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Composite Four-Terminal Floating Nullor with Variable Voltage and Current Gains Jirawat Hirunporm* Sumalee Unhavanich** Worapong Tangsrirat* Wanlop Surakampontorn* * Faculty of Engineering and Research Center for Communication and Information Technology (ReCCIT), King Mongkut’s Institute of Technology Ladkrabang (KMITL), Ladkrabang, Bangkok 10520, THAILAND ** Department of Industrial Electrical Technology (IET), Faculty of Engineering, King Mongkut’s Institute of Technology North-Bandkok (KMITNB), Bandsue, Bangkok 10800, THAILAND E-mail : [email protected] , [email protected] Abstract- A design technique for the practical implementation of a variable four-terminal floating nullor (FTFN) is presented, which contains three operational mirrored amplifiers (OMAs) and four grounded resistors. The proposed FTFN provides tunable both voltage-gain and current-gain with constant bandwidth property by varying the value of a single grounded resistor. PSPICE simulation results that agree with the theoretical analysis are obtained by modeling a variable-gain FTFN using commercial AD844 ICs. I. INTRODUCTION At present, current-mode circuits have been receiving significant attention owing to its advantage over the voltagemode, particularly for higher frequency of operation and simpler filtering structure [1]. Recently, the applications and advantages in the realization of transfer functions using fourterminal floating nullors (FTFNs) have received considerably attention. The designs of current-mode circuits employing FTFN as active devices such as amplifiers [2], current-mode filters [3-4], sinusoidal oscillators [5-6] and floating immittances [7], have been developed in the literature. Some previous-mentioned topologies have been demonstrated that an FTFN is a more flexible and all-round building block than an operational amplifier and a current conveyor [2],[4]. This is due to the fact that the nullor model of FTFN, the nullator and the norator, are isolated from each other, which is more flexible in active network synthesis. Moreover, the FTFNbased structures also provide a number of potential advantages, such as, complete absence of passive componentmatching requirement, minimum number of employed passive elements. In addition, the FTFN whose the gain can be independently tuned seems to be more attractive, flexible and suitable for design and implementation of the frequency selective systems, such as, biquads, oscillator and so forth. Although some tunable FTFNs have been recently reported [89], they can variable only current-gain between iw and iz. There are no circuit realization based on tunable FTFN that can variable both voltage-gain and current-gain. The aim of this paper is to propose a circuit technique for the practical implementation of the FTFN with variable voltage and current gains. The circuit realization uses only three operational mirrored amplifiers (OMAs) and four grounded resistors. The proposed tunable FTFN offers independently variable dc voltage and current gains while remaining a constant bandwidth. Moreover, it is interesting to show that the dc gains of the circuit can be tuned by adjusting grounded resistors without effecting the useful bandwidth. The performances of the proposed variable-gain FTFN using a commercial AD844 ICs are given with the simulation results, which will show that the characteristics of the resulting circuit become tunable. II. CIRCUIT DESCRIPTION An FTFN has the potential of being an extremely versatile analog active building block. It is a four-terminal active device with two input terminals (y, x) and two output terminals (w, z), whose circuit representation is shown in Fig.1. The terminal characteristics of the FTFN can be defined by means of the following relationship. i y " i x " 0 , v x " # .v y and iz " ! .iw (1) where # = 1-$, (|$| << 1), and $ denotes the voltage tracking error, and = 1-%, (|%| << 1), and % represents the current tracking error of an FTFN. The sign “+” is applied for the positive FTFN (FTFN+), whereas the sign “–” uses for the opposite polarity case, represented the negative FTFN (FTFN). For an ideal FTFN, the voltage and current tracking error are equal to zero, i.e., $ = % = 0, or # = = 1. The usefulness of the FTFN can be extended if equation (1) is implemented in such a way that the voltage and current transfer ratios can be varied, in which case a more generalized tunable FTFN should be investigated. ECTI-CON 2007 The 2007 ECTI International Conference ___________________________________________________________ 113 iy iz vy y vx x The proposed tunable FTFN with arbitrary voltage-gain and current-gain, named TFTFN, is shown in Fig.3. It mainly consists of three OMAs and four grounded resistors. A detail analysis results that the voltage-current characteristics of this device can be defined by : z FTFN w ix iw Figure 1 : Symbol of an FTFN +R ( +R ( i y " i x " 0 , v x " )) 1 &&v y and i z " )) 3 &&iw * R4 ' * R2 ' Fig.2 shows the circuit implementation and representation of the OMAs. The negative OMA (OMA-) comprising an opamp and two pairs of current mirrors as shown in Fig.2(a) is a more general and flexible device owing to it can be equivalent to an ideal nullor or FTFN+ [1-2], whereas the other type of OMA which requires only one pairs of current mirrors is named the positive OMA (OMA+) and is shown in Fig.2(b). Therefore, it can be concluded from Fig.2 that the port characteristics of the OMA can be characterized as : v2 " v1 i1 " i2 " 0 and , i4 " i3 (3) Also note that the proposed TFTFN of Fig.3 is more flexible, which can be varied the voltage-gain and the current-gain through the ratio of two grounded resistors. Furthermore, if the 3rd positive OMA (OMA+) of Fig.3(a) is used instead with the negative OMA (OMA-), then the variable-gain FTFN- will also be obtained. (2) III. PERFORMANCE ANALYSIS i1 i3 1 i1 i4 i3 1 3 One important issue that must to be taken into account is the non-idealities of each OMA on the frequency dependent performance. Fig.4 shows the macro-model of the OMA, where # and denote the non-ideal voltage- and current gains of the OMA. By applying the model from Fig.4 into the subcircuit between OMA1 and OMA2 of Fig.3(a), routine analysis obtains that 4 3 2 2 i2 i2 4 i4 (a) i1 i3 1 i1 i4 i3 1 3 ( v X + #1# 2 3 RA (+ 1 && &&)) " )) vY * R2 '* 1 , sRAC A ' 4 3 2 2 i2 i2 where RA = R1 -- Ry -- Rz , CA = Cy + Cz and #i and i are the voltage gain and current gain of the OMAi (i = 1, 2, 3). Typically, the values of Ry and Rz are too large and can also approximate to Ry , Rz >> R1, then equation (4) can be rewritten as : 4 i4 (b) Figure 2 : Possible implementation of OMAs (a) negative OMA (OMA-) (b) positive OMA (OMA+) 4 4 vY y R1 1 2 OMA+ vX 1 3 1 2 R2 4 2 R4 OMA- ( v X + #1# 2 3R1 (+ 1 && &&)) . )) vY * R2 '* 1 , sR1C A ' iZ z 1 R3 3 2 3 3 w iW v1 1 iz y vx x v2 z ix w iw 4 Cy i3 / 3 i3 2 Rx TFTFN i4 # Ry (a) iy (5) OMA+ x vy (4) Cx Rz Cz #v1 Figure 4 : Macro model for non-ideal OMA (b) Figure 3 : Proposed tunable FTFN (TFTFN) (a) circuit implementation (b) its symbol ECTI-CON 2007 The 2007 ECTI International Conference ___________________________________________________________ 114 Rw Cw According to equation (5), the dc voltage gain, #dc, and the high-frequency dominant pole between the port y and the port x, 0pv, can respectively be given by # dc " and #1# 2 0 pv " 21f pv " 3 R1 R2 1 1 " R1C A R1(C y , C z ) (6) (7) It can easily be noted from equations (6) and (7) that the dominant pole frequency can be adjusted by tuning the value of the resistor R1, while the dc voltage-gain of this circuit can be adjusted through the resistor R2 without affecting the bandwidth property. For example, if R1 = 5 k2, Cy = 2 pF and Cz = 4.5 pF, then this pole frequency will locate at 4.89 MHz. This means that the dc voltage-gain of the proposed TFTFN can be independently varied without changing the useful bandwidth. In the same way as above, the transfer characteristic between the currents iZ and iW can be considered by applying the model from Fig.4 into the sub-circuits formed of OMA2 and OMA3 of Fig.3(a). Reanalysis gives the relations : 0 pi " 21f pi " and 1 1 " R3C A R3 (C y , C z ) (12) From equations (11) and (12), R3 should be selected so as to meet the desired bandwidth, whereas R4 can be modified to change the gain without disturbing the bandwidth. Similarly, if R3 = 5 k2, Cy = 2 pF and Cz = 4.5 pF, then this pole frequency is also located at 4.89 MHz. It also concludes that the dc current-gain of the proposed TFTFN can be independently controlled without changing the useful bandwidth. IV. SIMULATION RESULTS The performances of the proposed variable-gain FTFN of Fig.3 have been simulated with PSPICE using an OMA, which consists of AD844 transimpedance op-amps as shown in Fig.5 [6]. The simulation was performed using macromodel of the AD844 IC shown in Fig.6 [12]. +i4 y 1 AD844 +z 5 i z 8 # 3 2 3 Rm R z 5 8 1 "6 3 36 i w 7 Rn ( R z , R L ) 4 7 (1 , sRm C A )(1 , sR L C z ) 4 4 -i4 x i3 x AD844 +z 2 3 y (8) Figure 5 : Realization of OMA+ with commercial available AD844 ICs where Rm = R3 -- Ry -- Rz , Rn = R4 -- Rx and RL is the load resistance connected to the port z. Since R3 and R4 are very small, comparable to those resistances, i.e., Ry , Rz >> R3, Rx >> R4. Thus equation (8) can be reduced to : 5 i z 8 # 3 2 3 R3 5 8 1 "6 3 36 iw 7 R4 4 7 (1 , sR3C A )(1 , sR L C z ) 4 x I'x C1 y Rb C9 ,iz #Rx ' vy z v'y /Rx Rx Cy ,:I'x Rz Cz (9) if we choose R3 >> RL, then the above equation becomes : 5 i z 8 # 3 2 3 R3 5 8 1 "6 3 36 iw 7 R4 4 7 (1 , sR3Ci ) 4 (10) Hence, the dc current-gain, dc, and the high-frequency dominant pole between the port w and the port z, 0pi, are dc " #3 2 3 R3 R4 (11) Figure 6 : Small signal equivalent circuit for the AD844 transimpedance amplifier [12] : Rb = 300 2, Rx = 50 2, #Rx = 20 k2, Rz = 2 M2, C9 = 2 pF, C1 = 26 pF, Cx = 2 pF and Cz = 4.5 pF Fig.7 shows the voltage frequency responses, vx / vy , when R1 = 5 k2 and R2 is changed to 5 k2, 2.5 k2, 1 k2 and 0.5 k2, which corresponds to the dc voltage gain # = 1, 2, 5 and 10, respectively. The ac current responses of the proposed TFTFN for R3 = 5 k2 are shown in Fig.8. From the simulated frequency responses in Figs.7 and 8, it is evidenced in both cases that the useful bandwidth is nearly constant with respect to the variation of the voltage-gain or the current-gain of the proposed TFTFN, which are well confirmed the theoretical analysis. ECTI-CON 2007 The 2007 ECTI International Conference ___________________________________________________________ 115 ideal case. The proposed tunable FTFN employs only three OMAs and four grounded resistors, and offers constant bandwidth, whereas both the dc voltage- and current-gains can be independently controlled through a single grounded resistor. PSPICE simulation results obtained from an implementation with the AD844 transimpedance op-amp have been demonstrated that its performance is quite satisfactory for discrete high-frequency circuit designs, such as, biquads, oscillators and so forth. 25 Voltage gain (dB) 20 0 : R2 = 0.5 k2 : R2 = 1.0 k2 : R2 = 2.5 k2 : R2 = 5.0 k2 -15 100 ACKNOWLEDGMENT 10k 1M 100M Frequency (Hz) Figure 7 : Voltage transfer characteristics of the proposed tunable FTFN for R1 = 5 k2 REFERENCES 25 Current gain (dB) 20 0 : R4 = 0.5 k2 : R4 = 1.0 k2 : R4 = 2.5 k2 : R4 = 5.0 k2 -15 100 10k 1M This work is funded by the Thailand Research Fund (TRF) through the Senior Research Scholar Program; grant number RTA4680003. 100M Frequency (Hz) Figure 8 : Current transfer characteristics of the proposed tunable FTFN for R3 = 5 k2 V. FURTHER APPLICATIONS Finally, the proposed FTFN with variable-gain can be applied for implementing active filters with electronic control of the important circuit parameters, such as, the natural angular frequency 0o, the quality factor (Q-factor) and the absolute bandwidth. Moreover, oscillator with electronic control of the frequency and the condition of oscillators can also be realized. But it is not demonstrated in this paper, because of some applications employing this device have been recently reported in references [7-11]. VI. CONCLUSIONS In this paper, a circuit configuration for an FTFN with variable voltage- and current-gains is proposed in order to simplify the representation of different building block in the [1] B. Wilson, "Recent development in current conveyors and current mode circuits", IEE Proceedings, vol.137, Pt. G., pp.63-77, 1990. [2] J.H. Huijsing, "Operational floating amplifier", IEE Proceedings, vol.137, Pt. G., pp.131-136, 1990. [3] M.T. Abuelma'atti and H.A. Al-zaher, "Universal twoinput two-output current-mode active biquad using FTFNs", International Journal of Electronics, vol.86, pp.181-188, 1999. [4] M. Higashimura, "Realization of current-mode transfer function using four-terminal floating nullor", Electronic Letters, vol.27, pp.170-171, 1991. [5] D.R. Bhaskar, "Single resistance controlled sinusoidal oscillator using single FTFN", Electronic Letters, vol.35, pp.190, 1999. [6] S.I. Liu, "Single-resistance-controlled sinusoidal oscillator using two FTFNs", Electronic Letters, vol.33, pp.1185-1186, 1997. [7] R. Senani, "A novel application of four-terminal floating nullors", Proceedings of the IEEE, vol.75, pp.1544-1546, 1987. [8] W. Tangsrirat, S. Unhavanich, T. Dumawipata and W.Surakampontorn, “FTFN with variable current gain”, Proceedings of TENCON 2001, Singapore, pp.209-212, August 19-21, 2001. [9] J. Hirunporm, W. Tangsrirat and W. Surakampontorn, “Electronically tunable multiple-output FTFN and its applications”, Proceedings of ECTI-CON 2006, Thailand, pp.805-808, May 10-13, 2006. [10] J. Hirunporm, W. Tangsrirat and W. Surakampontorn, “Current-controlled current-mode biquadratic filter using tunable multiple-output FTFNs”, Proceedings of The 2006 International Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2006), Thailand, pp.705-708, July 10-13, 2006. [11] J. Hirunporm, T. Pukkalanun and W. Tangsrirat, “Current-controlled current-mode biquadratic filter with two inputs and three outputs using multiple-output FTFNs”, Proceedings of International Joint Conference 2006 (SICE-ICCAS 2006), Korea, pp.5691-5694, October 18-21, 2006. [12] E. Bruun and O.H. Olesen, "Conveyor implementation of generic current mode circuits", International Journal of Electronics, vol.73, no.1, pp.129-140, 1992. ECTI-CON 2007 The 2007 ECTI International Conference ___________________________________________________________ 116 transfer function of the proposed filter in Fig.3 can be given by : %g g " I o1 ' & # m1 m2 I1 $ D( s ) ! (3) and % D( s) I 2 & (sC2 g m1 )I1 " I o2 ' # D( s ) ! $ (4) where D(s) = (s2C1C2 + sC2gm1 + gm1gm2) (5) and gmi denotes gm of the i-th MO-OTA (i = 1, 2). I1 + C1 I2 gm1 -- + - *o ' Io2 - + g + m2 + Io1 From equations (3)-(5), it can be seen that : a LP function is realized with I1 = Iin , I2 = 0 and Io1 = Iout. a BP function is realized with I1 = Iin , I2 = 0 and Io2 = Iout. a BS function is realized with I1 = I2 = Iin and Io2 = Iout. a AP function is realized with I1/2 = I2 = Iin and Io2 = Iout. a HP function is realized with I1 = I2 = Iin and Io1 +Io2 = Iout. Thus, the proposed TITO filter can realize all the five standard types of the biquadratic filtering functions from the same circuit configuration. Note also that the circuit needs no inverting-type current input signal for realizing any biquadratic functions. As seen from the proposed circuit configuration, it employs only grounded passive elements especially grounded capacitors and there are no critical component-matching conditions or cancellation constraints in the design, thus the circuit is very suitable for fully IC technology. Also from equations (3)-(5), the filter parameters *o and *o/Q are given by : 1) 2) 3) 4) 5) Fig.3 : Proposed TITO current-mode universal filter employing only MO-OTAs and grounded capacitors (6) *o g ' m1 Q C1 and C2 g m1 g m 2 C1C2 (7) It can be seen from above expressions that the *o for all the filter responses can electronically be tuned by varying gm2 and/or C2 without affecting the parameter *o/Q. +V +io +io v+ vIB -V Fig.2 : Circuit diagram of an ordinary MO-OTA ECTI-CON 2007 The 2007 ECTI International Conference ___________________________________________________________ 118 -io -io From these relations, the active sensitivities can be found as Moreover, the *o and *o/Q sensitivities can be given by (8) SG o ' 1 * * SC o ' SC o ' & 1 2 2 (9) SG o ' * /Q Sg o and * 1 Sg ' Sg ' m1 m2 2 *o m1 *o * /Q ' SC o 1 '1 i1 * i2 1 2 Gi1Gi 2 g m1 g m 2 + ( g m1 + Gi1 )Gi 2 2 1 2 (14) 1 2 (g m1 + Gi1 )Gi 2 g m1g m 2 + ( g m1 + Gi1 )Gi 2 2 1 2 (15) " Gi1C2 1% 1 2 # 2 $ C2 ( g m1 + Gi1 ) + C1Gi 2 ! 2 (16) " Gi 2C1 1% 1 2 # 2 $ C2 ( g m1 + Gi1 ) + C1Gi 2 ! 2 (17) * (10) SG o / Q ' i1 All the active and passive sensitivities are not more than unity in magnitude. and * SG o / Q ' III. NON-IDEAL STUDY i2 The circuit model of the non-ideal MO-OTA can be shown in Fig.4, where Gi and Go are the parasitic input and output conductances, and Ci and Co are the parasitic input and output capacitances, respectively. Therefore, re-analysis the proposed filter of Fig.3 by taking into account the nonidealities of the MO-OTA, the denominator polynomial of the non-ideal transfer function can be rewritten as : It can easily be observed from equations (14)-(17) that the entire active sensitivities are still less than 0.5 in magnitude. Thus, the proposed filter structure displays a low sensitivity performance. IV. SIMULATION RESULTS D(s)=s2C1C2+s[C2(gm1+Gi1)+(C1Gi2)]+[gm1gm2+(gm1+Gi1)Gi2] (11) where Gik represents the parasitic input conductance of the kth MO-OTA. io v+ + Gi Ci gm(v+-v-) Go Co io v- Gi Ci gm(v+-v-) Go Co To verify the theoretical prediction, the characteristics of the proposed current-mode universal filter of Fig.3 have been simulated with PSPICE program. The MO-OTA is simulated using the bipolar structure given in Fig.2 with DC supply voltages of 33V. The transistors model parameters are taken from the PR100N (PNP) and NP100N (NPN) of the bipolar arrays ALA400 from AT&T [8]. Fig.5 shows the simulated frequency responses of the LP, BP and HP filter functions of the proposed circuit in Fig.3. In simulations, equal bias current values of IB1 = IB2 = 100 4A, and capacitance values of C1 = C2 = 1 nF were chosen to obtain fo = *o/25 6 318 kHz and Q = 1. With the same setting, the gain and phase responses of the BS and AP filters are also given in Figs.6 and 7, respectively. All the simulation results agree quite well with the theory. 10 In this case, the modified parameters *o and *o/Q are calculated as *o ' g m1g m 2 + ( g m1 + Gi1 )Gi 2 C1C2 (12) Current gain (dB) Fig.4 : Circuit model of the non-ideal MO-OTA operating in linear region 0 LP HP BP -10 -20 -30 1k 10k 100k 1M 10M Frequency(Hz) and *o Q 1 g + Gi1 . 1 Gi 2 . ,, + // ,, ' // m1 C1 - 0 C2 0 (13) Fig.5 : LP, BP and HP current responses of the proposed current-mode universal filter in Fig.3. ECTI-CON 2007 The 2007 ECTI International Conference ___________________________________________________________ 119 100M ACKNOWLEDGMENT Gain Phase (dB) (degree) 40 100 This work is funded by the Thailand Research Fund (TRF) through the Senior Research Scholar Program; grant number RTA4680003. o 20 50o 0 0 -20 -50o -40 -100o 1k Gain Simulation Theory Phase Simulation Theory REFERENCES 10k 100k 1M 10M 100M Frequency (Hz) Fig.6 : BS current response of the proposed current-mode filter. Gain Phase (dB) (degree) 40 100o 20 50o 0 0 -20 -50o -40 -100o 1k Gain Simulation Theory 10k 100k 1M Phase Simulation Theory 10M 100M Frequency (Hz) Fig.7 : AP current response of the proposed current-mode filter. [1] J. Wu, “Current-mode high-order OTA-C filters”, International Journal of Electronics, vol.76, pp.11151120, 1994. [2] T. Tsukutani, M. Ishida, S. Tsuiki and Y. Fukui, “Versatile current-mode biquad filter using multiple current output OTAs”, International Journal of Electronics, vol.80, pp.533-541, 1996. [3] Y. Sun and J. K. Fidler, “Design of current-mode multiple output OTA and capacitor filters”, International Journal of Electronics, vol.81, pp.95-99, 1996. [4] J. Wu and E. I. El-Masry, “Current-mode band-pass ladder filters using OTAs”, International Journal of Electronics”, vol.85, pp.61-70, 1998. [5] C. M. Chang and S. K. Pai, “Universal current-mode OTA-C biquad with the minimum components”, IEEE Transaction on Circuits and Systems-I: Fundamental Theory and Applications, vol.47, pp.1235-1238, 2000. [6] M. Bhusan and R. W. Newcomb, “Grounding of capacitors in integrated circuits”, Electronics Letters, vol.3, pp.148-149, 1967. [7] K. Pal and R. Singh, “Inductorless current conveyor allpass filter using grounded capacitors”, Electronics Letters, vol.18, p.47, 1982. [8] D. R. Frey, “Log-domain filtering : an approach to current-mode filtering”, IEE Proceedings Part G, Circuits, Devices and Systems, vol.140, pp.406-416, 1993. V. CONCLUSIONS In this paper, a two-input two-output current-mode universal biquadratic filter that employs a minimum number of active and passive components has been described. The configuration consists of only two MO-OTAs and two grounded capacitors, which is advantageous from IC fabrication. The proposed filter can realize all the five standard biquadratic filter functions without any matching conditions. The filter parameters *o and *o/Q are tuned electronically and independently, and all the passive and active sensitivities are low. ECTI-CON 2007 The 2007 ECTI International Conference ___________________________________________________________ 120