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High-Input and Low-Output Impedance Voltage-Mode Universal Biquadratic Filter Using FDCCIIs Hua-Pin Chen1*, and Yi-Zhen Liao2 1 Department of Electronic Engineering, De Lin Institute of Technology, Taipei, Taiwan, R.O.C. Graduate Institute of Computer and Communication Engineering, National Taipei University of Technology, Taipei, Taiwan, R.O.C. *Email: [email protected] 2 Abstract—A novel high-input and low-output impedance voltage-mode universal filter with three inputs and single output employing two fully differential current conveyors, two resistors, and two capacitors is proposed. The proposed configuration can realize all the five standard biquadratic filter functions. It maintains the following advantages: (i) employment of only two current conveyors, (ii) employment of only grounded capacitors, (iii) employment of only grounded resistors, (iv) high-input and low-output impedance, (v) no need to employ inverting type input signals, (vi) no need to impose component choice conditions to realize specific filtering functions, and (vii) low active and passive sensitivity performances. Index Terms—active filters, current conveyors, analog electronics I. Introduction Current-mode active elements offer the main advantages like greater linearity, low power consumption and wider bandwidth over their voltage-mode counterparts [1-3]. Also, the design of filter circuits employing current-mode active elements may be used in phase-locked loop frequency modulation (FM) stereo demodulators, touch-tone telephone tone decoder and cross over networks used in a three-way high fidelity loudspeaker [4]. As a current-mode active device, the fully differential second-generation current conveyor [5] was proposed to improve the dynamic range processing is required. This element is a versatile building block whose applications appear in the literature 978-1-4244-2186-2/08/$25.00 ©2008 IEEE [6-10]. Active filters with high-input impedance are of great interest because it can be easily cascaded to synthesize high-order filters [11-14]. Besides, the difficulty of realizing the operations of addition and subtraction of a voltage-mode signal renders two special active elements, namely, differential difference current conveyor (DDCC) and fully differential current conveyor (FDCCII), both of which have the ability to perform the operations of addition and subtraction, to become very important for the design of voltage-mode analog filter design [15]. Recently, a new high-input and low-output impedance voltage-mode universal biquadratic filter using three DDCCs has been proposed by Chiu and Horng [16]. This proposed circuit offers the following features: realization of all the standard filter functions in the same configuration, no requirements for component matching conditions, the use of only grounded capacitors and resistors, high-input and low-output impedance, and low active and passive sensitivities. In this paper, a new configuration for realizing universal voltage-mode FDCCIIs filter is proposed. The proposed circuit employs one fewer active to realize the same voltage-mode universal biquadratic filter. It still maintains the following advantages: (i) the employment all grounded capacitors and resistors, (ii) high-input and low-output impedance, (iii) no need to employ inverting-type input signals, (iv) no need to impose component choice, and (v) low active and passive sensitivity performances. Fig. 1. Block diagram of the FDCCII. from the point of view of integrated circuit fabrications. Because the Y input terminal of the FDCCII enjoy very high input impedance, the proposed biquad filter can straight cascade with another block circuit at its input ports [15, 16]. Derived by each nodal equation of the proposed circuit, the input-output relationship matrix form of Fig. 2 can be expressed as G1Vi 2 ⎤ ⎡ sC1 G1 − G1 ⎤ ⎡V1 ⎤ ⎡ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢− G sC V 0 G V G V (2) = − + 2 2 i3 ⎥ , ⎥ ⎢ 2 ⎥ ⎢ 2 i1 ⎢ 2 ⎥⎦ ⎢⎣ 1 0 1 ⎥⎦ ⎢⎣Vo ⎥⎦ ⎢⎣ Vi1 where G1 = 1 1 and G2 = . R1 R2 From the above matrix form, the output voltage Vo can be derived as Vo = Fig. 2. Proposed high-input and low-output impedance universal voltage-mode filter. II. Circuit Description The block diagram of the FDCCII is shown in Fig. 1 and its terminal relations are given by ⎡I X + ⎤ ⎢ ⎥ ⎡V X + ⎤ ⎡0 0 1 − 1 1 0⎤ ⎢ I X − ⎥ ⎢V ⎥ ⎢ ⎥⎢ ⎥ ⎢ X − ⎥ = ⎢0 0 − 1 1 0 1⎥ ⎢ VY 1 ⎥ . (1) ⎢ I Z + ⎥ ⎢1 0 0 0 0 0⎥ ⎢VY 2 ⎥ ⎢ ⎥ ⎢ ⎥ 0 0 0⎦ ⎢VY 3 ⎥ ⎣ I Z − ⎦ ⎣0 1 0 ⎢ ⎥ ⎣⎢VY 4 ⎦⎥ It is shown that the ideal of FDCCII all the four Y terminals exhibit an infinite input resistance. The two ports X exhibit zero output resistance and the two ports Z exhibit an infinite input resistance. The proposed biquad filter, based on two FDCCIIs, is shown in Fig. 2. Only two current conveyors, two grounded capacitors, and two grounded resistors are employed in Fig. 2. The employment of grounded resistors and grounded capacitors are beneficial s 2C1C2Vi1 − sC2G1Vi 2 + G1G2Vi 3 . s 2C1C2 + sC2G1 + G1G2 (3) Depending on the voltage status of Vi1, Vi2, and Vi3 in the numerator of Eq. (3), one of the following five filter functions is realized: (i) low-pass: Vi1=Vi2=0, and Vi3=Vin; (ii) band-pass: Vi1=Vi3= 0, and Vi2=Vin; (iii) high-pass: Vi2=Vi3=0, and Vi1=Vin; (iv) notch: Vi2=0, and Vi1=Vi3=Vin; (v) all-pass: Vi1=Vi2=Vi3=Vin. Note that there are not any component matching conditions and inverting-type input signals needed in realizing filtering functions. The resonance angular frequency ωo and the quality factor Q are given by ωo = Q= G1G 2 . C1 C 2 (4) C1G2 . C2G1 (5) III. Effect of Non-Idealities Taking into account the non-idealities of a FDCCII, namely, VX + = α aVY 1 − α bVY 2 + α cVY 3 , VX − = −α dVY 1 + α eVY 2 + α f VY 4 , IZ + = βa I X + and I Z − = β b I X − , where β i = 1 − ε i and ε i ( ε i << 1 ) denotes the current tracking error and αV = 1 − ε V and ε v ( ε v << 1 ) denotes the differential voltage tracking error [10]. Reanalysis of the proposed circuit in Fig 2 that the denominator of the transfer functions becomes D( s ) = s 2 C1C2 + α a1α d 2 β a1 sC 2 G1 + α a 2α b1 β a1 β a 2 G1G2 . (6) The resonance angular frequency ωo and the quality factor Q are given by ωo = Q= α a 2α b1β a1β a 2G1G2 C1C2 1 α a1α d 2 . α a 2α b1β a 2C1G2 . β a1C2 G1 (7) (8) Using the classical definition of sensitivity co-efficient x ∂F S xF = . (9) F ∂x where F represents one of ωo, Q and x represents any of the passive elements (G1–G2, C1–C2) or the active parameters ( α i , β i ). Using the above definition the active and passive sensitivities of the proposed circuit shown in Fig. 2 are given as ωo ωo ωo ωo ωo o Sαωao2 = Sαωbo1 = S ω β a1 = S β a 2 = S G1 = S G2 = − S C1 = − S C2 = 1 ; SαQa 2 = SαQb1 = S βQa 2 = S CQ1 = S GQ2 = − S βQa1 = − S CQ2 = 2 1 ; SαQa1 = SαQd 2 = −1 . − S GQ1 = 2 (10) all of which are low and not larger than unity in absolute value. be seen, there is a close agreement between theory and simulation. The noise behavior of the filter was simulated using the INOISE and ONOISE statements of frequency responses of the bandpass response with Vi2=Vin, and Vi1=Vi3=0. Fig. 6 shows the simulated amplitude-frequency responses for the BP filter with INOISE and ONOISE designed R1=R2=15.9kΩ, and C1=C2=10pF. The total equivalent input and output noise voltages are 24mV and 0.22mV, respectively. Finally, to test the input dynamic range of the filter, the simulation has been repeated for a sinusoidal input signal at fo=1MHZ. Fig. 7 shows that the input dynamic range of the BP response with Vi2=Vin, Vi1=Vi3=0, R1=R2=15.9kΩ, and C1=C2=10pF, which extends up to amplitude of 0.8V (peak to peak) without signification distortion. V DD M14 IB M15 Z+ M16 M18 M19 M27 Vbp Vbp X+ M20 M17 M9 M22 M3 M4 Y3 Y1 M1 M2 Y2 Y4 M29 M33 M30 M34 X- M5 M6 Z- Vbn M10 M25 M24 M11 M12 M21 Vbn M31 M35 M32 M26 M23 M36 M28 I SB VSS Fig. 3. CMOS realization of the FDCCII. 10 high-pass IV. Simulation Results 0 magnitude(dB) To verify the theoretical prediction of the proposed biquad filter, a simulation using H-Spice simulation with TSMC 0.35μm process was performed and the CMOS implementation of an FDCCII is shown in Fig. 3 [8] with the NMOS and PMOS transistor aspect ratios (W/L=5μ/1μ) and (W/L=10μ/1μ), respectively. The supply voltages are VDD=-VSS=1.65V, the biasing voltages are Vbp=-Vbn=0V, and the biasing currents are IB=ISB=100μA. The component values of Fig. 2 were given by R1=10kΩ, R2=2kΩ, C1=79.5pF and C2=15.9pF, leading to a center frequency of fo=1MHZ and quality factor of Q=5. Fig. 4 shows the simulated and theoretical response of low-pass, band-pass and high-pass of Fig. 2. Fig. 5 shows the simulated and theoretical response of notch and all-pass of Fig. 2. As can M8 M7 M13 -10 -20 low-pass band-pass -30 fo=1MHz Q=5 -:theoretical -40 -50 5 10 o:simulation *:simulation x:simulation 6 10 frequency(Hz) 7 10 Fig. 4. Simulated frequency responses of low-pass, band-pass and high-pass of Fig.1 at fo=1MHz and Q=5. Table 1.Performance parameters of recently reported voltage-mode filter. 10 Criteria Circuits 0 magnitude(dB) all-pass The new circuit -10 -20 -30 fo=1MHz Q=5 -:theoretical o:simulation -40 *:simulation -50 5 10 Ref. [8] in 2005 notch 6 10 frequency(Hz) 7 Ref. [16] in 2007 Ref. [14] in 2004 10 Fig. 5. Simulated frequency responses of notch and all-pass of Fig.1 at fo=1MHz and Q=5. Ref. [13] in 2003 Ref. [12] in 2001 (i) one DDCC one FDCCI I one FDCCI I three DDCCs three CCIIs Two OTAs one CCII three CCIIs (ii) (iii) (iv) (v) (vi) (vii) yes yes yes yes yes yes no no no no yes no yes yes yes yes yes yes no no no no no no no no no no yes no no no no no yes no V. Conclusions Fig. 6. The equivalent input and output noises against frequency. In 2007, Chiu and Horng proposed a good high-input and low-output impedance voltage-mode universal biquadratic filter using three DDCCs, two grounded capacitors and resistors. In this paper, although the use of FDCCII can be divided into two separate DDCC’s, the proposed circuit still maintains the following advantages: (i) employment of two current conveyors, (ii) employment of only grounded capacitors, (iii) employment of only grounded resistors, (iv) high-input and low-output impedance, (v) no need to employ inverting type input signals, (vi) no need to impose component choice conditions to realize specific filtering functions, and (vii) low active and passive sensitivity performances. The main features of the proposed circuit are compared with those of previous works in Table 1. Acknowledgment The authors would like to thank the National Science Council and Chip Implementation Center of Taiwan, ROC. The National Science Council, Republic of China supported this work under grant number NSC 96-2221-E-237-009. References [1] Fig. 7. The input and output waveforms of the BP response for a 1 MHz sinusoidal input voltage of 0.8V (peak to peak). [2] B. Wilson, ‘‘Recent developments in current conveyor and current-mode circuits,’’ Proceedings of IEE, vol. 137, pp.63–77, 1990. G. W. Roberts and A. S. Sedra, ‘‘All current-mode frequency selective circuits,’’ Electron. Lett., vol. 25, pp. 759–761, 1989. [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] C. M. Chang, ‘‘Current mode allpass/notch and bandpass filter using single CCII,’’ Electron. Lett., vol. 27, pp. 1812–1813, 1991. M. A. Ibrahim, S. Minsri, and H. Kuntman, ‘‘A 22.5MHz current-mode KHN-biquad using differential voltage current conveyor and grounded passive elements,’’ Int. J. Electron. Commun. (AEÜ), vol. 59, pp. 311–318, 2005. A. A. El-Adwy, A. M. Soliman, and H. O. 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Wen, ‘‘Quadrature oscillators with grounded capacitors and resistors using FDCCIIs,’’ ETRI Journal, vol. 28, pp. 486-494, 2006,. J. W. Horng, J. R. Lay, C. W. Chang and M. H. Lee, ‘‘High input impedance voltage-mode multifunction filters using plus-type CCIIs,’’ Electron Letts, vol. 33, pp. 472-473, 1997. J. W. Horng, ‘‘High-input impedance voltage-mode universal biquadratic filter using three plus-type CCIIs,’’ IEEE Trans Circ Syst—II: Analog Digital Signal Process, vol. 48, pp. 996-997, 2001. J. W. Horng, ‘‘High-input impedance voltage-mode universal biquadratic filter using two OTAs and one CCII,’’ Int J Electron, vol. 90, pp. 185-191, 2003. J. W. Horng, ‘‘High input impedance voltage-mode universal biquadratic filters with three inputs using three plus-type CCIIs,’’ Int J Electron, vol. 91, no. 8, pp. 465-475, 2004. C. M. Chang, A. M. Soliman, and M. N. S. 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