Dual-Mode Biquadratic Filter Employing Second-Generation Voltage Conveyors

In this paper, a dual-mode biquadratic filter is suggested. The proposed filter employs two Second-Generation Voltage Conveyors (VCIIs) along with four resistors and two capacitors. The suggested filter can realize all five standard biquadratic filter functions such as lowpass (LP), bandpass (BP), highpass (HP), bandstop (BS), and allpass (AP) in both voltage-mode (VM) and current-mode (CM) without needing to modify its circuit structure. The quality factor (Q) and natural angular frequency (ωo) can be accurately and separately controlled through the passive component. It additionally offers the capability of providing the output voltage at the low-output impedance terminal in VM. The effects of the VCII non-idealities on the filter performance have been analyzed in detail. The proposed filter also offers low active and passive sensitivity features. Simulation results achieved with PSPICE software using TSMC CMOS 0.18 μm parameter have been validated and compared with the theoretical findings.


INTRODUCTION
Active filters play a crucial role in the areas of analog signal processing, electronic devices, and data communications, especially active filters that permit all five standard biquadratic filter functions simultaneously, including lowpass (LP), bandpass (BP), highpass (HP), bandstop (BS), and allpass (AP) responses with the same topology.In recent years, the design of dual-mode (DM) biquadratic filters has gained a lot of attention from researchers since they can operate in both voltage-mode (VM) and current-mode (CM) simultaneously.The DM filter can be served for wide applications since it can be operated with either voltage or current signals.This feature makes the DM filter more versatile and flexible for practical filtering applications and requirements.A variety of DM universal biquadratic filters based on various active components were recently introduced in the literature [1][2][3][4][5][6].In [1][2], they require more than two active components.Besides, in [2], a large number of passive components are needed for its realization.These cases cause high power dissipation and a large silicon chip area.The voltage-mode filter aims to provide a low output impedance for straightforward cascade connections to the voltage circuit.However, the filters described in [1,[3][4][5][6] fail to fulfill this criterion.Furthermore, table 1 shows a comparative analysis of the functional characteristics of the proposed DM filter to those suggested in the previously mentioned related works.
The Second-Generation Voltage Conveyor (VCII) was first mentioned in [7].Recently, many researchers have become interested in VCII due to its outstanding features, including its simple circuitry, high operating frequency, low power consumption, compact silicon chip area, and low impedance voltage output terminal [8][9].In the literature, VCII was used in the design of many various applications, i.e., capacitance multiplier [10][11], inductance simulator [9,[12][13] oscillator [14][15][16], and biquadratic filter [17][18].A DM biquadratic filter with multiple inputs and multiple outputs (MIMO) is, therefore, presented in this paper.Two VCIIs, four resistors, and two capacitors are required to be capable of providing all five of the standard filter responses in both VM and CM.The quality factor (Q) and natural angular frequency ( o ) of the proposed filter can be accurately and separately controlled.PSPICE simulation utilizing TSMC CMOS 0.18-m technology was used to verify the proposed circuit's functionality.

CIRCUIT DESCRIPTION 2.1 Second-Generation Voltage Conveyor (VCII)
Figure 1 shows the circuit symbol of the VCII, which is a threeterminal active building block.In the ideal case, the terminal relation of VCII is found as follows [7][8]: where the plus and minus signs in (1) denote the plus-type and minus-type VCII (VCII±), respectively.According to (1), the VCII device comprises the y and x terminals as low-and highimpedance current terminals, respectively, and the z terminal as a low-impedance voltage terminal.The output current at the x terminal (i x ) is transferred from the current flowing through the y terminal (i y ), whose direction depends on the type of VCII device.Furthermore, the voltage drop at the x terminal (v x ) is conveyed to the output voltage at the z terminal (v z ).The internal CMOS implementation of the VCII± is shown in Figure 2, where the transistors M 1 -M 16 perform a current buffer, whereas M 17 -M 23 serve as a voltage buffer [12].

Proposed DM biquadratic filter
The versatile DM biquadratic filter with multiple-input and multipleoutput (MIMO) terminals proposed in this communication is shown in Figure 3.The proposed filter consists of two VCIIs, four resistors, and two capacitors, which can be operated in both VM and CM without changing the circuit configuration.By taking the ideal VCII's characteristics in (1) into account, the output voltage (v out ) is achieved at the low-output impedance terminal and found to be: 2), the five standard biquadratic filter functions can be accomplished as follows: • LP response is acheviced with v in (input voltage) = v 1 , v 2 = v 3 = 0 (grounded); Moreover, if v 1 = v 2 = v 3 = 0, the proposed circuit can also be realized as a CM filter through the output currents (i LP , i BP , and i HP ).The five current transfer functions can be accomplished as follows: The BS response was achieved by summing the HP and LP signals, while the summing of HP, BP, and LP signals realizes the AP response as follows:  In all filter responses, the natural angular frequency ( o ) and the quality factor (Q) are found to be: From ( 9) and ( 10), the Q value can be adjusted separately from the o value by adjusting the R 2 value.Due to the fact that the proposed circuit yields a quality factor with a denominator exceeding the numerator, Q values greater than one cannot be achieved.

NON-IDEAL ANALYSIS
This section discusses the VCII's non-ideal performance, which influenced the suggested filter in Figure 3.In this scenario, the VCII characteristic mentioned in (1) can be rewritten as [8]: where and denote the current and voltage tracking errors, respectively.Reexamining the proposed circuit in Figure 3, the parameters o and Q with the non-ideality effects can be expressed as: = 2 ( 2 + 3 )  The active and passive sensitivities of the o and Q values are calculated and listed as follows: The investigation can easily deduce that all sensitivity coefficients of o and Q are no more than unity in both modes of operation.

SIMULATION VERIFICATIONS
In this section, the simulation results provided from PSPICE simulation employing the internal CMOS implementation of VCII in Figure 2 have been verified.The aspect ratios of transistors using TSMC 0.18-m CMOS real process parameters are tabulated in Table 2.The supply bias voltages of ±0.75 V and the bias currents of I B1 = I B2 = 15 A were taken.
In all simulations, the following component values were chosen:

CONCLUSIONS
This work proposes a biquadratic filter operating in both voltage and current modes.The proposed filter employs two VCIIs as active elements, along with four resistors and two capacitors.This circuit is capable of generating five standard biquadratic filtering functions, including LP, BP, HP, BS, and AP, in both operating modes with a single circuit structure.In VM, the output voltage can be realized at the low-impedance output terminal, which is suitable for cascading connection features for easily achieving a high-order filter.The impact of the non-ideal gain can be readily mitigated by adjusting the resistance values.The Q-and f o -values  can be separately controlled with low sensitivity coefficients.The workability of the proposed filter has been proven and shown to be in good agreement with the theory through PSPICE simulation software that utilizes TSMC CMOS 0.18 m process parameter.
Transistors W ( m)/L ( m) M 1 -M 2 , M 17 -M 18 10/0.18M 3 -M 4 , M 6 -M 10 , M 19 -M 20 5/0.18 M 5 , M 21 50/0.18M 11 -M 16 , M 22 -M 23 2.4/0.18 100 to realize the filter with f o = 1.59 MHz and Q = 0.67.The ideal and simulation results for the LP, BP, and HP voltage responses are given in Figure 4(a).Figures 4(b) -4(c) illustrate the simulated gain and phase plots of the BS and AP voltage responses compared with the theory.The current responses using the above component values are also simulated and plotted in Figure 5.The total power consumption of the circuit was estimated to be 0.57 mW.

Figure 4 :Figure 5 :
Figure 4: Ideal and simulation voltage responses of the circuit in Figure 3 (a) LP, BP and HP; (b) BS; (c) AP.

Figure 6 :
Figure 6: Simulated BP responses in VM by varying f o with Q = 0.67.

Figure 7 :
Figure 7: Simulated BP responses in VM by varying Q with f o = 1.59 MHz.

Table 1 :
A comparison of the proposed DM filter and its related works