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Electronically tunable universal filter and quadrature oscillator using low- voltage differential difference transconductance amplifiers

This paper presents a new electronically tunable universal filter and quadrature oscillator for low frequency biomedical and biosensor applications employing low-voltage differential difference transconductance amplifier (DDTA). The DDTA CMOS structure uses 0.5 V of supply voltage and consumes 277 nW of power. Unlike the previous universal filters, the proposed filter provides many transfer functions of the standard five transfer functions such as low-pass, high-pass, band-pass, band-stop and all-pass with both unity and controlled voltage gains as well as both inverting and non-inverting transfer functions. The natural frequency and the voltage gain of the five standard transfer functions can be controlled electronically. For the band-pass filter, the third intermodulation distortion (IMD3) was 0.37% for 20 mVpp input signal while the output integrated noise was 61.37 μV. The dynamic range (DR) was 53.27 dB for 1% IMD3. The quadrature oscillator has electronically and orthogonal control of the condition and frequency of oscillation. The proposed circuit and its applications were designed and verified via Cadence simulator tool using 0.13 μm UMC CMOS technology. Further, the circuit was evaluated by PSPICE simulation and experiment test using commercial OTA LM13700.


I. INTRODUCTION
Universal filters are a useful block that usually provide five second-order transfer functions into a single topology such as low-pass (LPF), high-pass (HPF), band-pass (BPF), band-stop (BSF) and all-pass (APF) transfer functions. The second-order filters can be applied to FM stereo demodulation [1], audio crossover network circuit [2], programmable universal filter as commercial ICs [3] and high-order filters [4][5][6][7].
The oscillator circuits are the systems that usually generate a sinusoidal signal, which can be applied in telecommunication, control and measurement systems such as single sideband generator [1] and voltage-controlled oscillator of a phase-locked loop [8]. In addition, quadrature oscillators are the systems that usually provide two sinusoidal signals with 90º phase difference, which can be applied to quadrature mixer [9], phase sensitive detector [10], vector generators and selective voltmeters [11]. In these applications, it is advantageous if a single circuit can serve as a universal filter or a quadrature oscillator. In addition, the universal filter and oscillator, which are implemented as a single integrated circuit (IC), can help circuit designers to easily find the required integrated circuits.
Nowadays, the low-power second-order filters can be used to realize high-order filters for biomedical and biosensor applications such as fourth-order low-pass filters [32][33][34][35] and band-pass filters [36][37][38] as well as the low-frequency oscillators that can be applied in the biomedical systems [39][40][41]. The LPF can be applied to bio-signal acquisition system [32], BPF can be applied to bionic ears [59], BSF can reduce the effect of the power line interference [60], APF can be used to realize audio delay line for use in hearing aids [61], HPF, LPF and BSF are used for signal conditioning for biosensors [62]. The voltage-controlled oscillator can be applied to biosensors [63,64].
Recently, low-voltage, low-power universal filters and quadrature oscillators have been reported [42][43][44][45][46]. In [42], low-voltage, low-power universal filter employing new active element, difference transconductance amplifiers (DDTA), has been presented. The circuit employs three DDTAs and two grounded capacitors that offers twenty filtering functions. In [43,44], a universal filter and quadrature oscillator that can be realized from a single topology has been proposed. The circuit in [43] employs four multiple-input operational transconductance amplifiers and two grounded capacitors that can realize eleventh filtering functions, but the circuit uses 1.2 V of voltage supply and consumes of 96 W of power. The circuit in [44] employs two DDTA and two grounded capacitors that uses 0.3 V of voltage supply and consumes 0.715 W of power, but in case the circuit realizing a quadrature oscillator, the condition of oscillation is controlled by adjusting the ratio of two capacitors which is not ideal for integrated circuit implementation. The structures in [45,46] provide only universal filter. It should be noted that the voltage gain of all universal filters in [42][43][44][45][46] cannot be controlled.
In this work a low-voltage, low-power universal filter and quadrature oscillator suitable for application of biomedical and biosensors has been proposed. The universal filter is based on low-voltage, low-power difference transconductance amplifiers that offers the advantages: (1) providing thirty-six filtering functions that cover both inverting and non-inverting standard filter responses such as LPF, HPF, BPF, BSF and APF, (2) offering both unity and controlled voltage gains of these standard filter responses, (3) offering a high-input impedance, hence no additional buffer circuits are required, (4) providing electronic tuning capability of natural frequency, (5) offering the orthogonal control of natural frequency and quality factor. The quadrature oscillator can be realized by slightly modifying the proposed universal filter. The condition and frequency of oscillations can be orthogonally and electronically controlled. The output terminals possess lowimpedance level which can be connected directly to a load without additional buffer circuit. Fig. 1 shows the electrical symbol of the DDTA. The input and output ideal characteristic can be given by

A. LOW-VOLTAGE DDTA
where 1 , 2 , 3 , 4 are the input voltages, is the output voltage, is the output current, and is the transconductance gain. It should be noted that this device offers the output voltage of addition and subtraction voltages as -terminal and the output current of addition and subtraction voltages as -terminal.
The innovative low-voltage DDTA CMOS structure was firstly presented in [44]. The modifications presented in this paper, compared with [44], are shown and highlighted in Fig.  2 a) the symbol and realization of the multiple-input MOS transistor (MI-MOST) is shown in b) and c), respectively. The original structure comprised of the differentialdifference current conveyor (DDCC) and the transconductance amplifier (TA). The circuit employed several non-conventional techniques: 1) the partial positive feedback (M7, M8) that creates a negative conductance boosting the gain of the DDCC [47], 2) the bulk-driven nontailed differential stages (M1A,1B, M2A, 2B, M3, M4. M5, M 6) that enable rail-to-rail operation under extremely low voltage supply (≤ 0.5V) [48,49,50], 3) multiple-input technique MI-MOST for the DDCC (M1A, M2B) that simplify the structure by reducing the number of the differential pairs from standard two to one [51,52], and 4) the linear resistor R used for optimum linearity of the TA [53]. However, along with the above-mentioned techniques, additional techniques have been used in the presented structure, in order to enhance the performance of this active element, i.e. the super class AB stage [54] and the self-cascoded MOS transistor [55] have been used. The self-cascoded transistor is very suitable solution for circuits with low-voltage supply (≈0.5V) since one transistor operates in saturation while the second one in linear region that results in drain-source voltage of both transistor close to the drain-source voltage of a single transistor while with much increased output resistance. In Fig. 2 a) for the DDCC block and in order to achieve power efficient class AB output stage of the DDCC a super class AB stage is used. This stage is simply obtained by using the capacitor CB that for ac operation boosts the dynamic current above the quiescent current that is settled by the high resistance RL by connecting the gate of M9 to the bias voltage VB. The high resistance RL is realized by two turned off diodes created by two identical MOS transistors MR as shown in Fig. 2 d). For the high linear TA that suffered from low output resistance value, which was around 5.1 MΩ [44], the self-cascode transistors M5, M5c-M10, M10c that significantly increase the output resistance up to 1.18 GΩ has been used. Note that none of the super class AB stage or the self-cascode technique consume extra power, which is a benefit. Also, note that the low output resistance value of the TA caused degraded attenuation at low frequency for the filter function like HPF and BPF [44]. It is worth mentioning that the optimum linearity for TA is achieved when = 1⁄ [53]. Therefore, TA with large transconductance value means low R and low chip area and vice versa.

B. MULTIPLE-INPUT MULTIPLE-OUTPUT UNIVERSAL FILTER
The proposed universal filter employing three DDTAs, two grounded capacitors and one grounded resistor is shown in Fig. 3. The circuit has eight input terminals with highimpedance level and six output terminals. Thus, the input terminals can be connected to any terminals without buffer circuit requirements. Using (1) and nodal analysis, the output voltages of Fig. 3 From (2)- (7), the five standard filtering responses such as LPF, HPF, BPF, BSF and APF can be achieved by appropriately applying the input signals and suitable connecting output terminals as shown in Table 1. It can be seen from Table 1 that the five standard filtering responses possess both non-inverting and inverting transfer functions as well as both unity and controlled voltage gain of the transfer functions. The proposed topology offers thirty-six filtering responses. The natural frequency ( ), the quality factor ( ) of filters can be given by The voltage gain of transfer function can be given by From (8) and (9) the quality factor can be given by 1 / 2 by letting 1 = 2 whereas the natural frequency can be obtained electronically by adjusting ( = 1 = 2 ). Therefore, the natural frequency and the quality factor can be orthogonally controlled. From (10), the voltage gain can be controlled electronically by 3 and constant 1 . Fig. 4 shows the modified quadrature oscillator using the proposed universal filter in Fig. 3. The non-inverting BPF having the voltage gain of Fig. 3 is used for creating the loopgain of the oscillator. Considering the output 5 ′ and the input 4 , the transfer function of the non-inverting BPF can be expressed by This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication.    This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication. ⁄ =1, the characteristic equation of the oscillator can be given by 2 1 2 + 2 1 (1 − 3 1 ) + 1 2 = 0 (12) The condition of oscillation (CO) and the frequency of oscillation (FO) of the oscillator can be given respectively by

C. MODIFIED QUADRATURE OSCILLATOR
The CO can be controlled electronically by 3 and the FO can be controlled electronically by 2 . The capacitor 1 can also be used to adjust the FO if required. Thus the CO and FO of the quadrature oscillation can be independently controlled.
The non-ideal transconductance gain of DDTA is caused by the parasitic capacitor and parasitic resistor at o-terminal. In the frequency range that generates these parasitic capacitance and resistance, can be modified as [56]  Using (17), the denominator of (18) From (24), the non-idealities of the DDTAs affect the circuit characteristics, which depart from ideal values. The parasitic effects from the DDTA can be made negligible by satisfying the following condition Therefore, the non-ideal natural frequency ( ) and the quality factor ( ) can be obtained respectively by If such as or is a function of such as capacitor or , the sensitivity of a parameter to an element is given by [57] = = (ln ) Using (29), the sensitivity of and with respect to circuit components and non-ideal parameters can be expressed by It can be concluded from (30)-(32) that all the sensitivities are within unity in magnitude. Thus, the proposed filter enjoys good active and passive sensitivities. Re-considering the output 5 ′ and the input 4 , the modified BPF can be expressed by From (35) and (36), the electronic tuning capability of the oscillator can easily compensate the non-idealities of DDTAs.

A. SIMULATION RESULTS
The circuit has been designed and simulated in Cadence environment using the 0.13 µm UMC CMOS technology.
The transistors aspect ratio of the DDTA are listed in Tab Fig. 5. The gain of the DDA and TA at low frequencies enjoy high value of 88 dB and 46.65 dB, due to the increased output resistance, caused by the partial positive feedback and the self-cascode techniques. The frequency characteristic of the output impedance of the TA is shown in Fig. 6. Thanks to the self-cascode technique, the resistance at low frequencies is increased to 1.18 GΩ. The gain of the DDA and TA at low frequencies enjoy high value of 88 dB and 46.65 dB, due to the increased output resistance, caused by the partial positive feedback and the self-cascode techniques. The frequency characteristic of the output impedance of the TA is shown in Fig. 6. Thanks to the self-cascode technique, the resistance at low frequencies is increased to 1.18 GΩ. The rail-to-rail operation capability in inverting and non-inverting configuration of the DDCC is shown in Fig. 7. It can be seen that the input range of DDTA is wide and near to the supply rails. Fig. 8 shows the relations of and versus input voltage 4 − when the bias current was varied. The wide input voltage range, railto-rail, and the good linearity are evident.    For the filter application in Fig. 3, the off-chip components have the following values: C1=C2=50 pF and R1= 12.9 MΩ. Fig. 9 shows the frequency magnitude responses of LPF, HPF, BPF, BSF and APF. The natural frequency fo was 231.7 Hz. Fig. 10 shows the frequency magnitude responses of BPF filter with different Iset=Iset1=Iset2= (30,50,70,90,110) nA while Iset3 was fixed as 50 nA. The corresponding fo was

Vy1-Vy2 Vy2-Vy1
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication.    Fig. 12 (a), (b) and (c), respectively. A slight deviation can be seen for temperature corner 55 °C and this is expected due the operation of transistors in weak inversion region that is sensitive for temperature variation. The variation of the magnitude response of the BP filter with 200 runs MC is shown in Fig. 12 (d). The mean value of the gain is 0.13 dB and the standard deviation is 0.72 dB as shown in the histogram in Fig. 13.
To determine the third order intermodulation distortion IMD3 of the BPF, two-tone test has been applied. The first tone was 10 mVpp @ 220 Hz and the second one was 10 mVpp @ 240 Hz. The spectrum of the output signal is shown in Fig.  14 indicating 0.37% IMD3. The IMD3 versus the input voltage Vinpp is shown in Fig. 15. The output noise of the BP filter is shown in Fig. 16. The RMS value integrated in the band pass was calculated to 61.37 µV. The dynamic range (DR) of the BP filter is then calculated as 53.27 dB for 1% IMD3. For the oscillator application in Fig. 4, the components had the following values: 1 = 2 =50 pF and 1 = 14 MΩ. The starting oscillation and the steady state are shown in Fig. 17  (a) and (b).The Vo4 and Vo5 oscillation frequency is 238 kHz and total harmonic distortion (THD) 1% and 1.1%, respectively.

B. EXPERMENTAL RESULTS
To confirm the workability of the proposed circuit, simulation and experiment tests have been performed simultaneously. The circuit was evaluated by PSPICE simulation and experiment test using commercial OTA LM13700. The DDTA is implemented using OTA LM13700 as shown in Fig. 18. The supply voltages were selected as = − = 5 V, the resistors 1 = 2 were fixed as 47 kΩ and resistor 3 was used to adjust the transconductance of DDTA. The capacitances 1 and 2 were 22 nF for both filter and oscillator.

Vo4 Vo5
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication.  This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication.  Note: * IMD3-two tones test, ** PD=power dissipation, N=order of filter.

Frequency [kHz]
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication.   Fig. 24 shows the quadrature output verifying through the X-Y mode. The measured result compared with the theoretical value of the FO by varying the value of transconductances 2 was shown in Fig. 25. In this figure, when the transconductance 2 was changed from 0.481 mS to 8.45 mS, the measured value of FO was changed respectively from 6.24 kHz to 25.21 kHz. Fig. 26 shows the plot for amplitude versus FO. It should be noted that the amplitude is not constant when 2 was varied. The amplitude-automatic gain control (AGC) circuit [58] must be used if the constant amplitude of output signals is needed. Fig. 27 shows the phase error of outputs between Vout1 and Vout2 that is deviated from 90. Finally, Fig. 28 shows the measured results of the frequency responses, Fig. 29 shows the breadboard implemented for the universal filter and Fig.  30 shows the experiment setup for the quadrature oscillator. It is worth noting that, the measured results are included in this work to confirm the functionality of the universal filter and oscillator in general also to show the advantages of the CMOS DDTA in form of reducing the count of active blocks needed for the application realization, i.e. 3DDTAs versus 6 LM3700.
The performance of the proposed circuit and compared with some previous works has been summarized in Table 3. The circuits in [20,23,24,42,44,45,46] have been used for comparison. Compared with [20,23,24], the proposed circuit enjoys low-power consumption. Compared with [42,45,46], the proposed structure can realize both universal filter and quadrature oscillator. Compared with [24,45,46], the proposed circuit offers better figure of merit (FOM). Finally, compared with all circuits [20,23,24,42,44,45,46], the proposed filter offers the controlled voltage gain for both of the non-inverting and inverting of transfer function

IV. CONCLUSION
The universal filter and quadrature oscillator using differential difference transconductance amplifier as active element for low frequency biomedical and biosensor applications has been presented in this paper. The proposed filter uses 0.5 V supply voltage and consumes 831 nW of power. The proposed universal filter provides thirty-six filtering functions of LPF, HPF, BPF, BSF and APF with This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication. both inverting and non-inverting version, as well as both unity voltage gain and non-unity voltage gain. The natural frequency and quality factor can be orthogonally controlled. The natural frequency also enjoys electronic tuning ability. The quadrature oscillator can be realized from the proposed filter by slightly adding a connection. The condition and frequency of oscillations can be controlled electronically and orthogonally. The output impedance of the oscillator is low thus they can be connected to a load without buffer circuits.