Multiple-Input Universal Filter and Quadrature Oscillator Using Multiple-Input Operational Transconductance Amplifiers

This paper presents a new multiple-input single −output voltage-mode universal biquad filter based on multiple−input operational transconductance amplifiers (MI-OTA). This work demonstrates that the multiple-input OTA−based universal filter can provide more filtering responses and other benefits, compared to conventional OTA−based one. The filter provides electronic and orthogonal control of the natural frequency and the quality factor. Furthermore, a two-phase quadrature oscillator can be obtained by slightly modifying the proposed universal filter while the condition and frequency of oscillation can be controlled orthogonally and electronically. The performance of the proposed circuit is evaluated in Cadence environment using the TSMC <inline-formula> <tex-math notation="LaTeX">$0.18~\mu \text{m}$ </tex-math></inline-formula> CMOS technology. The voltage supply is 1.2 V and the power dissipation of the MI−OTA is <inline-formula> <tex-math notation="LaTeX">$24~\mu \text{W}$ </tex-math></inline-formula>. For 1% third intermodulation distortion (IMD3) the dynamic range of the band−pass filter is 78.6 dB. In addition, the proposed filter and oscillator are investigated through experiment tests using LM13700 commercially available OTA.


I. INTRODUCTION
Analog filters are important signal processing blocks for electronic, communication and control systems applications. For instance, they are used to reject the out−of−band noise in electronic and control systems and to eliminate the carrier signal in communication systems [1]. Universal filters are the circuits that usually provide five standard filtering responses into single topology: low-pass (LP), high−pass (HP), band−pass (BP), band−stop (BS) and all−pass (AP) responses. The filters with orthogonal control of the natural frequency and the quality factor are the most desirable ones. Moreover, the voltage−mode filters with high input impedance and without inverting−type signal inputs are required to avoid additional buffers and inverting amplifiers.
The next important kind of electronic circuits are oscillators. They are used in electronic, telecommunication and The associate editor coordinating the review of this manuscript and approving it for publication was Dušan Grujić . control systems to generate waveforms of different shapes, amplitudes and frequencies. Quadrature oscillators are the systems that usually generate two sinusoidal signals with 90 • phase shift. They are often used in communication and measurement systems, such as quadrature mixers [1], vector generators, selective voltmeters [2], and many other. The circuits with orthogonal control of the condition of oscillation and the frequency of oscillations are the most desirable ones.
The operational transconductance amplifier (OTA) is the basic active block in OTA−C filter design [3]- [11]. However, more complex filters require relatively large number of OTAs, that increases the silicon area and power dissipation [12]. The multiple-input OTA (MI−OTA) appeared as an attractive alternative technique that reduces the number of single−input OTAs used in filter design [12]- [15]. The multiple−input OTA enables summing and subtracting signals at its inputs. It was claimed that the use of multiple-input OTAs could reduce the number of components, silicon area, and power dissipation by approximately the factor of k, where k is the VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ number of inputs of the OTA [12]. As representative examples, one could provide the third− and seventh−order elliptic and low−pass filters described in [12] and [15]. Nevertheless, the MI−OTAs used in the aforementioned designs were based on parallel connections of differential stages to obtain the multiple-input blocks, resulting not only in increased number of transistors and chip area, but mainly in increased number of current branches, thus leading to a higher power dissipation and a more complex internal structure. A simple structure of MI−OTA, using one differential pair, can be achieved by employing the multiple-input floating−gate transistor (MIFG) [16]. Nevertheless, the MIFG transistor is based on charge conversation making it unpractical with modern CMOS technologies that suffer from gate leakage [17]. Furthermore, the MIFG transistor suffers from a residual charge on its gate, that results in higher voltage offset compared to conventional design. This paper presents a new MI−OTA based universal filter, with more filtering responses and more versatility, and a quadrature oscillator. Unlike, the aforementioned MI−OTAs, the presented OTA use the multiple-input MOS transistor (MI−MOST) technique that allows simplifying its overall structure and decrease the power dissipation. It is worth noting that the first experimental results of MI-MOST were presented by Khateb et. al in [18]- [20]. Later, this technique has been used in several active blocks and applications [21]- [28].
This paper is organized as follows: Section 2 shows the multiple input OTA. Section 3 presents its applications in the active filter and oscillator circuit. Sections 4 and 5 present the non-ideal analysis and simulation results, respectively. The experimental results are shown in Section 6. Finally, the conclusion is given in Section 7. Fig. 1 (a) shows the circuit symbol of OTA. Its ideal characteristic can be described by

II. MULTIPLE-INPUT OTA
where I o is the output current, g m is the transconductance gain, V 1+ and V 1− denote, respectively, the voltage of the non−inverting and inverting input terminals. The symbol of multiple−input OTA is shown in Fig. 1 (b). Its ideal characteristic can be described by where n is the number of required inputs. In order to realize the multiple−input OTA, one could use n single-input OTAs with their outputs connected together, as shown in Fig. 1 (c). However, this realization results in increased chip area and power consumption that limits its usefulness in low−voltage and low−power applications. Alternative way to realize the multiple−input OTA is to use one OTA with n parallel-connected differential stages [12]- [14]. However, this method still suffers from increased chip area, and power consumption.   The MI-OTA can be simply realized, using the MI−MOST [18]- [20]. The symbol of the MI−MOST with n inputs is depicted in Fig. 2 (a). The arbitrary number of inputs can be obtained by coupling the input terminals (V 1 ,. . . , V n ) to the gate terminal (G) of the conventional MOST by n input capacitors (C G1 ,..,C Gn ). To ensure the DC signal path, the high resistances (R MOS1 ,..,R MOSn ), created by two MOSTs (M R ) operating in cut-off region, are connected in parallel to each input capacitor, as shown in Fig. 2 (b) and (c). Due to the employment of the transistor M R a high resistance value of the order of several G is simply obtained with minimum chip area. In this work, to realize the MI−OTA, a twostage OTA with two outputs denoted as out-R and out is used, as shown in Fig. 3. The differential stage consists of one MI−MOST differential pair M 1 , M 2 , a flipped voltage follower M 5 , and two current sources M 10 , M 11 . The second stage operates in so−called super class AB and consists of M 6 and M 12 . In this stage, R MOS ensures the DC biasing of the gate of M 12 while the capacitor C ensures the AC signal path to this gate [28]. The capacitor C C ensures the OTA stability. The negative feedback from the output terminal out-R to the input terminal of M 1 ensures transferring of the differential input voltages to the output terminal with the voltage gain equal to unity. The output terminal out−R is connected to a linear adjustable resistor R set that converts the output voltage to output current I Rset . This current is mirrored by M 7 and M 13 to the output terminal out. Hence, the transconductance stage is obtained.
It is worth mentioning that the proposed MI−OTA enjoys high linearity and increased input voltage range thanks to the negative feedback connection and the input capacitive divider, that attenuate the input signal. Furthermore, thanks to the flipped voltage follower, the minimum voltage supply is given by only one gate-source and one drain-source voltage

III. PROPOSED CIRCUITS
The proposed universal biquad filter using MI−OTAs is shown Fig. 4. It consists of four MI-OTAs and two grounded capacitors.
and V in7 are input voltages, the output voltage of the proposed filter can be expressed by where From (6), five standard filtering responses and ten filtering functions can be obtained as The parameters ω o and Q of all filtering responses can be expressed as (7) and (8) can be rewritten as From (9) and (10), the parameter ω o for all filtering responses can be controlled electronically through G mset (G mset = G mset1 = G mset2 ) with constant C 1 = C 2 while the parameter Q can be controlled orthogonally through G mset3 with VOLUME 9, 2021 In case of non −inverting and inverting all-pass responses, a condition G mset2 = G mset3 is required. The universal biquad filter in Fig. 4 can be transformed to a quadrature oscillator as shown in Fig. 5. To obtain orthogonal control of the condition of oscillation and the frequency of oscillations, the non-inverting band-pass response V in4 could be used to create a positive feedback loop, with inputs V in1 , V in2 , V in3 , V in5 , V in6 and V in7 connected to ground. The characteristic equation of the quadrature oscillator can be expressed by The condition of oscillations (CO) and the frequency of oscillations (FO) can be expressed, respectively, by From (12) and (13), it is evident that CO can be controlled electronically by G mset3 , while FO can be varied orthogonally by G mset1 with C 1 = C 2 constant. Thus, the quadrature oscillator can be orthogonally controlled. It should be noted that the quadrature oscillator in Fig. 5 provides three output terminals V out1 , V out2 and V out3 . The additional outputs still provide sinusoidal signals, with 90 o phase shift, and the relationships between output signals can be expressed as: With s = jω o , eqns. (14) and (15) can be rewritten respectively, as
In the frequency range of a few MHz, G msetnj can be modified as where µ j = 1 ω gj . The pole frequency ω gj , results from the parasitic input and output resistances (R + , R − , R o ) and the input and output capacitances (C + , C − , C o ), as shown in Fig. 6. The high-resistance and small-capacitance values will result in high value of ω gj and small value of µ j . Using (17), the denominator of the transfer function of the universal filter can be expressed as It can be made negligible by satisfying the following, condition: The various passive and active sensitivities of the parameters ω o and Q of the universal filter can be expressed as Thus, all the incremental parametric sensitivities for parameters ω o and Q are below 1.
Using (17), the characteristic equation of a quadrature oscillator can be written as It can be made negligible by satisfying the following condition:

V. SIMULATION RESULTS
The circuit was designed to work with 1.2 V supply, with 5 µA bias current and 24 µW power consumption. The Cadence environment has been used to design and simulate the circuit using a 0.18µm CMOS technology from TSMC. The parameters of the components are shown in Table. 1. For the filter design the capacitor C 1 = C 2 = 10 nF and R set1 = R set2 = R set3 = R set4 = 15 k were selected for natural frequency of 1 kHz. These R set resistors can be integrated on chip using a high resistance poly resistor while these 10 nF capacitors should be off-chip capacitors.
The simulated magnitude frequency responses of the universal filter showing the non-inverting LP, HP, BP, and BS responses are shown in Fig. 7. The simulated natural frequency is 1.03 kHz. The magnitude frequency response and the phase characteristic of the non-inverting AP filter are shown in Fig. 8. The total power consumption of the filter is 96 µW. Fig. 9 shows the tuning capability of the Q factor   for the BP filter by tuning R set3 = 5k , 10k , 15k , 20k and 25k , while R set1 = R set2 = R set4 = 15k .
A sine wave with different amplitudes (0.05V, 0.1V, 0.15V, 0.2V, 0.25V) and 1 kHz frequency was applied to the input of the BP filter. The output signals are shown in Fig. 10. The total harmonic distortion (THD) is less than 1.67 % for input amplitude of 0.3V as shown in Fig. 11. This confirms the high linearity of the filter with low THD.
To determine the third-order distortion products produced by the circuit nonlinearity, two tones that are close in frequency are applied to the input of the BP filter. The first VOLUME 9, 2021   tone is a sine wave with amplitude of 25mV@ 0.9kHz and the second one with 25mV@ 1.1kHz. The spectrum of the output signal is depicted in Fig. 12. The third intermodulation distortion (IMD3) is only -65.6 dBc. The relation between the IMD3 and the peak-to-peak value of the input signal is shown in Fig. 13. The IMD3 is around -33.7 dB for 350mV pp . The equivalent output noise of the BPF is shown in Fig. 14. The RMS output noise of the BP filter integrated in the band pass from 432Hz−2.523kHz was 12µV that results in 78.6dB dynamic range for 1% IMD3.      The low sensitivity of the design to process and mismatch variation was also proved by Monte Carlo (MC) analysis with 200 runs as shown in Fig. 16.
The quadrature oscillator was also simulated with C 1 = C 2 = 10nF, R set1 = R set2 = R set4 = 15k . To start the oscillation the R set3 was selected to 16k . The simulated oscillation frequency was 1.04kHz. Fig. 17 shows the growing oscillations of the oscillator output voltage V out1 , V out2 and V out3 while Fig. 18 shows the steady-state waveforms. The spectrum of the output signals was shown in Fig. 19, the THD of the output signals is 0.33%, 0.35% and 0.1% for V out1 , V out2 , V out3 , respectively.     20 shows the frequency versus R set1 . For all simulated frequencies, the THD was less than 0.4%.

VI. EXPERIMENTAL RESULTS
The proposed universal filter was also tested experimentally. The prototype circuit was realized using commercially available integrated circuits LM13700N [30]. Note, that the macro-model of the LM13700N has been also used, hence the simulation results based on macro-model and the measured results can be compared. The multiple input OTA was realized by a parallel connection of OTAs (LM13700N) as shown in Fig. 1 (c).    The supply voltages were V DD = −V SS = 5 V and the capacitances C 1 and C 2 were of 220 nF. The sinusoidal input signal and the output waveforms were measured using Agilent Technologies DSOX 1102G oscilloscope. The transconductances g mset1 = g mset2 = g mset3 = g mset4 = 1.512 mS were designed to obtain the filter with the natural frequency f o ∼ =1.09 kHz and the quality factor Q ∼ =1. Fig. 21 shows the measured and simulated magnitude responses of the non-inverting LP, HP, BP and BS filter with natural frequency f o = 1.09 kHz. Fig. 22 shows magnitude and phase responses   of the AP filter. Fig. 23 shows magnitude responses of the BP filters for different values of the transconductance g mset (g mset = g mset1 = g mset2 = g mset3 ) equal to 0.481 mS, 0.873 mS, 1.512 mS and 2.934 mS. Fig. 24 shows the magnitude responses of the BP filters for g mset3 equal to 0.481 mS, 0.873 mS, 1.512 mS and 2.934 mS.  The value of g mset3 was varied to obtain different values of the parameter Q, while the input signal was applied to V in3 , with g mset1 = g mset2 = 1.512 mS.
The proposed quadrature oscillator was experimentally tested as well. The capacitances C 1 and C 2 were 220nF. The measured output waveforms were taken using Tektronix MSO 4034 mixed signal oscilloscope. Fig. 25 shows the measured output wave forms of V out1 , V out2 and V out3 for g mset1 = g mset2 = g mset4 = 1.512mS and variable g mset3 , for controlling the condition of oscillation. The circuit generates the output waveform with frequency of 1.11 kHz, while the theoretical value was 1.09 kHz. The amplitudes were nearly equal in this case. The quadrature output waveform in Fig. 25 was verified through the XY mode to show the quadrature relationship. The quadrature relationships between V out1 and V out2 and between V out2 and V out3 were shown in Fig. 26, (a) and (b), respectively. The measured frequency of oscillations as a function of g mset1 is shown in Fig. 27. The achieved results agree well with (13). The frequency of oscillations was 0.607 kHz, 0.849 kHz, 1.11 kHz, 1.58 kHz, 2.21 kHz and 2.68 kHz for g mset1 equal to 0.481 mS, 0.873 mS, 1.512 mS, 2.934 mS, 5.81 mS and 8.45 mS, respectively. The plot showing the output amplitude versus frequency of oscillations is shown in Fig. 28. The THD of the output signals V out1 , V out2 and V out3 is shown in Fig. 29. The phase error between V out1 and V out2 , and between V out2 and V out3 , referred to 90 o , is shown in Fig. 30.    [11]. While the works in [7]- [9], [11] use only commercially available integrated circuit without CMOS structure, the works in [6], [10] use only a conventional CMOS OTA structure (i.e. well known OTA with one input).
Compared with [6], the proposed filter can be easily transformed into a quadrature oscillator. Although using the topology in [6] one can obtain five standard filtering responses, they are achievable only with the use of different modes of operation (voltage−mode, current−mode, transresistance−mode, transconductance−mode). Compared with [8]- [10], the proposed filter provides full non-inverting and inverting realization of five standard filtering responses and offers a three−phase quadrature oscillator. Furthermore, thanks to innovative and simple CMOS structure, the proposed filter offers improved linearity, lowest THD and IMD3, wide dynamic range and low power consumption and less amounts of active elements when it is realized using MI−OTAs. Finally, it is worth to mention that due to absence of MI-OTA fabrication the commercially available integrated circuit LM13700N is used only to confirm the functionality and benefits of the multiple-input technique on these new presented applications.

VII. CONCLUSION
In this paper, a new voltage-mode universal biquad filter employing four MI−OTAs and two grounded capacitors is proposed. It offers eleven filtering responses into single topology which can be possible using the MI−OTA−based circuit. The filter also provides orthogonal control of the natural frequency and the quality factor. By slightly modifying the proposed universal filter, a two−phase quadrature oscillator with orthogonal control of the condition and frequency of oscillation can be obtained. The performance of the proposed filter and oscillator circuit were evaluated in Cadence environment using the TSMC 0. 18  His research interests include the continuous and discrete-time analog filtering, including fractional-order filters, companding filters, current amplifier filters, CCII and CFOA filters, and sampled-data filters, and in the development of ultra-low voltage building blocks for biomedical applications. He is also a member of Nonlinear Circuits and Systems Technical Committee of the IEEE CAS Society. He also serves as an Area Editor for the International Journal of Electronics and Communications (AEU) journal, and an Editor for the International Journal of Circuit Theory and Applications. He is also an Associate Editor of the Circuits Systems and Signal Processing Journal and the Journal of Advanced Research. He is also a member of the Editorial Board of the Analog Integrated Circuits and Signal Processing Journal, Microelectronics Journal, and Journal of Low Power Electronics.