This paper presents a new technique for programming SC circuits using a single time-multiplexed capacitor bank, achieving a significant reduction in capacitance area. Simulation results of a programmable biquad low pass filter show the validity of the proposed method

García Franquelo, Leopoldo

Pérez Vega-Leal, Alfredo

Torralba Silgado, Antonio Jesús

idUS. Depósito de Investigación Universidad de Sevilla

Programmable SC Biquad Using One Single Capacitor Bank A. Torr.lb •. A. P. Vegaleal. L. O. Franquelo DpID. Ingenieria Eleclronica. Univ. Sevilla Abstract This paper presents a new technique for programming SC circuits using a single time-multiplexed capaci tor bank . achieving a significanr reduction in capaci tance area. Simulation results of a programmable biquad low pass Ii Iter show the valid ity of the propcsed method. D a significanl reduction in the overall capacitance area. Time-multiplexing is another techn ique that has been used to save area and to reduce power consumption in high order SC filters [4]-16]. Differen t multiplexing strategies have been • 8P -----~~J-1Krt -L ---L HP i I tPu/ ----------------~I ~ Figure 1. Universal biquad SC filter. I. Introduction SC filtering is a consolidated technique widely used in CMOS and BiCMOS analog and mixed-signal circuits. Many applications require filtering with programmable frequency responses. Most of previous implementations of programmable SC Iilters used digitally-controlled binary weighted capacitor arrays [J]-[21. leading to large area of silicon and hence, high cost of manufacturing. In [3]. twO capacitor quasi-passive algorithmic DAC1s were used for programming each capacitance value. leading to ,. used. In [4). several integrator capacitors were multiplexed onto a single op-amp. In [SJ. Ihe amplifiers were time-shared to realize two poles of filtering per amplifier in a ladder structure. in [6]. an amplifier time-sharing technique was propcsed to realize an arbitrary number of biquadratic cells with on ly twO amplifiers. In f7]. periodical nonuniform individual samplig of each SC structure in a filter was used to program SC circuits. All previous approaches used one bank of capacitors per amplifier input. In this paper, a new technique for programming SC circuits is proposed that uses one single time-multiplexed bank of capacitors for all the op-amp inputs. Using the by-inspection analysis method for multi phase SC networks proposed in [8J. the following transfer function is obtained ~~I ----~====~------~====~ ~F $tF ~A $tA ~E $'E ~G --, n n n n a) n n n n n , n : n n n n n n n $'G ~C $,C rI n b) Figure 2. Time diagram for the circuit in figure 1. a) Conventional and b) proposed clock signals II. Programmable SC biquad with one single capacitor bank The proposed technique will be illustrated using the universal second order filter shown in figure I as an example. This circuit can provide BP, LP, and HP transfer functions. by enabling the corresponding signal paths by proper switchi ng. Let's first consider the LP transfer function. Under conventional sampling operation. there are only two non-overlapping c lock phases fl}, and @, (figure 2a). In this case. clock signal s @,. i. {i :A.C £.F,Gj coincide with @landclocksignals @2./. (i :: A.C.£,F.Gj coincide with @1. The transfer function of the SC filter is given by: D(~~E) ' , -' H (Z)= - I_[I+B+F AC . z_,+B+F . ,,-2 B+E D(B+E) B+E (I ) Let's now divide the overall repetition period Ts into 10 equal-spaced intervals of duration T, / 10. and define @/-io (i :: A. .C. E,F,Gj and {!h.i. f i = It,e.E,F.G} with the liming shown in figure 2b. S9 H(, ) = AG _=_.,-5 D(B + E) I_[I+B+F AC ] .,_, +B+F,_" B+E D(B+E) - B+E (2) which. disregarding the ( .' unit delay. is idenlical to ( I) . Note that, under the timing proposed in figure 2b. capacitors A. C.E,F and G can be time-multiplexed using one single bank of capacitors, leadi ng to the circuit in figure 3. m. Simulation Results To demonstrate the validity of the proposed technique. SWlTCAP simu lations of the circuit in figure 3 have been done. Capacitor values were determined for a nominal cUloff frequency 10 = 10 KH<. quality factor Q = 0.707. and unity dc gain. The master clock cycle was chosen to be/, = I MHz, leading to the following nominal capaci tor va lues: A = 1.2 pF. B = 11.9 pF. C; F = G = 0.4 pF. D = 12 pF. and E = 1.6 pF. Capacitors {A.C.E.F.G} were implementod using one single bank of 8 binary weighted capacitors with 0.1 pF of minimum value. Many different transfer functions can be implemented in this way. Figure 4a shows the filter response when capacitors {A,C.E,F,G} are scaled for the same k factor, k= (1/4, 112. I. 2, 4, 8}. Figure 4b shows the filter response when the capacitor F changes from 0.1 to 1.4 pF and capacitors {A. C, E,G} have nominal values. As expected, cutoff frequency and quality factor follow the approx imate expressions 1 c-;:c 10 z 2~ rii(B~ and Q z_l_/ACCB+El E -F V D (3) D + Although the transfer functions in (I) and (2) are identical (except for the ,.5 unit delay), op-amp outputs are identical only during 1/5" of the whole period T,. Thi s effect can not be ignored when the ratio fol (5 J,) approaches 112. For instance. assumi ng [-1.11 to be the amplifier output signal swing in the LP SC filter of figure 3, the maximum input signal ampli tude is 882 mV for the nominal filter (k=/), and 48 1 mV for the least favorable case (k =8) , as confirmed by SWITCAP simulations. Similar results cou ld be obtained usi ng the BP and HP transfer functions of the circuit in figure I. For the HP function , capacitor I cannot be programmed with the time-multiplex ing technique proposed here. so a second capac itor bank would be required for programming capacitor I. 0 --+..-----I + Program. <1>u Capacitor Bank - 8 <P--v <Px <Pv - 0 ~~ I/Ju = I/J IG + I/JIC I/Jv = I/JIF + I/JI A + I/J I£ I/JIV = I/JIF + I/JIA + 1/J2£ + I/J 'G + I/J ,c I/Jx = I/J'F + I/J'A + 1/J 2£ + I/J'G + I/J,c Figure 3. Programmable Low Pass SC biquad using one single capacitor bank. The proposed technique can be also used with other time-multiplexing techniques to implement higher order filters. Furthenmore, a single quasi-passive algorithmic DAC [3] could have been used instead of the programmable capaci tor bank of figure 3, with similar results. It has to be mentioned that, in somes cases, swi tching capacitors with the timing of figure 2b may reduce the input dynamic range. 60 IV. Conclusions To the authors' knowledge, no other method has been reported allowing a biquad section to be programmed using one single capacitor bank. The proposed technique achieves a very compact and area efficient implementation of SC filters. Compared to a conventional programmable biquad using multiple capacitor banks, the filter in figure 3 has a 40% area occupancy. for a standard 0.35 Ilm CMOS technology. Concerning power consumption. the op-amps are required to swi tch faster. but '0 0 -------'0 .", ... " 0 .so ·EO -10 ..., -to 000 ""'00 a) with a lower capacitance load. Therefore. no a significant increase in power consumption is expected . ,......, ,. r-----------------------------r-------------~~------_, "U' ..... --,0 5 ·5 -, 0 -211 -.---"t.P c...dolf~ -~-",p-K.dU· .. _.-l..plA.QIf" --~-8:::: := v : s.dIL" ----~~----------------------~----------------~ '0000 b) Figure 4. a) Frequency and b) Quality factor programmability 61 References [I] ALLSTOT, D.1., BRODERSEN. R.W., and GRA Y, P.R.: "An Electrically-Programmable Switched Capacitor Filter". 1£££ J. Solid-Slale Circllils. 1979. 14 (6), pp. 1034-1041. [2] COX, D.B.: "A Digitally Programmable Switched-Capacitor Universal Active Filler/Oscillator". 1£££ J.Solid-SlOle CirCllils, 1983.18 (4), pp. 383-389. [3J PAULINO, N., FRANCA. I .E.. and MARTINS, F.P.: "Programmable CMOS Switched-Capacitor Biquad using Quasi-Passive Algorithmic DAC' s". 1£££ J.Solid·Slale Circllils, 1995,30 (6). pp. 7 15-719. [4] BOSSHART, P.W.: "A Multiplexed Switched-Capacitor Filter Bank". IEEE J.Solid-SlOle CirCllils, 1980, 15 (6). pp. 939-945 . [5J ALLSTOT, D.1.. and TAN, K.S.: "Simplified MOS Switched-Capacitor Ladder Filter Structures". IEEE J.Solid,Slate Circuils, 198!, 16 (6). pp. 724-729. [6] CASTELLO. R., GRASSI. A.1 ., and DONATI , S. : "A 500-nA Sixth Order Bandpass SC Filler". IEE£ J.Solid-Slate Circllils, 1990, 25 (3), pp. 669-676. [7] I . L. AUSIN , I . F. DUQUE - CARRILLO. G. TORELLI, E. SANCHEZ-SINENCIO, F.MALOBERTI:"Periodical nonuni form individual sampled switched-capacitor circuits", IEEE Proc. of Int. Symp .. on CAS. ISCAS 2000. vol. V. pp. 449-452. Geneva, Switzerland, May 2000. [8J DABROWSKI. A., and MOSCHYTZ, G.S.: "Direct Analys is of Multiphase Switched-Capacitor Networks Usi ng Signal-Flow Graphs". I£E£ TrailS. CircuilS SYSI .. 1990,37 (5), pp. 594-6. 62 

Programmable SC biquad using one single capacitor bank

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Programmable SC biquad using one single capacitor bank

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