Current-Mode Shadow Filter with Single-Input Multiple-Output Using Current-Controlled Current Conveyors with Controlled Current Gain

Citation: Kumngern, M.; Khateb, F.; Kulej, T.; Kyselak, M.; Lerkvaranyu, S.; Knobnob, B. Current-Mode Shadow Filter with Single-Input MultipleOutput Using Current-Controlled Current Conveyors with Controlled Current Gain. Sensors 2024,24, 460. https://doi.org/10.3390/ s24020460 Academic Editor: Mario Luiso Received: 22 November 2023 Revised: 21 December 2023 Accepted: 9 January 2024 Published: 11 January 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). sensors Article Current-Mode Shadow Filter with Single-Input Multiple-Output Using Current-Controlled Current Conveyors with Controlled Current Gain Montree Kumngern 1, Fabian Khateb 2,3,4,* , Tomasz Kulej 5, Martin Kyselak 4, Somkiat Lerkvaranyu 1 and Boonying Knobnob 6 1Department of Telecommunications Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand; montr[email protected] (M.K.); [email protected] (S.L.) 2Department of Microelectronics, Brno University of Technology, Technická10, 601 90 Brno, Czech Republic 3Faculty of Biomedical Engineering, Czech Technical University in Prague, Nám. Sítná3105, 272 01 Kladno, Czech Republic 4Department of Electrical Engineering, Brno University of Defence, Kounicova 65, 662 10 Brno, Czech Republic; [email protected] 5Department of Electrical Engineering, Czestochowa University of Technology, 42-201 Czestochowa, Poland; [email protected] 6Faculty of Engineering, Rajamangala University of Technology Thanyaburi, Pathum Thani 12110, Thailand; [email protected] *Correspondence: [email protected] Abstract: In this paper, a novel current-mode shadow filter employing current-controlled current conveyors (CCCIIs) with controlled current gains is presented. The CCCII-based current-mode shadow filters are resistorless and can offer a number of advantages such as circuit simplicity and electronic tuning capability. The proposed shadow filters offer five filtering functions, i.e., low-pass, high-pass, band-pass, band-stop, and all-pass functions, in the same topology. Furthermore, no component matching condition is required to realize all the transfer functions. The natural frequency and quality factor adjustment is possible by using the CCCII current gains without the need to use external amplifiers, all capacitors are grounded, and the filter terminals offer low-input and highoutput impedance. To verify the functionality and feasibility of the new topologies, the proposed circuits were simulated using SPICE and the transistor model process parameters NR100N (NPN) and PR100N (PNP) from AT&T’s bipolar arrays ALA400-CBIC-R. The simulation results are consistent with the theory. The CCCII experimental setup was designed using commercially available 2N3904 (NPN) and 2N3906 (PNP) transistors with a supply voltage of ± 2.5 V. The measurement results confirm the performance of the designed filters. Keywords: shadow filter; current-mode filter; current-controlled current conveyor; second-generation current conveyor 1. Introduction Over the last decade, second-generation current conveyors (CCIIs) have been used to realize current-mode analog circuits. This is because CCII-based circuits offer better signal bandwidth, higher linearity, circuit simplicity, and wider dynamic range performances compared with the operational amplifiers (op-amps)-based circuits [ 1 , 2 ]. In addition, a CCII is simpler to implement compared to the op-amp structure. Usually, a conventional CCII has three terminals (x-, y-, and z-terminal) [ 3 ]. Its electrical symbol is shown in Figure 1, while its terminal characteristics in ideal case are given by Equation (1). Sensors 2024,24, 460. https://doi.org/10.3390/s24020460 https://www.mdpi.com/journal/sensors Sensors 2024,24, 460 2 of 23   Iy Vx Iz =  000 100 010   Vy Ix Vz (1) Sensors 2024, 24, x FOR PEER REVIEW 2 of 24 Figure 1. Electrical symbol of CCII. 󰇭𝐼 𝑉 𝐼󰇮=000 100 010 󰇭𝑉 𝐼 𝑉󰇮 (1) It can be noted that the y-terminal is a voltage input that has a high impedance level (ideally infinity), the x-terminal is a voltage signal output and also a current signal input, with low impedance level (ideally zero), and the z-terminal is a current output with a high impedance level (ideally infinity). In practice, the parasitic resistance at the x-terminal (Rx) of the CCII can be controlled by its bias current, which can be used as a design parameter. Such a device is called a current-controlled current conveyor (CCCII) [4]. Circuits based on CCCII can thus reduce the number of passive resistors and offer the possibility of electronic control. It should be noted that in the ideal case is Vx = Vy for CCII and Vx = IxRx + Vy for CCCII, while Iz = Ix for both circuits. Note that the voltage and current gain in these formulas is equal to one. To increase the functionality, the CCCII with controlled current gain has also been proposed [5]. This device offers an adjustable current gain between the zand xterminals, which can be used as a design parameter for such applications as filters and oscillators. The CCII/CCCII can be realized using bipolar junction transistor (BJT) technology [5] or complementary metal oxide semiconductor (CMOS) technology [6,7]. In this work, a CCCII with controlled current gain is used to realize current-mode shadow filters. The shadow filter was first introduced in [8]. The concept of the conventional shadow filter is to use an external amplifier to adjust the natural frequency and the quality factor of the second-order filters without changing the value of parameters such as capacitances and resistances of the original topology. However, the shadow filter in [8] does not provide independent control of the natural frequency and the quality factor. To obtain independent control of the above-mentioned parameters, the shadow filter was further developed, and two new systems were proposed [9]. The first system in [9] consists of a secondorder filter and an amplifier. The LP and BP outputs are summed and amplified by the amplifier, and the output signal of the amplifier is summed with the input signal. Thus, the quality factor can be controlled by an external amplifier without changing the natural frequency. The second system in [9] was further developed by adding another amplifier to the first system. Thus, the second system in [9] consists of a second-order filter and two external amplifiers. The first amplifier is used to amplify the BP output, while the second one is used to amplify the LP output, and the output signals of the two amplifiers are summed with the input signal. Consequently, the quality factor can be modified by the first external amplifier, while the natural frequency can be modified by the second one. In this work, the two systems of shadow filters in [9] will be designed using CCCII with controlled current gain as active elements. It will be shown that the function of external amplifiers can be obtained using the current gains of CCCIIs. Many shadow filters (also known as frequency-agile filters) have been introduced [10–34]. These filters can be used for various radio applications and sensor networks including environmental monitoring, vital signs monitoring, and military applications. Considering the operating mode of these filters, they can be divided into three operating modes: voltage-mode [10–22], current-mode [23–31], and mixed-mode (or multi-mode) [32–34]. Figure 1. Electrical symbol of CCII. It can be noted that the y-terminal is a voltage input that has a high impedance level (ideally infinity), the x-terminal is a voltage signal output and also a current signal input, with low impedance level (ideally zero), and the z-terminal is a current output with a high impedance level (ideally infinity). In practice, the parasitic resistance at the x-terminal (R x ) of the CCII can be controlled by its bias current, which can be used as a design parameter. Such a device is called a current-controlled current conveyor (CCCII) [ 4 ]. Circuits based on CCCII can thus reduce the number of passive resistors and offer the possibility of electronic control. It should be noted that in the ideal case is V x =V y for CCII and V x =I x R x +V y for CCCII, while I z =I x for both circuits. Note that the voltage and current gain in these formulas is equal to one. To increase the functionality, the CCCII with controlled current gain has also been proposed [ 5 ]. This device offers an adjustable current gain between the zand x-terminals, which can be used as a design parameter for such applications as filters and oscillators. The CCII/CCCII can be realized using bipolar junction transistor (BJT) technology [5] or complementary metal oxide semiconductor (CMOS) technology [6,7] . In this work, a CCCII with controlled current gain is used to realize current-mode shadow filters. The shadow filter was first introduced in [ 8 ]. The concept of the conventional shadow filter is to use an external amplifier to adjust the natural frequency and the quality factor of the second-order filters without changing the value of parameters such as capacitances and resistances of the original topology. However, the shadow filter in [ 8 ] does not provide independent control of the natural frequency and the quality factor. To obtain independent control of the above-mentioned parameters, the shadow filter was further developed, and two new systems were proposed [ 9 ]. The first system in [ 9 ] consists of a second-order filter and an amplifier. The LP and BP outputs are summed and amplified by the amplifier, and the output signal of the amplifier is summed with the input signal. Thus, the quality factor can be controlled by an external amplifier without changing the natural frequency. The second system in [ 9 ] was further developed by adding another amplifier to the first system. Thus, the second system in [ 9 ] consists of a second-order filter and two external amplifiers. The first amplifier is used to amplify the BP output, while the second one is used to amplify the LP output, and the output signals of the two amplifiers are summed with the input signal. Consequently, the quality factor can be modified by the first external amplifier, while the natural frequency can be modified by the second one. In this work, the two systems of shadow filters in [ 9 ] will be designed using CCCII with controlled current gain as active elements. It will be shown that the function of external amplifiers can be obtained using the current gains of CCCIIs. Many shadow filters (also known as frequency-agile filters) have been introduced [10–34] . These filters can be used for various radio applications and sensor networks including environmental monitoring, vital signs monitoring, and military applications. Considering the operating mode of these filters, they can be divided into three operating modes: voltagemode [10–22], current-mode [23–31], and mixed-mode (or multi-mode) [32–34]. Considering the active devices used to realize the voltage-mode shadow filters in [10–22] , the circuit in [ 10 ] uses operational transresistance amplifiers (OTRA), the circuits in [ 11 – 13 ] Sensors 2024,24, 460 3 of 23 use current-feedback operational amplifiers (CFOA), the circuits in [ 14 , 16 – 18 ] use voltage differencing transconductance amplifiers (VDTA), the circuit in [ 15 ] uses voltage differencing differential difference amplifiers (VDDDA), the circuit in [ 19 ] uses voltage differencing gain amplifiers (VDGA), while the circuit in [ 21 ] uses operational transconductance amplifiers (OTA), and the circuits in [ 22 ] use differential difference transconductance amplifiers (DDTA). The shadow filters in [ 15 – 19 , 21 , 22 ] offer an electronic tuning capability, but only the filter in [ 15 ] offers five filtering functions, namely low-pass (LP), high-pass (HP), bandpass (BP), band-stop (BS), and all-pass (AP). However, the voltage-mode filter in [ 15 ] does not provide low-output impedance, which is required for voltage-mode circuits. This work is focused on the current-mode shadow filter that offers low-input and high-output impedances, which is required for current-mode circuits. With respect to the current-mode shadow filters in [ 23 – 31 ], the circuits in [ 23 – 27 ] use current difference transconductance amplifier (CDTA), the circuit in [ 28 ] uses operational floating current conveyor (OFCC), the circuit in [ 29 ] uses current backwards trans-conductance amplifier (CBTA), while the circuit in [ 30 ] uses current controlled current differencing cascadedtransconductance amplifier (CC-CDCTA), and the circuit in [ 31 ] uses current conveyor cascaded transconductance amplifier (CCCTA). The shadow filters in [ 23 – 27 , 29 – 31 ] offer an electronic tuning capability, but only the shadow filter in [ 31 ] can offer low-pass, high-pass, band-pass, band-stop, and all-pass filtering functions in one system. The circuit in [ 31 ] employs one CCCTA, one EX-CCCTA, and two capacitors. Although the circuit is based on a small number of active blocks, the structure of active blocks is rather complex. With respect to the mixed-mode shadow filters in [ 32 – 34 ], the circuit in [ 33 , 34 ] can realize low-pass, high-pass, band-pass, band-stop, and all-pass filtering functions in the same topology. However, when the mixed-mode circuit in [ 33 ] operates in current-mode, the input matching condition, namely I in =I in1 =I in2 , is required. This means that the circuit requires additional circuits to produce multiple copies of a single input signal. The filter in [ 33 ] employs two FD-CCCTAs (fully differential current conveyor cascaded transconductance amplifier), three capacitors, and two MOS resistors, while the filter in [ 34 ] employs two DDCCCTAs (differential current conveyor cascaded transconductance amplifiers), two capacitors, and one MOS resistor. However, the active block structures used in these filters [34,35] suffer from a relatively high complexity. This paper presents current-mode shadow filters using CCCIIs with controlled current gain as active elements. The circuits employ three CCCIIs and two grounded capacitors. This work shows that the current gains of the used CCCIIs can perform the role of external amplifiers to adjust the natural frequency and quality factor of the proposed universal filters without the need to modify their internal parameters. The proposed current-mode shadow filters offer low-pass, high-pass, band-pass, band-stop, and all-pass filtering functions in the same topology with low complexity. The natural frequency and the quality factor can be adjusted by the current gains of CCCIIs and can be electronically controlled. The proposed current-mode filters offer low-input and high-output impedances, which is desirable in current-mode circuits. The paper is organized as follows: Section 2describes the structure of the CCCII with controlled current gain, the proposed current-mode shadow filters and the nonideality analysis. The simulation results of the CCCII with controlled current gain and the shadow filter are shown in Section 3. Section 4presents the experimental results of the proposed filters and Section 5concludes the paper. 2. Proposed Circuit 2.1. CCCII with Controlled Current Gain The electrical symbol of the CCCII with controlled current gain and multiple current outputs is shown in Figure 2. In the ideal case, this element can be described by the following matrix equation: Sensors 2024,24, 460 4 of 23     Iy Vx Iz± Ikz±     =    0 0 0 0 1Rx0 0 0±100 0±k0 0        Vy Ix Vz± Vkz±     (2) Sensors 2024, 24, x FOR PEER REVIEW 4 of 24 2. Proposed Circuit 2.1. CCCII with Controlled Current Gain The electrical symbol of the CCCII with controlled current gain and multiple current outputs is shown in Figure 2. In the ideal case, this element can be described by the following matrix equation: 𝐼 𝑉 𝐼± 𝐼±=0000 1𝑅 00 0±100 0±𝑘00 𝑉 𝐼 𝑉± 𝑉± (2) Figure 2. Electrical symbol of the CCCII with controlled current gain. The CCCII with controlled current gain can be implemented using both BJT [5–7] as well as CMOS [6,7] technologies. This paper proposes a simple BJT implementation shown in Figure 3. The main circuit consists of the translinear loop (Q1-Q4) and the positive and negative current mirrors with adjustable gain (Q22-Q25, Q26-Q29). Assume that transistors Q1 to Q4 of a translinear loop are identical and are biased by the current Iset. The parasitic resistance at x-terminal is given by [4]: 𝑅=𝑉 2𝐼 (3) where VT is the thermal voltage (~26 mV at 27 °C) and Iset is the bias current. Note that Rx can be controlled by Iset. Figure 3. BJT implementation of the CCCII with controlled current gain. Assuming further that transistors Q22 to Q25 of positive current mirrors and transistors Q26 to Q29 of the negative current mirrors are identical, the current gain k of the CCCII in Figure 3 is given by [5]: 𝑘=𝐼 𝐼 (4) It should be noted that the current gain k can be linearly controlled. Moreover, it is independent of temperature variation. Figure 2. Electrical symbol of the CCCII with controlled current gain. The CCCII with controlled current gain can be implemented using both BJT [ 5 – 7 ] as well as CMOS [ 6 , 7 ] technologies. This paper proposes a simple BJT implementation shown in Figure 3. The main circuit consists of the translinear loop (Q 1 -Q 4 ) and the positive and negative current mirrors with adjustable gain (Q 22 -Q 25 , Q 26 -Q 29 ). Assume that transistors Q1to Q4of a translinear loop are identical and are biased by the current Iset. The parasitic resistance at x-terminal is given by [4]: Rx=VT 2Iset (3) where V T is the thermal voltage (~26 mV at 27 ◦ C) and I set is the bias current. Note that R x can be controlled by Iset. Sensors 2024, 24, x FOR PEER REVIEW 4 of 24 2. Proposed Circuit 2.1. CCCII with Controlled Current Gain The electrical symbol of the CCCII with controlled current gain and multiple current outputs is shown in Figure 2. In the ideal case, this element can be described by the following matrix equation: 𝐼 𝑉 𝐼± 𝐼±=0000 1𝑅 00 0±100 0±𝑘00 𝑉 𝐼 𝑉± 𝑉± (2) Figure 2. Electrical symbol of the CCCII with controlled current gain. The CCCII with controlled current gain can be implemented using both BJT [5–7] as well as CMOS [6,7] technologies. This paper proposes a simple BJT implementation shown in Figure 3. The main circuit consists of the translinear loop (Q1-Q4) and the positive and negative current mirrors with adjustable gain (Q22-Q25, Q26-Q29). Assume that transistors Q1 to Q4 of a translinear loop are identical and are biased by the current Iset. The parasitic resistance at x-terminal is given by [4]: 𝑅=𝑉 2𝐼 (3) where VT is the thermal voltage (~26 mV at 27 °C) and Iset is the bias current. Note that Rx can be controlled by Iset. Figure 3. BJT implementation of the CCCII with controlled current gain. Assuming further that transistors Q22 to Q25 of positive current mirrors and transistors Q26 to Q29 of the negative current mirrors are identical, the current gain k of the CCCII in Figure 3 is given by [5]: 𝑘=𝐼 𝐼 (4) It should be noted that the current gain k can be linearly controlled. Moreover, it is independent of temperature variation. Figure 3. BJT implementation of the CCCII with controlled current gain. Assuming further that transistors Q 22 to Q 25 of positive current mirrors and transistors Q 26 to Q 29 of the negative current mirrors are identical, the current gain kof the CCCII in Figure 3is given by [5]: k=Ia Ib (4) It should be noted that the current gain k can be linearly controlled. Moreover, it is independent of temperature variation. 2.2. Proposed Current-Mode Shadow Filter Figure 4a shows the block diagram of the current-mode shadow filter, which consists of a second-order filter (2nd-order filter) that provides three filtering functions i.e., LP, HP, and BP filters, and the amplifier (A) [ 9 ]. The outputs of the LP and HP filters are further summed and amplified by the amplifier A, and the output signal of the amplifier is then Sensors 2024,24, 460 5 of 23 summed with the input signal. Figure 4b shows the first proposed current-mode shadow filter based on the translinear current conveyors (CCCIIs) with controlled current gains, which is realized based on the block diagram in Figure 4a. The CCCII 1 to CCCII 3 , C 1 , and C 2 form a second-order filter that provides three outputs of, LP, HP, and BP filters. This is based on two integrator loops, of which CCCII 1 and C 1 create the first integrator, and CCCII 2 , and C 2 create the second. The current gains of CCCII 2 (k 2 ) and CCCII 3 (k 3 ) act as an external amplifier (i.e., k 2 =k 3 =k=A). The outputs of the LP and HP filters are amplified by k 2 and k 3 , respectively, and are next fed to the input node of the filter. Thanks to the multiple-output CCCII, the BS filter (I BS ) can be obtained by summing the outputs of the LP and HP filters. Sensors 2024, 24, x FOR PEER REVIEW 5 of 24 2.2. Proposed Current-Mode Shadow Filter Figure 4a shows the block diagram of the current-mode shadow filter, which consists of a second-order filter (2nd-order filter) that provides three filtering functions i.e., LP, HP, and BP filters, and the amplifier (A) [9]. The outputs of the LP and HP filters are further summed and amplified by the amplifier A, and the output signal of the amplifier is then summed with the input signal. Figure 4b shows the first proposed current-mode shadow filter based on the translinear current conveyors (CCCIIs) with controlled current gains, which is realized based on the block diagram in Figure 4a. The CCCII1 to CCCII3, C1, and C2 form a second-order filter that provides three outputs of, LP, HP, and BP filters. This is based on two integrator loops, of which CCCII1 and C1 create the first integrator, and CCCII2, and C2 create the second. The current gains of CCCII2 (k2) and CCCII3 (k3) act as an external amplifier (i.e., k2 = k3 = k = A). The outputs of the LP and HP filters are amplified by k2 and k3, respectively, and are next fed to the input node of the filter. Thanks to the multiple-output CCCII, the BS filter (IBS) can be obtained by summing the outputs of the LP and HP filters. It should be noted that the input current Iin is applied to the x-terminal of CCCII which provides a low impedance level, while the output currents ILP, IHP, IBP, and IBS are supplied from the z-terminals of the CCCII which provides a high impedance level. The circuit uses two grounded capacitors and no passive resistors, which reduces the chip area when it is realized in integrated form. (a) (b) Figure 4. First current-mode shadow filter: (a) block diagram, (b) first proposed current-mode shadow filter using CCCIIs. Using nodal analysis and (2), the output currents of the LP (𝐼), HP (𝐼), BP (𝐼), and BS (𝐼) filters in Figure 4b can be respectively expressed as 𝐼=1 𝑠𝐶𝐶𝑅𝑅󰇛1+𝑘)+𝑠𝐶𝑅+󰇛1+𝑘)𝐼 (5) 𝐼=𝑠𝐶𝐶𝑅𝑅 𝑠𝐶𝐶𝑅𝑅󰇛1+𝑘)+𝑠𝐶𝑅+󰇛1+𝑘)𝐼 (6) 𝐼=− 𝑠𝐶𝑅 𝑠𝐶𝐶𝑅𝑅󰇛1+𝑘)+𝑠𝐶𝑅+󰇛1+𝑘)𝐼 (7) 𝐼=𝑠𝐶𝐶𝑅𝑅+1 𝑠𝐶𝐶𝑅𝑅󰇛1+𝑘)+𝑠𝐶𝑅+󰇛1+𝑘)𝐼 (8) By combining the currents 𝐼 and 𝐼, the output current of the AP filter (𝐼) can be obtained as 𝐼=𝑠𝐶𝐶𝑅𝑅−𝑠𝐶𝑅+1 𝑠𝐶𝐶𝑅𝑅󰇛1+𝑘)+𝑠𝐶𝑅+󰇛1+𝑘)𝐼 (9) Figure 4. First current-mode shadow filter: (a) block diagram, (b) first proposed current-mode shadow filter using CCCIIs. It should be noted that the input current I in is applied to the x-terminal of CCCII which provides a low impedance level, while the output currents I LP , I HP , I BP , and I BS are supplied from the z-terminals of the CCCII which provides a high impedance level. The circuit uses two grounded capacitors and no passive resistors, which reduces the chip area when it is realized in integrated form. Using nodal analysis and (2), the output currents of the LP ( ILP ), HP ( IHP ), BP ( IBP ), and BS (IBS) filters in Figure 4b can be respectively expressed as ILP =1 s2C1C2Rx1Rx2(1+k3)+sC2Rx2+(1+k2)Iin (5) IHP =s2C1C2Rx1Rx2 s2C1C2Rx1Rx2(1+k3)+sC2Rx2+(1+k2)Iin (6) IBP =−sC2Rx2 s2C1C2Rx1Rx2(1+k3)+sC2Rx2+(1+k2)Iin (7) IBS =s2C1C2Rx1Rx2+1 s2C1C2Rx1Rx2(1+k3)+sC2Rx2+(1+k2)Iin (8) By combining the currents IBP and IBS , the output current of the AP filter ( IAP ) can be obtained as IAP =s2C1C2Rx1Rx2−sC2Rx2+1 s2C1C2Rx1Rx2(1+k3)+sC2Rx2+(1+k2)Iin (9) where Rx1 and Rx2 are, respectively, the parasitic resistances of CCCII 1 and CCCII 2 , while k2and k3are, respectively, the current gains of CCCII2and CCCII3. Assuming k2=k3=k ( k=A) , the natural frequency ( ωo ) and the quality factor ( Q ) can be respectively given by ωo=1 √C1C2Rx1Rx2 (10) Sensors 2024,24, 460 6 of 23 Q=(1+k)sC1Rx1 C2Rx2 (11) It should be noted that the parameter ωo can be electronically controlled by Rx1 and Rx2 via Iset1 and Iset2 (i.e., Iset1=Iset2 ) and the parameter Q can be electronically controlled via k(k=k2=k3). From (5), (6), (8), and (9), it can be seen that when the parameter Q is varied by k , the passband gains of the LP, HP, BS, and AP filters change. Namely, increasing the Q value will decrease the passband gains of these filters, except the passband gain of the BP filter, which will be constant. It should be noted that the shadow filter in Figure 4uses one external amplifier to modify only the quality factor. Figure 5a shows the block diagram for the second currentmode shadow filter which consists of a 2nd order filter and two amplifiers (A 1 and A 2 ) [ 9 ]. The output signals BP and LP are amplified, respectively, by A 1 and A 2 , and summed with the input signal. Thus, the quality factor and the natural frequency can be independently controlled using the amplifiers A1and A2. Sensors 2024, 24, x FOR PEER REVIEW 6 of 24 where 𝑅 and 𝑅 are, respectively, the parasitic resistances of CCCII1 and CCCII2, while 𝑘 and 𝑘 are, respectively, the current gains of CCCII2 and CCCII3. Assuming 𝑘=𝑘=𝑘 (𝑘=𝐴), the natural frequency (𝜔) and the quality factor (𝑄) can be respectively given by 𝜔=1  𝐶𝐶𝑅𝑅 (10) 𝑄=󰇛1+𝑘)𝐶𝑅 𝐶𝑅 (11) It should be noted that the parameter 𝜔 can be electronically controlled by 𝑅 and 𝑅 via 𝐼 and 𝐼 (i.e., 𝐼=𝐼) and the parameter 𝑄 can be electronically controlled via𝑘 (𝑘 = 𝑘 = 𝑘). From (5), (6), (8), and (9), it can be seen that when the parameter 𝑄 is varied by 𝑘, the passband gains of the LP, HP, BS, and AP filters change. Namely, increasing the 𝑄 value will decrease the passband gains of these filters, except the passband gain of the BP filter, which will be constant. It should be noted that the shadow filter in Figure 4 uses one external amplifier to modify only the quality factor. Figure 5a shows the block diagram for the second currentmode shadow filter which consists of a 2nd order filter and two amplifiers (A1 and A2) [9]. The output signals BP and LP are amplified, respectively, by A1 and A2, and summed with the input signal. Thus, the quality factor and the natural frequency can be independently controlled using the amplifiers A1 and A2. (a) (b) Figure 5. Second current-mode shadow filter: (a) block diagram, (b) second proposed currentmode shadow filter using CCCIIs. Figure 5b shows the proposed second realization of the current-mode shadow filter using CCCIIs with controlled current gains, which realizes the block diagram in Figure 5a. The CCCII1 to CCCII3, C1, and C2 form a second-order filter that provides three outputs of the LP, HP, and BP filters, which are similar to the ones in Figure 4b. Compared with Figure 5a, the gain A1 is realized by k1 of CCCII1 and A2 is realized by k2 of CCCII2. The output of the BP filter is amplified by k1 and the output of the LP filter is amplified by k2. The amplified output signals of the BP and LP filters are applied to the input node of the filter. Using nodal analysis and (2), the output currents of the LP (𝐼), HP (𝐼), BP (𝐼), and BS (𝐼) filters of Figure 5b can be respectively expressed as 𝐼=1 𝑠𝐶𝐶𝑅𝑅+𝑠𝐶𝑅󰇛1−𝑘)+󰇛1−𝑘)𝐼 (12) Figure 5. Second current-mode shadow filter: (a) block diagram, (b) second proposed current-mode shadow filter using CCCIIs. Figure 5b shows the proposed second realization of the current-mode shadow filter using CCCIIs with controlled current gains, which realizes the block diagram in Figure 5a. The CCCII 1 to CCCII 3 , C 1 , and C 2 form a second-order filter that provides three outputs of the LP, HP, and BP filters, which are similar to the ones in Figure 4b. Compared with Figure 5a, the gain A 1 is realized by k 1 of CCCII 1 and A 2 is realized by k 2 of CCCII 2 . The output of the BP filter is amplified by k 1 and the output of the LP filter is amplified by k 2 . The amplified output signals of the BP and LP filters are applied to the input node of the filter. Using nodal analysis and (2), the output currents of the LP ( ILP ), HP ( IHP ), BP ( IBP ), and BS (IBS) filters of Figure 5b can be respectively expressed as ILP =1 s2C1C2Rx1Rx2+sC2Rx2(1−k1)+(1−k2)Iin (12) IHP =s2C1C2Rx1Rx2 s2C1C2Rx1Rx2+sC2Rx2(1−k1)+(1−k2)Iin (13) IBP =−sC2Rx2 s2C1C2Rx1Rx2+sC2Rx2(1−k1)+(1−k2)Iin (14) Sensors 2024,24, 460 7 of 23 From ILP and IHP, the output current of the BS filter (IBS) can be obtained as IBS =s2C1C2Rx1Rx2+1 s2C1C2Rx1Rx2+sC2Rx2(1−k1)+(1−k2)Iin (15) From ILP IHP, and IBP, the output current of the AP filter (IAP) can be obtained as IAP =s2C1C2Rx1Rx2−sC2Rx2+1 s2C1C2Rx1Rx2+sC2Rx2(1−k1)+(1−k2)Iin (16) The natural frequency (ωo) and the quality factor (Q) of the filters are given by ωo=s1−k2 C1C2Rx1Rx2 (17) Q=√1−k2 1−k1sC1Rx1 C2Rx2 (18) As can be seen, the parameter ωo can be controlled by k 2 (A 2 ) in the range of 0 < k2< 1 and the parameter Q can be controlled by k 1 (A 1 ) in the range of 0 < k 1 < 1. Thus, the parameters ωo and Q can be independently controlled. It could be noted that adjusting the parameter ωo by k 2 will affect the parameter Q . In order to provide constant value of the parameter Q, when the parameter ωois varied by k2,k1must be used to adjust Q. From (12), (14)–(16), it can be seen that varying the parameter ωo by k 2 will affect the passband gains of the LP, BP, BS, and AP filters. Namely, increasing k 2 will increase the passband gains of these filters, except the passband gain of the HP filter, which will be constant. 2.3. Impact of Non-Idealities Taking into account the non-idealities of the CCCII with controlled current gain, its characteristics can be described by the following matrix equation     Iy Vx Iz± Ikz±     =    0 0 0 0 αRx0 0 0±β0 0 0±βkk0 0        Vy Ix Vz± Vkz±     (19) where α = 1 −εv (with εv « 1) denotes the voltage tracking error from yto x-terminal, β= 1 −εi(εi« 1) denotes the current tracking error from xto z-terminals, βk= 1 −εik (εik « 1 ) denotes the current tracking error from xto kz-terminals. The CCCII symbol with non-idealities is shown in Figure 6, where the additional passive elements represent the parasitic resistances and capacitances associated with each terminal of the device. The x-terminal has a parasitic serial resistance R x , the y-terminal has a high-value parasitic resistance R y in parallel with a low-value parasitic capacitance C y , the z-terminal has a high-value parasitic resistance R z in parallel with a low-value parasitic capacitance C z , and the kz-terminal has a high-value parasitic resistance R kz in parallel with a low-value parasitic capacitance Ckz. Sensors 2024, 24, x FOR PEER REVIEW 8 of 24 Figure 6. Parasitic resistances and capacitances of CCCII. Using (19) and nodal analysis, the denominator (D(s)) of the transfer functions of the filter in Figure 4b can be expressed by 𝐷󰇛𝑠)=𝑠𝐶𝐶𝑅𝑅󰇛1+𝑘𝛽)+𝑠𝐶𝑅𝛼𝛽+󰇛𝛼𝛼𝛽𝛽+𝑘𝛽) (20) The parameters ωo and 𝑄 in (10) and (11) can be respectively rewritten as 𝜔=1  𝐶𝐶𝑅𝑅𝛼𝛼𝛽𝛽+𝑘𝛽 1+𝑘𝛽 (21) 𝑄=1+𝑘𝛽 𝛼𝛽𝐶𝑅 𝐶𝑅∙𝛼𝛼𝛽𝛽+𝑘𝛽 1+𝑘𝛽 (22) Using (19) and nodal analysis, the denominator (D(s)) of the transfer functions of the filter in Figure 5b can be expressed by 𝐷󰇛𝑠)=𝑠𝐶𝐶𝑅𝑅+𝑠𝐶𝑅󰇛𝛼𝛽−𝑘𝛽)+󰇛𝛼𝛼𝛽𝛽−𝑘𝛼𝛽𝛽) (23) The parameters ωo and 𝑄 in (17) and (18) can be respectively rewritten as 𝜔=𝛼𝛼𝛽𝛽−𝑘𝛼𝛽𝛽 𝐶𝐶𝑅𝑅 (24) 𝑄=  𝛼𝛼𝛽𝛽−𝑘𝛼𝛽𝛽 𝛼𝛽−𝑘𝛽 𝐶𝑅 𝐶𝑅 (25) where αj is the voltage gain error, βj, and βkj are the current gain errors of j-th CCCII (j = 1, 2, 3). From (24) and (25), it can be seen that the voltage gain errors and the current gain errors of CCCIIs will affect the natural frequency and the quality factor of the proposed shadow filters in Figures 4b and 5b. However, this impact can be compensated by electronic tuning. Considering the proposed shadow filter in Figure 4b by including CCCII with the parasitic components in Figure 6, the denominator of all filtering functions is given by 𝐷󰇛𝑠)=𝑠𝐶𝐶𝑅𝑅󰇛1+𝑘)+𝑠𝐶𝑅1+𝐶𝐺𝑅𝑘+𝐶𝐺𝑅𝑘 𝐶  +󰇛1+𝑘)1+𝐺𝑅 1+𝑘 (26) where CT1 = C1 + Cz-3 + Cy1, CT2 = C2 + Cz-1 + Cy2, G1 = (1/Rz-3)//(1/Ry1), G2 = (1/Rz-1)//(1/Ry2). The parasitic impedance effects can be made negligible by satisfying the following condition: 𝐶𝐺𝑅𝑘+𝐶𝐺𝑅𝑘 𝐶 ≪1 𝐺𝑅 1+𝑘≪1 ⎭ ⎬ ⎫ (27) Figure 6. Parasitic resistances and capacitances of CCCII. Sensors 2024,24, 460 8 of 23 Using (19) and nodal analysis, the denominator (D(s)) of the transfer functions of the filter in Figure 4b can be expressed by D(s)=s2C1C2Rx1Rx2(1+k3βk3)+sC2Rx2α1β1+(α1α2β1β2+k2βk2)(20) The parameters ωoand Qin (10) and (11) can be respectively rewritten as ωo=1 √C1C2Rx1Rx2sα1α2β1β2+k2βk2 1+k3βk3 (21) Q=1+k3βk3 α1β1sC1Rx1 C2Rx2·α1α2β1β2+k2βk2 1+k3βk3 (22) Using (19) and nodal analysis, the denominator (D(s)) of the transfer functions of the filter in Figure 5b can be expressed by D(s)=s2C1C2Rx1Rx2+sC2Rx2(α1β1−k1βk1)+(α1α2β1β2−k2α1β1βk2)(23) The parameters ωoand Qin (17) and (18) can be respectively rewritten as ωo=sα1α2β1β2−k2α1β1βk2 C1C2Rx1Rx2 (24) Q=pα1α2β1β2−k2α1β1βk2 α1β1−k1βk1sC1Rx1 C2Rx2 (25) where αj is the voltage gain error, βj , and βkj are the current gain errors of j-th CCCII (j= 1, 2, 3). From (24) and (25), it can be seen that the voltage gain errors and the current gain errors of CCCIIs will affect the natural frequency and the quality factor of the proposed shadow filters in Figures 4b and 5b. However, this impact can be compensated by electronic tuning. Considering the proposed shadow filter in Figure 4b by including CCCII with the parasitic components in Figure 6, the denominator of all filtering functions is given by D(s)={s2CT1CT2Rx1Rx2(1+k3)+sCT2Rx21+CT1G2Rx1k3+CT2G1Rx1k3 CT2 +(1+k2)1+G2Rx1 1+k2}(26) where C T1 =C 1 +C z-3 +C y1 ,C T2 = C 2 +C z-1 +C y2 ,G 1 = (1/R z-3 )//(1/R y1 ), G2= (1/Rz-1)//(1/Ry2). The parasitic impedance effects can be made negligible by satisfying the following condition: CT1G2Rx1k3+CT2G1Rx1k3 CT2≪1 G2Rx1 1+k2≪1)(27) The parasitic capacitance will affect the natural frequency and the quality factor that can be expressed respectively by ωo= 1 /√CT1CT2Rx1Rx2 and Q=(1+k)√CT1Rx1/CT2Rx2 , where k2=k3=k. Considering the proposed shadow filters in Figure 5b by including the CCCII with the parasitic components in Figure 6, the denominator of all filtering functions is given by D(s)={s2CT1CT2Rx1Rx2+sCT2Rx2(1−k1)+CT1G2Rx1+CT2G1Rx1 CT2 +(1−k2)1+G1G2Rx1Rx2+G2Rx2−G2Rx2k1 1−k2}(28) Sensors 2024,24, 460 9 of 23 The parasitic impedance effects can be made negligible by satisfying the following condition: CT1G2Rx1+CT2G1Rx1 CT2≪1 G1G2Rx1Rx2+G2Rx2−G2Rx2k1 1−k2≪1)(29) The parasitic capacitance will affect the natural frequency and the quality factor that can be expressed, respectively, by ωo=p(1−k2)/CT1CT2Rx1Rx2 and Q= (√1−k2/ (1 −k1))√CT1Rx1/CT2Rx2. The parasitic impedances of CCCIIs that affect the parameters ωo and Q of the proposed shadow filters in Figures 4b and 5b can be absorbed by choosing C 1 >> C z-3 +C y1 , C2>> Cz-1 +Cy2,Rx1<< 1/G1,Rx2<< 1/G2. 3. Simulation Results The proposed current-mode shadow filters were simulated using SPICE. The CCCII in Figure 2was designed with the transistor model parameters of AT&T’s ALA400 CBIC-R process [ 35 ]. The DC supply voltage was ± 2.5 V. The bias currents I bi were fixed to 25 µ A and the bias current I ai was used to control the current gain k i (i = 1, 2, 3). The simulated performances of the CCCII with controlled current gain used in this paper are given in [ 36 ]. The capacitors C1and C2were 30 nF. The first proposed filter in Figure 4b was simulated and the theoretical value was added for comparison. The first simulation was performed with A = 0 (k 2 = k 3 = 0), by setting the bias currents I a2 = I a3 = 0 µ A and the bias currents I set1 = I set2 = I set3 = 25 µ A. This setting resulted in natural frequency (f o ) of 10.2 kHz and the quality factor (Q) of 1. Figure 7shows the magnitude frequency responses of the LP, HP, BP, and BS filters and Figure 8shows the magnitude and phase frequency responses of the AP filters. The simulated natural frequency was 10 kHz and was different from the theoretical value by 1.96%. The bandwidth of the filter was approximately 9 MHz. Sensors 2024, 24, x FOR PEER REVIEW 10 of 24 Figure 7. Simulated magnitude frequency responses of the LP, HP, BP, and BS filters of the first current shadow filter in Figure 4b without modification of the natural frequency and the quality factor (sim = simulation, the = theoretical). Figure 8. Simulated magnitude and phase frequency responses of the AP filter of the first currentmode shadow filter in Figure 4b without modification of the natural frequency and the quality factor (sim = simulation, the = theoretical). Figure 7. Simulated magnitude frequency responses of the LP, HP, BP, and BS filters of the first current shadow filter in Figure 4b without modification of the natural frequency and the quality factor (sim = simulation, the = theoretical). Sensors 2024,24, 460 16 of 23 natural frequency was affected by the temperature variations. From our investigation, for the temperatures of − 20 ◦ C and 85 ◦ C, the natural frequencies were, respectively, 11.09 kHz and 8.81 kHz. Thus, the natural frequency was varied by about ±1.04 kHz. Sensors 2024, 24, x FOR PEER REVIEW 17 of 24 (a) (b) (c) Figure 17. Simulated magnitude responses of the proposed current-mode shadow filter: (a) process corner, (b) voltage corner, and (c) temperature corner. Figure 17. Simulated magnitude responses of the proposed current-mode shadow filter: (a) process corner, (b) voltage corner, and (c) temperature corner. The BP response was simulated by setting 5% tolerances of the capacitor C 1 and C 2 at the cut-off frequency of 10 kHz and 200 Gaussian distribution runs. Figure 18 shows the derived histogram of the center frequency. The standard deviation ( σ ) of f o was 0.317 kHz and the maximum and minimum values of f o were, respectively, 10.805 kHz and 9.231 kHz. The proposed current-mode shadow filters were compared with previous shadow filters in Table 1. The voltage-mode shadow filters in [ 15 , 22 ], the current-mode shadow filters in [ 27 , 28 , 30 ], and the multi-mode shadow filters in [ 34 ] were selected for comparison. Compared with [ 22 , 27 , 28 ], the proposed filter can provide five filtering functions of LP, HP, BP, BS, and AP filters. Compared with [ 15 , 30 ], the proposed filter does not possess a buffer circuit at input or output terminals. Compared with [ 15 , 34 ], the proposed filter has no resistors and has a simpler structure. As can be seen, the proposed filters have the following features which the others do not: they offer the highest number of responses without the need for a buffer circuit at the input and output, have no resistors, all capacitors are grounded, and they have the possibility of electronic tuning of the natural frequency and quality factor. Sensors 2024,24, 460 17 of 23 Figure 18. The histogram of the center frequency of the BP filter with 200 runs of MC analysis. 9.00k 9.25k 9.50k 9.75k 10.00k 10.25k 10.50k 10.75k 0 5 10 15 20 25 11.0k Frequency, Hz Percent of samples n samples = 200 n divisions = 10 mean = 9,924.34 sigma = 317.779 minimum = 9,231.86 10th % = 9,526.88 median = 9,905.19 90th % = 10,353.4 maximum = 10,805.7 Figure 18. The histogram of the center frequency of the BP filter with 200 runs of MC analysis. Table 1. Comparison of the proposed design with previous works. Factor Proposed [15] [22] [27] [28] [30] [34] Number of active devices 3 CCCII 3 VDDDA 4 DDTA 7 CDTA 4 OFCC 4 CDCTA, 1 CCII 2 DCCCTA Realization BJT process (ALA400 CBIC-R) 0.18 µm CMOS structure & commercial IC 0.18 µm CMOS structure 0.18 µm CMOS structure 0.15 µm CMOS structure & commercial IC 0.18 µm CMOS structure & commercial IC 0.18 µm CMOS structure Number capacitors 2C 2C,1R 2C,3R 2C 2C,5R 2C 2C,2R Type of filter SIMO SIMO MISO SIMO SIMO MIMO SIMO Operation mode CM VM VM CM CM CM MM Number of offered responses 5 5 4 1 (BP) 1 (BP) 5 5 No need of buffer circuit at input or output Yes No Yes Yes Yes No Yes All grounded capacitors Yes Yes Yes No Yes No Yes Electronic control Yes Yes Yes Yes Yes Yes Yes Technique to control Q and ωo CG EG EG EG EG EG EG Sensors 2024,24, 460 18 of 23 Table 1. Cont. Factor Proposed [15] [22] [27] [28] [30] [34] Simulated power supply (V) ±2.5 ±0.9 0.5 ±0.9 ±1.5 ±1.25 ±1.7 Simulated power dissipation (mW) 9.9 - 0.000873 8.53 - 2.23 2.5 Total harmonic distortion (%) 0.937@100 µ A pp 1@280mVpp 2@60mVpp <5@100µApp - <1@600µApp <1@200 µ A pp Verification of result Sim/Exp Sim/Exp Exp Sim Sim/Exp Sim/Exp Sim/Exp Note: DCCCTA = differential current conveyor cascaded transconductance amplifier, MM = multi-mode, DDTA = differential difference transconductance amplifier, CG = current gain, EG = external gain (i.e., g m R, R1/R2, and gm1/gm2). 4. Experimental Results To confirm the functionality of the proposed shadow filters, an experimental setup of CCCII was designed using commercially available 2N3904 (NPN) and 2N3906 (PNP) transistors with supply voltage of ± 2.5 V. Figure 19 shows the experimental setup for the current-mode shadow filter. Passive capacitors were chosen as C 1 = C 2 = 330 nF and passive resistors 10 k Ω were used for voltage-to-current (V-I) converter as input and current-tovoltage (I-V) converter as output. The resistor that was connected in series with terminal I in works as a V-I converter to convert the voltage signal from the function generator to the current signal I in and the grounded resistors that were connected to terminals I LP , I HP , I BP , I BS , and I AP were used as I-V converter to convert current signals to voltage signals. The input and output waveforms ware measured using a KEYSIGHT DSOX1204G oscilloscope; the input signal was also provided by this oscilloscope. Sensors 2024, 24, x FOR PEER REVIEW 19 of 24 Electronic control Yes Yes Yes Yes Yes Yes Yes Technique to control Q and 𝜔 CG EG EG EG EG EG EG Simulated power supply (V) ±2.5 ±0.9 0.5 ±0.9 ±1.5 ±1.25 ±1.7 Simulated power dissipation (mW) 9.9 - 0.000873 8.53 - 2.23 2.5 Total harmonic distortion (%) 0.937@100µA pp 1@280mVpp 2@60mVpp <5@100µApp - <1@600µApp <1@200µApp Verification of result Sim/Exp Sim/Exp Exp Sim Sim/Exp Sim/Exp Sim/Exp Note: DCCCTA = differential current conveyor cascaded transconductance amplifier, MM = multimode, DDTA = differential difference transconductance amplifier, CG = current gain, EG = external gain (i.e., gmR, R1/R2, and gm1/gm2). 4. Experimental Results To confirm the functionality of the proposed shadow filters, an experimental setup of CCCII was designed using commercially available 2N3904 (NPN) and 2N3906 (PNP) transistors with supply voltage of ±2.5 V. Figure 19 shows the experimental setup for the current-mode shadow filter. Passive capacitors were chosen as C1 = C2 = 330 nF and passive resistors 10 kΩ were used for voltage-to-current (V-I) converter as input and current-tovoltage (I-V) converter as output. The resistor that was connected in series with terminal Iin works as a V-I converter to convert the voltage signal from the function generator to the current signal Iin and the grounded resistors that were connected to terminals ILP, IHP, IBP, IBS, and IAP were used as I-V converter to convert current signals to voltage signals. The input and output waveforms ware measured using a KEYSIGHT DSOX1204G oscilloscope; the input signal was also provided by this oscilloscope. Figure 19. Experimental setup for proposed shadow filters. The experimental frequency responses of the shadow filter in Figure 4b without modification of the natural frequency and the quality factor (A = 0, Q = 1) of (a) LP, (b) HP, (c) BP, (d) BS, and (e) AP are shown in Figure 20. Figure 21 shows the experimental frequency responses of the shadow filter in Figure 4b upon setting the quality factor of the amplifier A ≈ 3 of (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. Figure 19. Experimental setup for proposed shadow filters. The experimental frequency responses of the shadow filter in Figure 4b without modification of the natural frequency and the quality factor (A = 0, Q = 1) of (a) LP, (b) HP, (c) BP, (d) BS, and (e) AP are shown in Figure 20. Figure 21 shows the experimental Sensors 2024,24, 460 19 of 23 frequency responses of the shadow filter in Figure 4b upon setting the quality factor of the amplifier A ≈3 of (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. Figure 22 shows the experimental frequency responses of the second shadow filter in Figure 5b, setting the quality factor by the amplifier k 1 with k 2 = 0 for: (a) LP, (b) HP, (c) BP, (d) BS. Figure 23 shows the experimental frequency responses of the second shadow filter in Figure 5b, setting the natural frequency by k 2 , while k 1 is used to adjust Q for (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. Sensors 2024, 24, x FOR PEER REVIEW 20 of 24 (a) (b) (c) (d) (e) Figure 20. Experimental frequency responses of the first shadow filter in Figure 4b without modification of the natural frequency and the quality factor (A = 0, Q = 1) of (a) LP, (b) HP, (c) BP, (d) BS, and (e) AP. (a) (b) (c) (d) Figure 20. Experimental frequency responses of the first shadow filter in Figure 4b without modification of the natural frequency and the quality factor (A = 0, Q = 1) of (a) LP, (b) HP, (c) BP, (d) BS, and (e) AP. Sensors 2024, 24, x FOR PEER REVIEW 20 of 24 (a) (b) (c) (d) (e) Figure 20. Experimental frequency responses of the first shadow filter in Figure 4b without modification of the natural frequency and the quality factor (A = 0, Q = 1) of (a) LP, (b) HP, (c) BP, (d) BS, and (e) AP. (a) (b) Figure 21. Cont. Sensors 2024,24, 460 20 of 23 Sensors 2024, 24, x FOR PEER REVIEW 21 of 24 (c) (d) (e) Figure 21. Experimental frequency responses of the first shadow filter in Figure 4b, setting the quality factor by the amplifier A ≈ 3 of (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. Figure 22 shows the experimental frequency responses of the second shadow filter in Figure 5b, setting the quality factor by the amplifier k1 with k2 = 0 for: (a) LP, (b) HP, (c) BP, (d) BS. Figure 23 shows the experimental frequency responses of the second shadow filter in Figure 5b, setting the natural frequency by k2, while k1 is used to adjust Q for (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. (a) (b) (c) (d) Figure 21. Experimental frequency responses of the first shadow filter in Figure 4b, setting the quality factor by the amplifier A ≈3 of (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. Sensors 2024, 24, x FOR PEER REVIEW 21 of 24 (c) (d) (e) Figure 21. Experimental frequency responses of the first shadow filter in Figure 4b, setting the quality factor by the amplifier A ≈ 3 of (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. Figure 22 shows the experimental frequency responses of the second shadow filter in Figure 5b, setting the quality factor by the amplifier k1 with k2 = 0 for: (a) LP, (b) HP, (c) BP, (d) BS. Figure 23 shows the experimental frequency responses of the second shadow filter in Figure 5b, setting the natural frequency by k2, while k1 is used to adjust Q for (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. (a) (b) (c) (d) Sensors 2024, 24, x FOR PEER REVIEW 22 of 24 (e) Figure 22. Experimental frequency responses of the second current-mode shadow filter in Figure 5b setting the quality factor by the amplifier k1 with k2 = 0 for: (a) LP, (b) HP, (c) BP, (d) BS, and (e) AP. (a) (b) (c) (d) (e) Figure 23. Experimental frequency responses of the second shadow filter in Figure 5b, setting the natural frequency by k2, while k1 is used to adjust Q for: (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. 5. Conclusions This paper proposes two current-mode shadow filters using CCCIIs with controlled current gains. The circuits employ three CCCIIs with controlled current gains and two grounded capacitors. The proposed architecture can realize LP, HP, BP, BS, and AP filters in the same topology. The current gains of CCCIIs can be used to modify the natural Figure 22. Experimental frequency responses of the second current-mode shadow filter in Figure 5b setting the quality factor by the amplifier k 1 with k 2 = 0 for: (a) LP, (b) HP, (c) BP, (d) BS, and (e) AP. Sensors 2024,24, 460 21 of 23 Sensors 2024, 24, x FOR PEER REVIEW 22 of 24 (a) (b) (c) (d) (e) Figure 23. Experimental frequency responses of the second shadow filter in Figure 5b, setting the natural frequency by k2, while k1 is used to adjust Q for: (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. 5. Conclusions This paper proposes two current-mode shadow filters using CCCIIs with controlled current gains. The circuits employ three CCCIIs with controlled current gains and two grounded capacitors. The proposed architecture can realize LP, HP, BP, BS, and AP filters in the same topology. The current gains of CCCIIs can be used to modify the natural frequency and the quality factor of all filtering functions. The proposed shadow filters have the advantages of low-input and high-output impedances and low circuit complexity; they do not require passive resistors; they are suitable for integrated circuits by using grounded capacitors; and they have electronic tuning capability. To show the workability and performance of the proposed filters, SPICE simulation was performed. The simulated results were in agreement with the theoretical values and the experimental results confirm the functionality and the performance of the proposed filters. Author Contributions: Conceptualization, M.K. (Montree Kumngern), F.K. and T.K.; methodology, M.K. (Montree Kumngern), F.K., B.K. and S.L.; software, M.K. (Montree Kumngern), B.K. and S.L.; validation, M.K. (Montree Kumngern), F.K.; formal analysis, M.K. (Montree Kumngern); investigation, M.K. (Martin Kyselak), F.K. and T.K.; resources, M.K. (Martin Kyselak); data curation, M.K. (Martin Kyselak) and F.K.; writing—original draft preparation, M.K. (Montree Kumngern), F.K., B.K. and S.L.; writing—review and editing, M.K. (Montree Kumngern), F.K., B.K., S.L. and T.K.; visualization, M.K. (Martin Kyselak) and M.K. (Montree Kumngern); supervision, M.K. (Montree Kumngern) and F.K.; project administration, M.K. (Montree Kumngern) and F.K.; funding Figure 23. Experimental frequency responses of the second shadow filter in Figure 5b, setting the natural frequency by k2, while k1is used to adjust Q for: (a) LP, (b) HP, (c) BP, (d) BS, (e) AP. 5. Conclusions This paper proposes two current-mode shadow filters using CCCIIs with controlled current gains. The circuits employ three CCCIIs with controlled current gains and two grounded capacitors. The proposed architecture can realize LP, HP, BP, BS, and AP filters in the same topology. The current gains of CCCIIs can be used to modify the natural frequency and the quality factor of all filtering functions. The proposed shadow filters have the advantages of low-input and high-output impedances and low circuit complexity; they do not require passive resistors; they are suitable for integrated circuits by using grounded capacitors; and they have electronic tuning capability. To show the workability and performance of the proposed filters, SPICE simulation was performed. The simulated results were in agreement with the theoretical values and the experimental results confirm the functionality and the performance of the proposed filters. Author Contributions: Conceptualization, M.K. (Montree Kumngern), F.K. and T.K.; methodology, M.K. (Montree Kumngern), F.K., B.K. and S.L.; software, M.K. (Montree Kumngern), B.K. and S.L.; validation, M.K. (Montree Kumngern), F.K.; formal analysis, M.K. (Montree Kumngern); investigation, M.K. (Martin Kyselak), F.K. and T.K.; resources, M.K. (Martin Kyselak); data curation, M.K. (Martin Kyselak) and F.K.; writing—original draft preparation, M.K. (Montree Kumngern), F.K., B.K. and S.L.; writing—review and editing, M.K. (Montree Kumngern), F.K., B.K., S.L. and T.K.; visualization, M.K. (Martin Kyselak) and M.K. (Montree Kumngern); supervision, M.K. (Montree Kumngern) and Sensors 2024,24, 460 22 of 23 F.K.; project administration, M.K. (Montree Kumngern) and F.K.; funding acquisition, M.K. (Montree Kumngern). 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