40 B Kh 10Kh 100Kh 1.0Mh 10Mh 100Mh 1.0Gh

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1 Transistor-Only Band-Pass Filters with High Q Factor Andrzej Kie lbasinski Institute of Electronics Technical University of Koszalin ul. Partyzantow 17, Koszalin, Poland tel ext. 245 fax ak@man.koszalin.pl, March 24, 1997 Abstract The concept of two lumped-distributed RC band-pass lters with a high Q factor realized in the transistor-only lters domain is presented. A simple example of VLSI CMOS implementation of such lters is proposed. Both circuits are based on a dierential amplier with a unity gain and a simple lumped-distributed RC notch lter. The schems are obtained using the complementary transformation. The analysis results are presented. 1

2 1 Introduction Over 10 years ago Khoury, Tsividis and Banu [1] used a single enhancement MOS transistor as a tunable distributed RC low-pass lter. They noticed, that a MOS transistor operated in the strong inversion non-saturated region with bias V DS = 0 has similar properties to the uniform distributed RC line. Such a discovery was a return to the theory of distributed RC lines, very well-known for the 60's. A MOS transistor as a distributed RC line has several advantages. The main advantage is the tunability of the time-constant. The distributed capacitance of the thin oxide in a MOSFET is constant, but the channel distributed resistance can be tuned by the voltage V GS. In the classical distributed RC lines there was a lack of control of the time-constant. The theory of distributed and lumped-distributed circuits is more complex then the theory of lumped circuits, so currently, these rst are little forgotten. In [3] professor Y. Tsividis has realized a simple four transistor low-pass lter, consisted of a single MOSFET working as a distributed RC line and a source follower. The source follower is a bias circuitry for the long distributed MOSFET, and can be used as an amplier like in well-known distributed RC active lters [15]. Such selective circuits Tsividis named Transistor-Only Filters. He has proved, that they occupy small chip area, require very low power and can be realized for very high frequencies. There are several schemes of simple transistor-only low-pass and high-pass lters [3, 8, 10, 11, 12, 13, 14]. In [8] is presented also a transistor-only version of the Renze's band-pass distributed RC active lter. In [17] the concept of the transistor-only notch lumped-distributed RC lter was introduced. The notch lter can be used to realize a band-pass active lter with high Q factor. In the next section the idea of the notch 2

3 lumped-distributed RC lter is reminded and two band-pass lumped-distributed RC active lters are introduced. 2 Band-pass lumped-distributed RC active lters A very important element for lumped-distributed RC active lters is a notch lter [17]. It allows a simple realization of lters with conjugate zeros of the transfer function on the imaginary axis as well as band-pass lters with high Q factor. From the theory of distributed lters we know, that the network of Figure 1 realizes a selective band-rejection lter. Figure 1: Lumped-distributed notch rejection lter A voltage-transfer function of the notch network shown in Figure 1 has the following form: v out (s) v in (s) = R R 1 + p src sinh( p src) R R 1 cosh( p src) + p src sinh( p src) (1) The dominant complex conjugate zeros of the transfer function lie on the imaginary axis for the value = R=R 1 17:78, while the imaginary part of the zeros can be expressed as 2f 0 11:19=RC, where f 0 is a frequency of the maximum attenuation. The most important application of the notch network was in conjunction with an operational amplier to provide an amplier with a narrow band. The notch rejection lter characteristic is inverted in the feedback of the operational amplier. In Figure 2(a) 3

4 a band-pass lumped-distributed RC active lter with operational amplier is shown. If the gain of the operational amplier A is suciently high, then the transfer function of the band-pass lter has the following form: R v out (s) v in (s) = R 1 cosh( p src) + p src sinh( p src) R R 1 + p src sinh( p src) (2) and is simply the inversion of the notch network transfer function. Figure 2: Lumped-distributed band-pass RC active lters 1: (a) with an operational amplier A! 1 (b) with a unity gain amplier a! 1 The operational amplier has a limited gain and is a little complex, so the band-pass lter shown in Figure 2(a) is not ecient for very high frequencies. Basing on the complementary transformation [18, 19] the band-pass lter of Figure 2(a) can be transformed into the circuit as shown in Figure 2(b). Transmittances of these two lters are the same, if the gain of the amplier in Figure 2(b) is equal to a = A=(A + 1). It means that if A! 1 then a! 1. The band-pass lter 1 shown in Figure 2(b) is the rst band-pass lter proposed in this paper. In Figure 3, frequency responses of band-pass lter 1 for the gain a = 0.999, 0.99, 0.95, 0.90 are shown. We can see that Q factor can be tuned by the gain a. This is one way of Q factor tuning. Q factor can be tuned also by the coecient = R=R1. In the classical theory of lumped-distributed RC active lters, another band-pass lter 4

5 with a high-gain operational amplier is known. The scheme of this lter is shown in Figure 4(a). The same way, using the complementary transformation [18] we can transform 60 A 40 B C 20 D Kh 10Kh 100Kh 1.0Mh 10Mh 100Mh 1.0Gh Figure 3: Theoretical frequency responses of the band-pass lter 1 for A) a = 0:999, B) a = 0:99, C) a = 0:95, D) a = 0:90 Figure 4: Lumped-distributed band-pass RC active lters 2: (a) with an operational amplier A! 1 (b) with a unity gain amplier a! 1 the band-pass lter of Figure 4(a) into the band-pass lter 2 shown in Figure 4(b). The transfer function of these band-pass lters has a form: v out (s) v in (s) = R R 1 (cosh( p src)? 1) R R 1 + p src sinh( p src) (3) 5

6 The denominator of these transmittance is the same as in the transfer function of the band-pass lter 1. Notice also, that the schemes in Figures 2 and 4 are very similar. 60 A 40 B 20 C -0 D Kh 10Kh 100Kh 1.0Mh 10Mh 100Mh 1.0Gh Figure 5: Theoretical frequency responses of the band-pass lter 2 for A) a = 0:999, B) a = 0:99, C) a = 0:95, D) a = 0:90 In Figure 5 frequency responses of band-pass lter 2 for the gain a = 0.999, 0.99, 0.95, 0.90 are shown. We can see that frequency responses of the band-pass lter 2 are more selective then frequency responses of the band-pass lter 1. In the next section a CMOS implementation of both band-pass lters are presented. 3 CMOS implementation of band-pass lters with a unity gain amplier A simple CMOS dierential pair can be used as a unity gain amplier in band-pass lters of Figure 2(b) and 4(b). The rst proposal of CMOS implementation of both band-pass lters is shown in Figure 6 (a) and (b). Both lters consist of a dierential pair M 1 -M 2 6

7 with a current source M 5 -M 6. Transistors M 3 and M 4 connected as diodes form an active load. Figure 6: Transistor-only version of lumped-distributed RC active lters: (a) band-pass 1, (b) band-pass 2 Transistor M 7 is working as a uniform distributed RC line. Its gate is connected to the output of the dierential pair, which is also a bias circuitry for M 7. The time constant RC of M 7 can be tuned by voltage V dd. The output resistance of the dierential pair at node 1 used as the lumped resistance R 1 can be tuned by current I r. The gain jv out =v in j of the dierential pair shown in Fugure 6 is independent of the current I r, but it cannot be tuned. It should be near 1 to obtain high Q factor. The output resistance of the dierential pair at node 1 is equal to: R 1 1 g m3 = 1 K P p (W=L) 3 (V SG3? jv T p j) (4) 7

8 where K P p is a transconductance parameter of the pmosfet and V T p is a treashold voltage of the pmosfet. Voltage V SG3 is determined by the current I r and can be expressed by a formula: V SG3 = s I r K P p (W=L) 3 + jv T p j (5) The current I r can be used for independent tuning of R 1. The channel resistance of the M 7 is equal to: R = 1 K P n (W=L) 7 (V GS7? V T n ) (6) where K P n is a transconductance parameter of the nmosfet and V T n is a treashold voltage of the nmosfet. The voltage V GS7 = V dd? V SG3 can change the time constant RC, but it depends on both I r and V dd. As we can see the independent tuning of the time constant RC and the coecient R=R 1 is impossible in these circuits. However, setting of the central frequency and the Q factor is possible. Both lters have been designed in cmn16 standard CMOS 1.6 m technology from VLSI Technology Inc., using the COMPASS Design Automation tools. The channel width to length ratios of transistors M 1 -M 6 are the same and are equal to (W=L) 1?6 = 4=4, where = 0:8 m is a technology unit. The channel width to length ratio of transistor M 7 is (W=L) 7 = 200=20. Frequency responses of both lters are shown in Figure 7 and in Figure 8. In all simulations of the band-pass lters, in the SPICE netlist, transistor M 5 has been changed by a chain of twenty short MOS channels, like in [16]. The SPICE model without overlap capacitances has been used for these short channels. 8

9 60 B A C Kh 100Kh 1.0Mh 10Mh 100Mh Figure 7: Frequency responses of the band-pass lter 1 for constant I r = 60 A, for dierent V dd : A) V dd = 3:55 V, B) V dd = 3:625 V, C) V dd = 3:70 V 60 B A C Kh 100Kh 1.0Mh 10Mh 100Mh Figure 8: Frequency responses of the band-pass lter 2 for constant I r = 60 A, for dierent V dd : A) V dd = 3:55 V, B) V dd = 3:625 V, C) V dd = 3:70 V 9

10 4 Conclusion Two band-pass lters with high Q factor consisted of a unity gain dierential amplier and a simple notch lter have been introduced. The simple CMOS transistor-only implementation of these lters has been proposed. The simulation results proved theoretical concept. For practical realization better unity gain dierential amplier must be investigated. It have to be accurate for independent tuning of the gain, the time constant RC, and the coecient = R=R1. References [1] J. Khoury, Y. P. Tsividis, and M. Banu, \Use of MOS transistor as a tunable distributed RC lter-element", Electronics Letters, vol. 20, pp , Nov [2] M. Bagheri, and Y. P. Tsividis, \A Small-signal dc-to-high-frequency non-quasistatic model for the four-terminal MOSFET valid in all regions of operation", IEEE Transactions on Electron Devices, vol. ED-32, pp , Nov [3] Y. P. Tsividis, \Minimal transistor-only micropower integrated VHF active lter", Electronics Letters, vol. 23, pp , Jul [4] Y. P. Tsividis, \The transistor in a box puzzle", IEEE Circuits and Devices Magazine, vol. 4, p. 62, Jan. 1988, and pp , May [5] J. Khoury and Y. P. Tsividis, \Synthesis of arbitrary rational transfer functions in s using uniform distributed RC active circuits", IEEE Transactions on Circuits and Systems, vol. 37, no. 4, pp , April

11 [6] L. J. Pu and Y. P. Tsividis, \Small-signal parameters and thermal noise of the fourterminal MOSFET at very high frequencies", Solid-State Electronics, vol. 33, pp , May [7] L. J. Pu and Y. P. Tsividis, \Harmonic distortion of the four-terminal MOSFET in non-quasistatic operation", Proc. Inst. Elec. Eng., pt. G, vol. 137, pp , May [8] Lih-Jiuan Pu, Y. P. Tsividis, \Transistor-only frequency-selective circuits", IEEE Journal of Solid-State Circuits, vol. 25, no. 3, pp , Jun [9] R. P. Jindal, \Giga hertz band high gain low noise AGC ampliers in ne line NMOS", IEEE J. Solid-State Circuits, vol. SC-22, pp , [10] R. P. Jindal, \Low-Pass Distributed RC Filter Using an MOS Transistor with Near Zero Phase Shift at High Frequencies", IEEE Transactions on Circuits and Systems, vol. 36, pp , Aug [11] W. Li and E. I. El-Masry, \Distributed MOSFET high-pass lters", IEEE Transactions on Circuits and Systems, vol. 39, no. 3, pp , Mar [12] W. Li, \A transistor-only high-pass lter with adjustable Q factor", IEEE Transactions on Circuits and Systems, vol. 40, no. 2, pp , Feb [13] W. Li, \A transistor-only low-pass lter with adjustable bias and small phase shift at high frequencies", IEEE Journal of Solid-State Circuits, vol. 28, no.5, pp , May

12 [14] W. Li, \Transistor-only low-pass and high-pass lters", Ph. D. dissertation, Technical University of Nova Scotia, NS, Canada, Sep [15] M. Ghausi and J. Kelly, \Introduction to Distributed-Parameter Networks", New York: Holt, Reinhart, and Winston, [16] Y. P. Tsividis, \Operation and Modeling of the MOS Transistor", New York: Mc- Graw Hill, [17] A. Guzinski, A. Kie lbasinski, \Novel Notch Filter in Transistor-Only Filters Domain", Proceedings of the Third IEEE International Conference on Electronics, Circuits, and Systems, October 13-16, 1996, Rodos, Greece, Vol. 1, pp [18] N. Fliege, \Complementary Transformation of Feedback Systems", Proceedings of IEEE ISCAS, Los Angeles, USA, April 18-21, 1972, pp [19] A. Guzinski, M. Guzinski, Z. J. Staszak, \Eective Transformation of Voltage-Mode circuits into Current-Mode Ones", Proceedings of XVI-th National Conference Circuit Theory and Electronic Circuits, Ko lobrzeg, Poland, October 26-28,