CURRENT-MODE FOUR-PHASE QUADRATURE OSCILLATOR

CURRENT-MODE FOUR-PHASE QUADRATURE OSCILLATOR YI LI 1,, CHUNHUA WANG 1, SHIQIANG CHEN 3 Key words: Current differencing transconductance amplifier (CDTA), Current mode, Quadrature oscillator. This paper presents a current-mode four-phase third-order quadrature oscillator (QO) using current differencing transconductance amplifiers (CDTA). The proposed thirdorder QO consists of three CDTAs and three grounded capacitors, and it could generate four quadrature current outputs. The oscillation condition and oscillation frequency could be electronically and independently adjusted. Moreover, the proposed third-order QO has low active and passive sensitivities. Cadence IC Design Tools post-layout simulation and experimental results are included to confirm all the theory. 1. INTRODUCTION As the current-mode circuits have the advantages of low power consumption, inherently wide bandwidth and larger dynamic range, they have become a useful method in analog signal processing circuit design [1]. The current differencing transconductance amplifier (CDTA) is a recently introduced current mode building block by D. Biolek in 003 []. It is a really current-mode element whose input and output are current form, and it is widely used in designing active filters [3 8], current limiters [9], oscillators [10, 11] and many other analog signal processing circuits. Oscillator is an important basic building block in electrical and electronic engineering applications. For example, it can be found in communication systems to be a carrier in a modulator, instrumentation and measurement systems to generate a signal employed in sensor application, and etc. Among the several kinds of oscillators, the quadrature oscillator is widely used because it can realize two or four identical frequency sinusoidal signals with 90 phase difference, for example, in telecommunications for quadrature mixers and single-sideband modulators [1] or for measurement purposes in vector generator or selective voltmeters [13]. Especially, 1 College of Computer Science and Electronic Engineering, Hunan University, Changsha, P.R.China, 41008, E-mail: 15308406988@189.cn, wch17164@hnu.edu.cn Hunan Post & Telecommunication Planning and design Institute Ltd. 3 College of Computer Science, Sichuan University, Chengdu, P.R.China, E-mail: chensq- 8808@gmail.com Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 60, 3, p. 93 301, Bucarest, 015

94 Yi Li, Chunhua Wang, Shiqiang Chen the four-phases quadrature oscillators are suitable for the sub-harmonic mixer to reduce the noise and inter-modulation distortion [14, 15]; and the multi-phases oscillators can be used in sub-harmonically pumped frequency conversion circuits [16]. The CDTA based quadrature oscillators are reported in [17 4]. However, the works in [17 4] can not provide electronically controlled CO and FO, which can not be used as variable frequency oscillator; the works in [17, 18, ] suffer from floating capacitors, and the work in [17 0, 3, 4] use resistors, and they are not suitable for monolithic integration; the BJT technology is used in [4], and it is not compatible with the CMOS digital integrated circuit to realize monolithically integration. In this paper, a new CDTA-based current-mode four-phase QO with three CDTAs and two grounded capacitors is presented. The attractive advantage of the proposed QO is the condition of oscillation (CO) and frequency of oscillation (FO) of the quadrature oscillator can be adjusted electronically and independently by a bias voltage, and it is suitable for variable frequency oscillator (VFO). Moreover, the proposed QO is completely resistor-less, and it can provide four quadrature outputs at high impedance nodes. The performance of the proposed QO is demonstrated by Cadence IC Design Tools post-layout simulation results.. CIRCUIT DESCRIPTION.1. CURRENT DIFFERENCING TRANSCONDUCTANCE AMPLIFIERS The CDTA circuit representation and an equivalent circuit are shown in Fig.1. Equation (1) presents the terminal relations of the CDTA. Fig. 1 Symbol and equivalent circuit of current differencing transconductance amplifier. V p = Vn = 0 iz = i p in ix ± = ± gmv z = g m Z i z z, (1)

3 Current-mode four-phase quadrature oscillator 95 where g m is the transconductance gain of the CDTA, which could be controlled electronically and independently through an auxiliary port current I b, and V z is the voltage at the terminal Z. The CDTA provides output current i x in both directions, but they are equal in magnitude. The CMOS implementation of CDTA is provided in Fig.. The circuit is comprised of a current differencer and an operational transconductance amplifier (OTA). The current differencer consists of transistors M 1 M 15. The voltage buffers provide low-input impedance and also keep the input terminals at virtual grounded. Transistors M 16 M 7 form an OTA, which is composed of transconductance circuit and current mirrors circuit. Fig. The CDTA in this work... THE PROPOSED CURRENT MODE QUADRATURE OSCILLATOR The proposed four-phase third-order quadrature oscillator is shown in Fig.3, which employs three CDTAs and three grounded capacitors. Fig. 3 The proposed current-mode quadrature oscillator. Analysing the circuit in Fig.3 with equation (1), it is easy to get the characteristic equation of the third-order QO: 3 s C C C s g C C + sg g C + g g g = 0, () 1 3 + 1 3 m1 3 m1 m3

96 Yi Li, Chunhua Wang, Shiqiang Chen 4 where g m1, g and g m3 stand for the transconductance of the CDTA 1, CDTA and CDTA 3, respectively. From equation (), we can get the CO and FO of the QO: gm C3 = gm3c, (3) g g m1 ω 0 =. (4) C1C From equations (3) and (4), it is clear that the FO can be controlled by g m1, and the CO can be independently controlled by g m3, the CO and FO of the oscillator can be electronically and independently controlled. From Fig.3, we can know the current transfer function between i o1 and i o should be: () s () s ( jω) ( jω) io g i g. (5) i 1 o1 j90 = = = e o sc io sc From equation (5), it is clear that the phase difference between i o1 and i o is 90 o, and the two currents are quadrature. Because the CDTA can provide the other two inverted output currents i o3 and i o4, and the relations of the four output currents is: io1 = io3. (6) io = io4 From equations (5, 6), it is clear that the proposed third-order QO could provide four quadrature outputs. 3. NON-IDEAL ANALYSIS Taking the tracking errors of the CDTA into account, the port relations of the non-ideal CDTA can be rewritten as: vp = vn = 0 iz = αpip α nin, ix ± = ± βgmvz (7) where α p =1 ε p denotes the current tracking error from terminal p to z, α n =1 ε n denotes the current tracking error from terminal n to z, β is transconductance inaccuracy factor from the z to x terminals of the CDTA, and γ is transconductance inaccuracy factor from the z to x terminals of the CDTA, respectively. The CO and FO of the proposed QO get modified and are given as:

5 Current-mode four-phase quadrature oscillator 97 α, (8) nγ gc3 = αn3gm3c αn1α pβ1γ gm1g ω o =, (9) C C where α p1, α n1 are the tracking errors of CDTA 1 ; α p, α n are the tracking errors of CDTA, β 1 is transconductance inaccuracy factor of CDTA 1. It can be seen from equations (8, 9) that if the tracking errors of CDTA 1 and CDTA are equal, the CO of the proposed QO will not be affected; however, the FO of the QO will deviate from the ideal value, because of the tracking errors. In this case, the deviation of the FO can be compensated by trimming the transconductance g m3. From equation (10), the active and passive sensitivities of ω o are low, and they could be expressed as: 1 S S S ωo α n1,α p,β 1,γ,g m1,g ωo C1, C 1 = 1 = ωo α n,α n3,α p1,α p3,β,β 3,γ 1,γ 3,g m3, C3. (10) = 0 4. SIMULATION RESULTS The proposed third-order QO is verified using Cadence IC Design Tools Spectre simulator with standard Charted 0.18 μm CMOS technology. The chip layout is designed as symmetrically as possible to minimize the mismatch in the signal paths. Figure 4a is the simulated V o1, V o, V o3 and V o4 during initial state with 500 Ω load resistors, and it is clear that the starting time of the proposed QO is about 0.5 μs; Fig. 4b is the simulated quadrature outputs V o1, V o, V o3 and V o4 from 0.35 μs to 3.55 μs with 500 Ω load resistors. Figure 5 is the harmonic balance post-layout simulation result of V o1. From Fig. 5, we can know that the post-layout simulated frequency of the third-order QO is about 74.3 MHz, and the output power of V o1 is about 9.46 dbm, the output power of other harmonic signals are relatively small. Figure 6 is the phase noise simulation of the quadrature oscillator. Figure 6 is the phase noise of the QO. The phase noise of the QO at 1 MHz offset is 84.9 dbc/hz while the carrier is 74.3 MHz.

98 Yi Li, Chunhua Wang, Shiqiang Chen 6 (a) Fig. 4 The simulated V o1, V o, V o3 and V o4 : a) during initial state; b) from 3.5 μs to 3.55 μs. (b) Fig. 5 The harmonic balance simulation of V o1. Fig. 6 The phase noise of the quadrature oscillator. Fig. 7 The output frequency versus the bias voltage of CDTA 3.

7 Current-mode four-phase quadrature oscillator 99 Fig. 8 The layout of the proposed QO (1. 1.mm ). Because the proposed QO has the attractive advantage of independently adjusting the FO by the transconductance of CDTA 3 without disturbing the CO, the output frequency versus the bias voltage of CDTA 3 is presented in Fig.7. From the markers M 0 and M 1 in Fig.7, it is clear that the output frequency tuning range of the QO is about 63.7MHz when the control voltage changing from 1.08 V to 0.1 V, which means that the proposed QO can be used as variable frequency oscillator (VFO). The layout of the proposed QO is presented in Fig. 8. The QO takes a compact chip area of 1.44 mm including the testing pads. 5. EXPERIMENTAL EVIDENCE To further verifying the third-order QO in Fig. 3, the CDTA is realized using commercially available ICs. Fig. 9 is the block diagram of realizing the CDTA using AD844 and CA3080. The current differencing unit is realized using the two AD844 ICs, and the two CA3080 ICs realize the transconductance section of the CDTA. Fig. 9 Possible implementation of CDTA.

300 Yi Li, Chunhua Wang, Shiqiang Chen 8 Fig. 10 Experimental results of the four quadrature outputs. Figure 10 is the experimental results of the four quadrature output waveforms. From Fig.10, it is clear that the proposed QO could provide four different quadrature output signals. The left side picture of Fig. 10 are the 0 and 90 signals, the right side picture of Fig. 10 are the 180 and 70 signals. From the simulation results in Fig. 4b and the experimental results in Fig. 10, we can know that, the proposed QO could provide four quadrature output signals. 6. CONCLUSIONS A current-mode four-phase third-order quadrature oscillator using CDTA is presented in this paper. The Cadence IC Design Tools post-layout simulation results reveal that the frequency tuning range of the third-order QO is 41.71 MHz, and it is could be used as VFO. The capacitors used in the QO are all grounded, and the proposed QO is suitable for monolithic integration. Moreover, the proposed thirdorder QO only takes a compact chip area of 1.44mm including the testing pads. ACKNOWLEDGMENTS We would like to thank the editors and anonymous reviewers for their valuable comments which helped in improving this manuscript, and also thank the authors whose works we have cited in our paper. This work is supported by the National Natural Science Foundation of China (No. 617400), the natural science foundation of Hunan Province(NO.14JJ706) and the Open Fund Project of Key Laboratory in Hunan Universities (No.13K015). Received on May 0, 014 REFERENCES 1. C. Toumazou, F.J. Lidjey, D. Haigh, Analog IC design: The currentmode approach, UK, Peter Peregrinus Press, 1990, pp.195 07.. D. Biolek, CDTA Building block for current-mode analog signal processing, Proc. ECCTD 03, Krakow, Poland, 003, pp. 397 400. 3. T. Dumawipata, W. Tangsrirat, W. Surakampontorn, Current-mode Universal Filter with Four Inputs and One Output using CDTAs, IEEE Asia Pacific Conference on Circuits and Systems, Singapore, 006, pp. 89 895.

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