0.5 V Universal Filter and Quadrature Oscillator Based on Multiple-Input DDTA

This paper presents a universal voltage-mode filter and quadrature oscillator based on low-voltage multiple-input differential difference transconductance amplifier (MI-DDTA). Unlike the previous published DDTAs, that utilize the bulk-driven (BD) multiple-input MOS transistor technique (MI-MOST) in the differential pair of the first stage only, the proposed DDTA, for the first time, utilize the BD MI-MOST in the second stage of the DDTA. This results in capability of providing more arithmetic operations without additional current branches or power dissipation. Hence, simplify the topology of the filter and oscillator applications, by decreasing the count of active blocks. The voltage-mode filter offers high-input and low-output impedances, and both non-inverting and inverting versions of five types of transfer functions, namely low-pass, high-pass, band-pass, band-stop, and all-pass characteristics. The oscillator offers three-phase of quadrature signals, and orthogonal control of the condition and frequency of oscillations. The circuit was designed in Cadence environment using 180 nm CMOS TSMC technology. The voltage supply is 0.5 V and the power consumption of the filter is 472 nW. The simulation results are in accordance with theory and confirm the performance of the proposed circuit.


I. INTRODUCTION
The differential difference amplifier (DDA) is a versatile building block that was proposed as a circuit alternative for the conventional operational amplifier (op-amp) [1]. Thanks to the increased number of inputs, the DDA can realize the operations of addition and extraction of input voltages without the need for passive elements [2]. When operating with a negative feedback loop, and doubled output stage, the DDA can be used for the realization of the differential difference current conveyor (DDCC) [3]. Unfortunately, DDCC does not provide an electronic tuning capability; hence, DDCC-based circuits usually require passive resistors [4], [5], [6], [7], [8], [9], [10].
The associate editor coordinating the review of this manuscript and approving it for publication was Xi Zhu .
The operational transconductance amplifier (TA) is a circuit implementation of a voltage-controlled current source. This is another building block that can be used for synthesis of analog circuits. The TA is a simple one-stage amplifier, without high-impedance internal nodes. Its transfer characteristics are characterized mainly by its transconductance (g m ), which can easily be tuned with external current (I set ). The TA-based circuits are most often realized without passive resistors, and their characteristics can easily be tuned by means of I set [11].
Nowadays, low-voltage and low-power active filters have received considerable attention because they can be applied in biomedical and biosensor systems. The analog filters are used to select the required frequency range (in case of the bandpass filters) and to eliminate the out-of-band noise (in case of the low-pass filters). There are many low-voltage and low-power analog filters [21], [22], [23], [24], [25], [26], [27], [28], as well as signal generators [29], [30], [31], [32] available in the literature. The universal filters and oscillators based on low-voltage and low-power DDTAs have been proposed in [21] and [22]. The circuit in [21] employs three DDTAs and uses a 0.5 V supply, while the circuit in [22] employs two DDTAs and uses a 0.3 V supply voltage.
In this work a new universal voltage-mode filter and quadrature oscillator employing two low-voltage multipleinput DDTAs and two grounded capacitors is proposed. It will be shown that thanks to the MI-DDTAs many filtering responses can be obtained. Moreover, the proposed filter offers several advantages such as high-input and lowoutput impedance which is desirable in voltage-mode circuits, providing both non-inverting and inverting types of five basic transfer functions, namely low-pass (LPF), highpass (HPF), band-pass (BPF), band-stop (BSF), and all-pass (APF) responses. The structure uses only grounded capacitors, which is suitable for integrated circuit implementations. The proposed filter can be modified to work as a quadrature oscillator with orthogonal control of the condition and the frequency of oscillation.

A. PROPOSED MI-DDTA
The symbol of the MI-DDTA is shown in Fig. 1 (a). The properties of this MI-DDTA are similar to the previous DDTAs [21], [22], [23], [24], except the input terminals of the transconductance amplifier stage. Unlike the conventional solutions, in the proposed version the multiple-input inverting and non-inverting terminals of the transconductance amplifier are available, thus creating a more versatile active element that offers more arithmetic operations that simplify circuit structures of many applications. It is worth noting that the advantages of using multiple-input transconductors in reducing the number of components in OTA-C filters design was confirmed in the literature [39], [40]. It was confirmed that the multiple-input OTA can reduce the number of components, silicon area, and power dissipation by approximately factor k, where k is the number of OTA inputs [39].
In ideal case the main characteristics of the proposed MI-DDTA are given by The CMOS structure of the proposed MI-DDTA is shown in Fig. 1 (b). The circuit operates in subthreshold region and can be seen as a modification of the DDTA presented in [23]. It consists of a differential difference amplifier (DDA) followed by transconductance amplifier (TA). The DDA employs the bulk-driven multiple-input MOS transistor as a differential pair M 1A , M 2A , M 1B , M 2B [23]. The symbol and the CMOS realization of the BD MI-MOST is shown in Fig. 2. The multiple-input are simply obtained by a parallel connection of capacitors C B with high resistance anti-parallel connection of two minimum-size transistors M L . The MI-MOST technique was experimental verified in [33], [34], [35], and [36]. Since the input capacitive divider decreases the voltage gain, a partial positive feedback (PPF) technique was applied. Transistors M 7 , M 8 and M 9 , M 10 form two PPF circuits that generate negative resistances at gate/drain nodes of the diode-connected transistors M 2AB and M 5 /M 6 , respectively. Note, that in order to maintain the circuit stability, the transconductances of the PPF transistors should not exceed the transconductances of the corresponding diode-connected transistors, also in the presence of transistor mismatch and process, supply voltage, temperature (PVT) variations. Moreover, as the difference between the transconductances of the transistors in PPF circuits and the transconductances of the diode connected transistors is decreasing, then the circuit sensitivity to transistor mismatch is increasing, which can lead to increased variations of the gain bandwidth product (GBP), phase margin (PM), etc. As it was shown in [23], application of two PPF circuits with larger difference of transconductances can provide the same improvement of the voltage gain, with smaller overall sensitivity to transistor mismatch. Overall, the first stage of the proposed DDTA can be seen as a two-stage OTA, with MI differential stage at the input and 100% negative feedback, between output and one of the inputs. The capacitor C C is used for frequency compensation.
Compared to [23] the main modification is related to the TA where the bulk-driven multiple-input MOS transistor is also used in the differential pair M 1 , M 2 . This modification enables more arithmetic operations without additional current branches or power dissipation. The TA also employs the source degeneration technique M 11 , M 12 to increase the linear range of the TA. The overall structure can be seen as a current mirror TA, where the current mirrors M 3 -M 4 , M 5 -M 6 and M 9 -M 10 are composed of self-cascode transistors to improve the overall voltage gain of the circuit.
The small-signal transconductance of the TA is given by [33]: where η = g mb1,2 /g m1,2 at the operating point, β ≈ 1/n where n is the number of differential inputs of the pair (here n = 2), n p is the subthreshold slope factor and U T is the thermal potential. The coefficient m = (W/L) 11,12 /(W/L) 1,2 . For optimum linearity m = 0.5 [33]. Note the circuit transconductance can be easily tuned with I set .
Thanks to the BD MI-MOST and the source degeneration, the TA enjoys good linearity with nearly rail-to-rail input voltage range. Note, that the input noise of the MI-TA will be increased due to the lower transconductance, being a result of an input capacitive divider combined with a BD technique. However, the input range is extended in the same proportion, and hence, the dynamic range will not be affected [33]. Further improvement in circuit's performance could be achieved by employing the multiple-input bulk-driven quasifloating-gate MOS transistor, where the MI-MOST is driven simultaneously from its gate and bulk terminal [35]. This results in increased total transconductance and reduced input noise, however at the cost of increased chip area [36].
It worth mentioning that although the standalone TA was firstly presented and experimentally verified in [33], this is the first time where it is used as a part of the DDTA in order to increase its performance and its arithmetic operation.

B. ANALOG FILTER USING MI-DDTAS
The proposed analog filter using MI-DDTAs is shown in Fig. 3. The circuit employs two MI-DDTAs and two grounded capacitors. It should be noted that the inputs V +in1 , V −in1 , V +in2 , V −in2 , V +in3 , and V −in3 are fed to the high impedance terminals of DDTAs while the outputs V o1 and V o2 are the low-impedance outputs W of the MI-DDTAs. Thus, a single input signal can be fed to variant input terminals whereas the outputs can be connected directly to the loads, without buffer circuits. Note that since the circuit offers inverting input terminals, the inverting-type input signal requirement is absent. The use of inverting-type input signal means that additional circuit is required to convert the conventional positive signal to negative (i.e., from function generator). Using (1) and nodal analysis, the output voltages of the filter in Fig. 3 can be expressed by The filtering functions can be obtained by appropriately selecting the output terminals and appropriately applying the input signals as shown in Table 1. The natural frequency (ω o ) and the quality factor (Q) are given by The parameter ω o can be controlled by varying g m1 = g m2 and keeping C 1 and C 2 to be constant whereas the parameter Q can be determined by the ratio C 1 /C 2 while maintaining g m2 /g m1 to be constant. It should be noted that the parameter ω o can also be controlled electronically.
The proposed analog filter can be modified to work as a quadrature oscillator as shown Fig. 4. The transfer function V o1 /V −in1 of the band-pass filter of Fig. 3 is used and it can be expressed by Letting V o1 /V −in1 = 1 (V o1 and V −in1 are connected), the characteristic equation of the oscillator can be given by Letting g m1 = g m2 , the condition of oscillation is The frequency of oscillation is The frequency of oscillation can be controlled electronically by g m (g m = g m1 = g m2 ) while the condition of oscillation can be controlled by C 1 and/or C 2 . Therefore, the frequency and condition of oscillation can be orthogonally controlled. From Fig. 4, the transconductance amplifier of DDTA2 (g m2 ) along with C 2 form a lossless integrator and its transfer function can be expressed as Thus, the magnitude and phase difference (∅) between V o1 and V o2 of this transfer function at oscillating frequency (ω = ω o ) are respectively |g m2 /C 2 | and 90 • . From Fig. 4, the output V o2 and V o3 are out of phase, thus the phase difference between V o1 and V o3 is −90 • .

III. NONIDEALITIES ANALYSIS
To consider the non-ideal effect of a MI-DDTA, by taking the non-idealities properties of the DDTAs into account, the characteristics of the MI-DDTA can be rewritten as where β k1 is the voltage gain from V y1 to V w of k-th DDTA, β k2 is the voltage gain from V y2 to V w of k-th DDTA, β k3 is the voltage gain from V y3 to V w of k-th DDTA, g mnk is the non-ideal transconductance gain of k-th DDTA. The voltage gains β k1 , β k2 , β k3 are unity for ideal case. The non-ideal transconductance g mnk of k-th DDTA can be expressed by [37] g mnk (s) ∼ = g mk (1 − µ k s) (13) It is the frequency dependence of transconductance that usually considered around the operation frequency ω o [38], where µ k = 1/ω gmk , ω gmk denotes the first pole of k-th transconductance.
Using (12), the output voltages of the circuit in Fig. 3 Using (13), the denominator of (14)- (15) can be modified as The parasitic effects from the transconductance amplifiers can be made negligible by satisfying the following condition The natural frequency (ω o ) and the quality factor (Q) can be modified as Eq. (7) can be rewritten as The characteristic equation of oscillator can be modified as Letting g m1 = g m2 , the modification of the condition of oscillation is The frequency of oscillation become The error of voltage gains of MI-DDTAs will affect the frequency of oscillation of the oscillator whereas the effect on the condition of oscillation is relatively weak because voltages β 21 and β 22 can be compensated.

IV. SIMULATION RESULTS
The circuit was designed in Cadence environment using the 180 nm TSMC CMOS technology. The voltage supply was 0.5 V (±0.25V for the purpose of simulation) and the bias current for the MI-DDA was set to 40 nA and the nominal value of the setting current for the TA was set to I set = 10 nA. The power consumption of the MI-DDTA was 236 nW. The transistors aspect ratio, capacitors value and bias voltage are included in Table 2.
To demonstrate the advantages of the TA, Fig. 5 shows the simulated results of the DC transfer characteristic of the used TA (a) that was firstly presented in [33] with the TA (b) presented in [23]. Here it is evident the high linearity offered by the TA based on MI-MOST and source degeneration.  . VOLUME 11, 2023 The simulated frequency responses of the proposed filter are shown in Fig. 6. The values of C 1 = C 2 = 15 pF and the setting current I set = 10 nA. The simulated cut-off frequency was 281 Hz and the calculated value was 286.6 Hz. The power consumption of the filter was 472 nW.  The transient response of the LPF and its spectrum are shown in Fig. 10. To the input terminal of the LPF was applied a sine wave signal of 200 mV pp @100 Hz. The Spurious Free Dynamic Range (SFDR) was −42.72 dB and the Total Harmonic Distortion (THD) was 0.82 %. The output noise characteristic of the LPF is shown in Fig. 11. The integrated noise was found 190 µV that results in dynamic range (DR) 51.4 dB.
By applying two tones test with 50mV amplitude at 281.83 Hz and at 291.83Hz, the third-order intermodulation distortion (IMD3) of the LPF was found −46 dB as shown in Fig. 12.
For the proposed oscillator in Fig. 4, the capacitor values were selected C 1 = C 2 = 100 pF. Fig. 13 shows the starting oscillation (a) the steady state (b) and the output spectrum (c), respectively. The frequency was 45 Hz and the second harmonic was around −40 dB below the fundamental. The simulated phase noise shows −68.5 dBc/Hz at 10 Hz offset from the center frequency. Table 3 shows the performance comparison with previous universal filters. Compared with [21], [23], [27] the proposed filter has less count of active devices, compared with [22]  the proposed filter offers low output impedance and both non-inverting and inverting of five type filtering functions. Compared with [27], [28] the proposed filter is absent from minus-type input signal [27] and input voltage gain, i.e., 2V in [28].  It can be concluded that the proposed voltage-mode DDTA provides more arithmetic operation that can be served for minimum active/passive requirements of the proposed filter and oscillator. It should be noted that the multiple input of DDTA can offer many transfer functions of filter, both noninverting and inverting filtering responses of LP, HP, BP, BS, and AP filters, and enables easy feedback connection for realizing filter or oscillator without additional passive components. Please note that many transfer functions with minimum active elements can be possible by using MI-DDTA based circuit.
Compared with the conventional op-amp-based (or OTAbased) application, arithmetic operation (i.e. addition and subtraction) that usually required for realizing filter or oscillator, the single differential pair of these devices limit the applications such as applying the input signal or connecting  the negative or positive feedback (in case oscillator). Thus, these op-amp-based (or OTA-based) addition and subtraction are usually required many passive resistors, which results in  complex realization and extra consumed chip area. This is evident compared with [22] that has equal active and passive components, the proposed filter can offer both non-inverting and inverting filtering responses of LP, HP, BP, BS, and AP filters, and low-output terminal which is ideal of VM circuits for applications.

V. CONCLUSION
This paper presents a low-voltage and low-power universal voltage-mode filter and quadrature oscillator using only two MI-DDTAs and two grounded capacitors. Unlike the previous presented DDTAs, where the MI-MOST forms only the differential pair of the DDA stage, in the presented DDTA this technique forms also the differential pair of the TA. This results in a simple CMOS structure that offers more arithmetic operation without increasing in current branches and power dissipation. The presented filter and oscillator applications were designed and verified in Cadence environment using 0.5 V supply voltage and 180 nm TSMC CMOS technology.