CHAPTER 4 FOUR TERMINAL FLOATING NULLOR BASED BIQUAD FILTER

Transcription

1 CHAPTE FOU TEMINAL FLOATING NULLO BASED BIQUAD FILTE This chapter deals with the realization of a multifunction biquad filter usg Four Termal Floatg Nullor (FTFN), a new current mode device. Two biquad filters havg high put impedance have been realized with sgle put and two outputs simultaneousl. The proposed filter circuits simultaneousl implement high-pass and band-pass filterg functions. Each circuit emplos two FTFN, two capacitors and two resistors which is the absolute mimum requirement for a biquad filter. B slight modification the topolog of the circuit band-pass and low-pass responses can also be realized at the same outputs. Further, the proposed circuits emplo lesser number of passive components than the one reported b Liu and ung []. The followg sections troduce the basic FTFN, a four termal floatg nullor device and the current state of its applications as filters. Next the proposed circuits and their performances are discussed.. FOU TEMINAL FLOATING NULLO (FTFN) Current-mode circuits have been receivg significant attention as the have the potential advantages of accurac and wide bandwidth over their voltage-mode counterparts []. The current-mode circuits ma be realized usg active devices such as FTFN, DDA, OTA, DDCC, DCC etc. The noise immunit is of great concern mixed signal sstems that combe analogue as well as digital parts. It is therefore necessar to design analogue circuits which have a full balanced architecture. The active device such as DDA, OFA, FTFN etc offer full balanced architecture. Amongst these FTFN, four termal floatg nullor, is more flexible and versatile than others. It provides floatg output, which is ver useful some application such as current-amplifiers, voltage to current converters, grators, floatg impedances etc. [9-]. Besides beg flexible, FTFN is a more all-round buildg block than the operational amplifier and current conveor. 7

2 In 9, FTFN was implicitl proposed b Tellegen as an ideal amplifier [88-89]. It was demonstrated that an active circuit can be realized b this active element and passive components. In 96 Carl referred this element as a four port nullor [9]. The traditional representation of the FTFN as nullor model is shown Figure.. This figure shows that FTFN ma be considered to comprise of an put Nullator and Norator at the output port. It is known as Nullor Model of FTFN or Nullator - Norator pair [9]. In the nullor model of FTFN it is observed that nullator and the norator are isolated from each other, which gives more flexibilit the active network snthesis. I I I I Figure.: Nullor model of FTFN The smbolic representation of FTFN is shown Figure.. I I I I Figure.: A smbolic representation of FTFN The port characteristics of this active device ma be described as: I I, and I I (.) w The output impedance of and port of an FTFN are arbitrar. In the present analsis that output impedance of -port has been considered to be ver low and that of the -port ver high. 7

3 FTFN based structure provides a number of potential advantage such as complete absence of the passive component matchg requirement, mimum number of passive elements [97]. Sce its troduction the FTFN has remaed as a theoretical element. ith the advent of technolog and current mode circuit evolution, implementation of FTFN became feasible. Presentl FTFN is not commerciall available the chip form. However, there are various techniques for the realization of FTFN usg available active devices such as Op-amp, OTA, CCII, etc. The discrete I.C. AD8 can be used for the realization of FTFN as shown Figure.. Figure.: ealization of FTFN usg AD8 All four basic tpe amplifiers: oltage Amplifier, Current Amplifier, Transconductance Amplifier and Transresistance Amplifier ma be realized with FTFN as shown Figure.. FTFN is therefore called a universal amplifier. 7

4 Figure.(a): FTFN as voltage amplifier I Figure.(b): FTFN as transconductance amplifier I I out Figure.(c): FTFN as current amplifier out I Figure.(d): FTFN transresistance amplifier 7

5 . EISTING EALIATIONS OF FILTES USING FTFN Beg a universal active device FTFN has a wide range of applications. It is used various applications such as oscillators and realization of admittance, filters etc. M. T. Abuelma atti proposed current mode susoidal oscillator usg one FTFN and six passive components for low and medium range of frequenc []. Chipipop also realized current mode FTFN based verse filter low-pass and high pass filters [6]. These filter circuits provide one filter response at a time. The chaotic circuit has also been realized usg FTFN [9,]. The implementation of higher order filters, usg these circuits cascaded mode, often necessitates the use of additional buffers. Thus there is overwhelmg need to develop high put impedance voltage mode (M) filters to evade the practical difficulties realizg higher order filters. This high put impedance feature of voltage mode filters permits their use cascade mode thereb circumventg the need for impedance matchg devices. Toward this end some high put impedance M filter circuits based on FTFN, second generation current conveors (CCIIs) and current feedback amplifiers (CFAs) have been reported the literature [,,, 7, 8, 89, ]. However, not much work has been reported for the realization of high put impedance filter usg FTFN, which is a more flexible and versatile buildg block than operational amplifier or a CCII [, 8, 89] to meet the varg and strgent requirements of the circuit designers. Liu [] proposed a current mode second order band pass filter usg one FTFN and 6 passive components as shown Figure.. This circuit ma be used to realize all filter functions with high sensitivit b changg the passive components onl. 76

6 I 6 I I out Figure.: Liu s circuit for band-pass filter usg FTFN The transfer function of the Liu s circuit ma be obtaed as: I I (.) Table. shows the combations of passive components for realization of various filters. Table.: arious filter responses from Liu s circuit 6 All-pass Filter Band-eject Filter

7 High-pass Filter + Low-pass Filter + Band-pass Filter + The filters realized with these combations have different qualit factors and the cutoff frequencies. Abuelma'atti proposed a cascadable current mode filter usg sgle FTFN [] as shown Figure.6. The circuit uses one FTFN and passive components for the realization of low pass, high pass, band pass filter separatel, while the realization of the all-pass and notch filter requires the six passive components. It gives low active and passive sensitivities. I I out Figure.6: Current mode filter b Abuelma'atti usg FTFN 78

8 The transfer function of the Abuelma atti circuit ma be expressed as I : I I out (.) The circuit realizes different filter responses b proper selection of the component as shown Table.. Table.: arious filter realizations from Abuelma atti circuit High-pass Filter + Low-pass Filter + Band-pass Filter + Though, same cutoff/center frequenc ma be obtaed for all the realizations with all the capacitors and resistors kept unaltered, the qualit factor differ. Later Liu and Lee [] proposed voltage mode universal filter emplog two FTFNs, three resistances and two capacitors as shown Figure.7. Their circuit realizes two filter responses simultaneousl. The band-pass and high-pass filter responses are respectivel obtaed at output termal o and o. 79

9 C C o o Figure.7: Liu and Lee s voltage mode universal filter usg FTFN The transfer function of the universal filter, shown Figure.7 can be expressed as: s C C + + o + + s CC (.) ( ) o o (.) The natural frequenc and the qualit factor of this filter can be expressed as: ω C C (.6) and Q C C (.7) ith proper selection of the put the transfer function, various filter realizations, havg same qualit factor and the cutoff/central frequenc, ma be obtaed at the output termal o as shown Table.. 8

10 Table.: arious filter realizations from Liu and Lee s circuit Low-pass Filter Band-pass Filter High pass Filter The passive and active sensitivities of this filter circuit are ver low. This circuit has limited application due to its low put impedance. Subsequentl Liu and ung [] realized high put voltage mode filter usg FTFN as shown Figure.8. Figure.8: Liu and ung s high put impedance filter usg FTFN The transfer function of this filter circuit ma be expressed as follows: 8

11 ( + ) + ( ) + (.8) B substitutg the admittances,,, and equation (.8) ma be modified as equation (.9) to realize a band-pass filter as follows: s CC + s( C + C) + (.9) The center frequenc ω and the qualit factor Q of the band-pass filter realization are given b equation (.) and (.): ω C C (.) Q ( C + C) CC (.) This circuit ma also be used for realization of high-pass filter response b proper selection of the admittance such as,,, and function of the circuit is then obtaed as:. The transfer s CC s CC + s( + ) C + (.) This realization has low cutoff/center frequenc and the qualit factor sensitivities with respect to active and passive components. But the circuit realizes onl one filter response at a time. Several circuits have been reported the literature for the realization of all these filters with high impedance usg one FTFN and other active devices [,, ]. For example, Liu and ung proposed a high put impedance filter emplog one FTFN and positive second generation Current Conveor (CCII+) havg five passive components as shown Figure.9. 8

12 CCII + Figure.9: High put impedance filters usg FTFN and CCII+ The transfer functions of this circuit given b: + ( + ) + ( ) (.) This circuit realizes low-pass, high-pass and band-pass filter b proper selection of the passive components as shown Table.. Table.: arious filter responses from high put impedance filters usg FTFN and CCII+ band-pass low-pass high-pass 8

13 In the followg sections we propose two new filter circuits emplog two FTFN and four passive components. These circuits realize two filter responses simultaneousl. Further, the filter functions obtaed with these circuits do not impose an component matchg or cancellation constrats. The high put impedance feature of the circuit permits cascadg to obta higher order filters. The resonance frequenc ω and bandwidth ω /Q are dependentl controllable. The proposed circuit enjos low active and passive components parameter variation.. POPOSED CICUIT The two proposed circuits provide combation of two filter responses. First circuit gives band pass and high pass filter, while second circuit provides band pass and low passes filter responses. These circuits are realized b the positive FTFN and passive components. The analsis of the circuit of Figure.9 ields the high pass and band pass filter responses. O C O C Figure.: Proposed band pass- high pass (BP-HP) filter circuit usg FTFN The two transfer function of the filter circuit shown Figure. is given b equations (.) and (.): 8

14 o s s C C CC + + (.) (.) o s C C + s C + The circuit provides the same characteristic equations (.) and (.). Thus, parameter ω, ω Q and Q are same for these two filters and are given b equation (.), (.6) and (.7) respectivel: ω C C (.) ω Q (.6) C Q C C (.7) ANALSIS ITH NON IDEAL FTFN: Analsis of the circuit considerg non-ideal behavior of FTFN ma be carried out b usg followg relations α and I βi (.8) w where α ε and ε (ε <<) denotes the voltage trekkg error of FTFN; and β ε and ε (ε <<) is the current trekkg error. The transfer functions of the filter circuits shown Figure. ma be therefore written as: o α βs CC (.9) s β CC + ( + β) + o sα βc (.) s β C C + + β ) s C + ( 8

15 The active and passive sensitivities of the cutoff\center frequenc ω and the qualit factor are small and are given b: S ω C, C,,, β S Q S C, S Q C, β β ( + ) Q β β (.) (.) (.) (.) ω S,, Q α α β S, (.) α α, β Thus the active and passive sensitivities are not more than one. The magnitude and phase responses of the high-pass and band-pass filters are shown Figure. respectivel, match with the theoretical results. Figure.(a): High pass filter magnitude response of BP-HP filter circuit usg FTFN 86

16 Figure.(b): High pass filter phase response of BP-HP filter circuit usg FTFN Figure.(c): Band pass filter magnitude response of BP-HP filter circuit usg FTFN 87

17 Figure.(d): Band pass filter phase response of BP-HP filter circuit usg FTFN SECOND CICUIT The second proposed circuit is a modification of the first circuit for the realization of voltagemode low pass and band pass filter, shown Figure.. O C O C Figure.: Band pass-low pass (BP-LP) filter circuit usg FTFN The transfer functions of the modified circuit of Figure. are given as: 88

18 o s C C s C + + (.6) o s C C + s C + (.7) It ma be observed that characteristic equation for the both filter realization are same. Thus the parameter ω, ω Q and Q are the same for two filter realizations and are given b equations (.8) to (.). ω (.8) C C ω Q C (.9) C C Q (.) The characteristic equations (.)-(.) are same as (.6)-(.7). From equation (.8) and (.9) it can be seen that band pass ga the two circuits can be controlled b the ratios C C and respectivel however this will change the cutoff/central frequenc ω. If the adjustment is made b C and the bandwidth remas unaffected but the cutoff/central frequenc ω changes. An examation of (.) and (.6) shows that non -teractg tung of ω /Q and ω can be obtaed b adjustg former parameter of terest through the components C and/or and the latter through C and/or. The frequenc responses of the band-pass and low-pass filter realizations usg modified circuit of Figure. are shown Figure. match with ideal response. 89

19 Figure.(a): Band pass magnitude response of BP-LP filter circuit usg FTFN Figure.(b): Band pass phase response of BP-LP filter circuit usg FTFN 9

20 Figure.(c): Low pass magnitude response of BP-LP filter circuit usg FTFN Figure.(d): Low pass phase response of BP-LP filter circuit usg FTFN 9

21 . SIMULATION AND ESULT Bread board realizations were done to verif the response of the circuit. The positive FTFN can be implemented b cascadg two AD8 of Analog Devices, to realize high pass and band pass responses with the passive components chosen as kω, kω, C nf and C nf. The band pass and low pass realizations ma be obtaed with passive components chosen as kω, kω, C nf and C nf. Figure. show magnitude and phase responses of the high-pass and band-pass filter, where Figure. shows the magnitude and phase responses of band-pass and low-pass filters respectivel. Both the choices give the same frequenc resonant frequenc ω 9. khz at Q.. The results shown figures agree with the analsis.. CONCLUSION This chapter first considers the concept of FTFN as a combation of nullator and the norator. Subsequentl realizations of all four tpes of amplifier, emplog FTFN are discussed. Next the available circuits emplog FTFN are presented. In the subsequent sections of the chapters two voltage-mode circuits emplog two FTFN are proposed. These circuits have high put impedance and low passive components as compared to existg one reported the literature. The proposed circuit provides two filter realizations simultaneousl. First circuit offers high-pass and band-pass filter realizations, where as bandpass and low-pass are obtaed from the second circuit. The proposed circuits do not impose an component matchg constrats. The proposed circuits have low sensitivit figures. The proposed circuit offers lear phase responses which are not generall available the filers realized with mimum number of active elements. These circuits ma be used the video signal processg where phase has ver significant role to pla. 9