Multiple-Input Single-Output Voltage-Mode Multifunction Filter Based On Vdddas

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER Multiple-Input Single-Output Voltage-Mode Multifunction Filter Based On Vdddas Pintira HUAIHONGTHONG1, Peerawut SUWANJAN1, Surapong SIRIPONGDEE1, Winai JAIKLA1, Amornchai CHAICHANA1 1Department of Engineering Education, School of Industrial Education and Technology, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand [email protected], peera[email protected], surap[email protected], [email protected], amornchai.c[email protected] DOI: 10.15598/aeee.v21i4.5159 Article history: Received Apr 09, 2023; Revised Jul 19, 2023; Accepted Oct 09, 2023; Published Dec 31, 2023. This is an open access article under the BY-CC license. Abstract. In recent years, the voltage differencing differential difference amplifier (VDDDA) has been used in various analog signal processing circuit designs. A second-order multifunction filter with multiple-inputs and single-output (MISO) voltage mode using VDDDA as active elements is proposed in this paper. The structure of the proposed filter comprises two VDDDAs, two grounded capacitors, and two resisters. The proposed filter has a cascadability feature in a voltage-mode system, producing voltage input and voltage output at high and low impedance ports, respectively. It can offer responses for all-pass (AP), band-reject (BR), band-pass (BP), low-pass (LP), and high-pass (HP) filters without additional inverting and double gain amplifiers, as well as the matching conditions. Choosing the appropriate input signals provides these five filter responses in the same circuit topology. With two VDDDAs, the bias currents can be utilized to electronically tune the natural frequency (ω0) independently from the quality factor (Q). Experimental results using available commercial ICs have supported the theoretical expectations and confirmed the practical operation of the proposed multifunction biquad filter. Keywords Multifunction filter, VDDDA, voltage-mode circuit, MISO, electronical controllability, LM13700, AD830. 1. Introduction. A filter is an electrical network that is designed to pass or reject an electrical signal in a certain way when it is connected to its input terminals [1]. Active filters, in particular, are versatile, low-cost configurations that are simple to design and tune. Communications, electronic music, medical electronics, seismology, instrumentation, and many other fields use active filters in important ways [2]. A multiple-input, single-output (MISO) multifunction biquad filter is one of the most popular categories of analog filters [3]. In the same circuit topology, it can offer various filter responses. Based on suitable input signals, the MISO filter’s various output transfer functions can be chosen. The most common way to control the input signal at the filter’s input nodes is to turn on or off the input signals. This digital selection can be done by a microcontroller or microprocessor [4]. The voltage differencing differential difference amplifier (VDDDA) [5] combines the functions of both the transconductance amplifier (TA) and the unitygain voltage differential difference amplifier (DDA). It is an immensely useful and flexible active building block (ABB) for designing a voltage-mode active filter. Where the TA is at the VDDDA input stage, the filtering parameters of the VDDDA-based filter, such as the passband voltage gain, bandwidth, cut-off frequency, quality factor, and phase response, may be tuned via the transconductance (gm). With a DDA at the VDDDA output stage, it is also very useful for building voltage-mode filters without the need for extra or external voltage summation or voltage difference circuits. Moreover, certain VDDDA-based voltage-mode filters c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 340 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER Tab. 1: Some results with accuracy. Ref. Filter sort No. Of ABB No. Of R+C High input impedance Low output impedance Availability of LP,HP,BP,BR, and AP responses No need for matching condition No need of additional circuits for selecting the filtering responses Independent control of ω0 and Q Electronic control [4] MISO 1 2+2 No No Yes Yes No No Yes [6] MIMO 3 1+2 Yes Yes Yes No Yes Yes Yes [7] MIMO 1 1+2 Yes No No No Yes Yes Yes [8] MISO 1 1+2 No No Yes Yes No No Yes [9] MISO 2 0+2 Yes Yes Yes Yes Yes No Yes [10] MISO 3 1+2 Yes Yes Yes Yes Yes Yes Yes [11] MISO 1 1+2 No No Yes No No No Yes [12] MISO 2 1+2 Yes Yes Yes No No No* Yes [13] MISO 1 2+2 Yes No Yes Yes No No Yes [14] SIMO 2 2+2 Yes No No Yes Yes Yes Yes [15] SIMO 3 1+2 Yes No Yes Yes Yes Yes Yes [16] SIMO 2 0+1 No No No Yes Yes No Yes [17] SIMO 3 1+2 Yes No Yes Yes Yes Yes Yes [18] MISO 2 3+2 No Yes Yes Yes Yes Yes No [19] MIMO 3 4+2 No Yes No Yes Yes No* No [20] MIMO 3 5+2 No Yes No Yes Yes No* No [21] MIMO 2 3+2 No Yes No Yes Yes No* No [22] SIMO 3 2+2 Yes Yes No Yes Yes No No [23] MIMO 3 1+2 Yes No Yes Yes Yes No Yes [24] MIMO 3 0+2 Yes No Yes Yes Yes No Yes [25] MIMO 2 0+2 Yes No Yes Yes No No Yes [26] SIMO 3 1+2 Yes Yes No Yes Yes No* Yes This work MISO 2 2+2 Yes Yes Yes Yes Yes Yes Yes *The multifunction filters provide only the orthogonal control of ω0and Q(Qis tuned without affecting the ω0). can be connected without the use of additional buffer devices [12]. The voltage-mode multifunction filters using a family of voltage differential difference amplifiers can be found in the open literature. These are based on VDDDA [4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], AD830-based DDA [18, 19, 20, 21, 22], and a differential difference transconductance amplifier (DDTA) [23, 24, 25, 26]. The comparison and review of a proposed filter with the referenced single-input multiple-output (SIMO), multiple-input multiple-output (MIMO), and MISO in voltage-mode filters are given in Table 1. It is found that filters in [4], [8], [11], [16], and [18, 19, 20, 21] cannot provide high input impedance at all input voltage nodes. Low output impedance is not obtained for all standard function responses [4], [7], [8], [11], [13, 14, 15, 16, 17], and [23, 24, 25]. Five different filter responses cannot be realized in the same circuit topology [7], [14], [16], [19, 20, 21, 22], and [26]. The voltagemode filters in [6], [7], [11], and [12] need matching conditions, and in [4], [8], [11, 12, 13], and [25] they need additional circuits for selecting the filtering responses. The parameters ω0and Qof the filters in [4], [8, 9, 11, 12, 13, 16], and [19, 20, 21, 22, 23, 24, 25, 26] cannot be independently adjusted. the parameters ω0 in [18, 19, 20, 21, 22] cannot be electronically controlled. It is also found that with two VDDDAs, the independent control of the parameters ω0and Qis not achieved. The two VDDDA-based MISO multifunction filters in [12] only control ω0and Qorthogonally (Qis tuned without affecting ω0). This paper introduces a voltage-mode multifunction filter based on VDDDAs that has multiple-inputs and a single-output voltage. Two grounded capacitors, two resistors, and two VDDDAs are used in the proposed multifunction filter. Without matching requirements, it can provide all typical filter responses, such as HP, LP, BP, BR, and AP. It features high input impedance and low output impedance for all functions, with no need for additional circuits for selecting the filtering responses. The parameters ω0and Qcan be independent, where ω0can be electronically tuned using bias current and Qcan be adjusted via a grounded resistor. The results of the experiment supports the viability of the proposed circuit. 2. Proposed Filter 2.1. VDDDA A voltage differencing differential difference amplifier (VDDDA) as a voltage-mode active device is used in the proposal filter. Fig. 1(a) denotes the VDDDA’s symbol. Fig. 1(b) is the equivalent circuit of the VDDDA. It comprises a transconductance amplifier (TA) and a differential difference amplifier (DDA). The terc 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 341 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER (a) (b) Fig. 1: The VDDDA’s symbol and equivalent circuit. Fig. 2: The VDDDA’s symbol and equivalent circuit. minal relation of the ideal VDDDA can be characterized by the following set of equations [5]. iz=gm(v+−v−) vw=vz−vn+vp.(1) According to the equivalent circuit and symbol of the VDDDA in Fig. 1, v+,v−,n, and pare high-impedance voltage input terminals, zis a high-impedance current output terminal, and wis a low-impedance voltage output terminal. By using bias current (IB), the transconductance of VDDDA is electronically tuned. For the real experiment, the VDDDA comprises commercially available ICs [9], as illustrated in Fig. 2. LT1228 is an OTA, and AD830 is a DDA. The bias current of the LT1228 can be used to control the value gm. The relationship between gmand IBis given by gm= 10IB.(2) Fig. 3: The proposed multifunction filter using VDDDAs. Tab. 2: Some results with accuracy. Output response Vin1Vin2Vin3Vin4 Non-inverting low-pass GND GND Vin GND Inverting high-pass GND Vin Vin GND Non-inverting band-pass GND GND GND Vin Inverting band-pass Vin GND GND GND Inverting band-reject GND Vin GND GND Inverting all-pass GND Vin GND Vin 2.2. Proposed filter According to Fig. 3, the proposed filter is constructed using VDDDA as the active component. It has two grounded capacitors (C1and C2), two resistors (R1 and R2), and two voltage-amplifying components (VDDDA1 and VDDDA2). One output voltage node and four high-impedance input voltage nodes make up the proposed circuit. Without requiring both active and passive element matching conditions, it can provide HP, LP, BP, BR, and AP responses in the same topology. It should be noted that R1should be shorted (R1= 0) for an AP response. The following gives the equation for the proposed filter’s output voltage: Vo=R1+R2 R2    −s2Vin2+gm1 C1 sVin4−gm1 C1 sVin1 +gm1gm2 C1C2 Vin3−gm1gm2 C1C2 Vin2    s2+R1+R2 R2gm1 C1s+gm1gm2 C1C2 . (3) It is obvious from Eq. (3) that the proposed filter may achieve all standard second-order filter responses in the same circuit topology by selecting the proper input terminals according to Table 2, where the gain of the BP function is unity, and the gain of the other functions is (R1+R2)/R2. From Eqs. (2) and Eqs. (3), the parameters ω0and Qare given by: ω0=rgm1gm2 C1C2 = 10rIB1IB2 C1C2 ,(4) and Q=R2 R1+R2sgm1C1 gm2C2 =R2 R1+R2rIB1C1 IB2C2 . (5) c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 342 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER Fig. 4: The proposed multifunction filter with parasitic impedances. From Eqs. (4) and (5), if C1=C2=Cand the bias currents, IB1and IB2are simultaneously tuned (IB1=IB2=IB), the parameter ω0and Qcan be rewritten as ω0=gm C=10IB C,(6) and Q=R2 R1+R2 .(7) From Eqs. (6) and (7), it is discovered that the parameter ω0can be adjusted linearly and electronically by bias current (IB). Moreover, both the ω0and Q can be independently tuned. The Qcan be controlled without disturbing ω0by the resistors, R1and R2. 2.3. Circuit sensitivities From Eqs. (4) and (5), the active and passive sensitivities of the parameters ω0and Qof a proposed filter are given by Sω0 IB1=Sω0 IB2=SQ IB1=SQ C1=1 2,(8) Sω0 C1=Sω0 C2=SQ IB2=SQ C2=−1 2,(9) SQ R1=−R1 R1+R2 , SQ R2=R1 R1+R2 .(10) 2.4. Analysis of non-ideal cases For the sake of practicality, it is important to consider the non-ideal characteristics of the VDDDA that affect the circuit’s performance. Firstly, taking into account the voltage tracking error from the voltage and current terminals of VDDDA, the terminal relationships in Eq. (1) can be rewritten as vW=βzvz−βnvn+βpvp,(11) Where βz,βn, and βpare the voltage transfer gain errors from the z,n, and pterminals to the wterminal Fig. 5: Experimental gain responses of LP, HP, BR, and BP functions. Fig. 6: Experimental gain and phase responses of AP functions. of VDDDA, respectively. Thus, the voltage-tracking error transfer functions can be expressed as V∗ O= R1+R2 R2+R1(1−βp1)            −βn1Vin2s2−βz1 gm1 C1 sVin1 +βp2βz1 gm1 C1 sVin4 +βz2βz1 gm1gm2 C1C2 Vin3 −βn1βz2 gm1gm2 C1C2 Vin2                 s2+ (R1+R2)βn2βz1gm1 C1s R2+R1(1 −βp1)! +βz2 gm1gm2 C1C2      . (12) From Eq. (12), the non-ideal parameters filter is given by: ω∗ 0=rβz2 gm1gm2 C1C2 ,(13) Q∗=1 βn2βz1 −βp1 βn2βz1R1 R1+R2sβz2gm2C1 gm1C2 . (14) c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 343 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER It can be seen from Eq. (12) that parameters βz, βnand βpaffect gain and filter responses. Also, the voltage tracking errors have a slight effect on the ωz and Q. as illustrated in Eq. (13) to (14). Secondly, this section considers the VDDDA’s parasitic impedance effect. The high-impedance terminals v+,v−,z,n, and pof VDDDA have a parallel parasitic resistance and a parasitic capacitance. The low-impedance terminal whas a parasitic series resistance (Rw), as illustrated in Fig. 4, the nonideal transfer functions will be expressed as where Yn2=sCn2+Gn2,Yv+1 =sCv+1 +Gv + 1,Y1= sCT1+GT1,Y2=sCT2+GT2,Y3=sCp1+Gp1+G1, CT1=C1+Cz1+Cv−2,CT2=C2+Cz2,CT3=Cp1, GT1=Gz1+Gv−2, and GT2=Gz2. If the operational frequency (fop) of the proposed biquad filter is much less than 1/[2πCp1(R1//R2)] and Rp1 is much more than R1, then Y3is approximately equal to Y3∼ =1/R1. Also, if the operational frequency is much less than 1/[2πCv+1(Rv+1//Rw2)] and 1/[2πCn2(Rn2//Rw1)], then the admittances Yn2and Yv+1 are neglected. Thus, the voltage transfer functions in (15) can be rewritten as V∗∗∗ O= R1+R2 R2                   −Vin2s2+sGT2 CT2 +sGT1 CT1 +GT1GT2 CT1CT2 +gm1 CT1 s+GT2gm1 CT1CT2Vin4 −s CT1 +GT2 CT1CT2gm1Vin1 +gm1gm2 CT1CT2 Vin3−gm1gm2 CT1CT2 Vin2                                    s2+ R2 R1+R2gm1 CT1 +GT2 CT2 +GT1 CT1s +gm1gm2 CT1CT2 +R2 R1+R2 ×GT2gm1 CT1CT2 +GT1GT2 CT1CT2                  . (16) From Eq. (16), the non-ideal filter parameters are given as ω∗∗∗ 0=sgm1gm2 CT1CT2 +R2 R1+R2GT2gm1 CT1CT2 +GT1GT2 CT1CT2 , (17) Q∗∗∗ =rgm1gm2 CT1CT2+R2 R1+R2GT2gm1 CT1CT2+GT1GT2 CT1CT2 h R2 R1+R2gm1 CT1+GT2 CT2+GT1 CT1i(18) The parasitic impedances of VDDDA have an impact on the voltage gain, ω0,Q, and the filter response, as Fig. 7: Tuning of f0for BP filter via IB. Fig. 8: Tuning of the quality factor for BP filter via R1. can be observed from Eq. (18). In a while, C1and C2can absorb the parameters Cz1and Cz2at ports Z1 and Z2. 3. Experimental results The proposed multiple-input single-output voltagemode multifunction filter based on VDDDAs is experimentally tested. In Fig. 3, the VDDDA is implemented by using commercially available ICs LT1228 and AD830. To design all standard functions of the proposed filter with gain = 1.1 dB, Q= 0.9, and f0= 300 kHz. The circuit components are chosen as: C1=C2= 1 nF, R1= 100 Ω for LP, HP, and BP functions. R2= 1 kΩ,IB1=IB2= 185 µA and the supply voltage =±5V. The experimental and theoretical results of the frequency gain response for all filtering functions are illustrated in Fig. 5. The experimental f0is 299 kHz. So, the deviation between experimental and theoretical values is ∼0.3%. It is found that the experimental LP response at high frequency is inconsistent with the theoretical response because of the effect of the parasitic impedances of VDDDA as studied in Eq. (15). The parasitic elements in VDDDA also affect the HP response at low frequency. The experimental c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 344 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER VO=     −Vin2+gm1 Y11 1 + Yv+1Rw2Vin4−gm1 Y1 Vin1 +gm1gm2 Y1Y21 1 + Yv+1Rw2Vin3−gm1gm2 Y1Y21 1 + Yv+1Rw2Vin2            Y3Yn2+Y3R2+1+Rw1Yn2(Y3R2+ 1) Y3Yn2+Y3R2+ 1 −1 1 + R2Y3+gm1 Y11 1 + Yv+1Rw2 +gm1gm2 Y1Y21 1 + Yv+1Rw2Y3Yn2+Y3R2+1+Rw1Yn2(Y3R2+ 1) Y3Yn2+Y3R2+ 1 −1 1 + R2Y3       .(15) gain and phase responses of the AP function are depicted in Fig. 6. It is found that the phase shift begins at 180 degrees at low frequency and transitions to -180 degrees at high frequency. With this phenomenon, the proposed AP function can provide the leading phase shift from low frequency to natural frequency and the lagging phase shift from the natural frequency to high frequency. As stated above for an AP response, R1 should be shorted (R1= 0). Experimental results in Fig. 7 demonstrate that f0can be tuned without affecting Q, where IBwas changed to 61 µA, 127 µA, and 246 µA, while other elements were as follows: C1=C2 = 1 nF, R1= 100 kΩ, and R2= 1 kΩ. The experimental results show that f0obtained from these tuning IBvalues are 97.9 kHz, 203 kHz, and 390 kHz. The deviations from experimental and theoretical values are 0.1%, 0.09%, and 0.5%, respectively. It is found that when f0is tuned by IB1, it slightly affects the pass band gain due to the parasitic elements as analysed in Eq. (16). Experimental results in Fig. 8 demonstrate that Qcan be tuned without affecting f0, where R1was varied to 100Ω,940Ω, and 2 kΩ, while other elements were as follows: C1= 10 nF, C2= 1 nF, IB1=IB2= 202µA, R2= 1 kΩ. The experimental results show that Qobtained from these tuning R1values are 2.87,1.63, and 1.05. The deviations from experimental and theoretical values are 2.8%, 1.2%, and 0.9%, respectively. It is found that when Qis tuned by R1, it slightly affects the pass band gain due to the parasitic elements as analysed in Eq. (16). The measured output and input sinusoidal waveforms of the LP, HP, BP, BR, and AP functions for three frequencies are depicted in Figs. 10, 11, 12, 13, and 14 respectively 4. Conclusion This study describes a voltage-mode multifunction filter based on VDDDAs that has multiple-input and a single-output voltage node. Two VDDDAs, two grounded capacitors, and two resistors are used in the proposed filter. It can acquire all standard filter responses such as HP, LP, BP, BR, and AP without requiring matching conditions. The proposed filter can perform all functions with a high input impedance and a low output impedance. The ω0and Qcan be independently tuned. The parameters ω0can be electronically and linearly controlled by bias current (IB) without disturbing Q. Moreover, the Qis not electronically tuned (Qis controlled by a resistor (R1)) without disturbing ω0. The experimental results show strong performance and support the theoretical hypothesis. Acknowledgment This work was financially supported by King Mongkut’s Institute of Technology Ladkrabang, grant number 2566-02-03-010. Author Contributions Conceptual framework, P.H., W.J., and P.S.; Simulation, P.H., and W.J.; Experimental, P.H, and W.J.; Formal analysis and writing-original draft preparation, P.H., W.J., S.S., and A.C.; Verified the analytical methods, P.H.; All authors have discussed the results and contributed to the final manuscript. References [1] WATERS, A. Active Filter Design. Macmillan Publishers Limited, 1991. ISBN 978-1-349-213115 DOI: 10.1007/978-1-349-21311-5. [2] LANCASTER, D. Active-filter Cookbook. Newnes. 2nd edition, 1996. ISBN 978-0750629867. [3] JAIKLA, W., S. SIRIPONGDEE, and P. SUWANJAN, MISO Current-mode Biquad Filter with Independent Control of Pole Frequency and.Quality Factor. Radioengineering, 2012, vol.21, no. 3, pp. 886-891. [4] CHAICHANA, A., S. SANGYEAM, and W. JAIKLA. Multifunction Voltage-Mode Filter c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 345 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER (a) (b) (c) Fig. 9: Measured waveforms of non-inverting VLP and Vin (a) f= 10 kHz, (b) f= 300kHz and (c) f= 1MHz. (a) (b) (c) Fig. 10: Measured waveforms of inverting VHP and Vin (a) f= 10kHz, (b) f= 300kHz and (c) f= 1MHz. c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 346 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER (a) (b) (c) Fig. 11: Measured waveforms of non-inverting VBP and Vin (a) f= 10kHz, (b) f= 300kHz and (c) f= 1MHz. (a) (b) (c) Fig. 12: Measured waveforms of inverting VBP and Vin (a) f= 10kHz, (b) f= 300kHz and (c) f= 1MHz. c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 347 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 4 |2023 |DECEMBER (a) (b) (c) Fig. 13: Measured waveforms of inverting VBR and Vin (a) f= 10kHz, (b) f= 300kHz and (c) f= 1MHz. (a) (b) (c) Fig. 14: Measured waveforms of inverting VAP and Vin (a) f= 10kHz, (b) f= 300kHz and (c) f= 1MHz. c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 348