Conveyor-Based Single-Input Triple-Output Second-Order LP/BP and Cascaded First-Order HP Filters

Abstract

In this paper a new single-input independent multiple-output universal tunable filter employing second-generation current conveyors (CCII) and second-generation voltage conveyors (VCII) as active elements is presented. The proposed filter has been analyzed at transistor level, using a CMOS standard AMS 0.35 μm technology, and implemented using discrete components based on the commercially available AD844. A detailed mathematical analysis is carried out, considering also parasitic impedances and non-ideal parameters. The low-pass, band-pass, and high-pass responses are simultaneously obtained and experimentally verified at 10 kHz central frequency where the voltage gain is about 27 dB for each output. THD analysis has been performed to evaluate the proposed work.

1. Introduction

Electronic filters are fundamental building blocks in many signal-processing applications, including audio amplifiers, phase correction, phase-locked loop (PLL) demodulators, and loudspeaker crossover networks [1,2,3,4]. Traditionally, active filters have been realized using operational amplifiers (op-amps) in voltage mode (VM). However, VM circuits exhibit intrinsic drawbacks such as low bandwidth, limited dynamic range, and relatively higher power consumption [5]. These drawbacks are particularly serious for projects designed employing modern CMOS technologies, where supply voltage is strongly reduced [6]. In addition, VM-based implementations often rely on a large number of components or floating passive elements, both of which impede efficient integrated circuit (IC) realization [3,7].

Current-mode (CM) circuits constitute a valid alternative, especially attractive for high-frequency and low-voltage applications, offering higher bandwidth, larger dynamic range, improved linearity, lower power consumption, and reduced sensitivity to parasitic node capacitances [5,8,9]. Universal (or multifunction) filters are of particular interest, as they can provide multiple second-order responses—such as low-pass (LP), high-pass (HP), band-pass (BP), band-stop (BS), and all-pass (AP)—from a single input [3,4,5]. Then, single-input multiple-output (SIMO) architectures [10,11] are often preferred to multiple-input multiple-output (MIMO) realizations [12,13,14], due to their reduced circuit complexity and ease of design [15,16,17].

Despite these advantages, reported SIMO filters still present several limitations. Many topologies need a significant number of active and passive elements [5,15,17], or employ floating resistors and capacitors, which are generally undesirable in IC fabrication [3,5]. Conversely, solutions employing only grounded passive elements are better suited for IC integration. Some works aim to reduce the component count [6,8,18] or to realize resistor-less architectures [11,19,20]. Furthermore, not all reported filters are capable of simultaneously providing the complete set of biquadratic responses [21]. Several designs implement only LP, BP, and HP functions [15,19], whereas BS and AP responses often require additional circuitry or output interconnections [15]. Moreover, the output impedance is not always compatible with direct cascading, while proper CM or VM operation ideally requires high- and low-impedance outputs, respectively [21]. Additionally, in many reported topologies the filtering responses are not fully independent, since some outputs are derived from others or share passive components. This internal dependence complicates design flexibility, makes parallel analysis of the same input signal difficult, and may introduce unwanted interactions between responses.

Electronic tunability is another critical design issue. Some proposals do not have orthogonal control of the natural frequency (ω₀) and quality factor (Q), or exhibit coupling between tuning parameters [6,14]. High-frequency performance is also frequently limited by parasitic effects [17,18,22]. For example, series capacitors connected to the X terminals of current-feedback operational amplifiers (CFOAs) [3], or second-generation current conveyors (CCIIs) [8], may interact with intrinsic parasitic resistances, causing performance degradation. Similarly, MOS-only implementations, although compact, often suffer from higher-order effects due to parasitic capacitances [19].

This work introduces a SIMO multifunction filter mainly based on the second-generation voltage conveyor (VCII). The principle underlying the proposed design is the use of independent, grounded passive networks connected to the active core, ensuring that the low-pass, band-pass, and high-pass responses are obtained simultaneously and without internal component dependance. The aim of this work is to realize a low-power solution capable of simultaneously providing LP, BP, and HP responses with well-defined output impedances, and robustness against nonidealities using current mode active blocks. As a result, each filtering path operates autonomously and the same input signal can be processed in parallel across different frequency bands, without interaction or degradation among the responses.

The paper is organized as follows. Section 2 describes the active element employed in the proposed design. Section 3 details the circuit configuration and presents the theoretical analysis of the filtering responses. Section 4 reports simulation and measurement results validating the proposed approach. Finally, Section 5 concludes the paper by highlighting the main features and advantages of the presented solution.

2. Current-Mode Active Blocks Overview

In this section, the two main current-mode active blocks employed for analog signal processing are presented: the second-generation current conveyor (CCII) and the second-generation voltage conveyor (VCII) [23,24,25].

The CCII is a three-terminal device (X, Y, Z) that behaves as a voltage buffer from Y to X and as a current buffer from X to Z.

Figure 1 illustrates the CCII symbol (a) and its equivalent circuit (b). The equivalent impedances at the Y and Z terminals are typically of the parallel RC type, while the X terminal impedance is generally of the RLC type. This configuration is comprised as follows:

• Y is a high-impedance (ideally infinite) voltage input terminal;
• X is a low-impedance (ideally zero) current input/voltage output terminal;
• Z is a high-impedance (ideally infinite) current output terminal.

The ideal voltage–current relationships of a CCII are defined by the following matrix:

$$\left[\begin{array}{c}{I}_Y\\ V_X\\ I_Z\end{array}\right]=\left[\begin{array}{ccc}0& 0& 0\\ \alpha & 0& 0\\ 0& \pm \beta & 0\end{array}\right]\left[\begin{array}{c}{V}_Y\\ I_X\\ V_Z\end{array}\right]$$

(1)

where $\alpha$ and $\beta$ are ideally unity voltage and current gains, respectively. The sign of β indicates whether the device is a positive or negative type CCII, denoted as CCII+ and CCII-, respectively.

In addition, the real voltage–current relationships of a CCII, considering terminal parasitic impedances (shown also in Figure 2), are defined by

$$\left[\begin{array}{c}{I}_Y\\ V_x\\ I_z\end{array}\right]=\left[\begin{array}{ccc}{sC}_y& 0& 0\\ \alpha & \left(r_x+{sL}_x\right)//{\displaystyle \frac{1}{{sC}_x}}& 0\\ 0& \pm \beta & {\displaystyle \frac{1}{r_z//\frac{1}{{sC}_z}}}\end{array}\right]\left[\begin{array}{c}{V}_y\\ I_x\\ V_z\end{array}\right]$$

(2)

with $C_y$, $r_x$, $L_x$, $C_x$, $r_z,$ and $C_z$ being the parasitic capacitance at Y terminal, the parasitic resistance, inductance and capacitance associated with X terminal, and the parasitic resistance and capacitance at Z terminal, respectively. The VCII is the dual of the CCII and shares most of its characteristics. However, unlike the CCII, the VCII provides a voltage output, which simplifies signal acquisition in applications requiring voltage monitoring. Since its introduction, the CCII and VCII have been widely applied in the realization of amplifiers [26,27,28], sensor read-out circuits [29,30], instrumentation amplifiers [31], voltage-to-current conversions, and various other analog processing systems [32,33,34].

Figure 3 presents the VCII symbol and its equivalent circuit. An ideal VCII works as a current buffer from Y to X and as a voltage buffer from X to Z. This configuration is comprised as follows:

• Y is a low-impedance (ideally zero) current input terminal;
• X is a high-impedance (ideally infinite) voltage input and current output terminal;
• Z is a low-impedance (ideally zero) voltage output terminal.

The ideal voltage–current relationships of a VCII are defined by the following matrix:

$$\left[\begin{array}{c}{I}_X\\ V_Y\\ V_Z\end{array}\right]=\left[\begin{array}{ccc}0& \pm \beta & 0\\ 0& 0& 0\\ \alpha & 0& 0\end{array}\right]\left[\begin{array}{c}{V}_X\\ I_Y\\ I_Z\end{array}\right]$$

(3)

Here, the plus or minus sign of β corresponds to the positive or negative type VCII, denoted as VCII+ and VCII-, respectively. The non-ideal voltage–current relationships of a VCII are defined by the following matrix:

$$\left[\begin{array}{c}{I}_x\\ V_y\\ V_z\end{array}\right]=\left[\begin{array}{ccc}{\displaystyle \frac{1}{r_x}}+{sC}_x& \pm \beta & 0\\ 0& r_y+{sL}_y& 0\\ \alpha & 0& r_z+{sL}_z\end{array}\right]\left[\begin{array}{c}{V}_x\\ I_y\\ I_z\end{array}\right]$$

(4)

where $r_x$ and $C_x$ represent the parasitic resistance and capacitance at X terminal, $r_y$ and $L_y$ are the parasitic resistance and inductance at Y terminal, and, finally, $r_z$ and $L_z$ are the parasitic resistance and inductance associated with Z terminal, respectively. The VCII symbol with parasitic terminal impedances is also shown in Figure 4. Figure 5 and Figure 6 illustrate the practical transistor-level implementations of the CCII and VCII employed in this work, respectively. As seen from Figure 6, the less-known VCII is composed of a current buffer and a voltage buffer. The input current to the Y terminal is transferred to the X terminal with a current gain of about 1 by a current buffer made of M₁-M₇ transistors. The voltage buffer between X and Z terminals is a flipped voltage follower (FVF) made by M₉ and M₁₀ transistors. The used FVF provides a low output impedance at Z terminal. The feedback loop formed by M₁-M₅ transistors provides a low input impedance at the Y terminal. The voltage and current gains and node impedances of the CCII and VCII used for the filter are shown in

Table 1. CCII and VCII characteristic parameters.

Parameter	α	β	ZX	ZY	ZZ
CCII	1	0.99	7.4 kΩ	10 MΩ	2 MΩ
VCII	1	1	1.7 MΩ	54 Ω	202 Ω

.

All values were calculated at a frequency of 10 kHz, where all the parasitic impedances are of resistive kind. The CCII and VCII used have been designed and simulated using standard AMS 0.35 μm CMOS technology. The circuit operates at a ±1.65 V supply voltage; the aspect ratios of the used transistors are reported in

Table 2. Aspect ratio of the used transistors.

CCII	W (μm)	L (μm)	VCII	W (μm)	L (μm)
M1–M2	50	0.35	M1–M2	30	0.35
M3–M4	35	1.2	M3–M4	4.2	0.35
M5–M10	22.05	0.35	M5	7	0.35
M6–M7–M8–M9	10	2.1	M6–M7	50	3.5
			M8–M9	28.7	1.4
			M10	14	52
			MB0–MB1–MB2–MB3	2.1	0.7
			MB4–MB5	4.2	0.7

.

3. The Proposed Multifunction Filter

The proposed multifunction analog filter, designed for kHz-range frequencies, is suitable for applications such as pre-/post-filtering in audio ADC/DAC chains, signal recovery in specific frequency bands, and sensing systems. The filter is centered, as an example, at 10 kHz frequency and is employed using CCII and VCIIs. In the following, we present the general equation of the trans-resistance (in absolute value) for the circuit shown in Figure 7, considering ideal active blocks, where the passive components are represented by their equivalent impedances:

$$v_{OUT}=v_X=-Z_3{i}_y=-Z_3({\displaystyle \frac{Z_2}{Z_1+Z_2}}{i}_{IN}+{\displaystyle \frac{v_{OUT}}{Z_4}})$$

(5)

$${\displaystyle \frac{v_{OUT}}{i_{IN}}}={\displaystyle \frac{-{Z_{2}Z}_3{Z}_4}{(Z_1+Z_2)(Z_3+Z_4)}}$$

(6)

The impedances $Z_n$ (with n = 1, 2, 3, 4) correspond to passive components employed in signal filtering and $v_{out}$ is the output voltage obtained from the generic block in Figure 5 by injecting a current $i_{in}$into the input. Replacing each impedance with its corresponding passive element, in particular Z₁ = R₁, Z₂ = 1/(sC₁), Z₃ = R₂, and Z₄ = (1/sC₂), the equivalent circuit for a second-order low-pass (LP) filter is obtained, whose transfer function, with respect to the input current, and for ideal active blocks, is given by

$${\displaystyle \frac{v_{OUT,LP}}{i_{IN}}}={\displaystyle \frac{-R_2}{\left({1+sR}_1{C}_1\right)\left(1+{sR}_2{C}_2\right)}}$$

(7)

A value of 16 kΩ was selected for $R_1$ to establish the gain in the bandwidth, while $R_2$was set to 10 kΩ. The pole frequencies were chosen to be 10 kHz and 40 kHz, ensuring sufficient distance to prevent interference between them. The values of $C_1$and $C_2$were determined by deriving the equations that describe the behavior of each pole and substituting the known parameters, namely the selected frequencies and resistances. The equations representing the poles are the following:

$$f_{L{P}_1}={\displaystyle \frac{1}{2\pi R_1{C}_1}}$$

(8)

$$f_{L{P}_2}={\displaystyle \frac{1}{2\pi R_2{C}_2}}$$

(9)

Using these equations, the capacitor values were calculated as C₁ = 1 nF and C₂ =0.4 nF. In Equations (8) and (9), the variables $f_{L{P}_1}$ and $f_{L{P}_2}$ represent the pole frequencies of the low-pass filter and are functions of the impedance values.

Applying the same procedure, the following types of elements to be implemented for a band-pass (BP) filter have been chosen: Z₁ = 1/(sC₃), Z₂ = R₃, and Z₃ = (1/sC₄) and Z₄ = R₄. The related transfer function is the following:

$${\displaystyle \frac{v_{OUT,BP}}{i_{IN}}}={\displaystyle \frac{-s{C_3{R}_{3}R}_4}{(1+s{C}_3{R}_3)(1+s{R}_4{C}_4)}}$$

(10)

The pole frequencies of the transfer function in Equation (10) are given in (11) and (12). For the bandpass filter, the resistor and capacitor values were set to 16 kΩ and 1 nF, respectively, to obtain a center frequency of 10 kHz. This choice follows the canonical form given in Equation (13), from which the characteristic equations for the natural frequency ω₀ (Equation (14)) and the quality factor Q (Equation (15)) with Q = 0.5 are derived.

Recalling the typical canonical forms of the BP filters, the main characteristics are the following:

$$f_{B{P}_1}={\displaystyle \frac{1}{2\pi R_3{C}_3}}$$

(11)

$$f_{B{P}_2}={\displaystyle \frac{1}{2\pi R_4{C}_4}}$$

(12)

$$H\left(s\right)={\displaystyle \frac{Ks}{s^2+\left(\frac{{\omega }_0}{Q}\right)s+{\omega }_0^2}}={\displaystyle \frac{-s{C_3{R}_{3}R}_4}{(1+s{C}_3{R}_3)(1+s{R}_4{C}_4)}}$$

(13)

$${\omega }_0={\displaystyle \frac{1}{\sqrt{Kx}}}={\displaystyle \frac{1}{\sqrt{R_3{R}_4{C}_3{C}_4}}}$$

(14)

$$Q={\displaystyle \frac{\sqrt{\alpha Kx}}{K\alpha +x}}={\displaystyle \frac{\sqrt{R_3{R}_4{C}_3{C}_4}}{C_3{R}_3+C_4{R}_4}}$$

(15)

Applying the well-known definition of sensitivity,

$$S_x^F={\displaystyle \frac{\raisebox{1ex}{$∆F$}\!\left/ \!\raisebox{-1ex}{$F$}\right.}{\raisebox{1ex}{$∆x$}\!\left/ \!\raisebox{-1ex}{$x$}\right.}}\cong {\displaystyle \frac{x}{F}}{\displaystyle \frac{\partial F}{\partial x}}$$

(16)

where F represents one of filter parameters (ω₀, Q) and x one of the passive elements (R,C).

According to Equations (14)–(16), the sensitivity of the proposed second order band-pass filter can be expressed as

$$S_x^F=S_{R_3}^{{\omega }_0}=S_{R_4}^{{\omega }_0}=S_{C_3}^{{\omega }_0}=S_{C_4}^{{\omega }_0}=-{\displaystyle \frac{1}{2}}$$

(17)

$$S_x^F=S_{R_3}^Q=S_{C_3}^Q={\displaystyle \frac{1}{2}}-{\displaystyle \frac{R_3{C}_3}{\left(R_3{C}_3+R_4{C}_4\right)}}$$

(18)

$$S_x^F=S_{R_4}^Q=S_{C_4}^Q={\displaystyle \frac{1}{2}}-{\displaystyle \frac{R_4{C}_4}{\left(R_3{C}_3+R_4{C}_4\right)}}=-{\displaystyle \frac{1}{2}}+{\displaystyle \frac{R_3{C}_3}{\left(R_3{C}_3+R_4{C}_4\right)}}$$

(19)

Considering $R_3=R_4$ and $C_3=C_4$ in Equations (18) and (19), we obtain

$$S_x^F=S_{R_3}^Q=S_{C_3}^Q=S_{R_4}^Q=S_{C_4}^Q=0$$

(20)

Finally, the high-pass (HP) output was ensured, which was obtained by choosing Z₄ = ∞, which represents a sub-case of the general model, so the impedances Z₁ = 1/(sC₅), Z₂ = R₅, and Z₃ = R₆, were substituted, obtaining the related transfer function

$${\displaystyle \frac{v_{OUT,HP1}}{i_{IN}}}={\displaystyle \frac{{-Z}_2{Z}_3}{Z_2+Z_1}}={\displaystyle \frac{-s{R}_5{R}_6{C}_5}{1+s{R}_5{C}_5}}$$

(21)

The transfer function expressed in Equation (21) represents the mathematical model describing the behavior of the output voltage $v_{OUTHP}$with respect to the injected input current. It features a single pole and thus corresponds to a first-order high-pass filter. In this relationship, the value of $R_6$has been set at 10 kΩ and is independently chosen as the gain factor or trans-resistor. The cut-off frequency of the high-pass filter (set at 10 kHz) is given by

$$f_{HP}={\displaystyle \frac{1}{2\pi R_5{C}_5}}$$

(22)

As in the previous cases, the capacitance value is derived from already known values of resistance and relative cut-off frequency; in this case of study, $R_5$is assumed at 16 kΩ and $C_5$ is consequently set at 1 nF to achieve a cut-off frequency of about 10 kHz.

To achieve a second-order high-pass response with a steeper roll-off of 40 dB/decade (instead of 20 dB/decade), two first-order stages have been cascaded. In this configuration, the output voltage from the first stage, taken at terminal Z of the first VCII, is applied to the input of the second stage. The second stage is an RC first-order high-pass filter whose output is connected to the X terminal of a second VCII. Due to the inherent voltage follower characteristic between the X and Z terminals of the VCII, the overall output is taken from the Z terminal of the second VCII, as shown in Figure 8. This cascaded configuration yields a slope of −40 dB/decade, thus approximating the behavior of a second-order HP filter, although each stage is intrinsically first-order.

Analyzing the circuit demonstrated in Figure 8, the overall transfer function of the cascaded configuration is given by

$${\displaystyle \frac{v_{OUT,HP2}}{i_{IN}}}={\displaystyle \frac{-s{R}_5{R}_6{C}_5}{1+s{C}_5{R}_5}}{\displaystyle \frac{R_5}{R_5+\left(\frac{1}{s{C}_5}\right)}}{=R_6\left({\displaystyle \frac{s{R}_5{C}_5}{1+s{R}_5{C}_5}}\right)}^2$$

(23)

The proposed complete multifunction filter is shown in Figure 9. Each transfer function discussed involves current input and voltage output; the overall filter is designed as a single voltage input and three voltage outputs. Using a CCII in a V-I converter configuration, as schematized in Figure 9 and expressed in Equation (24), and considering that the output current is approximately 3 times larger than the input current of each filter, due to the circuit symmetry, current partitioning into equal parts was employed as a reasonable approximation for analysis, and the transfer function was derived accordingly.

$$i_{OUT}=-i_Z=-\left(-{\displaystyle \frac{v_Y}{R_7}}\right)={\displaystyle \frac{v_{in}}{R_7}}$$

(24)

By observing the mathematical model associated with each output, a passive attenuation factor is observed due to the conversion of voltage into current. The value for the input stage conversion resistance was determined as an experimentally derived standard value, and since it has to be the minimum possible, the value of 100 Ω for $R_7$ was chosen.

$${\displaystyle \frac{v_{OUT,LP}}{v_{in}}}={\displaystyle \frac{{-R}_2}{3R_7\left({1+sR}_1{C}_1\right)\left(1+{sR}_2{C}_2\right)}}$$

(25)

$${\displaystyle \frac{v_{OUT,BP}}{v_{in}}}={\displaystyle \frac{-s{C_3{R}_{3}R}_4}{3R_7(1+s{C}_3{R}_3)(1+s{R}_4{C}_4)}}$$

(26)

$${\displaystyle \frac{v_{OUT,HP}}{v_{in}}}={{\displaystyle \frac{{-R}_6}{3R_7}}\left({\displaystyle \frac{s{R}_5{C}_5}{1+s{R}_5{C}_5}}\right)}^2$$

(27)

Using Equations (25)–(27), it is possible to make a tunable filter by keeping some parameters fixed and by varying the poles in Equations (8), (11), (12), and (24) in the first RC group of each filter and both cut-off frequencies in the case of the band pass filter synchronously, so as to introduce a slope of −40 dB/decade immediately after the cut-off frequency.

The real transfer function of the proposed filter, considering the real active block with parasitic impedances of VCII (shown in Figure 4), was first obtained by assuming the non-unitary $\mathsf{\alpha }$ and β parameters; starting from Equation (6), it is expressed as

$${\displaystyle \frac{v_{OUT}}{i_{IN}}}={\displaystyle \frac{-\alpha \beta {Z_{2}Z}_3{Z}_4}{(Z_1+Z_2)(\alpha \beta Z_3+Z_4)}}$$

(28)

Adding the parasitic impedances (ignoring Z_y), the resulting relation is

$${\displaystyle \frac{v_{OUT}}{i_{IN}}}={\displaystyle \frac{-\alpha \beta {Z_2(Z}_3//Z_x\left)\right(Z_4+Z_z)}{\left(Z_1+Z_2\right)\left[\right(\alpha \beta Z_3//Z_x)+Z_4+Z_z]}}$$

(29)

In this study, parasitic impedances are considered purely resistive at the operating frequency of 10 kHz, as inductive and capacitive effects typically become significant only beyond 1 MHz. The real transfer function becomes the following:

$${\displaystyle \frac{v_{OUT}}{i_{IN}}}={\displaystyle \frac{-\alpha \beta {Z_2(Z}_3//r_x\left)\right(Z_4+r_z)}{\left(Z_1+Z_2\right)\left[\right(\alpha \beta Z_3//r_x)+Z_4+r_z]}}$$

(30)

To summarize the methods adopted in this work, the design procedure followed three main steps. First, the passive component values were selected according to the transfer functions to set the desired pole frequencies for each response (Equations (8) and (9) for LP, Equations (11) and (12) for BP, and Equation (22) for HP). Second, sensitivity analysis was performed (Equations (16)–(20)) to evaluate the robustness against parameter variations. Finally, the independence of the three filtering paths and the transimpedance characteristics of the outputs was verified analytically (Equations (25)–(27)), ensuring that each function operates separately without internal component dependence.

4. Simulations and Measurements

The proposed multifunction filter has been simulated using LTspice 17.2 software, firstly designing the current-mode active blocks, as CCII and VCII at transistor level using a CMOS standard AMS 0.35 μm technology (shown in Figure 5 and Figure 6). After simulations, experimental measurements to validate the architecture were conducted. A discrete version of the proposed filter was prototyped using the commercial device AD844: a current feedback op-amp (CFOA) that can implement both a CCII and a VCII, only if the current mirror output node is connected to an output terminal of the chip. Tz, V-, and vout correspond to the X, Y, and Z terminals of the VCII, while the V-, V+, and Tz act as the X, Y, and Z terminals of CCII, respectively.

The tunability of the multifunction filter was analyzed and simulated, highlighting the non-linear trend of the pole frequency as a function of the varied parameter. It is observed that the cutoff frequency adjustment is closely linked to the variation in the resistor $R_1$ for the low-pass filter and of $R_5$ for the high-pass one. This dependence is characterized by the following relationship, which expresses the slope of the frequency variation with respect to $R_1$ (sensitivity):

$${\displaystyle \frac{d{f}_{LP1}}{d{R}_1}}={\displaystyle \frac{-1}{2\pi {R_1}^2{C}_1}}$$

(31)

As highlighted, this relation shows that the slope is inversely proportional to the square of the resistor value, resulting in a strong non-linearity in the variation in the pole frequency, particularly for higher values of $R_1$.

Regarding the band-pass filter, it was necessary to vary the values of $R_3$and $C_4$ simultaneously to maintain symmetry and obtain a uniform trend. The slope of the pole frequency with respect to $C_4$is described by the following expression:

$${\displaystyle \frac{d{f}_{BP2}}{d{C}_4}}={\displaystyle \frac{-1}{2\pi R_4{C_4}^2}}$$

(32)

The results further indicate that, although the pole frequency can be predictably tuned through component variation, its dependence on the circuit parameters is non-linear, in agreement with the theoretical equations.

To experimentally validate the proposed architecture, a prototype of the multifunction filter was implemented on PCB (see Figure 10a) and characterized using the measurement setup shown in Figure 10b. The input signal was generated by a KEYSIGHT 33600A Series Waveform Generator, Keysight Technologies, Santa Rosa, CA, USA, while the output responses were acquired with a KEYSIGHT MSOX3054T oscilloscope (500 MHz, 5 GSa/s), Keysight Technologies, Santa Rosa, CA, USA. The circuit was supplied by a KEYSIGHT E36313A DC power supply, Keysight Technologies, Santa Rosa, CA, USA.

In Figure 11, the simulated and measured frequency responses of the multifunction filter, centered at 10 kHz, are shown. Specifically, the blue traces correspond to transistor-level simulations in CMOS technology, the red traces report the simulated frequency response of the three outputs using a discrete AD844 chip as the active block, while the green traces represent the measured responses obtained with the setup of Figure 10. Frequency responses were measured by applying a sinusoidal input (200 mV amplitude) and sweeping the input frequency from 100 Hz to 1 MHz.

The total harmonic distortion (THD) values of the proposed filter were determined using LTspice simulations and experimental measurements (see Figure 12a–d).

Concerning the simulations, we have applied a sinusoidal input voltage with two different peak-to-peak values (20 mV and 200 mV) at three different frequencies (1 kHz, 10 kHz and 100 kHz). The resulting simulated THD values (Figure 12a) show maximum values of 3.1% (−30 dB), 4% (−27.9 dB), and 3.73% (−28.6 dB) for THD in the low-pass filter, band-pass filter, and high-pass filter, respectively.

The second analysis, shown in Figure 12b, is obtained by measuring the voltage at each output terminal sweeping the sinusoidal input amplitude from 20 mVpp to 200 mVpp.

In Figure 12c,d, the THD experimental measurements are reported, showing a performance improvement when compared to the previous simulations. The resulting measured THD values show maximum values of 1.78% (−34.9 dB), 1.05% (−39.6 dB), and 1.6% (−35.9 dB) for THD in the low-pass filter, band-pass filter, and high-pass filter, respectively. The comparison reveals an error between the simulated and measured results (1.32% (−37.6 dB) for LP, 2.95% (−30.6 dB) for BP, and 2.13% for HP (−33.4 dB)). These improved results in the measured values can be attributed to several factors: the limited resolution and dynamic range of the measurement setup, which may prevent the detection of very small harmonic components; the presence of background noise and instrument noise floors, which can hide higher-order harmonics; and the intrinsic filtering effects of the acquisition system, which can attenuate out-of-band distortion components.

Although the VCII architecture already benefits from internal local feedback via the FVF, and the regulated common gate stage, additional improvements can be considered. For instance, optimizing the biasing of transistors in the current buffer and voltage follower stages can extend the linear operating region and reduce distortion. Moreover, source degeneration techniques or increasing the bias current in key transistors (e.g., M9 in the FVF) could further improve linearity at the cost of higher power consumption.

5. Comparison with the Literature

A comparison between the proposed SIMO multifunction filter and other reported works [4,6,8,11,15,18,20,22,35,36,37,38,39,40,41] was carried out and is shown in

Table 3. Comparison from the literature of SIMO multifunction filters.

Reference	Operation Mode Filter Order	Main Active Block (Total Transistor Number)	No. Active Blocks	No. Passive Elements	Filter Operations	Technol. (μm)	Supply (V)	Power Consumption	THD Worst Case (%)	Internal Dependance	FOM
[6]	VM 2nd order	DDCCTA (44)	2	4 (2R,2C)	LP, BP, HP, AP, BS	Mietec 0.5	±2	3.74 mW	1.5–7	yes	0.089
[35]	CM 2nd order	CCII (Not available)	4	4 (2R,2C)	LP, BP, HP	Not available	10	Not available	Not available	yes	Not available
[36]	VM 2nd order	DDCCTA (22)	1	3 (1R,2C)	LP, BP, HP	Mietec 0.5	±3	0.83 mW	1.5–5.5	yes	0.6
[20]	CM 2nd order	CDTA (72)	3	2 (2C)	LP, BP, HP, BR	Mietec 0.5	±2.5	19.6 mW	Not available	yes	0.02
[4]	CM 2nd order	OTA+ Current Follower (44)	3 (2 OTA + 1 CF)	2 (2C)	LP, BP, HP, BR, AP	TSCM 0.18	±1	Not available	4–10	yes	Not available
[15]	MM 2nd order	DVCC (54)	3	5 (3R,2C)	LP, BP, HP, Notch	TSCM 0.35	±1.5	5.76 mW	Not available	yes	0.043
[37]	CM 2nd order	MOCCII (59)	3	4 (2R,2C)	LP, BP, HP	Not available	±2.5	Not available	Not available	yes	Not available
[11]	Dual-Mode (VM, CM) 2nd order	VDTA (36)	2	2 (2C)	LP, BP, HP,	TSCM 0.25	±1	2.47 mW	8–9	yes	0.2
[38]	VM 2nd order	CFA (N/A)	3	5 (3R,2C)	LP, BS, BP	AD844	±6	255 mW	Not available	yes	0.001
[22]	CM 1st order	DD-DXCCII (30)	1	1 (1C)	LP, HP, AP	Standard CMOS 0.18	±1.25	2 mW	Not available	yes	0.25
[39]	CM 1st order	CCCII (70)	2	2 (2C)	LP, HP, AP	BJT (ALA400 CBIC-R)	±2.5	2.72 mW	1.8	yes	0.091
[18]	CM 1st order	MOCDTA (35)	1	1 (1R)	LP, HP, AP	CMOS TMC 0.13	±1	2.5 mW	Not available	yes	0.2
[40]	MM 1st order	EX-CCCII (35)	1	1 (1C)	LP, HP, AP	Standard CMOS 0.18	±0.9	0.558 mW	0.69	yes	0.89
[8]	CM 2nd order	CCII (30)	3	4 (2R,2C)	LP, BP, HP	0.7	±1.65	Not available	Not available	no	Not available
[41]	VM/CM 1st/2nd order	VCII (63)	2/3	3/6	INVERSE	Not available	±0.75	0.25/0.5 mW	1.5–2	yes	0.44
Proposed CMOS	TIM and VM 2nd order	VCII (64)	5 (4 VCII + 1 CCII)	14 (8R, 6C)	LP, BP, HP	Standard CMOS 0.35	±1.65	0.876 mW	4	no	0.12
Proposed AD844	TIM and VM 2nd order	CFA (Not available)	5 AD844	14 (8R, 6C)	LP, BP, HP	AD844	±10	326 mW	4 (sim) 1.78 (meas)	no	0.00032

.

Table 3 highlights that the proposed solution (where both the CMOS and the AD844-based simulations are reported together with the corresponding AD844 measurements) employs a relatively simpler active block compared to most other implementations. Although a higher number of passive components is used, the configuration enables the realization of the three fundamental filter responses (low-pass, band-pass, and high-pass) in a fully independent manner. Each filtering function is achieved through a distinct set of passive components, with no shared elements among them. Furthermore, none of the three outputs is derived from another, ensuring complete functional and structural separation. Despite the relatively higher count of active and passive components compared to some recent works, this design choice ensures complete structural independence among the three filtering paths (LP, BP, HP), avoiding shared elements or signal coupling. Nevertheless, potential optimizations can be considered. The resistive elements may be replaced with switched-capacitor equivalents, facilitating CMOS integration. For current-mode input signals, the first CCII can be omitted. The LP and BP sections employ only one active block and four passive components. Additionally, a first-order implementation of the HP section can be considered, depending on system requirements. Moreover, a trade-off could involve partially sharing passive components between filter stages or exploring composite active blocks to reduce transistor count. However, such modifications would compromise modularity and potentially affect filter independence.

Such independence behavior allows the same input signal to be simultaneously analyzed for different applications at distinct frequency bands, each with its own tailored filtering behavior. For example, it is possible to observe the low-pass response of the signal at a certain frequency while simultaneously analyzing its band-pass response at another, simply by adjusting the passive components of the corresponding paths. This flexibility enables more advanced and targeted signal analysis across multiple frequency ranges.

Another relevant observation from Table 3 is that the CMOS AMS 0.35 µm implementation exhibits a power consumption of only 876 µW at ±1.65 V, placing it among the lowest-power second-order SIMO filters in the comparison. While a few first-order or highly specialized designs report lower absolute values, these are not directly comparable in terms of functionality and architecture. The THD values are comparable to those of several state-of-the-art solutions, despite the more complex single-input triple-output functionality. To provide an objective benchmark among the surveyed solutions, a Figure of Merit (FoM) was calculated and defined as

$$FoM={\displaystyle \frac{Order}{PowerConsumption\left(mW\right)\ast ComponentCount}}$$

(33)

where Order is the filter order, Power consumption is expressed in mW, and Component Count is the sum of active and passive components. This metric rewards higher-order filters with low power and reduced complexity.

Although the proposed CMOS implementation does not achieve the very highest FoM values in the table, this is mainly due to the relatively large number of components required to realize the single-input triple-output functionality. Nevertheless, thanks to its low power consumption (0.876 mW), it still achieves a competitive FoM compared to other second-order solutions.

A representative application of the proposed SIMO filter can be found in surface electromyography (sEMG), where different frequency bands carry distinct physiological information. The low-pass output can be used to monitor motion artifacts or muscle tone fluctuations below 50 Hz, the band-pass section can isolate voluntary muscle activity in the 50–150 Hz range, and the high-pass path may reveal high-frequency features such as fiber-type recruitment or tremor signatures above 150 Hz. This parallel and independent analysis enhances both diagnostic accuracy and the performance of biomedical systems such as prosthetic control interfaces or neuromuscular monitoring tools.

6. Conclusions

This paper reports a novel SIMO multifunction filter based on VCII and CCII active building blocks which realizes low-pass, band-pass, and high-pass responses from a single input, with each path operating independently. This property enables parallel analysis of different frequency bands without mutual interference. The proposed topology combines internal component independence with implementation flexibility, as confirmed by both transistor-level simulations in standard CMOS technology and experimental validation using the commercial device AD844. Sensitivity and total harmonic distortion (THD) analyses further demonstrated the robustness of the filter against component tolerances. The availability of three independent outputs makes the proposed architecture attractive for actual applications such as parallel signal processing, electronic interfaces, and biomedical instrumentation requiring multi-band monitoring, providing an efficient alternative to traditional solutions, thanks to a trade-off between complexity, performance, and integration suitability.