1 V Tunable High-Quality Universal Filter Using Multiple-Input Operational Transconductance Amplifiers

This paper presents a new multiple-input single-output voltage-mode universal filter employing four multiple-input operational transconductance amplifiers (MI-OTAs) and three grounded capacitors suitable for low-voltage low-frequency applications. The quality factor (Q) of the filter functions can be tuned by both the capacitance ratio and the transconductance ratio. The multiple inputs of the OTA are realized using the bulk-driven multiple-input MOS transistor technique. The MI-OTA-based filter can also offer many filtering functions without additional circuitry requirements, such as an inverting amplifier to generate an inverted input signal. The proposed filter can simultaneously realize low-pass, high-pass, band-pass, band-stop, and all-pass responses, covering both non-inverting and inverting transfer functions in a single topology. The natural frequency and the quality factors of all the filtering functions can be controlled independently. The natural frequency can also be electronically controlled by tuning the transconductances of the OTAs. The proposed filter uses a 1 V supply voltage, consumes 120 μW of power for a 5 μA setting current, offers 40 dB of dynamic range and has a third intermodulation distortion of −43.6 dB. The performances of the proposed circuit were simulated using a 0.18 μm TSMC CMOS process in the Cadence Virtuoso System Design Platform to confirm the performance of the topology.


Introduction
An operational transconductance amplifier (OTA) is a voltage-controlled current source that offers numerous advantages in circuit design, such as providing electronic tuning capability, easy implementation of the OTA structure, and the powerful ability to realize various applications.In addition, OTA-based circuits are usually absent from resistor requirements, making them suitable for integrated circuit (IC) implementation [1,2].
Biquad filters are very useful blocks for applications in measurement, communication, and control systems.From the general form of second-order filter functions [3], there are five frequency responses that are possible to obtain, namely low-pass filter (LPF), high-pass filter (HPF), band-pass filter (BPF), band-stop filter (BSF), and all-pass filter (APF).These are the so-called five standard filtering functions.A biquad filter can be used to realize high-order filters by cascading multiple first-order and second-order sections, as used in phase-lock loops (PLL) for loop filtering (usually an LP filter), FM stereo demodulators (usually LP and BP filters), and crossover networks in three-way high fidelity (usually LP, Sensors 2024, 24, 3013 2 of 16 BP, and HP filters) [3].A filter that can provide several second-order filters in a single topology is classified as a universal filter.There are many universal filters available in the literature using varying active devices, such as second-generation current conveyors (CCIIs) [4][5][6] and current feedback operational amplifiers (CFOAs) [7][8][9].Unfortunately, these filters lack electronic tuning capabilities, which is important when parameters such as the natural frequency and quality factor deviate by process-voltage-temperature (PVT) variations.Some universal filters that offer the possibility of electronic tuning and minimal active elements have been introduced by using the voltage differencing inverting buffered amplifier (VDIBA) [10,11] and inverters [12].However, these filters supply the input signals through capacitors, and therefore, an additional buffer circuit is required, and these capacitors become floating.
It should be noted that these universal filters are not designed for low-voltage lowpower signal-processing applications.Nowadays, low-voltage low-power filters are required for biomedical applications, such as biosensors [3].Universal filters using OTAs operating with a low supply voltage and with low power consumption are available in the literature [42][43][44][45][46][47].However, these configurations cannot benefit from independent and electronic control of the quality factor and the natural frequency and cannot provide a high-quality (high-Q) filter.In modern applications, high-Q filters are strictly desirable for processing weak signals, such as the detection, measurement, and quantification of biomedical signals [48,49].The bio-signal has the attributes of a low amplitude and a low frequency (≤10 kHz).
This paper presents a low-voltage low-power universal biquadratic filter that allows the natural frequency and quality factor to be independently and electronically controlled.A high-Q filter can also be obtained.The filter is realized using multiple-input operational transconductance amplifiers (MI-OTAs).In the filter's input differential stage, the MI-OTAs are realized using the multiple-input MOS transistor technique (MI-MOST), which obtains a minimal differential pair and minimal power consumption.Using an MI-OTA-based filter shows that both the non-inverting and the inverting transfer functions of LP, HP, BP, BS, and AP filters can be obtained without inverted input signals.The proposed filter uses a 1 V supply voltage and 120 µW of power consumption for a 5 µA setting current.The filter was designed and simulated in the Cadence Virtuoso environment using 0.18 µm TSMC CMOS technology.

Multiple-Input OTA
The multiple-input OTA is used to realize the filter application.Its circuit symbol is shown in Figure 1.Ideally, the transfer characteristic of this OTA is given by the following equation: where I o is the output current, and g m is the small-signal transconductance.Note that the circuit in the general case has n non-inverting and n inverting inputs; thus, its input voltage can be considered as the difference of two sums of voltages applied to the non-inverting V +1,...,+n and inverting V −1,...,−n inputs, respectively.
Sensors 2024, 24, x FOR PEER REVIEW 3 of 16 current.The filter was designed and simulated in the Cadence Virtuoso environment using 0.18 µm TSMC CMOS technology.

Multiple-Input OTA
The multiple-input OTA is used to realize the filter application.Its circuit symbol is shown in Figure 1.Ideally, the transfer characteristic of this OTA is given by the following equation: where  is the output current, and  is the small-signal transconductance.Note that the circuit in the general case has n non-inverting and n inverting inputs; thus, its input voltage can be considered as the difference of two sums of voltages applied to the noninverting  ,…, and inverting  ,…, inputs, respectively.
The transistor-level schematic of the OTA proposed in this work with n = 3 is shown in Figure 2. The circuit consists of an OTA with folded-cascode topology with a linearized input stage consisting of the transistors M1-M2 and M1SD, M2SD, and biased by the current sinks M3 and M4.The transistors M13-M18 were used for biasing.The multiple inputs were realized in a simple way by adding a capacitive voltage divider to the transistors M1 and M2, thus creating a multiple-input device, as shown in Figure 3.The input capacitors CBi were bypassed by large RMOSi resistances, which were realized as an anti-parallel connection of MOS transistors operating in a cutoff region.The large resistances provided the DC biasing of the M1 and M2 gates.The linearization technique used in this work is similar to the technique with gatedriven input stages operating in strong inversion introduced in [50].However, in this work, the bulk-driven devices operating in weak inversion were applied to the proposed structure.Operation in weak inversion generally leads to a narrower linear range The transistor-level schematic of the OTA proposed in this work with n = 3 is shown in Figure 2. The circuit consists of an OTA with folded-cascode topology with a linearized input stage consisting of the transistors M 1 -M 2 and M 1SD , M 2SD , and biased by the current sinks M 3 and M 4 .The transistors M 13 -M 18 were used for biasing.The multiple inputs were realized in a simple way by adding a capacitive voltage divider to the transistors M 1 and M 2 , thus creating a multiple-input device, as shown in Figure 3.The input capacitors C Bi were bypassed by large R MOSi resistances, which were realized as an anti-parallel connection of MOS transistors operating in a cutoff region.The large resistances provided the DC biasing of the M 1 and M 2 gates.
Sensors 2024, 24, x FOR PEER REVIEW 3 of 16 current.The filter was designed and simulated in the Cadence Virtuoso environment using 0.18 µm TSMC CMOS technology.

Multiple-Input OTA
The multiple-input OTA is used to realize the filter application.Its circuit symbol is shown in Figure 1.Ideally, the transfer characteristic of this OTA is given by the following equation: where  is the output current, and  is the small-signal transconductance.Note that the circuit in the general case has n non-inverting and n inverting inputs; thus, its input voltage can be considered as the difference of two sums of voltages applied to the noninverting  ,…, and inverting  ,…, inputs, respectively.The transistor-level schematic of the OTA proposed in this work with n = 3 is shown in Figure 2. The circuit consists of an OTA with folded-cascode topology with a linearized input stage consisting of the transistors M1-M2 and M1SD, M2SD, and biased by the current sinks M3 and M4.The transistors M13-M18 were used for biasing.The multiple inputs were realized in a simple way by adding a capacitive voltage divider to the transistors M1 and M2, thus creating a multiple-input device, as shown in Figure 3.The input capacitors CBi were bypassed by large RMOSi resistances, which were realized as an anti-parallel connection of MOS transistors operating in a cutoff region.The large resistances provided the DC biasing of the M1 and M2 gates.The linearization technique used in this work is similar to the technique with gatedriven input stages operating in strong inversion introduced in [50].However, in this work, the bulk-driven devices operating in weak inversion were applied to the proposed structure.Operation in weak inversion generally leads to a narrower linear range compared to the strong inversion version of the circuit.On the contrary, the use of bulkdriven terminals extends the linear range compared to the gate-driven realization.Moreover, the input capacitive divider further extends the linear range.The result is the relatively large linear range of the OTA, even for weakly inverted devices biased with very low currents.A similar input stage was first described and verified experimentally in [51,52].The M1SD and M2SD transistors operate in a triode region, introducing negative feedback to the input pair M1 and M2.Controlling their characteristics by the signals seen at the gates of the main transistors of the pair M1 and M2 further improves the linearity of the input stage [51].Assuming that all the capacitances CBi are identical, the small-signal transconductance of the OTA is given by: where   , / , is the bulk to gate transconductance ratio at the operating point, n is the number of input terminals, np is the subthreshold slope factor for the p-channel The linearization technique used in this work is similar to the technique with gatedriven input stages operating in strong inversion introduced in [50].However, in this work, the bulk-driven devices operating in weak inversion were applied to the proposed structure.Operation in weak inversion generally leads to a narrower linear range compared to the strong inversion version of the circuit.On the contrary, the use of bulk-driven terminals extends the linear range compared to the gate-driven realization.Moreover, the input capacitive divider further extends the linear range.The result is the relatively large linear range of the OTA, even for weakly inverted devices biased with very low currents.A similar input stage was first described and verified experimentally in [51,52].The M 1SD and M 2SD transistors operate in a triode region, introducing negative feedback to the input pair M 1 and M 2 .Controlling their characteristics by the signals seen at the gates of the main transistors of the pair M 1 and M 2 further improves the linearity of the input stage [51].
Assuming that all the capacitances C Bi are identical, the small-signal transconductance of the OTA is given by: where η = g mb1,2 /g m1,2 is the bulk to gate transconductance ratio at the operating point, n is the number of input terminals, n p is the subthreshold slope factor for the p-channel transistors, U T is the thermal potential, I set is the biasing current and k is the ratio of aspect ratios of the triode-region transistors M 1SD , M 2SD and the main transistors of the input pair M 1 and M 2 : Note that the best linearity performance is obtained for k = 0.5 [51].In such a case, the circuit transconductance can be expressed as: The use of an input capacitive divider and bulk-driven devices extends the linear range of the OTA, but on the other hand, it increases the input noise and decreases the voltage gain.For instance, with η = 1/3 and 3 inputs, the circuit transconductance is lowered 9 times as compared to a gate-driven input pair.Consequently, the low-frequency voltage gain of the circuit is decreased by around 19 dB.To counteract this effect, we applied a cascode high-impedance output stage, composed of the transistors M 5 -M 12 .With the applied output stage, the low-frequency gain of the OTA can be approximated as: Consequently, this gain is improved by the factor of g m r ds (intrinsic voltage gain of an MOS transistor), which for the applied technology and operating point exceeds 30 dB.
As was already mentioned, the applied technique increases the linear range of the OTA.On the other hand, however, it increases its input noise due to signal attenuation.Since the input noise is increased in the same proportion, the dynamic range (DR) of the OTA remains unchanged and is equal to the DR of the GD OTA with a single differential input and the applied linearization technique.Nevertheless, the larger linear range allows for avoiding hard nonlinearities for the large voltage swings and V DD , as applied in the considered design.

Proposed Tunable High-Q Voltage-Mode Universal Filter
Figure 4 shows the proposed tunable high-Q voltage-mode universal filter using OTAs.Figure 4a shows the proposed voltage-mode universal filter using conventional OTAs and Figure 4b shows the proposed voltage-mode universal filter using MI-OTAs.It should be noted from Figure 4a,b that the universal filter using MI-OTAs has a significantly reduced number of OTAs (10 OTAs vs. 4 MI-OTAs).The input terminals of the universal filter in Figure 4b are connected to the high-input impedance of the OTA; thus, the proposed universal filter offers high input impedance, which is ideal for voltage-mode circuits.The output impedance can be given by 1/g m4 .
Figure 4 shows the proposed tunable high-Q voltage-mode universal filter OTAs. Figure 4a shows the proposed voltage-mode universal filter using conven OTAs and Figure 4b shows the proposed voltage-mode universal filter using MI-OT should be noted from Figure 4a,b that the universal filter using MI-OTAs has a s cantly reduced number of OTAs (10 OTAs vs. 4 MI-OTAs).The input terminals universal filter in Figure 4b are connected to the high-input impedance of the OTA the proposed universal filter offers high input impedance, which is ideal for voltagecircuits.The output impedance can be given by 1/ .Letting g m1a = g m1b = g m1 , g m2a = g m2b = g m2 , g m3a = g m3b = g m3c = g m3 , g m4a = g m4b = g m4c = g m4 , and using nodal analysis, the output voltage of Figure 4a,b can be given by: where + g m1 g m2 .The variant filtering functions are shown in Table 1.It should be noted that the variant non-inverting and inverting transfer functions of the LPF, BPF, HPF, BSF, and APF can be obtained without inverted input signal requirements.For the BPF, if the input signals are V in3 and V in4 , varying the quality factor will increase the gain of the transfer functions.Conversely, if the input signals are V in5 or V in6 and V in7 or V in8 , varying the quality factor will not affect the gain of the transfer functions.
Table 1.Obtaining the variant filtering functions of the proposed universal filter.

LPF
Non-inverting Non-inverting , the transfer function of the non-inverting APF can be expressed as in (7), and letting the transfer function of the inverting APF can be expressed as in (8).
These transfer functions can be used to express the magnitudes and phase responses of APFs.
The natural frequency (ω o ) and the quality factor (Q) can be given by: The parameter ω o can be controlled electronically by g m1 and g m2 and the parameter Q can be controlled by C 3 and/or g m3 .If C 3 is used as a parameter, C 1 and C 2 could be constant (C 1 = C 2 ), and if g m3 is used as a parameter, g m1 and g m2 could be constant (g m1 = g m2 ).Thus, the parameter Q can be tuned by varying the values of the capacitance and resistance.

Effects of the Nonidealities of the MI-OTA
Figure 5 shows the nonideal model of the OTA [53].There are three components that have been considered: (i) the input capacitances C + , C − , and input resistances R + , R − ; (ii) the output capacitance C o and output resistance R o (or conductance g o ); and (iii) the frequency-dependent transconductance g m .

Effects of the Nonidealities of the MI-OTA
Figure 5 shows the nonideal model of the OTA [53].There are three componen have been considered: (i) the input capacitances C+, C−, and input resistances R+, R−; output capacitance Co and output resistance Ro (or conductance  ); and (iii) t quency-dependent transconductance  .The frequency-dependence of  ( ) can be approximated [54] as: where  1  ⁄ and  denotes the second pole of the OTA.The first consideration can be rewritten by using (9) and the denominator of ( where  is the output capacitance of the j-th  , and  and  are the input itances of the j-th  (j = 1, 2, 3, 4).
The parasitic effects on the natural frequency and the quality factor of the pro universal filter can be avoided by choosing:

Simulation Results
The proposed MI-OTA and the filter application were simulated in the Caden tuoso System Design Platform using the 0.18 µm CMOS technology from TSMC (T Semiconductor Manufacturing Company, Taiwan).The aspect ratio of the The frequency-dependence of g m (g mn ) can be approximated [54] as: where τ = 1/ω p and ω p denotes the second pole of the OTA.
The first consideration can be rewritten by using ( 9) and the denominator of (6) as: It can be seen that the parasitic poles (τ i ) of the i-th OTA affect the filter performance.The influence of the parasitic pole can be neglected if the following conditions are met: Next, the parasitic capacitances and resistances (or conductance) have been considered by letting the transconductance g m be ideal.Considering Figure 4b, the values of the capacitors C 1 , C 2 , and C 3 can be represented, respectively, by C ′ 1 , C ′ 2 , and C ′ 3 , where , where C oj is the output capacitance of the j-th g m , and C +j and C −j are the input capacitances of the j-th g m (j = 1, 2, 3, 4).
When the parasitic resistances are considered, the capacitors , where R oj is the output resistance of the j-th g m , R +j and R −j are the input resistances of the j-th g m (j = 1, 2, 3, 4).
The parasitic effects on the natural frequency and the quality factor of the proposed universal filter can be avoided by choosing:

Simulation Results
The proposed MI-OTA and the filter application were simulated in the Cadence Virtuoso System Design Platform using the 0.18 µm CMOS technology from TSMC (Taiwan Semiconductor Manufacturing Company, Taiwan).The aspect ratio of the MOS transistors of the MI-OTA in Figure 1 is listed in Table 2.The voltage supply was 1 V (V DD = −V SS = 0.5 V).The proposed MI-OTA consumed 30 µW for a 5 µA setting current.To obtain the dynamic characteristic of the MI-OTA, a sine wave of 1 kHz was applied to the input of the OTA.The extended linearity of the MI-OTA with various setting currents Iset = (2.5, 5, 10, 20) µA is shown in Figure 7a.The transconductance AC characteristic of the MI-OTA with various setting currents Iset = (2.5, 5, 10, 20) µA is shown in Figure 7b.The transconductance was (2.9, 4.9, 7.9, 12.6) µS, respectively.The transconductance AC characteristic with Iset = 5 µA was repeated for the Monte Carlo (MC) analysis with 200 runs and process, voltage, and temperature (PVT) corners, as shown in Figure 8.To obtain the dynamic characteristic of the MI-OTA, a sine wave of 1 kHz was applied to the input of the OTA.The extended linearity of the MI-OTA with various setting currents I set = (2.5, 5, 10, 20) µA is shown in Figure 7a.The transconductance AC characteristic of the MI-OTA with various setting currents I set = (2.5, 5, 10, 20) µA is shown in Figure 7b.The transconductance was (2.9, 4.9, 7.9, 12.6) µS, respectively.The transconductance AC characteristic with I set = 5 µA was repeated for the Monte Carlo (MC) analysis with 200 runs and process, voltage, and temperature (PVT) corners, as shown in Figure 8.
Sensors 2024, 24, x FOR PEER REVIEW 8 of 16 transistors of the MI-OTA in Figure 1 is listed in Table 2.The voltage supply was 1 V (VDD = −VSS = 0.5 V).The proposed MI-OTA consumed 30 µW for a 5 µA setting current.To obtain the dynamic characteristic of the MI-OTA, a sine wave of 1 kHz was applied to the input of the OTA.The extended linearity of the MI-OTA with various setting currents Iset = (2.5, 5, 10, 20) µA is shown in Figure 7a.The transconductance AC characteristic of the MI-OTA with various setting currents Iset = (2.5, 5, 10, 20) µA is shown in Figure 7b.The transconductance was (2.9, 4.9, 7.9, 12.6) µS, respectively.The transconductance AC characteristic with Iset = 5 µA was repeated for the Monte Carlo (MC) analysis with 200 runs and process, voltage, and temperature (PVT) corners, as shown in Figure 8. acceptable range.The frequency and phase characteristics of the filter with Iset1-4 = 5 µA and C1-3 = 100 pF are shown in Figure 9.The cutoff frequency was 7.85 kHz.The simulation of the LPF was repeated with MC and PVT corners analyses, as shown in Figure 10.While the curves for the PVT overlapped, for the MC, the gain variation at low frequencies was in the range of −3.1 dB to 1.6 dB and the cutoff frequency variation was in the range of 0.72 kHz to 9.3 kHz, which can be realigned by adjusting the setting current.To determine the third intermodulation distortion (IMD3) of the BPF, two closed tones were applied to the input of the BPF.Both tones were a sine wave with an amplitude of 25 mV but with different frequencies: 7.5 kHz and 8.2 kHz.The transient analyses of the input and output signal are shown in Figure 13a    To determine the third intermodulation distortion (IMD3) of the BP tones were applied to the input of the BPF.Both tones were a sine wave with of 25 mV but with different frequencies: 7.5 kHz and 8.2 kHz.The transie the input and output signal are shown in Figure 13a  To determine the third intermodulation distortion (IMD3) of the BPF, two closed tones were applied to the input of the BPF.Both tones were a sine wave with an amplitude of 25 mV but with different frequencies: 7.5 kHz and 8.2 kHz.The transient analyses of the input and output signal are shown in Figure 13a and the spectrum of the output signal is shown in Figure 13b.The IMD3 was −43.6 dB, which indicates a 0.66% THD.
The equivalent output noise is shown in Figure 14.The integrated noise in the filter bandwidth of 4.8 kHz to 12.5 kHz was 485.7 µV; hence, the dynamic range DR was calculated to be 40 dB for 1% IMD3.
The OTA-based universal filters in [16,34,41,45,46] were used as a comparison, as shown in Table 3.Compared with the filters in [16,34], which offer independent/electronic control of the ω o and Q as well as a high-Q filter, the proposed filter offers larger transfer functions that cover both the non-inverting and the inverting transfer functions of the LPF, HPF, BPF, BSF, and APF.Compared with the filters in [41, 45,46], which provide sub-volt supply voltage, the proposed filter offers independent/electronic control of the ω o and Q and a high-Q filter.Compared with the filters in [16,34,41], the proposed filter offers low voltage and low power consumption.
To determine the third intermodulation distortion (IMD3) of the BPF, two closed tones were applied to the input of the BPF.Both tones were a sine wave with an amplitude of 25 mV but with different frequencies: 7.5 kHz and 8.2 kHz.The transient analyses of the input and output signal are shown in Figure 13a and the spectrum of the output signal is shown in Figure 13b.The IMD3 was −43.6 dB, which indicates a 0.66% THD.The equivalent output noise is shown in Figure 14.The integrated noise in the filter bandwidth of 4.8 kHz to 12.5 kHz was 485.7 µV; hence, the dynamic range DR was calculated to be 40 dB for 1% IMD3.The OTA-based universal filters in [16,34,41,45,46] were used as a comparison, as shown in Table 3.Compared with the filters in [16,34], which offer independent/electronic control of the ωo and Q as well as a high-Q filter, the proposed filter offers larger transfer functions that cover both the non-inverting and the inverting transfer functions of the LPF, HPF, BPF, BSF, and APF.Compared with the filters in [41, 45,46], which provide sub-volt supply voltage, the proposed filter offers independent/electronic control of the ωo and Q and a high-Q filter.Compared with the filters in [16,34,41], the proposed filter offers low voltage and low power consumption.Note: a = the capacitance varies from 25 to 800 pF, b = the biasing current varies from 0.312 to 10 µA, c = the capacitance varies from 2 to 128 nF, d = the biasing current varies from 1 to 70 µA, e = the g m varies from 1 to 3 mS.

Conclusions
In this paper, a new multiple-input single-output voltage-mode universal filter using MI-OTAs is proposed.In this filter, the pole-Q can be tuned by varying the capacitance and setting current.The natural frequency can also be electronically controlled.The proposed filter uses four MI-OTAs that its differential pair realizes using the multiple-input MOS transistor technique, which does not increase the power consumption of the OTA.This work shows that an MI-OTA-based filter with 10 transfer functions, namely the non-inverting and inverting transfer functions of the LPF, HPF, BPF, BSF, and APF, can be obtained without changing the circuit topology.The proposed filter is suitable for low-voltage-supply, lowpower-consumption and low-frequency applications like the biomedical one, since it is capable of operating with a 1 V supply voltage and consumes 120 µW of power for a 5 µA setting current.

Figure 2 .
Figure 2. CMOS realization of the MI-OTA using the MIBD-MOST technique.

Figure 1 .
Figure 1.Electrical symbol of the MI-OTA.

Figure 1 .
Figure 1.Electrical symbol of the MI-OTA.

Figure 2 .
Figure 2. CMOS realization of the MI-OTA using the MIBD-MOST technique.

Figure 2 .
Figure 2. CMOS realization of the MI-OTA using the MIBD-MOST technique.
and C ′ 3 are expressed, respectively, by C ′′ −300 mV, V B2 = 200 mV The parasitic impedances of the MI-OTA are shown in Figure 6, where R +,− = 42 GΩ, C +,− = 0.25 pF for the input terminal, and R o = 32.4MΩ, C o = 52.8fF for the output terminal.

Figure 9 .Figure 10 .
Figure 9.The frequency and phase characteristics of the filter.

Figure 12 .
Figure 12.The frequency characteristic of the BPF with different Iset1-4.

Figure 13 .
Figure 13.(a) The transient characteristic of the BPF and (b) the spectrum of the output signal.

Figure 11 .Figure 11 .
Figure 11.The frequency characteristic of the BPF with different values for (a) the capacitor C 3 and (b) the setting current I set3 .

Figure 12 .
Figure 12.The frequency characteristic of the BPF with different Iset1-4.

Figure 12 .
Figure 12.The frequency characteristic of the BPF with different I set1-4 .

Figure 13 .Figure 13 .
Figure 13.(a) The transient characteristic of the BPF and (b) the spectrum of the output signal.

Figure 14 .
Figure 14.The output noise of the BPF.

Figure 14 .
Figure 14.The output noise of the BPF.
It can be seen that the parasitic poles ( ) of the i-th OTA affect the filter perform The influence of the parasitic pole can be neglected if the following conditions are Next, the parasitic capacitances and resistances (or conductance) have been c ered by letting the transconductance  be ideal.Considering Figure4b, the values capacitors C1, C2, and C3 can be represented, respectively, by  ,  , and  , wher

Table 2 .
Parameters of the components of the MI-OTA.

Table 2 .
Parameters of the components of the MI-OTA.

Table 2 .
Parameters of the components of the MI-OTA.

Table 3 .
Comparison of the properties of this work with those of high-Q universal filters.

Table 3 .
Comparison of the properties of this work with those of high-Q universal filters.