Generation of Voltage-Mode OTRA-R/MOS-C LP, BP, HP, and BR Biquad Filter

Transcription

1 Recent Researches in Instrumentation, Measurement, ircuits and Systems eneration of Voltage-Mode OTRA-R/MOS- LP, BP, HP, and BR Biquad Filter hun-ming hang, Young-Ja Ko, Zhe-Yu uo, hun-li Hou*, and Jiun-Wei Horng* epartment of Electrical/*Electronic Engineering hung Yuan hristian University hung-li, Taiwan R. O. hina Abstract: The operational transresistance amplifier (OTRA) is attractive to be used in circuit design, with the dual input-and-output characteristics of the well-known operational transconductance amplifier (OTA). A low-pass, band-pass, high-pass, and band-reject biquad filter using two OTRAs, three capacitors, and several resistors is presented through a new analytical synthesis method. Since the realized filter structure has no capacitors in feedback loops, rather precise output signals can be obtained. H-Spice simulations validate filter feasibility and null group sensitivities. Key Words: Active filters, analog circuit design, continuous-time filters, low-pass filters, band-pass filters, high-pass filters, band-reject filters, operational transresistance amplifiers. Introduction (i) OTRA-based circuit structures may be the dual An operational transconductance amplifier (OTA) [], simultaneously representing both an active element and an electronically tunable conductor and leading to no resistors necessarily used in a circuit, is one of the most prospective active elements in the field of analogue circuit design. Its input-and-output characteristics includes (i) the two and terminal input currents, I =I - =, (ii) the output current, I o =(V -V - )g m in which g m is the transconductance of an OTA, and V and V - are the two and terminal input voltages, (iii) very high input impedance, and (iv) very high output impedance. On the other hand, another active element called operational transresistance amplifier (OTRA) [-6] has the following input-and-output relationships: (i) the two and terminal input voltages, V =V - =, (ii) the output voltage, V o =(I -I - )R m in which R m is the transresistance of an OTRA, and I and I - are the two and terminal input currents, (iii) very low input impedance, and (iv) very low output impedance. Based upon the above two sets of input-and-output characteristics, it is apparent that an OTRA is the dual of an OTA and vice versa. In addition to this, the main advantage of eliminating the parasitics at the input port of an OTRA due to virtually grounded input terminals is an extra benefit and very attractive for designers. ote that the OTAs cannot enjoy this benefit. Therefore, we may make the predictions as follows. of OTA-based circuit structures. (ii) OTRA-based circuits may have better performance through some particular design methods than OTA-based circuits. Hence, several distinct OTRAs have been proposed in the literature since 99 [-6]. So do many different kinds of analog circuits, such as integrators [7], immittance simulators [8], oscillators [9-], square or triangular waveform generators [-4], monostable [5-6] and bistable [7] multivibrators, first- [, 8-] and second-order [] all-pass filters, and other secondorder single- [, ] and multi-function [4, 4] and high-order [5] filters. A low-pass Tow-Thomas biquad filter was presented [] using two pseudo-differential OTRAs, four capacitors, and several resistors. Four single-function biquad filters were also proposed [] using a single OTRA, two or three (one more) capacitors, in addition to some resistors. A universal biquad filter [4] employing four (two more) capacitors was presented. An OTRA-based universal biquad filter using two OTRAs, three capacitors, and several resistors, was also published [4]. Since the two of the three capacitors were synthesized and put in feedback loops, the non-ideal analysis exhibits that the ideal s has been replaced by practical s m where m =/R m, and R m is the transresistance function of an OTRA. This arrangement produced additional poles in the transfer function. ote ISB:

2 Recent Researches in Instrumentation, Measurement, ircuits and Systems that this main disadvantage has been improved in this paper.. Analytical Synthesis ive a generic voltage-mode second-order high-pass (V in =V in and V in =), low-pass (V in = and V in =V in ), and band-reject (V in =V in =V in ) filter transfer function as below. bsv in bv in Vout = as as a ross multiplying (), and re-arranging it, yield ( ) ( ) V a s a s = a V b s V bv () out out in in ividing by as yields a a b s b V s = V V V out out in in a as a as a b Let Vout = V out Vin (4) as as () becomes a b s V s = () V V out out in a a From (4), if V in =, then (4) becomes () () (5) circuit is a low-pass (LP), band-pass (BP), high-pass (HP), and band-reject (BR) biquad filter. ote that no capacitors in feedback loops. V in R - R m V out V in R R 4 - R R m Fig. OTRA-based LP, BP, HP and BR biquad filter V out Since the two input terminals of an OTRA are virtually grounded, the resistor shown in Fig. may be replaced by two parallel MOS transistors M and M, shown in Fig., both of which are matched and operating in ohmic region. The current passing through an MOS transistor is given by i i I = K ( V V )( V V ) a ( V V ) (8) T S The transistors M and M have the same drain and source voltages leading to the cancellation [4] of the odd and even nonlinearities shown in (8). The current difference shown in Fig. is W I I = μox ( Vi V ) (9) L i S V out a = as V out (6) Substituting (6) into (), we obtain V out ( bas a ) a b s V a V = = as as as a as as as a (7) in in It means that V out is an inverting-type band-pass signal. The realizations of (4) and (5) are shown in the right and the left parts of Fig., respectively, in which =, =a, =b /a, =a /a, =, =a, and 4 =b. The realized Fig. on-linearity cancellation in two matched MOS transistor circuit. Applying the replacement of a resistor with two parallel MOS transistors, Fig. may be transformed to another second-order OTRA-MOS- low-pass, band-pass, high-pass, and band-reject filter shown in Fig.. ISB:

3 Recent Researches in Instrumentation, Measurement, ircuits and Systems with respect to each passive component are H s H s s S, H s H S H (5) Fig. Second-order OTRA-MOS- LP, BP, HP and BR filter derived from Fig.. omponent Sensitivity The transfer function of Fig. is V s V V out in 4 in () = = = Vin s s H s The resonant angular frequency and the quality factor are () Thus, we obtain that H (i) S S =, (ii) S S S = (6) For a band-reject biquad transfer function, H s H s s s S, H s H s H 4 S =, S, H H 4 S = (7) 4 From (7), we find out ω (i) S S = o = (), (ii) S H S S S S = 4 (8) For a band-pass biquad transfer function, Q = () Vout sv in H() s = = = (9) Vin s s respectively. Obviously, the sensitivities of the resonant angular frequency and the quality factor with respect to each passive component are ±/, or -. The component sensitivity of the transfer function H(s) is shown as below. The sensitivities of high-pass transfer function H(s) with respect to each passive component are H s H s s H S, S =, H s H s s H S,, S, S =, H s H H S () H s H H S () From (), we find out From (), we find out (i) S S S S =,(ii) S S = () (i) S S =, (ii) S S S S = (4) And the sensitivities of low-pass transfer function H(s) There are two null group sensitivities in (4), (6), (8), and (). It shows that if the components in a null group have the same sensitivity tendency (increment or ISB:

4 Recent Researches in Instrumentation, Measurement, ircuits and Systems decrement) and identical variation rate, the group sensitivity equals null. This result may offer a prospective research work for eliminating output deviations due to component variations in an integrated circuit. 4. on-ideal Analysis onsidering the non-ideal input-and-output characteristic of an OTRA in a circuit structure, that is, V o =(I -I - )R m, the non-ideal transfer function of the second-order LP, BP, HP, and BR filter shown in Fig. is presented below in which the non-ideal numerator and denominator are (HP) = s (BP) = s ( m) (LP) = ( 4 m) = s ( ) (BR) 4 m m m = s s ( )( ) () omparing the above four non-ideal results, we may say that the most accurate numerator is the high-pass one, the worst numerator is the low-pass or band-pass one, and the band-reject one has the medium accuracy in numerator. However, the deviations of the denominators for the three different cases are the same. ote that the total accuracy of whole transfer function depends on the deviation percentages of both the numerator and the denominator. If both the deviation percentages are identical, then the whole transfer function has perfect output responses without any errors. A comparison with the previous OTRA-based low-pass, band-pass, high-pass, band-reject, and all-pass biquad filter (Fig. in [4]) is essential. The non-ideal numerator and denominator are (HP) = (s m)s (BP) = s 4, (LP) = 4, (BR) = (s m)s (AP) = (s m)s (s m) = (s )(s ) () m 5 m 4 From (), the numerators of high-pass, band-reject, and all-pass biquad transfer functions are added by extra and unnecessary term(s). For example, there is an extra and unnecessary term, s m, in the numerator of the high-pass biquad transfer function. Thus, () has more serious non-ideal effect than () due to the following main reason: in (), s involves in m ; since s and m are two different kinds of elements, it leads to the distortion of output signals. However, there is no such an involvement in (). 5. H-Spice Simulations To verify theoretical predictions, the second-order lowpass, band-pass, high-pass, and band-reject filter shown in Fig. is simulated using the H-Spice with.5μm process ( ±.65V supply voltages), and the MOS implementations, shown in Fig. 4, of the OTRA (with V B =-.65V) presented in [5]. The W/L of the MOSFET in the OTRA [5] is shown in Table I. Table I: W/L of the MOSFET in the OTRA [ 5] MOSFET W( μm)/l(μm) M-M, M-M 7/.75 M4, M7 7/.75 M5-M6 /.75 M 8-M 5/.75 M4 5/.5 Fig. 4 MOS implementation of the OTRA [5] The component values are given by = = =4pF, and R =R =R 4 =8.k Ω, R =56.7k Ω. The simulated LP, BP, HP, and BR amplitude-frequency responses are respectively shown in Figs. 5, 6, 7, and 8. The simulated f db =.8kHz (LP),.86kHz (BP),.6kHz (HP), and.46khz (BR) have the errors of.8%,.86%,.6%, and.46% when compared to the theoretical operating f db =khz. Rather accurate output signals may be obtained from the ISB:

5 Recent Researches in Instrumentation, Measurement, ircuits and Systems realized OTRA-based LP, BP, HP, and BR biquad filter. Fig. 5 Amplitude-frequency responses for the low-pass biquad Fig. 8 Amplitude-frequency responses for the bandreject biquad Some group sensitivities exhibit the cancellation of component sensitivities in a group. Figs. 9 to show the band-pass and band-reject null group sensitivities for the four groups, (i) and, (ii),,, and, (iii) and, and (iv),,,, and 4, respectively. Figs. 9 and (resp. and ) show the component sensitivities in a group and the null group sensitivity for the band-pass biquad (resp. band-reject biquad). In this regard, the fabrication of integrated circuits may be oriented to make the group components have identical variation tendency and amount such that the defect due to component variations may be eliminated. Fig. 6 Amplitude-frequency pass biquad responses for the band- Fig. 7 Amplitude-frequency responses for the highpass biquad Fig. 9 BP ull group sensitivity curves (dashed line, with % tolerance; dotted line, with % tolerance, real line, nominal; circle line, all with % tolerance) ISB:

6 Recent Researches in Instrumentation, Measurement, ircuits and Systems all with % tolerance) 6. onclusions A new OTRA-based low-pass, band-pass, high-pass, and band-reject biquad filter is presented applying a new analytical synthesis method. Since the proposed filter structure has the structure without a capacitor in feedback loops unlike the previously reported work [4], H-Spice simulations validate that the four generic biquad filters have rather accurate output signals within the error of.86%. Moreover, null group sensitivities are also verified in this paper. Fig. BP ull group sensitivity curves (dashed line, with % tolerance; dotted line, with % tolerance, real line, or with % tolerance and the nominal curve; circle line, all with % tolerance) Fig. BR ull group sensitivity curves (dashed line, with % tolerance; dotted line, with % tolerance, real line, nominal; circle line, all with % tolerance) Fig. BR ull group sensitivity curves (dashed line, with % tolerance; dotted line, 4 with % tolerance, real line, or or with % tolerance and the nominal curve; circle line, 4 References [] Tu, S. H., hang,. M., Ross,. J., and Swamy, M.. S., Analytical synthesis of current-mode highorder single-ended-input OTA and equal-capacitor elliptic filter structures with the minimum number of components, IEEE Trans. ircuits & Syst.-I, Vol. 54, o., 7, pp [] hen, J. J., Tsao, H. W., and hen,.., Operational transresistance amplifier using MOS technology, Electron. Lett., 99, Vol. 8, o., 99, pp [] hen, J. J., Tsao, H. W., Liu, S. I., and hiu, W., Parasitic-capacitance-insensitive current-mode filter using operational transresistance amplifiers, IEE Proc. ircuits evices Syst., Vol. 4, o., 995, pp [4] Salama, K.., and Soliman, A. M., MOS operational trans-resistance amplifier for analog signal processing, Microelectron. J., Vol., 999, pp [5] Mostafa, H., and Soliman, A. M., A modified MOS realization of the operational transresistance amplifier (OTRA), Frequenz, Vol. 6, o. -4, 6, pp [6] Kafrawy, A. K., and Soliman, A. M., A modified MOS differential operational transresistance amplkifier (OTRA), Int. J. Electron. ommun. (AEU), Vol. 6, 9, pp [7] hiu, W. W., Jsay, J. H., Liu, S. I., Tsao, H. W., hen, J. J., Single-capacitor MOSFET- integrator using OTRA, Electron. Lett., Vol., o., 995, pp [8] Kacar, F., am, U., icekoglu, O., Kuntman, H., Kuntman, A., ew parallel immittance simulator realizations employing a single OTRA, The Midwest Symposium on ircuits and Systems (MWAS), Vol.,, pp. I--6. ISB:

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