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Minimum Components Universal Filters Chun-Ming Chang and Hua-Pin Chen Dept. of Electrical Engineering, Chung Yuan Christian University, Chung-Li, Taiwan 32023, R. O. China Abstract: Two new universal biquads based on the recently introduced fully differential current conveyor (FDCCII) are presented. The universal biquads employ a single FDCCII, two grounded resistors and two grounded capacitors, which are the minimum components, necessary to simultaneously realize five 2nd-order generic filtering responses (low-pass, high-pass, band-pass, notch, and all-pass) unlike the biquads reported in [1] employing more active and passive components, and [2] without voltage-mode all-pass output signals or employing an extended 12-terminal FDCCII for the current-mode realization. Simulation results validate the theoretical analysis. Key-Words: Analogue circuit design, active filters, current conveyors, voltage-mode circuits, currentmode circuits. 1 Introduction current-mode signals. This paper describes two In 2000, a new active element called the fully new minimum components filter biquads. The differential current conveyor (FDCCII) has been voltage-mode one has all-pass signals in proposed [1] to improve the dynamic range in addition to four other generic filtering (low-pass, mixed-mode fully band-pass, high-pass, and notch) signals, and the differential signal processing is required. The current-mode one employs a 9-terminal FDCCII application of FDCCII in filter design was also smaller in size than the 12-terminal FDCCII demonstrated in [1], where three filter biquads used in [2]. applications where were described. Each biquad employs three FDCCIIs, two grounded capacitors and three 2 Circuit Descriptions resistors, which have been implemented using Two minimum components universal biquads, MOS transistors. From the wealth of knowledge one of which is a voltage mode one, and the on RC active filters, it is known that it is other of which is a current mode one, are possible to design filter biquads using a single proposed as follows. active element, two resistors and two capacitors. Such filters are known as minimum components 2.1 Voltage-Mode Universal Filter count circuits and were realized recently [2]. The proposed voltage-mode universal biquad is However, in [2], the voltage-mode all-pass shown in Fig.1. It is based on one FDCCII, two signal cannot be realized and the 8-terminal grounded resistors, and two grounded capacitors. FDCCII is expanded to be a 12-terminal The matrix input-output relationship of the FDCCII for realizing five generic biquadratic eight-terminal FDCCII [1] is shown as follows. 1 0 1 1 0 1 1 0 0 0 1 0 0 V X 0 V 0 X I Z 1 I Z 0 1 0 0 0 I X 0 I X 1 VY 1 0 VY 2 0 VY 3 VY 4 Vo 5 Vo3 Vo 4 Vin Vin s 2 C C sC 2 G2 G1G2 2 1 2 s C1C 2 sC 2 G2 G1G2 (0) (9) Note that no component matching conditions are Circuit analysis yields the following voltage- required in the design. mode filter transfer functions: Vo1 Vi1 sC1G1 Vi 3 G1G2 V sC G G G 1 1 1 2 i2 s 2 C1C 2 sC 2 G2 G1G2 Vo 2 On the other hand, the specializations of the numerator in Eq. (3) result in the following filter (1) Vi1 sC1G1 s 2 C1C 2 Vi 2 sC1G1 Vi 3 G1G2 sC 2 G2 2 s C1C 2 sC 2 G 2 G1G2 functions: (i) low-pass: Vi1 = Vi3 = 0, and Vi2= Vin; (ii) band-pass: Vi1 = Vi2 = 0, and Vi3 = Vin; (iii) high-pass: Vi2 = Vi3 = 0, and Vi1 = Vin; (iv) notch: Vi3 = 0, and Vi1 = Vi2 = Vin; (2) (v) capacitor C2 be floating, and insert the voltage Vo 3 input signal Vi3 into the floating terminal of the Vi1 s C1C 2 Vi 2 G1G2 Vi 3 sC 2 G2 s 2 C1C 2 sC 2 G2 G1G2 2 Vo 4 If we make the resistor R2 be grounded, the Vi1 sC 2 G2 G1G2 V G G V sC G 1 2 i3 2 2 i2 s 2 C1C 2 sC 2 G2 G1G2 capacitor C2, then (3) Vo 3 Vi1 s 2 C1C 2 Vi 2 G1G2 Vi 3 sC 2 G2 (10) s 2 C1C 2 sC 2 G2 G1G2 The all-pass signal can be obtained from the (4) output terminal Vo3 provided Vi1=Vi2=Vi3=Vin. The resonance angular frequency ωo and the If Vi1=Vi2=Vin, and Vi3=0, then quality factor Q are given by Vo1 G1G2 2 Vin s C1C 2 sC 2 G2 G1G2 (5) o Vo 2 s 2 C1C 2 2 Vin s C1C 2 sC 2 G2 G1G2 (6) Q Vo3 s 2 C1C 2 G1G2 Vin s 2 C1C 2 sC 2 G2 G1G2 Vo 4 sC 2 G2 2 Vin s C1C2 sC 2 G2 G1G2 G1G2 C1C 2 C1G1 C 2 G2 (11) (12) This shows that the biquad o and Q can not be (7) tuned orthogonally. This is not a limitation associated with just the proposed biquad since it (8) is known that active RC filters based on a single 2 active element have non-independent o and Q To realize the above all-pass output signal, one tunability [3]. It is possible for the biquad of more output terminal Z+, which can be easily Fig.1 to provide non-interactive tunability if realized by using a current mirror [4] with four more FDCCIIs are added to the circuit. However, MOS transistors, in an FDCCII is needed for this is in conflict with the motivation of the producing an extra output current Io2. The presented work, which is the design of filter resonance angular frequency ωo and the quality biquads using a single FDCCII. factor Q are shown in Eqs. (11) and (12) by the replacement of G1 with G2 and vise versa. 2.2 Current-Mode Universal Filter On the other hand, the proposed current-mode 3. Simulation Results universal biquad is shown in Fig.2. It is also To validate the theory predict of the proposed based on one FDCCII, two grounded resistors, minimum components universal biquads shown and two grounded capacitors. Routine analysis in Fig. 1 with Vi1=Vi2=Vin, and Vi3=0, and Fig. 2, yields the following current transfer functions: we use level-49 H-Spice with 0.5 μm process to I o1 I i1 sC 2 G2 I i 2 G1G2 2 I in s C1C2 sC 2 G1 G1G2 I o2 I in do the simulation. The CMOS implementation of the fully differential second-generation (13) current conveyor is shown in [1]. The simulation circuits are built with R1=R2=15.9k, C1=C2= I i1 sC 2 G1 G1G2 I i 2 sC1G1 s 2 C1C 2 sC 2 G1 G1G2 10pF (for voltage mode), and R1=R2=3.18k, (14) C1=C2=50pF (for current mode), with the supply voltages: VDD = -Vss = 5V (for voltage mode) and 3.5V (for current mode), Vbp = -Vbn = I o3 I in 1V, and the bias currents: IB = ISB = 1.65mA (for I i1 sC 2 G1 G1G2 I i 2 sC1G1 (15) 2 I i 3 s C1C 2 sC 2 G1 G1G2 2 s C1C 2 sC 2 G1 G1G2 voltage mode) and IB = ISB = 1.2mA (for current The specializations of the numerators in Eqs. be seen, they agree very well with theory. So do (13) to (15) result in the following filter transfer the voltage-mode and current-mode phase (all- functions: pass only)-frequency responses, shown in Figs. mode). The voltage-mode and current-mode amplitude-frequency responses with fo = 1MHz are shown in Figs. 3 and 5, respectively. As can 4 and 6, respectively. (i) low-pass: Ii2=Iin, Ii1=0, and Io1= Iout; (ii) band-pass: Ii2=Iin, Ii1=0, and Io2=Iout; or Ii1=Iin , 4. Discussion and Conclusions Ii2=0, and Io1=Iout; This paper has presented two new filter biquads that employ the minimum number of active elements (i.e. one FDCCII) and passive components (i.e. two resistors, and two capacitors). It is useful to give insight (iii) high-pass: Ii1=Iin, Ii2=0, and Io3=Iout; (iv) notch: Ii2=Iin, Ii1=0, C1=C2, and Io3=Iout; (v) all-pass: Ii2=Iin, Ii1=0, C1=C2, and Io3+ Io2=Iout. 3 into how biquad filters based on a single (Chapter 9, p. 481): Matrix Publishers, Inc., FDCCII compare with other alternatives. 1. For example, if we are to compare the proposed voltage-mode biquad (Fig.1) with an op-amp based filter, a very good example is the Sallen-Key circuit. Both filter 2. configurations employ the same number of active elements (i.e. one) and passive components (i.e. four). However, the SallenKey filter requires additional passive and active circuitry if notch or all-pass is 1978. [4] CHANG, C. M., and PAI, S. K.: “Universal current-mode OTA-C biquad with the minimum components”, IEEE Trans. Circuits Syst. I, Vol. 47, No. 8, 2000, pp. 1235-1238. [5] TU, S. H., CHANG, C. M., and LIAO, K. P.: “Novel versatile insensitive universal currentmode biquad employing two second-generation current conveyors”, Int. J. Electron., Vol. 89, No. 12, 2002, pp. 897-903. required [3], which is not the case with the proposed biquad since it is capable of achieving all filter functions (LP, HP, BP, NH and AP) using the circuit shown in Fig.1. Fig. 1 is also better than the recently reported single-FDCCII-based voltage-mode biquad filter [2] without the all-pass function. Similarly, the proposed currentmode universal biquad (Fig.2) is simpler than the current conveyor-based universal R2 Y1 Y2 Vi1 Y3 Z+ FDCCII Vo1 Z- Y4 X+ Vi3 Vo2 X- C2 Vo4 - V + V o5 o3 C1 filter [5] and the recently reported one [2] employing a 12-terminal FDCCII in addition to two capacitors and two resistors. R1 Vi2 Fig. 1 Proposed voltage-mode universal biquad. References [1] EL-ADAWY, A. A., SOLIMAN, A. M., and ELWAN, H. O.: “A novel fully differential Y4 Y3 Y2 Y1 current conveyor and applications for analog R1 Ii1 VLSI”, IEEE Trans Circuits Syst. II, Vol. 47, No. R2 Ii2 X+ FDCCII X- 4, 2000, pp. 306-313. [2] CHANG, C. M., AL-HASHIMI, B. M., Z+ C1 WANG, C. L., and HUNG, C. W.: “Single fully Ii3 differential current conveyor biquad filters” IEE Z- C2 Io2 Io3 Io1 Proc.-Circuits Devices Syst., Vol. 150, No. 5, 2003, pp.394-398 Fig. 2 Proposed current-mode universal biquad [3] SEDRA, A. S., and BRACKETT, P. O., Filter Theory and Design: Active and Passive 4 Fig. 3 Amplitude-frequency responses of the Fig. 5 Amplitude-frequency responses of the proposed voltage-mode universal biquad proposed current-mode universal biquad Fig. 4 Phase-frequency response of the proposed Fig. 6 Phase-frequency response of the proposed voltage-mode all-pass biquad current-mode all-pass biquad 5