tuning the resistor R without affecting the characteristic frequency ωo.

Proposed Dual-Mode Quadrature Oscillator
In Figure 3, by taking vi1 = vi2 = vi3 = iin = 0, and connecting terminal z− to x of the VDGA, the proposed mixed-mode universal biquadratic filter can be worked as a quadrature sinusoidal oscillator. Figure 4 shows the proposed dual-mode quadrature oscillator based on the proposed mixed-mode universal filter in Figure 3. It is worth noting that in this design, all of the passive components are grounded. The characteristic equation of the proposed dual-mode quadrature oscillator in Figure 4 is found as [54]:  From Equation (29), the oscillation condition (OC) and the oscillation frequency (OF) are evaluated by [55]: and OF : ω osc = 2π f osc = g mA g mB C 1 C 2 .
As can be observed from Equations (30) and (31), the OC can be controlled simply by changing the value of a grounded resistor R without altering the OF, which can be tuned separately using the transconductance g mB . As a result, the parameters OC and OF of the proposed quadrature oscillator in Figure 4 are orthogonal controllable.
For sinusoidal steady state, the relationship between the output voltages v osc1 and v osc2 is v osc1 = g mA g mB Thus, the proposed circuit produces the two marked voltages v osc1 and v osc2 in quadrature signal.
Also from Figure 4, the output current relations from i osc1 to i osc2 and i osc3 at the OF are found as: According to Equation (33), the phase differences between i osc1 and i osc2 , as well as i osc1 and i osc3 , are 90 • and 180 • , respectively. This demonstrates that the three output currents are not only 90 • out of phase, but also 180 • out of phase.

Non-Ideal Analyses
This section investigates the impact of VDGA non-idealities on the performance of the proposed mixed-mode universal biquad filter and dual-mode quadrature oscillator. In fact, the non-idealities of the VDGA arise mostly from two significant consequences. The first set of effects is caused by finite tracking errors, whereas the second group is caused by the existence of all VDGA terminal parasitics.
In presence of the VDGA tracking defects, the expressions for the parameters ω o and Q of the proposed mixed-mode universal biquad filter in Figure 3 are modified as: and Through the tracking error effects, the values of ω o and Q clearly depart slightly from their ideal values. These variations may be accommodated by altering the transconductance gains g mA and g mB via the bias currents of VDGA.
For the proposed dual-mode quadrature oscillator in Figure 4, the modified OC and OF can be derived as: and OF : ω osc = α A α B g mA g mB C 1 C 2 .
It is evident that the non-ideal factors clearly cause the OC and OF parameters to deviate slightly. However, the OC and OF can still be altered through adjusting R and g mB , respectively.

Effect of Parasitics
The non-ideal behavior model of the VDGA including finite parasitic impedances at each terminal is represented in Figure 5. These parasitics consist of resistance in parallel with capacitance for the p, n, z+, z−, x and o terminals, and serial resistance at the w terminal [53][54][55]. Because of the presence of these undesired parasitics, the circuit performance may differ from ideality. As a result, the suggested circuits in Figures 3 and 4, including the VDGA parasitics, must be thoroughly examined.
Using the non-ideal model of VDGA shown in Figure 5, the non-ideal ω o and Q of the filter configuration in Figure 3 are found as: and where R = R R n R x , C 1 = C 1 + C z+ , and C 2 = C 2 + C n + C x .  Similarly, the non-ideal OC and OF of the oscillator configuration in Figure 4 are also found as: OC: and OF: where R″ = R ∥ Rn ∥ Rz-∥ Rx and C″2 = C2 + Cn + Cz-+ Cx. From Equations (39)-(42), the frequency characteristics of the proposed filter and oscillator circuits would be unaffected, if the following constraints were fulfilled: maximum R << parasitic resistances (Rn, Rz-, Rx), and minimum (C1, C2) >> parasitic capacitances (Cn, Cz+, Cz-, Cx).

Simulation Results
In this section, a PSPICE simulation program was carried out to demonstrate the performance of the proposed configurations in Figures 3 and 4. The VDGA was simulated using the CMOS circuit of Figure 2 with TSMC 0.18 μm transistor parameters, and with symmetrical supply voltages of ±0.9 V. Table 2 illustrates the aspect ratios of the CMOS transistors employed for the VDGA circuit in Figure 2. The capacitor settings for global simulations were C1 = C2 = 50 pF.  Similarly, the non-ideal OC and OF of the oscillator configuration in Figure 4 are also found as: and OF : ω osc = g mA g mB where R" = R R n R z-R x and C 2 = C 2 + C n + C x− + C x . From Equations (39)-(42), the frequency characteristics of the proposed filter and oscillator circuits would be unaffected, if the following constraints were fulfilled: and minimum (C 1 , C 2 ) >> parasitic capacitances (C n , C z+ , C z-, C x ).

Simulation Results
In this section, a PSPICE simulation program was carried out to demonstrate the performance of the proposed configurations in Figures 3 and 4. The VDGA was simulated using the CMOS circuit of Figure 2 with TSMC 0.18 µm transistor parameters, and with symmetrical supply voltages of ±0.9 V. Table 2 illustrates the aspect ratios of the CMOS transistors employed for the VDGA circuit in Figure 2. The capacitor settings for global simulations were C 1 = C 2 = 50 pF.

Simulation Verifications of the Proposed Mixed-Mode Universal Filter
The suggested mixed-mode universal filter in Figure 3 was performed with g mA = g mB = g mC = 1 mA/V (I BA = I BB = I BC = 80 µA), and R = 1 kΩ, to actualize all the four-mode universal filter responses with f o = 3.18 MHz and Q = 1. Figures 6-9 illustrate the simulated and theoretical frequency responses of VM, CM, TAM, and TIM filters, respectively. The disparity between simulated and theoretical gain responses in the HP filters of VM, CM, and TAM, as well as the BP filter of TIM, is greater in the low-frequency range of roughly 1 kHz to 100 kHz. This phenomenon may be explained by the fact that the input or output signals of the circuits were sensed with C 2 and R, introducing an undesirable pole that caused significant deviations in low operating frequencies. In Figures 6c and 7c, the phase shifting between input and output signals was measured as −190.70 • and −192.74 • , respectively, and the gain response was 0.84 dBV and 1.067 dBA down from zero for the frequency ranges varying from 1 kHz to 1 MHz. The simulated f o and corresponding percentage errors are given in Table 3. It is to be observed that all simulation results are found to be in good consistent with the theoretical values. Figures 10-13 depict the transient responses of the proposed filter to the following input signals: (i) a 3.18 MHz sinusoidal input voltage signal with an amplitude of 100 mV (peak-to-peak) applied to the VM and TAM filters; and (ii) 3.18 MHz sinusoidal input current signal with an amplitude of 100 µA (peak-to-peak) applied to the CM and TIM filters. Table 4 shows the total harmonic distortions (THDs) and DC components of the VM, CM, TAM, and TIM outputs in Figures 10-13. As can be seen, the THD value is less than 1.92% in all four modes. Thus, there is no significant distortion in the biquad design. The entire power consumption of the circuit was 1.31 mW at ±0.9 V biased voltages. The effect of temperature variation on the filter parameters is now being investigated. For this purpose, the proposed filter was simulated under ambient temperature changes ranging from 0 to 100 °C with a step of 25 °C. Figure 15 demonstrates the gain and phase variations of the AP filter in VM operation. The findings reveal that, for different temperatures, the gain and phase at fo vary from −0.44 to −0.5 dBV and from −172 to −223°, respectively.                         In addition, the orthogonal tunability of a high-Q value for a BP filter in VM is shown in Figure 14. The filter is designed to operate at f o = 3.18 MHz with g mA = g mB = g mC = 1 mA/V. By simply adjusting the R value for 0.5 kΩ, 10 kΩ, and 50 kΩ, the BP responses with various Q values of 0.5, 10, and 50 are achieved, respectively. Based on the measured data, the Q value was evaluated as 0.495, 8.273, and 44.25, respectively. The relative variation of the Q factor remained less than 12%, even when Q reached 50.  Figure 13. Time-domain responses of the LP and BP filters in TIM.   The effect of temperature variation on the filter parameters is now being investigated. For this purpose, the proposed filter was simulated under ambient temperature changes ranging from 0 to 100 • C with a step of 25 • C. Figure 15 demonstrates the gain and phase variations of the AP filter in VM operation. The findings reveal that, for different temperatures, the gain and phase at f o vary from −0.44 to −0.5 dBV and from −172 to −223 • , respectively.

Simulation Verifications of the Proposed Dual-Mode Quadrature Oscillator
Based on previous component settings, the simulated quadrature voltages v osc1 and v osc2 of the proposed dual-mode quadrature oscillator in Figure 4 are displayed in Figure 16. Figure 16a shows the steady-state waveforms of v osc1 and v osc2 , whereas Figure 16b presents the frequency spectrums of the oscillation output voltages. As per the findings, the simulated f osc was found to be 2.76 MHz, and the phase shift between v osc1 and v osc2 was 85.76 • . The attenuations at the second harmonic for v osc1 and v osc2 were 30.30 dBm and 31.45 dBm, respectively. Further, the percentage of THD was 2.46% for v osc1 and 4.28% for v osc2 . 16. Figure 16a shows the steady-state waveforms of vosc1 and vosc2, whereas Figure 16b presents the frequency spectrums of the oscillation output voltages. As per the findings, the simulated fosc was found to be 2.76 MHz, and the phase shift between vosc1 and vosc2 was 85.76°. The attenuations at the second harmonic for vosc1 and vosc2 were 30.30 dBm and 31.45 dBm, respectively. Further, the percentage of THD was 2.46% for vosc1 and 4.28% for vosc2.
Due to the VDGA transconductance gain gmk is tuned by the bias current IBk, the fosc of the proposed circuit is a current tunable function. Figure 18   Similarly, the simulated steady-state responses and the corresponding frequency spectrums of i osc1 , i osc2 , and i osc3 are also given in Figure 17. The phase shifts between i osc1 and i osc2 , and i osc1 and i osc3 were measured to be 92.73 • and 177.82 • , respectively. The second-harmonic attenuations for i osc1 , i osc2 , and i osc3 were 30.05 dBµ, 30.88 dBµ, and 30.87 dBµ, respectively, while the percentage THDs of i osc1 , i osc2 , and i osc3 were 3.86%, 4.16%, and 3.50%, respectively.  Due to the VDGA transconductance gain g mk is tuned by the bias current I Bk , the f osc of the proposed circuit is a current tunable function. Figure 18

Experimental Verifications of the Proposed Mixed-Mode Universal Filter
To further support the theory, the suggested circuits in Figures 3 and 4 were experimentally verified. As shown in Figure 19, the VDGA was built-in hardware utilizing off-the-shelf IC dual-OTA LM13600s from National Semiconductor [58]. To bias the LM13600, DC supply voltages of ±5 V were employed. A prototype hardware setup for verification purposes of the proposed circuit is illustrated in Figure 20. The component values were set as follows: gmA = gmB = gmC = 1 mA/V (IBA = IBB = IBC = 50 μA), R = 1 kΩ, and C1 = C2 = 680 pF, actually results in fo = 234 kHz, and Q = 1. In order to measure the input signals for the CM and TIM, a voltage-to-current converter with IC AD844 [59] and a converting resistor RC of 1 kΩ was used, as illustrated in Figure 21. In Figure 22, two extra AD844s and RC were used as a current-to-voltage conversion for output signal measurements in CM and TAM operations.

Experimental Verifications of the Proposed Mixed-Mode Universal Filter
To further support the theory, the suggested circuits in Figures 3 and 4 were experimentally verified. As shown in Figure 19, the VDGA was built-in hardware utilizing off-the-shelf IC dual-OTA LM13600s from National Semiconductor [58]. To bias the LM13600, DC supply voltages of ±5 V were employed. A prototype hardware setup for verification purposes of the proposed circuit is illustrated in Figure 20. The component values were set as follows: g mA = g mB = g mC = 1 mA/V (I BA = I BB = I BC = 50 µA), R = 1 kΩ, and C 1 = C 2 = 680 pF, actually results in f o = 234 kHz, and Q = 1. In order to measure the input signals for the CM and TIM, a voltage-to-current converter with IC AD844 [59] and a converting resistor R C of 1 kΩ was used, as illustrated in Figure 21. In Figure 22, two extra AD844s and R C were used as a current-to-voltage conversion for output signal measurements in CM and TAM operations.

Experimental Verifications of the Proposed Mixed-Mode Universal Filter
To further support the theory, the suggested circuits in Figures 3 and 4 w perimentally verified. As shown in Figure 19, the VDGA was built-in hardware u off-the-shelf IC dual-OTA LM13600s from National Semiconductor [58]. To b LM13600, DC supply voltages of ±5 V were employed. A prototype hardware se verification purposes of the proposed circuit is illustrated in Figure 20. The com values were set as follows: gmA = gmB = gmC = 1 mA/V (IBA = IBB = IBC = 50 μA), R = 1 k C1 = C2 = 680 pF, actually results in fo = 234 kHz, and Q = 1. In order to measure th signals for the CM and TIM, a voltage-to-current converter with IC AD844 [59 converting resistor RC of 1 kΩ was used, as illustrated in Figure 21. In Figure 22, tw AD844s and RC were used as a current-to-voltage conversion for output signa urements in CM and TAM operations.             [23][24][25][26][27] show the measurements of the input and output waveforms and the relevant output spectrums for the proposed VM filter with a 20 mV (peak) sinewave input voltage at 234 kHz. The THD values of the LP, BP, HP, BS, and AP output responses were 1.88%, 0.25%, 0.57%, 1.84%, and 2.66%, respectively. As can be seen from Figures 23b, 24b, 25b, 26b and 27b, the spurious-free dynamic range (SFDR) for the cases of LP, BP, HP, BS, and AP were measured at 35.03 dBc, 52.65 dBc, 45.68 dBc, 36.35 dBc, and 34.33 dBc, respectively. Figure 28 also shows the experimental gain-frequency responses of the proposed VM filter. The measured results of f o of VM, CM, TAM, and TIM were found to be 241.13 kHz (error~+3%), 227.08 kHz (error~−2.98%), 227.38 kHz (error~−2.87%), and 233.32 kHz (error~−0.33%), respectively. In all cases, the practically observed behavior of the circuit was found to be consistent with the theoretical predictions. The experimental test results, thus, verify the practicability of the suggested design. Nevertheless, one observes that the discrepancy between the theoretical and measured results was originally caused by non-ideal gain and parasitic impedance effects of the LM13600s and AD844s. The stray capacitances generated by the breadboard circuit realization also affect the frequency performance of the circuit in experimental testing. In all cases, the practically observed behavior of the circuit was found to be consistent with the theoretical predictions. The experimental test results, thus, verify the practicability of the suggested design. Nevertheless, one observes that the discrepancy between the theoretical and measured results was originally caused by non-ideal gain and parasitic impedance effects of the LM13600s and AD844s. The stray capacitances generated by the breadboard circuit realization also affect the frequency performance of the circuit in experimental testing.

Experimental Verifications of the Proposed Dual-Mode Quadrature Oscillator
According to the experimental measurements for the proposed dual-mode quadrature oscillator in Figure 4, the oscilloscope output waveforms in time-domain and Lissajous pattern of vosc1 and vosc2 are given in Figure 29. By using the same component values as in the previous filter case, the oscillator was constructed to oscillate at an OF of fosc = 234 kHz. The fosc observed was 234.1 kHz, which is extremely close to the theoretical value. The phase angle difference between vosc1 and vosc2 was roughly 95.1°, resulting in an absolute phase deviation of 5.67%. Figure 30 also shows the measured frequency spectrum of the vosc1 output. From the experimental testing, the THD and SFDR values for the output vosc1 were 2.85% and 31.38 dBc, respectively.

Experimental Verifications of the Proposed Dual-Mode Quadrature Oscillator
According to the experimental measurements for the proposed dual-mode quadrature oscillator in Figure 4, the oscilloscope output waveforms in time-domain and Lissajous pattern of v osc1 and v osc2 are given in Figure 29. By using the same component values as in the previous filter case, the oscillator was constructed to oscillate at an OF of f osc = 234 kHz. The f osc observed was 234.1 kHz, which is extremely close to the theoretical value. The phase angle difference between v osc1 and v osc2 was roughly 95.1 • , resulting in an absolute phase deviation of 5.67%. Figure 30 also shows the measured frequency spectrum of the v osc1 output. From the experimental testing, the THD and SFDR values for the output v osc1 were 2.85% and 31.38 dBc, respectively.
For i osc1 , i osc2 , and i osc3 measurements, the current-to-voltage converter circuit as shown in Figure 22 was also employed. The time-domain waveforms and the corresponding Lissajous figures of the oscillator output currents i osc1 and i osc2 , and i osc2 and i osc3 are illustrated in Figures 31 and 32, respectively. The quadrature-phase shifts between i osc1 and i osc2 , and i osc2 and i osc3 were 96.1 • and 85.3 • , respectively, deviating from the calculations by 6.78% and 5.22%. The frequency spectrum of the i osc1 output was also recorded and exhibited in Figure 33, with percentage THD and SFDR values of 2.05% and 34 dBc, respectively. Clearly, the generated waveforms observed in the experimental data validate the quadrature relationship of the suggested quadrature oscillator in both VM and CM.   For iosc1, iosc2, and iosc3 measurements, the current-to-voltage converter circuit as shown in Figure 22 was also employed. The time-domain waveforms and the corresponding Lissajous figures of the oscillator output currents iosc1 and iosc2, and iosc2 and iosc3 are illustrated in Figures 31 and 32, respectively. The quadrature-phase shifts between iosc1 and iosc2, and iosc2 and iosc3 were 96.1° and 85.3°, respectively, deviating from the calculations by 6.78% and 5.22%. The frequency spectrum of the iosc1 output was also recorded and exhibited in Figure 33, with percentage THD and SFDR values of 2.05% and 34 dBc, respectively. Clearly, the generated waveforms observed in the experimental data validate the quadrature relationship of the suggested quadrature oscillator in both VM and CM.    For iosc1, iosc2, and iosc3 measurements, the current-to-voltage converter circuit as sh in Figure 22 was also employed. The time-domain waveforms and the correspon Lissajous figures of the oscillator output currents iosc1 and iosc2, and iosc2 and iosc3 are         Figure 33. Measured frequency spectrum of iosc1 output. Figure 33. Measured frequency spectrum of i osc1 output.

Discussion
At this point, we would like to briefly discuss the superiority of the proposed MUBF and DMQO design over similar existing designs in the literature. The following observations are based on Table 1.
In the QO configurations [47,48], there are floating passive elements that are not encouraged for further integration. Several QO designs operated in either VM [44,47,49] or CM [42,43]. As compared to the proposed DMQO circuit, it not only uses grounded passive elements, but it also provides both voltage and current quadrature outputs simultaneously.
As a conclusion, it should be noted that the proposed MUBF and DMQO circuit in this study is capable of fulfilling all of the performance features described above simultaneously and without trade-offs.

Conclusions
This work proposes a compact mixed-mode universal biquadratic filter and dual-mode quadrature oscillator circuit using a single voltage differencing gain amplifier (VDGA). In this design, a canonical structure with one resistor and two capacitors is employed. The proposed universal biquad filter is able to realize generic second-order filter functions in all four modes of operation, namely, VM, CM, TAM, and TIM. It has the feature of orthogonal control of ω o and Q characteristics, and simultaneously the ability to implement a high-Q filter with a single resistance adjustment. The quadrature oscillator, which generates both voltage and current output signals simultaneously, is also feasible by slight modification of the proposed configuration. Both the oscillation condition and the oscillation frequency of the proposed quadrature oscillator are non-interactively controlled. The circuits are subjected to non-ideal analysis, including tracking error and parasitic element effects. The simulation and experimental findings prove that the suggested circuit performs in both the mixed-mode universal biquad filter and the dual-mode quadrature oscillator.

Informed Consent Statement: Not applicable.
Data Availability Statement: The data supporting the results presented in this work are available on request from the authors.
Acknowledgments: This work was supported by King Mongkut's Institute of Technology Ladkrabang (KMITL).

Conflicts of Interest:
The authors declare no conflict of interest.