* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Quadrature oscillator using CDTA-based integrators
Nanofluidic circuitry wikipedia , lookup
Surge protector wikipedia , lookup
Josephson voltage standard wikipedia , lookup
Schmitt trigger wikipedia , lookup
Power MOSFET wikipedia , lookup
Transistor–transistor logic wikipedia , lookup
Superheterodyne receiver wikipedia , lookup
Switched-mode power supply wikipedia , lookup
RLC circuit wikipedia , lookup
Current source wikipedia , lookup
Phase-locked loop wikipedia , lookup
Index of electronics articles wikipedia , lookup
Valve audio amplifier technical specification wikipedia , lookup
Power electronics wikipedia , lookup
Two-port network wikipedia , lookup
Negative-feedback amplifier wikipedia , lookup
Operational amplifier wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Wilson current mirror wikipedia , lookup
Radio transmitter design wikipedia , lookup
Opto-isolator wikipedia , lookup
Regenerative circuit wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Rectiverter wikipedia , lookup
Quadrature oscillator using CDTA-based integrators DALIBOR BIOLEK, ALI ÜMIT KESKIN*), VIERA BIOLKOVA Depts. of Microelectronics and Radioelectronics, Brno University of Technology Dept. of EE, University of Defence, Brno, Czech Republic *) Department of Biomedical Engineering, Yeditepe University, Istanbul, Turkey [email protected] http://user.unob.cz/biolek Abstract: A current mode quadrature oscillator consisting of two CDTA (Current Differencing Transconductance Amplifier) –based integrators is introduced. The oscillation frequency can be made adjustable by internal transconductances of active elements without affecting the oscillation condition. Three methods of stabilizing the oscillation amplitude are proposed. PSpice simulations are preformed, which verify the circuit performance. Keywords: - Quadrature oscillator, CDTA, current mode 1 Introduction Quadrature oscillators (QOs) employing various types of active elements are reported in the literature. Current conveyors and other active components, enabling highspeed current-mode or mixed-mode operation, have been increasingly used. A QO in [1] consists of two operational transresistance amplifiers (OTRAs), but six virtually grounded passive R and C components are required. Horng [2] reported a QO with two current differencing buffered amplifiers (CDBAs), two grounded capacitors, and four virtually grounded resistors. A more economical QO in [3] uses three current-controlled current conveyors CCCII and only one grounded and one virtually grounded capacitor. However, it generates relatively low-amplitude and unequal sinusoidal output signals. Salama and Soliman [4] proposed a pair of lossy and lossless integrators in a feedback loop, implemented by two CDBAs and six virtually grounded CMOS transistors, with the possibility of digital control of oscillation frequency. The OTA-C tunable QO in [5] contains four operational transconductance amplifiers (OTAs), two grounded capacitors, and special circuits for current-mode amplitude control. The QO in [6] consists of two allpass sections, each employing one current differencing transconductance amplifier (CDTA) and a virtually grounded pair of R and C components. The frequency of generated waveforms is insensitive to transconductances gm of CDTAs and is given by passive R and C components. Most of the reported oscillators provide noninteracting controls for the frequency of oscillation (FO) and condition of oscillation (CO). There are several methods of amplitude control, from simple nonlinear limiters [7] to sophisticated control loops which can represent more complicated circuitry on the chip than the primary oscillator [5]. In this paper, a novel QO is proposed. Similarly to [6], it employs CDTA active elements. However, the circuitry consists of two integrators in a feedback loop. That is why the QO is compounded of only two CDTAs and two grounded capacitors, plus auxiliary circuitry for automatic gain control. 2 CDTA element The CDTA elements [8] in Fig. 1 (b) are exploited for integration in a simple way: the difference of currents, flowing into low-impedance p and n terminals, flows out of the z-terminal into a load Z, causing a voltage Vz at the z terminal. Internal transconductance gm, controllable by an outside current source Ig, converts this voltage into a couple of bidirectional output currents Iout. Therefore, this active element can be characterized by the following equations: Vp = Vn = 0 , Iz = Ip - In , Ix+ = gmVz , Ix-= - gmVz. (1) CDTA can be thought of as a combination of a current differencing unit followed by a dual-output operational transconductance amplifier, DO-OTA. Ideally, the OTA is assumed to be an ideal voltagecontrolled current source and can be described by the formula Ix = gmVin, where Ix is the output current, and Vin denotes the input voltage of the OTA. Note that gm is a function of the bias current. With dual output available, the condition Ix+ = −Ix− is assumed. A possible CMOS-based CDTA circuit realization suitable for the fabrication of a monolithic IC is displayed in Fig. 2 [6, 9]. In this circuit, transistors from M1 through M12 perform the current differencing operation while transistors from M13 through M24 convert the voltage at the z terminal to output currents at the two outputs of the DO-OTA section. DO-OTA’s transconductance (gm) is controllable via its bias current IB3. Also, an impedance Z connected at the z terminal can be used to adjust the gain of CDTA, while the voltage at the input of DO-OTA is Vz = Iz. Z. The gate terminals of output transistors M11 and M12 in the current-differencing section are connected to bias-voltages to provide drain output and high impedance at the z terminal (ideal current-controlled current source, CCCS). The multiple-output (MO) CDTA can be easily implemented by copying the structure of transistor couples M16-M21 and M20-M24. Then one can use more I+ and I- outputs, which is advantageous in many applications. Examples of such MO-CDTAs are given in [10, 11]. Note that total parasitic capacitance on the chip increases, causing lowering the bandwidth. Bipolar CDTA structures are given in [12-14]. Ig Ip In x+ p x- z Vz Table 1.Transistor W/L ratios used in CDTA model. W / L ( µm ) 8 /1 5/1 20 / 2 16 / 1 6/1 4/1 Transistor M1 - M6 M7 - M10 M11 - M12 M13 - M14 M15 - M20 M21 - M24 3 QO basic configuration The proposed economical oscillator is shown in Fig. 3. It consists of one inverting and one noninverting lossless current integrator in a feedback loop. Ideally, such configuration represents a 2nd order system with infinite quality factor, enabling harmonic oscillation. g mVz CDTA n All the PSpice simulations in this paper were performed using a PSpice subcircuit based on the structure in Fig. 2. Here, 0.5 µ MIETEC real transistor model parameters are implemented for all transistors. Transistor aspect ratios are indicated in Table 1. I p − In Z Fig. 1: CDTA symbol indicating a possibility of gm control and loading the z terminal. x+ CDTA 1 p z x- C1 x+ CDTA 2 n z xp n I out 1 I out 2 C2 Fig. 3: Proposed QO circuit employing CDTA elements, without a gain control circuitry. Fig. 2: CMOS-based CDTA: IB1=IB2=85 µA, IB3=(20-700)µA for controlling gm within (200-635) µS, bandwidth=400MHz, V DD=-VSS=2.5V. Note that the structure in Fig. 3 represents a special case of two-CDTA KHN (Kerwin– Huelsman – Newcomb) filter, previously reported in [9,13], without negative feedback, control-ling the quality factor. CDTA elements in Fig. 3 seem to be employed uneconomically because the p-terminal of CDTA1 and the n-terminal of CDTA2 are not utilized. From this point of view, such 2 nd-order system could be employed by two OTAs. There are two reasons why to use CDTAs: 1 Current outputs of internal OTAs operate into lowimpedance input terminals of CDTAs, which increases the bandwidth of the operation, 2 Input terminals will be used by a circuitry for amplitude stabilization as well as for prospective external compensation of current offsets of active elements. In the first step, let us analyze the ideal linearized model of QO in Fig. 3, considering frequency independent internal transconductances gm1 and gm2 as the only parameters of CDTAs No. 1 and 2. Let us disconnect the feedback path from the output of CDTA2 to the n-terminal of CDTA1 and analyze the open loop gain AOL. The current gains of CDTA integrators are given by the ratios of transconductances and capacitor susceptances. That is why AOL becomes AOL = − g m1 g m 2 . sC1 sC 2 (2) Setting AOL=1 shows the characteristic equation of the harmonic oscillator with zero damping factor: s +ω = 0, 2 2 0 (3) where ω0 = g m1 g m 2 . C1C 2 (4) Because the harmonic signal Iout2 represents the integral of signal Iout1, there exists a 90° phase shift between them. For identical time constants of both integrators, i.e. for g m1 g m 2 (5) = = ω0 , C1 C2 the ideal model in Fig. 3 will generate two harmonic waveforms in a quadrature, of equal magnitudes. For practical design, we choose identical integrator sections, i.e. (6) g m1 = g m 2 = g m , C1 = C 2 = C . Then ω0 = gm . C (7) For control current IB3=600 µA, the transconductance gm is 625µS. For C1=C2=10pF, the theoretical oscillation frequency (7) is 9.947 MHz. Note that this frequency is valid for the small-signal linear model, i.e. for the start-up process. In the steadystate, when the amplitude is large, the transconductance is decreased due to the nonlinearity of the shape Ix = f(Vz), causing harmonic distortion as well as decreasing the oscillation frequency according to Eq. (7). The start-up process and steady-state operation will be analyzed in the following Chapter with the above values of IB3, gm and C. 4 QO without amplitude stabilization For the oscillator without the circuitry for stabilizing the amplitude, the start-up behavior will depend on two real parameters of the CDTA: internal resistance Rz of the z-terminal, and the frequency dependence of gm, which is determined by the cutoff frequency ωm0. Serial resistances of p- and n- input terminals have no effect due to their current excitations from the CDTA x+ terminals. The steady-state behavior will be determined by the nonlinear characteristics of CDTAs, namely by the trade-off between Ix and Vz. For the CDTA structure in Fig. 2 and IB3=600 µA, PSpice simulation leads to the following small-signal parameters: gm = 625µS, Rz = 347kΩ, (8) fm0 = 787MHz ⇒ ωm0 = 6.945GigaRads/s. Considering identical CDTAs in both integrators with internal resistances Rz and transconductances gm, the current gain AI of one integrator becomes AI = gm , sC + G z (9) where Gz = 1/Rz. As shown in [5], in order to analyze the oscillator stability, the one-pole model of OTA with the low-frequency value gm0 of the transconductance and with the cutoff frequency ωm0 can be approximated by the formula s g m ≈ g m 0 1 − ω m0 . (10) By substitution from Eqs. (6), (9) and (10), the open loop gain (2) becomes 2 g (1 − s / ω m 0 ) AOL = − m 0 . sC + G z (11) 200u 100u After a small arrangement, the equality AOL=1 leads to the following characteristic equation: s 2 + 2d x s + ω 02x = 0 , (12) with the following damping factor dx and oscillation frequency ω0x: CG z − dx = C + 2 ω0x = g m2 0 + G zě g2 C 2 + m2 0 ω m0 = ω0 g m2 0 ω m0 , g m2 0 FO: 0.6u 1.2u 1.8u 1 + [ g m 0 /(ω m 0 C )] 2 . (14) 5 QO with amplitude stabilization In order to adjust and stabilize the amplitudes of generated waveforms and decrease the harmonic distortion, as well as to move the frequency towards the designed value (7), three types of methods for stabilizing the amplitude have been proposed. 1 Connecting a nonlinear resistor RN (see Fig. 5 a) as an amplitude limiter in parallel to C1. (15) IN IN 2 3.0u Fig. 4: PSpice simulation of starting up the oscillator without circuitry for stabilizing the amplitude. 1 + (G z / g m 0 ) 2 1 + (G z / g m 0 ) 2 2.4u T (Secs) (13) ω m2 0 1 + (ω 0 / ω m 0 ) -200u 0.0u ω0 G = z , ω m0 g m0 ω0x = ω0 -100u ix1 (A) Ix2 (A) Let us assume that the oscillator operates in the frequency range below the cutoff frequency ωm0. Then the original oscillation frequency (7) is given by the ratio of gm0 to C. The condition of oscillation dx = 0 and the frequency of oscillation can be rewritten as follows: CO: 0u ≈ ω0 . G (16) The squared terms in Eq. (16) are much less than 1. That is why the oscillation frequency is practically not affected by the finite resistance of z-terminal and the finite cutoff frequency of internal OTA. Note that equality (15) means a steady amplitude of oscillation within the linear regime, whereas the smaller left side term than the right-side term results in a growing amplitude. Numerical values (8) and an oscillation frequency of 9.947MHz give ω0 G ω =& 0.0126 , z =& 0.00461 , 0 x =& 0.99993 . ω0 ω m0 g m0 The first term is smaller than the second one, which indicates soft-start oscillations. The amplitude is growing, effective gm is decreasing due to the nonlinear curve Ix versus Vz, and the second term is continuously decreasing. In the steady-state, Eq. (15) is dynamically fulfilled. The results of PSpice simulation in Fig. 4 confirm the above. In the steady state, the oscillating frequency is about 6.5MHz with large THD=23%. C1 -E VN RN (a) G E VN (b) Fig. 5: (a) Nonlinear resistor as an amplitude limiter, (b) its I/V characteristic [7]. According to the I/V characteristic in Fig. 5 (b), if the amplitude of a voltage across C1 does not exceed the value E, or alternatively, if the output current of the CDTA does not exceed the value of Egm, this resistance does not have any effect. The peaks above this value will cause an additional current IN which will cause conductance losses. Two examples of circuit implementation are proposed in [7]. Computer simulations indicated some imperfections of this method of controlling the amplitude for the oscillator in Fig. 3, consisting in an unacceptable nonlinear distortion of output waveforms. For the current-mode oscillator, it is more advantageous to use current limiters. 2 Using a current-to-current feedback limiter The THD of generated waveforms is 3.48% for Ix1 and 1.64% for Ix2. The repeating frequency is 9.59MHz. Its decrease below the theoretical value 9.947MHz is due to the decrease of the effective value of transconductance. IFB x+ CDTA 1 p z x- n b -IE IX IE b IX (b) C1 IX IFB (a) R IFB (c) Fig. 6: (a) Current-to-current limiter in the feedback loop, (b) its I/I characteristic, c) an example of simple implementation. Fig. 6 (a) demonstrates a more effective method for amplitude stabilization. In contrast to the above method, this nonlinear negative feedback does not create a DC path from the z-terminal to the ground, which is the main source of nonlinear distortion in the case of the method from Fig. 5 (a). A simple implementation of current-to-current limiter is in Fig. 6 (c). For a relatively low current Ix, when the voltage drop on the resistance R is below the threshold voltage VTH≈0.6V, the diodes are in the OFF state and IFB = 0. If the absolute value of Ix is increased above the value of IE=VTH/R, the diode is switched to the ON state and IFB is increased or decreased according to the slope b=gDR/(1+gDR). Here gD is the small-signal conductance of the diode. A more sophisticated current limiter can be implemented by means of a current comparator [15]. The PSpice simulation in Fig. 7 has been accomplished for limiter parameters IE = 50µA and b = 1. 80u As shown in Fig. 7, the waveforms generated exhibit a current offset which is caused by the offset and other DC imperfections of CDTA structure. These imperfections can be compensated by combining the auxiliary DC current sources Icp, Icn, I1+, and I1- in Fig. 8. It is obvious that the sources I1+ and I1- compensate the individual offsets of oscillator output signals without affecting the internal state of oscillator. As shown in [13], the transfer functions from Icp to Iout1 and from Icn to Iout2 are of bandpass character whereas the transfer functions from Icp to Iout2 and from Icn to Iout1 represent lowpass filters with unity DC gains. That is why DC current Icp has no effect on the output current terminals of CDTA1 but it is reflected as an additional offset current at the output terminals of CDTA2 (as a positive offset value at x+ and a negative value at x-). Similarly, Icn can independently control the offset at the output terminals of CDTA1. x+ CDTA 1 p z x- Icp x+ CDTA 2 n z xp n I out 1 I1- Icn C1 I out 2 I2- C2 I out 1 Fig. 8: The principle of independent offset control via auxiliary current sources. 60u 40u 3 Using a linear inertial feedback control 20u 0u An auxiliary circuitry, represented in Fig. 9 by a controlled current source I FB = ßIX, stabilizes the amplitude of generating waveform and dynamically fulfills the CO by local feedback from the output to positive input of CDTA1. -20u -40u -60u -80u 0n ix1 (A) 120n ix2 (A) 240n 360n 480n 600n T (Secs) Fig. 7: PSpice simulation of steady-state oscillation with amplitude stabilization by means of current-tocurrent limiter. For ideal model of the oscillator, the condition of oscillation is independent on the frequency of oscillation (4): CO: β = 0. (17) x+ CDTA 1 p z x- n β IX IX IX β C1 I amplitude amplitude p x+ I adjust z p x+ A x- IFB IX B n x- z n Fig. 9: Linear current-controlled current source in the feedback loop for inertia-type amplitude control; β depends on the amplitude of generated waveforms. Fig. 10: Proposed circuit for automatic gain control. The current gain ß is controlled according to the formula (18) β = I amplitude (t ) / I adjust − 1 , where Iamplitude is instantaneous amplitude of generated waveforms, sensed by rectifying, Four-Phase MAX [5] or other method, and Iadjust is adjustable value of the required amplitude. In the initial state, the value of ß = -1 provides flat soft-start of the oscillation. In steadystate operation, amplitude is dynamically perturbed around the nominal value Iadjust, causing changes of ß around zero which subsequently stabilize the amplitude. For well-matched control laws gm(Ig) of both the CDTAs, ß = 0 when Iamplitude = Iadjust. For the simulation, Iadjust has been set to 50µA. Amplitude sensing was simulated by a block which performed squared root of the sum of powers of quadrature output currents, followed by a simple RC filter. PSpice simulation led to the similar results as in Fig. 7. The THD of generated waveforms was about 2.5%. It can be decreased by eliminating the offset of output waveforms, because it influences the algorithm of amplitude sensing. Finally, the THD has been minimized below 1%. It can be further decreased by improving the loop gain stabilization circuitry. For the nonideal case, the simplified CO and FO are as follows: 4 Conclusions CO: β= 2ω 0 ω m0 − FO: ω0x = ω0 Gz C ≈ 0, 1 − ( 2 − β )G z / g m 0 ≈ ω0 . 1 + (2 − β )ω 0 / ω m 0 (19) (20) For concrete values of Gz, gm0 and ω0, we get practically values, corresponding to the ideal case. The proposed circuit solution of linear currentcontrolled current source from Fig. 9 is shown in Fig. 10. It consists of two CDTAs. The element “B” utilizes internal OTA for simulating the gmB conductance at the z-terminal. The CDTA “A” is connected as current amplifier which current gain is given by a ratio of gmA/gmB. The current source connected at the x+ output of CDTA “A” simulates subtraction of this current from the output current of the current amplifier. This source can be implemented by a current mirror or by simple applying the x-terminal of multiple-output CDTA [11]. The current gain ß is then given by the relation β = g mA / g mB − 1 . (21) The quadrature oscillator circuit proposed has the following features: (i) use of two CDTAs for providing direct current-to-current integration; (ii) use of only two grounded capacitors; (iii) dynamical fulfilling the CO by simple auxiliary circuitry; (iv) electronic gmcontrol of FO, which does not affect the CO. All these features have not been achieved simultaneously in any of the previous QOs published in [1 – 7] including those cited therein. As follows from (i) and (ii), the new QO also represents an economical circuit solution because its core consists of only two active elements and two grounded capacitors. One can choose a circuitry for stabilizing the amplitude from simple nonlinear limiter to complicated systems of loop gain control. Acknowledgments This work has been supported by the Grant Agency of the Czech Republic under grants No. 102/04/0442 and 102/05/0277, and by the research programmes of Brno University of Technology and University of Defence Brno. References [1] Salama, K. N., and Soliman, A. M. ‘Novel oscillators using the operational transresistance amplifier’, Microelectronics Journal, 2000, 31, (1), pp. 39–47. [2] Horng, J.-W. ‘Current differencing buffered amplifiers based single resistance controlled quadrature oscillator employing grounded capacitors’, IEICE Trans. Fundamental (Japan), 2002, E85-A, (2), pp.1416- 1419. [3] Maheshwari, S. ‘New voltage and current mode APS using current controlled conveyor’, International Journal of Electronics, 2004, 91, (12), pp.735-743. [4] Salama, K. N., and Soliman, A. M. ‘Novel MOSC quadrature oscillator Using the differential current voltage conveyor’. Proc. Midwest Symposium on Circuits and Systems (MWSCAS), 1999, Vol. 1, pp. 279 -282. [5] Linares-Barranco, B., Rodríguez-Vánquez, A., Sánchez-Sinencio, E., Serrano-Gotarredona, T., Ramos-Martos, J., Ceballos-Cáceres, J., Mora, J.M., and Linares-Barranco, A. ‘A precise 90 ° quadrature OTA-C oscillator tunable in the 50130-MHz range‘, IEEE Trans. On CAS-I, 2004, 51 (4), pp. 649-663. [6] Keskin, A. Ü., and Biolek, D. ‘Current mode quadrature oscillator using current differencing transconductance amplifiers (CDTA)’, IEE Proceedings - Circuits, Devices and Systems, 2006, Vol. 153, No. 3, pp. 214 - 218. [7] Linares-Barranco, B., Rodríguez-Vánquez, A., Sánchez-Sinencio, E., Huertaz, J.L. ‘10MHz CMOS OTA-C controlled quadrature oscillator’, Electron. Lett., 1989, 25, pp. 765-767. [8] Biolek, D. ‘CDTA – Building Block for CurrentMode Analog Signal Processing’. Proc. European Conference on Circuit Theory and Design (ECCTD), 2003, Vol. III , pp. 397-400. [9] Keskin, A.U., Biolek, D., Hancioglu, E., Biolková, V. ‘Current-mode KHN filter employing current differencing transconductance amplifiers’. AEU International Journal of Electronics and Communications, 2006, Vol. 60, No. 6, pp. 443 446. [10] Uygur, A., and Kuntman, H. ‘Novel current-mode biquad using a current differencing transconductance amplifier’. Proceedings of Applied Electronics (AEE), 2005, Pilsen, Czech Republic, pp. 349-352. [11] Uygur, A., Kuntman, H., and Zeki, A. ‘Multi-input multi-output CDTA-based KHN filter’, Proc. Of ELECO 2005: The 4th Int. Conference on Electrical and Electronics, Bursa, Turkey, 2005, pp. 46-50. [12] Tanjaroen, W, Dumawipata, T., Unhavanich, S., Tangsrirat, W., Surakampontorn, W. ‘Design of current differencing transconductance amplifier and its application to current-mode KHN biquad filter’, Proceedings of the ECTI-CON 2006, Thailand, May 2006. [13] Tangsrirat, W., Dumawipata, T., and Surakampontorn, W. ‘Multiple-input single-output current-mode multifunction filter using current differencing transconductance amplifiers’, AEU International Journal of Electronics and Communications, accepted for publication, 2006. [14] Jaikla, W., Siripruchyanun, M. ‘Current Controlled Current Differencing Transconductance Amplifier (CCCDTA): A New Building Block and Its Applications’, Proceedings of the ECTI-CON 2006, Thailand, May 2006, pp. 348-351. [15] Biolek, D., Biolková, V. ‘Current-Mode CDTABased Comparators’. In the 13th Electronic Devices and Systems 2006 IMAPS CS/SK International Conference, EDS2006, pp. 6-10, September 14-15, 2006.