Third order low-pass filter using synthetic immittance elements with current conveyors

THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE THIRD ORDER LOW-PASS FILTER USING SYNTHETIC IMMITTANCE ELEMENTS WITH CURRENT CONVEYORS Pavel BRANDSTETTER1, Lukas KLEIN1 1Department of Electronics, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic pavel.brandst[email protected], [email protected] Abstract. The paper deals with a theoretical proposal of the resulting circuit of the frequency filter using synthetic immittance elements of higher order with current conveyors. The text pays particular attention to design process of synthetic immittance elements, explains the principle of increasing of order, which is then reflected to the frequency filter order. The text then deals less with the theory of current conveyors, which has already been discussed, in detail, in previous papers. Universal current conveyor (UCC) is discussed more. This active element is used for the theoretical implementation of the synthetic element solution used in the frequency filter. The theoretical knowledge is then demonstrated in the design of 3rd order low-pass frequency filter. The final functionality of the proposed frequency filter circuit solution is validated by PSpice simulation. Keywords Current conveyor, frequency filter, low-pass filter, synthetic immittance element. 1. Introduction Method of the synthetic elements is primarily based on the needs of classical inductors substitution by synthetic equivalents in electronic circuits. It is not a new method, but its use in combination with new modern active components (current conveyors), for the design and realization of frequency filters, is a relatively new idea [1], [2], [3], [4], [5], [6], [7], [8]. The basic advantages of using current conveyors [1] include a wide frequency range, ease of integrability of the resulting circuit solutions, low supply voltage of active elements and the possibility of use of battery supply in resulting circuit, when it is used in the mobile devices. Current conveyors [1] can be basically regarded as universal elements, because four basic functional block structures can be realized by combinations of these active elements. However, the basic disadvantage is low commercial availability of current conveyors and commercial unavailability of universal current conveyor (UCC), which was selected for the realization of filter proposed in this paper. Selection of UCC has its important reasons. This element seems to be very promising, especially in the design of circuit solutions with current conveyors, because it could be used for the implementation of all current conveyors variations. Universal current conveyor currently exists only as a laboratory sample and the wider extension yet to come. The paper tries to show its importance and the advantages. 2. Synthetic Immittance Elements of Higher Orders Synthetic dipoles with immittance of higher order [2] are divided into four groups – DP, DS, EP, ES. They are consisting of serial or parallel elementary dipoles connections. Synthetic elements DP, DS are created by elementary D type dipoles of order 0 to ND,max. Synthetic elements EP, ES are created by elementary E type dipoles of order 0 to NE,max. The linear circuits theory discusses that stable frequency filters can be realized, if the elementary dipoles of all orders from the lowest (nd,min, ne,min) to highest (nd,max, ne,max) will be connected in the synthetic elements. Most of the values of nd,min, ne,min equal to 0 or 1, values of nd,max, ne,max set the order of the synthetic element. In the most cases, these values also set the order of frequency filter transfer function, respectively. As stated above, there are four connections of synthetic elements with immittance of higher order [2]: © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 89 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE  dipole DP ND,min ND,max consists of a parallel connection of synthetic elementary dipoles of type Dn for n = ND,min, ND,min + 1, ..., ND,max - 1, ND,max,  dipole DS ND,min ND,max consists of a serial connection of synthetic elementary dipoles of type Dn for n = ND,min, ND,min + 1, ..., ND,max - 1, ND,max,  dipole EP NE,min NE,max consists of a parallel connection of synthetic elementary dipoles of type En for n = NE,min, NE,min + 1, ..., NE,max - 1, NE,max,  dipole ES NE,min NE,max consists of a serial connection of synthetic elementary dipoles of type En for n = NE,min, NE,min + 1, ..., NE,max - 1, NE,max. 2.1. The Conditions of Synthetic Immittance Elements Realization If suitable synthetic immittance elements of higher order should be designed, then an appropriate form of input impedance, respectively input admittance is searched [3]. The required input impedance respectively input admittance form of synthetic immittance elements of DS and ES type should be: VWV U IN YYY Y Z1  , WU WV IN YY YY Y . (1a, b) Increase of synthetic element order is done by repeatedly replace of admittance YV with circuit with input admittance (1b). Increase of order of synthetic immittance element can also be achieved by replacing the admittance YU with circuit with the input admittance (2b). For synthetic immittance elements of DP and EP type, it is required input impedance respectively admittance in form:  WVU W IN YYY Y Z , U W VU IN Y Y YY Y . (2a, b) Admittance YV is repeatedly replaced with circuit with the input admittance (2b), if we want to increase order of synthetic immittance element. 3. Universal Current Conveyor Universal current conveyor (see Fig. 1) was created on the base of the universal element idea, which could easily implement every current conveyor generation or variation in practice. This element would allow a different application use of current conveyors and their wider expansion. Universal current conveyor has met these requirements [4]. It can realize all the known types of current conveyors. It is the basic principle of its versatility. Implementation of the various types of current conveyors is provided by use of only certain input and output terminals of universal current conveyor, the remaining terminals are properly connected or grounded. Another advantage of the element is that it contains several input and output terminals, which provides an opportunity to sum signals at the input of conveyor or to divide the output signals to multiple locations [4]. The active element is not currently mass produced, and therefore not widely available. Fig. 1: Schematic symbol of universal current conveyor (UCC). Terminals Y1+, Y2-, Y3+ are the voltage inputs, X is the current input (see Fig. 1). Terminals Z 1+ and Z2+ are current outputs with a positive transfer of current, Z1and Z2are current outputs with a negative transfer of current from terminal X. The universal current conveyor is generally described by equations [4]: 321 YYYX uuuu    , , 0 321  YYY iii XZZ iii    21 , . (3a, b, c, d) XZZ iii   21 4. Realization of Synthetic Immittance Elements with Current Conveyors If the appropriate structure of synthetic immittance dipoles of type DP, DS, EP and ES type is searched, then the particular form of input admittance or impedance is primarily required. It is very difficult to find the exact expressions that equal to the formulas (1a, b) respectively (2a, b). We can more often find the expressions approaching these forms than exact forms. They can be also used. However, it is necessary to theoretically verify their suitability for use in frequency filters. The main target is to get forms of equations that will be most similar to the equations (1a, b) respectively (2a, b). The general circuit network for searching of suitable circuit structures was used to implement synthetic immittance element. The general circuit network consists of nine passive elements (admittances) and one general four-port current conveyor [2]. Final © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 90 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE structure is shown in Fig. 2. Fig. 2: Default admittance network to search the synthetic element solution. The synthetic element searching procedure is quite simple. The selected admittances are removed from the general circuit network. The resulting circuit structure should consist of three admittances and general four-port current conveyor. Three admittances are enough to realize the synthetic immittance element. Any of the general current conveyor terminals Y, X, Z1 or Z2 can be used as the input of the resulting circuit structure [5]. The input admittance form is then edited again by the suitable choice of the general current conveyor coefficients a, b, c11, c22. It is final change of the input admittance. The final input admittance of the resulting circuit is then deducted, if it equals (1a, b), (2a, b) or forms close to these equations. Several dozens of combinations were examined this way. Figure 3 shows one of the found structures that can be used for the realization of synthetic element. The circuit is suitable for implementing filters of higher order. Fig. 3: Circuit structure suitable for realization of synthetic element. The input admittance general form of the circuit shown in Fig. 3 has the form: 22711771122 9722929222722272 1172117272727272 IN cYcYYcYY abYYacYYabYYacYYcYY acYYcYYabYYbYYaYYYY Y   . (4) There the values of the general current conveyor coefficients from the possible combinations were chosen. Best suited combination is a=-1, b=0, c11 =-1, c22=1. This combination of values simplifies the input admittance general form and brings it to its ideal form. General circuit structure is suitable to implement the synthetic immittance elements DP or EP (1a, b). Selected coefficients correspond to the inverting current conveyor of second generation ICCII+/-. After this adjustment, the input admittance of the circuit is transformed into the form: 2 7 92 IN 2Y Y YY Y , )2( 792 7 IN YYY Y Z . (5a, b) Targeted selection of passive elements and their substitution for general admittance in the circuit structure create the synthetic immittance element DP of second order. The circuit structure is shown in Fig. 4. Fig. 4: Circuit structure of second order synthetic element DP. The resulting input admittance of synthetic immittance element shown in Fig. 4 has the form: . (6) 2927 2 IN 2CpCCRpY  4.1. Synthetic Immittance Element Order Increasing Increasing of the synthetic element order will be demonstrated on the synthetic element shown in Fig. 4. Increasing of the synthetic element order is cascade, i.e. there is a repeated replacement of a passive element for a whole circuit structure of identical synthetic element in the structure of synthetic element. Increasing of order of synthetic element in Fig. 4 to third order shows Fig. 5. As can be seen from Fig. 5, the capacitor marked in Fig. 4 as C9 was replaced by circuit structure of synthetic element DP shown in Fig. 4. Fig. 5: Third order synthetic immittance element DP. © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 91 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE The number of capacitors in the structure of a synthetic element was increased. The result is also increasing of the synthetic element order. The input admittance of the newly created synthetic element of third order has form as follows: . (7) 1211 2 32121 32CpCCRpCCCRRpYIN  The new increasing of order of synthetic element would be made by replacing the capacitor C3 for the whole synthetic element structure shown in Fig. 4. Forms of other input admittance caused by increasing of the synthetic immittance element order are shown in Tab. 1. Tab.1: Input admittance forms. Order of Synthetic Element Input Admittance Form 4. YIN = p4R1R2R3C1C2C3C4 + p32R1R2C1C2C3 + p2R1C1C2+ p2C1 5. YIN = p5R1R2R3R4C1C2C3C4C5 + p42R1R2R3C1C2C3C4 + p32R1R2C1C2C3 + p2R1C1C2 + p2C 1 6. YIN = p6R1R2R3R4 R5C1C2C3C4C5C6 + p52R1R2R3R4C1C2C3C4C5 + p42R1R2R3C1C2C3C4 + p32R1R2C1C2C3 + p2R1C1C2 + p2C1 7. p52R1R2R3R4C1C2C3C4C5 + p42R1R2R3C1C2C3C4 + p32R1R2C1C2C3 + p2R1C1C2 + p2C1 YIN = p7R1R2R3R4 R5R6C1C2C3C4C5C6C7+ p62R1R2R3R4 R5C1C2C3C4C5C6 + 5. Frequency Filters Using Synthetic Immittance Elements There was used synthetic immittance element DP shown in Fig. 5 for the realization of low-pass filter of third order. Circuit solution of third order low-pass is shown in Fig. 6. FThird order low-pass using synthetic element with current conveyors. Two universal current conveyors were used in the final circuit solution of active frequency filter. With its help, ICCII+/- was implemented. There was also used passive low-pass at the input of active filter to smooth the final frequency responses at higher frequencies. Resistor R ig. 6: ther with capacitor C1. Transfer function of active third order low-pass shown in Fig. 6 has form as follows: 1 was divided into two parts, and it creates passive lowpass toge 1442 213221 2 432321 3 CRpCCRRpCCCRRRp KU Specific values of passive components were calculated with gen 1 )( p. (8) eral design relations for active third rder low-pass [6]: o 432321 3 0 33 2 cCCCRRR  , (9) 3221 2 0 32 4 cCCRR  , (10) 21 0  Butterworth approximation was chosen. The coefficients of this approximation for filters of third order have values c 31 4 cCR. (11) resistors (12), (13), (14) are expressed from equations (9), (10), (11): 31=c32=2, c33=1 [6]. As already mentioned in the previous text, the values of capacitors are chosen and values of resistors are calculated. The values of passive elements of frequency filter are also based on the chosen value of cut-off frequency 1 MHz and the coefficients of chosen approximation. The forms for calculation of values of 20 31 14 c C R  , (12) 3310 32 2 c2 Cc R  , (13) 4320 3Cc  Values of resistors are calculated after substituting of specific values. Optimization in PSpice was also used to determine the ideal values of passive elements. The resulting values of the passive elements were determined R 33 c2 R. (14) 1=2,7 kΩ, R2=5,6 kΩ, R3=1,2 kΩ, C1=C2=C3=22 pF, C4=100 pF. The resulting amplitude frequency response and phase response of a real model of third order lowpass is shown in Fig. 7. There are two traces here. First trace is for circuit solution of active low-pass and second trace describes the behavior of circuit solution of active low-pass using also passive low-pass. As can be seen, use of passive low-pass in the circuit structure of third order active low-pass changes the position of cut-off frequency. However, this solution also gives good results at higher frequencies, where the gain increase is reduced. Cut-off frequency of the filter is defined as a decrease of magnitude about 3 dB [6]. Cut-off frequency in this case was chosen 1 MHz. The simulated characteristic shown in Fig. 7 does not exactly match those requirements. The selected cut-off frequency of 1 MHz is defined as a decrease of amplitude frequency response about 4,43 dB. Such a large deviation can be tolerated. Some of © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 92 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING NUMBER: 2 | 2012 | JUNE VOLUME: 10 | © 2012 IN ELECTRICAL AND ELECTRONIC ENGINEERING 93 ideal oper hange of cut-off frequency of active low-pass depends cular traces depending on the variable tolerance of C2. the factors that could cause the deviation are the pr ties of the used universal current conveyor model and the passive low-pass at the input of active filter. Also, sensitivity analysis was carrying out. The mostly on capacitor C2. The amplitude frequency response and phase response shown in Fig. 8 describe parti c Fig. 7: Amplitude frequency response and phase response of third order low-pass using synthetic element with current conveyors. Fig. 8: Monte Carlo analysis of amplitude frequency response and phase response of third order low-pass with passive filter. f the final circuit solution. This ty is a disadvantage and ADVANCES 6. Conclusion The paper tries briefly describe the realization of frequency filters with synthetic immittance elements of higher order with current conveyors. Application use of synthetic immittance elements brings a lot of advantages. One of the most important advantages is the easy integrability o is a very important factor especially in electroindustrial production. It is advantageous to use universal current conveyor in design. UCC is able to substitute all previous generations of current conveyors but its commercial unavailabili THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE un sal current conveyor can be used only as a theoretical element now. The described theory and the final circuit solution of third order low-pass indicate that the described method produces relatively good results. The article describes only one of total three found synthetic elements. Despite further attempts no other elements were found. It can therefore be assumed to find another solution of synthetic immittance elements with current conveyors is very difficult. However, other solutions of synthetic immittance elem iver ents can be found with combinations of different types of current conveyors or with other active elements. SP2012/85, which was supported by Student Grant Competition of VSB-Technical University of Ostrava. urrent ctions using Universal Current Conveyor. In: Conference 3868-6. ISSN 0925-1030. DOI: 10.1007/s10470onics. 2009, vol. 96, iss. 8, iwice: IEEE, tional amplifiers. Praha: BEN, 2002. ISBN 80-7300-047-4. nts, Acknowledgements In the paper, there are the results of the project References [1] SMITH, K. C. and A. S. SEDRA. The current conveyor: a new circuit building block. IEEE Proceedings of the CAS. 1968, vol. 56, iss.1, ISSN 0018-9219. [2] SPONAR, R. and K. VRBA. Synthetic dipole elements with higher-order immittances in frequency filters with c conveyors. Elektrorevue [online]. 2004, vol 2004, no. 13. ISSN 1213-1539. Available at: http://www.elektrorevue.cz/clanky/04013/index.html. [3] HORNG, J.-W., Ch.-L. HOU, Ch.-M. CHANG, H. YANG and W.-T SHYU. Higher-order immittance fun current conveyors. Journal Analog Integrated Circuits and Signal Processing. 2009, vol. 61, no. 2, pp. 205-209. ISSN 0925-1030. DOI: 10.1007/s10470-009-9298-6. [4] ZHANG, Q., Ch. WANG and Y. LENG. A Novel Building Block: Proceedings of IEEE 8th International Conference on ASIC. Changsha: IEEE, 2009, pp 1109-1112. ISBN 978-1-4244- [5] PSYCHALINOS, C. and G. SOULIOTIS. Low-Voltage Current Controlled Current Conveyor. Journal Analog Integrated Circuits and Signal Processing. 2010, vol. 63, no. 1, pp. 129-135. 009-9416-5. [6] KOTON, J., K. VRBA and HERENCSAR. Tuneable Filter Using Voltage Conveyors and Current Active Elements. International Journal of Electr pp. 787-794. ISSN 0020-7217. [7] BRANDSTETTER, P. and L. KLEIN. Applications of NonInverting Positive Second Generation Current Conveyor as a Commercially Available Versatile Active Element. In: Conference Proceedings of International Conference on Signals and Electronic Systems - ICSES´10. Gl 2010, pp. 157-160. ISBN 978-1-4244-5307-8. [8] PUNCOCHAR, J. History and present of opera About Authors Pavel BRANDSTETTER was born in Ostrava, Czech Republic, 1955. He received the M.Sc. and Ph.D. degrees in Electrical Engineering from Brno University of Technology, Czech Republic, in 1979 and 1987, respectively. He is currently full professor in Electrical Machines, Apparatus and Drives and vice dean of Faculty of Electrical Engineering and Computer Science at VSB-Technical University of Ostrava. His current research interests are applied electronics, microcomputer control systems and modern control methods of electrical drives. Lukas KLEIN was born in Uherske Hradiste in 1984. He obtained Bachelor’s degree at Brno University of Technology in field of Teleinformatics in 2007 and then he obtained his Master’s degree in field of Mobile technologies in 2009 at VSB-Technical University of Ostrava. He is currently pursuing Ph.D. study at Department of Electronics on Faculty of Electrical Engineering and Computer Science. His research area includes application of modern active eleme especially current conveyors, in electronic circuits. © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 94