Generation of Voltage-Mode OTRA-Based Multifunction Biquad Filter

Transcription

1 eneration of Voltage-Mode OTRA-Based Multifunction Biquad Filter Chun-Ming Chang, Ying-Tsai Lin, Chih-Kuei Hsu, Chun-Li Hou*, and Jiun-Wei Horng* epartment of Electrical/*Electronic Engineering Chung Yuan Christian University Chung-Li, Taiwan R. O. China Abstract: With the dual input-and-output characteristics of the well-known operational transconductance amplifier (OTA), the operational transresistance amplifier (OTRA) is attractive to be used in circuit design. Applying a new analytical synthesis method, a low-pass, band-pass, and high-pass biquad filter without capacitors in feedback loops using three OTRAs, two capacitors, and several resistors is presented. Based upon component sensitivity tendency and variation amount, just properly adjusting one or two resistances by a small difference, or giving approximate component values for achieving precise output responses is investigated and developed in this paper. Null group sensitivities are also simulated and validated in this paper. Key Words: Active filters, analog circuit design, continuous-time filters, low-pass filters, band-pass filters, high-pass filters, operational transresistance amplifiers. Introduction An operational transconductance amplifier (OTA) [], simultaneously representing both an active element and an electronically tunable conductor, becomes one of the most prospective active elements in the field of analogue circuit design. Its input-and-output characteristics are (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. Note that the OTAs cannot enjoy this benefit. Therefore, we may make the predictions as follows. (i) OTRA-based circuit structures may be the dual 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 [-], monostable [5-6] and bistable [7] multivibrators, first- [, 8-] and second-order [] all-pass filters, and other secondorder single- [, ] and multi-function [, ] 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 [] employing four (two more) capacitors was presented. An OTRA-based low-pass, band-pass, and high-pass biquad filter using only two capacitors, was also published []. Since the two capacitors were synthesized and put in feedback loops, the non-ideal analysis exhibits that the ideal sc has been replaced by practical sc+ m where m /R m, and R m is the trans-resistance function of an OTRA. This arrangement produced additional poles in the transfer function. Note that this main disadvantage has been improved in this paper. ISBN:

2 . Analytical Synthesis ive a generic voltage-mode second-order high-pass filter transfer function as below. Vout bs V a s + a s + a in () Cross multiplying (), dividing it by a s, yield a a b Vout + + V in as as () a a b a a a a a Since a a a a a () () becomes a a a b V out + + V in as as as a () Fig. OTRA-based LP, BP, and HP biquad filter namely, V ( ab a) a a a b V () out + Vout Vout Vin Vin as as a as + as as (5) + + a () which is equivalent to Hence, Fig. is a band-pass (from output voltage V ) -a and low-pass (from output voltage V ) in addition to a -a -a b Vout() -Vout () Vout () Vin a s + a s a s (6) a high-pass filter. We may let Since the two input terminals of an OTRA are virtually - a grounded, the resistor shown in Fig. may be replaced - a a V Vout Vout (7) by two parallel NMOS transistors M and M, shown as s in Fig., both of which are matched and operating in (6) is then simplified as ohmic region. The current passing through an NMOS transistor is given by - a b i i Vout () -V () + V () Vin as (8) I K N ( V VT )( V VS ) + ai ( V VS ) () a The transistors M and M have the same drain and - a - a a And let V source voltages leading to the cancellation [] of the V V (9) a s s odd and even nonlinearities shown in (). The current (8) becomes difference shown in Fig. is W b I I μncox ( Vi V ) () Vout() -V () + V () Vin () L a Each of Eqs. (7), (9), and () may be realized using one OTRA, several resistors, and one or without capacitor(s). The combination of these three sub-circuitries is shown in Fig.. From (7) and (9), we obtain V ( ab a) s () Vin as + as+ a Fig. Non-linearity cancellation in two matched ISBN:

3 NMOS transistor circuit. Applying the replacement of a resistor with two parallel NMOS transistors, Fig. may be transformed to another second-order OTRA-MOS-C low-pass, band-pass, and high-pass filter shown in Fig.. H S 5 - S H 6 Thus, we obtain that H H H H S + S, S + S, 5, (8) C C 5 H H H H S + S + S + S, 6 H H H H H H H H S + S + S + S + S + S + S + S (9) C C 5 6 Fig. Second-order OTRA-MOS-C LP, BP, and HP filter derived from Fig. There are four null group sensitivities in (9). It shows that if the components in a null group have the same sensitivity tendency (increment or 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.. Non-ideal Analysis Considering 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, and HP filter shown in Fig. is presented below in which the non-ideal numerator and denominator are. Component Sensitivity N(HP) s CC The transfer function of Fig. is V N(BP) sc 6( m) out N s CC 6 (5) Vin s CC + sc 5 N(LP) 6( m)(5 m) The resonant angular frequency and the quality factor s CC + sc( m) + are () ( m)( m)(5 m) 5 ω o (6) Comparing the above three non-ideal results, we may CC say that the most accurate numerator is the high-pass C one, the worst numerator is the low-pass one, and the 5 Q (7) band-pass one has the medium accuracy in numerator. C However, the deviations of the denominators for three respectively. Obviously, the sensitivities of the resonant different cases are the same. Note that the total accuracy angular frequency and the quality factor with respect to of whole transfer function from theoretical point of each passive component are ±/, or -. view depends on the deviation percentages of both the The sensitivities of transfer function H(s) with respect numerator and the denominator. If both the deviation to each passive component are percentages are identical, then the whole transfer function has perfect output responses without any errors. H s CC H s CC + sc SC -, SC - A comparison with the previous OTRA-based low-pass, band-pass, and high-pass biquad filter (Fig. in []) is essential. The non-ideal numerator and denominator are H s CC H sc S - S - N(HP) (sc m )(sc m ) N(BP) (sc m) H 5 H sc 5 S - S - N(LP) ISBN:

4 s(c (sc m ) m )(sc 5 m 6 )( m ) + () () has more serious non-ideal effect than () due to the following main reason: in (), sc involves in ; since sc and are two different kinds of elements, it leads to the distortion of output signals. However, there are no such involvements in (). 5. H-Spice Simulations To verify theoretical predictions, the second-order high-pass, band-pass, and low-pass filter shown in Fig. is simulated using the H-Spice with.5μm process ( ±.65V supply voltages), and the CMOS Implementations, shown in Fig., of the OTRA (with V B -.97V) 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 M, M7 7/.75 M5-M6 /.75 M8-M 5/.75 M 5/.5 f db khz with peak., and f db.9588mhz with peak.9869 (LP),.86 MHz with peak.97 (BP), and.79mhz with peak.97 (HP) when the theoretical operating f db MHz with peak.. We notice that the error,.86%, of the f db of the highpass response at khz is a little bit higher. This deviation is mainly due to the approximation design rule: approaching all trans-resistances to infinity. It means that the deviation is inevitable under the rule. Therefore, how to improve the output accuracy is an important matter for OTRA-based circuits. And since precise component values lead to the deviations of output signals, a set of proper variations of component values may make a more accurate output signal. Table I shows the variation percentage of f db and V peak when each component value is added by %. Based upon the sensitivity tendency and variation amount shown in Table I, we choose R to increase by.86/.98.86%, that is, replacing R by 5.76k Ω from.5kω.thus, the output parameters, f db and V peak.of the high-pass filter are much improved and shown in Table II. If we just tune R by only 6 k Ωmuch simpler than the precise value 5.76kΩ for eliminating the difficulty of fabricating such a precise resistor in an integrated circuit, the simulated results are also shown in Table II. As can be seen, the approximation value still produces very precise output signals. Fig. CMOS implementation of the OTRA [5] The component values are given by C C C pf (for khz) or pf (for MHz), and R R R R 6 kω, R.5kΩ, R 5 5.8kΩ. The simulated amplitude-frequency responses are respectively shown in Figs. 5, 6, and 7 having the simulated f db.8khz with peak.9869 (LP),.kHz with peak.9868 (BP), and.8khz with peak.9868 (HP) when the theoretical operating Table I Variation percentage of f db and V peak when the component value is added by % (for HP) Param. f db (%) V peak (%) Comp. R (+%) R (+%) R (+%) -.. R (+%) R 5 (+%).7.6 R 6 (+%) Table II Improved output parameters after adding R by.86% Param. f db and V peak f db and V peak Filter (R 5.76 kω) (R 6 kω) Low-Pass.85 (.85%) (.85%).9869 Band-Pass.9(.9%) (.69%).9867 High-Pass (.%) (.5%).9867 ISBN:

5 If we feel that the error of the above low-pass response is not good enough, we may do component-value tuning once again. Similar to Table I, we obtain the variation percentage of f db and V peak when each component value is added by % for the low-pass filter and shown in Table III. Based upon the sensitivity tendency and variation amount shown in Table III, we choose R 5 to increase by.857/ %, that is, replacing R 5 by 7.kΩ from 5.8kΩ.Thus, the output parameters, f db and V peak.of the low-pass filter are much improved and shown in Table IV. If we just tune R 5 by only 7 kωmuch simpler than the precise value 7.kΩ for eliminating the difficulty of fabricating such a precise resistor in an integrated circuit, the simulated results are also shown in Table IV. As can be seen, the approximation value still produces very precise output signals. Fig. 5 Amplitude-frequency responses for the low-pass biquad (red for khz and black for MHz) Some group sensitivies exhibit the cancellation of component sensitivities in a group. Figs. 8 to show these null group sensitivities for the three groups, (i) C, C,,,, and 6, (ii) C and, and (iii) C and 5, respectively. 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. Table III Variation percentage of f db and V peak when the component value is added by % (for LP) Param. f db (%) V peak (%) Comp. R (+%).56.5 R (+%).99.8 R (+%) R (+%)..7 R 5 (+%) R 6 (+%) Fig. 6 Amplitude-frequency responses for the bandpass biquad (red for khz and black for MHz) Table IV Improved output parameters after adding R 5 by.86% Param. f db and V peak f db and V peak Filter (R 5 7. kω) (R 5 7 kω) Low-Pass. (.%).9869.(.%).9869 Band-Pass.(.%).9868.(.%).9868 High-Pass 99.77(.7%) (.6%).9868 Fig. 7 Amplitude-frequency responses for the highpass biquad (red for khz and black for MHz) ISBN:

6 rather errors. Based upon sensitivity tendency and variation amount, appropriately varying some resistor may lead to very precise output responses. H-Spice simulations validate null group sensitiities in addition to filter feasibility and low component sensitivities Fig. 8 Null group sensitivity curves (dashed line, C with % tolerance; dotted line, with % tolerance, real line, nominal; circle line, C + with % tolerance) Fig. 9 Null group sensitivity curves (dashed line, C with % tolerance; dotted line, 5 with % tolerance, real line, nominal; circle line, C + 5 with % tolerance) Fig. Null group sensitivity curves (dashed line, 6 with % tolerance; dotted line, with % tolerance, real line, nominal or with % tolerance or with % tolerance; circle line, all with % tolerance) 6. Conclusions A new OTRA-based low-pass, band-pass, and highpass biquad filter is presented without a capacitor in feedback loops using a new analytical synthesis method. The difference between finite tranresistance and infinite transresistance makes output signals with References [] Tu, S. H., Chang, C. M., Ross, N. J., and Swamy, M. N. 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. Circuits & Syst.-I, Vol. 5, No., 7, pp [] Chen, J. J., Tsao, H. W., and Chen, C. C., Operational transresistance amplifier using CMOS technology, Electron. Lett., 99, Vol. 8, No., 99, pp [] Chen, J. J., Tsao, H. W., Liu, S. I., and Chiu, W., Parasitic-capacitance-insensitive current-mode filter using operational transresistance amplifiers, IEE Proc. Circuits evices Syst., Vol., No., 995, pp [] Salama, K. N., and Soliman, A. M., CMOS operational trans-resistance amplifier for analog signal processing, Microelectron. J., Vol., 999, pp [5] Mostafa, H., and Soliman, A. M., A modified CMOS realization of the operational transresistance amplifier (OTRA), Frequenz, Vol. 6, No. -, 6, pp [6] Kafrawy, A. K., and Soliman, A. M., A modified CMOS differential operational transresistance amplkifier (OTRA), Int. J. Electron. Commun. (AEU), Vol. 6, 9, pp [7] Chiu, W. W., Jsay, J. H., Liu, S. I., Tsao, H. W., Chen, J. J., Single-capacitor MOSFET-C integrator using OTRA, Electron. Lett., Vol., No., 995, pp [8] Kacar, F., Cam, U., Cicekoglu, O., Kuntman, H., Kuntman, A., New parallel immittance simulator realizations employing a single OTRA, The Midwest Symposium on Circuits and Systems (MWCAS), Vol.,, pp. I--6. [9] Salama, K. N., and Soliman, A. M., Novel oscillators using the operational transresistance amplifier, Microelectron. J., Vol.,, pp [] Hou, C. L., Chang, C. W., and Horng, J. W., A quadrature oscillator employing the dominant poles of the OTRAs, J. Advanced Engineering, Vol., No., 7, pp ISBN:

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