Mixed-Mode Third-Order Quadrature Oscillator Based on Single MCCFTA

This paper presents a new mixed-mode thirdorder quadrature oscillator based on new modified current-controlled current follower transconductance amplifier (MCCFTA). The proposed circuit employs one MCCFTA as active element and three grounded capacitors as passive components which is highly suitable for integrated circuit implementation. The condition and frequency of oscillations can be controlled orthogonally and electronically by adjusting the bias currents of the active device. The circuit provides four quadrature current outputs and two quadrature voltage outputs into one single topology, which can be classified as mixed-mode oscillator. In addition, four quadrature current output terminals possess high-impedance level which can be directly connected to the next stage without additional buffer circuits. The performance of the proposed structure has been verified through PSPICE simulators using 0.25 μm CMOS process from TSMC and experimental results are also investigated.


Introduction
At present, current-mode technique is very interesting approach due to the fact that it is easy as operating of arithmetic such as addition and subtraction signals, multiplication and division signals by a constant signal and potential to operate at lower supply voltage compared their voltage-mode circuits [1].Regarding to a current-mode building block, the current differencing transconductance amplifier (CDTA) [2] is a really current-mode active building block, due to its input and output signals are current forms.The structure of this device is consisted of a unity-gain current source controlled by the difference of two inputs and an output transconductance amplifier providing electronic tuning capability through its transconductance gain (g m ).Therefore, CDTA is highly suitable for realizing current-mode analog signal processing and CDTA-based circuits can also reduce number of passive resistors.
A quadrature oscillator (QO) usually provides sinusoids having a phase difference of 90° that is useful in communication and measurement systems such as quadrature mixers and single sideband generators for communication system [3], vector generators and selective voltmeters for measurements system [4].Several QOs using CDTAs as active element have been proposed in the literature; see, for example [5][6][7][8][9][10][11][12].However, some structures do not exploit the full capability of the CDTA where typically one of two input terminals of the CDTA is floated and not used [8][9][10][11][12].Unfortunately, floating terminal may increase the area of chip when these CDTA-based QOs build as IC's forms and also may cause some noise injection into the monolithic circuit.
Recently, a new concept of active building block with one current input and two kinds of current outputs, the socalled "current follower transconductance amplifier (CFTA)", has been introduced [13].This device is modified from an original CDTA by removing the negative terminal.When subtraction current circuit as input stage is absent, the structure of CFTA is simple.Compared with CDTA, the number of transistor used for CFTA is lesser.Therefore, several CFTA-based analog signal processing circuits are reported [14][15][16][17][18][19].The CFTA has been already used to realize QOs [20][21][22][23][24][25][26].They, in conjunction, exhibit high potential for bring drown the number of components.However, all structures are second-order QOs.This work focuses on the third-order QOs, which enjoys the requirement of QOs such as orthogonal adjustability and electronic tunability of the condition of oscillation (CO) and frequency of oscillation (FO), and uses grounded capacitors and minimum number of active elements.Because of highorder network the circuit provides better frequency response and quality, compared with lower-order network [27].This mention has been expressed in [28] by mathematical formulation, especially, to confirm phase noise reduction.Compared with a second-order oscillator, the third-order oscillator (three-stage oscillator) also offers lower phase noise [29].As a result, a number of third-order QOs based on different active building blocks have been proposed .The early system using operational transconductance amplifier (OTA) [30] enjoys electronic tuning capability, but its CO and FO are not decoupled and difficult to control.The QOs using active building blocks such as operational amplifier [31], second-generation current conveyor (CCII) [32][33][34], differential voltage current conveyor (DVCC) [35], operational transresistance amplifier (OTRA) [36], [37], [50], offer orthogonal control of CO and FO, but these structures lack the electronic tuning capability.A number of electronic-controlled third-order QOs have been reported using active building blocks such as current-controlled CCII (CCCII) [38], [39], current difference transconductance amplifier (CDTA) [40], [41], current-controlled CDTA (CCDTA) [42], current-controlled current conveyor transconductance amplifier (CCCTA) [43], [44], OTRA and MOS-C [45], DDCC and VDTA [46], [51], [52], differential voltage current conveyor transconductance amplifier (DVCCTA) [47].They exhibit high potential for enjoying up the electronic tunability.However, they require an excessive number of active components and the structures are not compact.The thirdorder oscillator QO based on log-domain technique is proposed in [48].However, this structure is suitable only in bipolar technology.The structure in [49] proposed thirdorder QO using a single current-controlled current conveyor transconductance amplifier (CCCCTA), but the circuit does not exploit the full capability of the CCTA when y-terminal of CCTA is not used and attached to ground.Until now, there is no CCCFTA-third-order QO available in open literature.
Therefore, this paper presents a new mixed-mode third-order QO employing a modified current-controlled current follower transconductance amplifier (MCCFTA) and three grounded capacitors.The concept of MCCFTA is similar to conventional CFTA [13], except f-terminal provides parasitic resistance R f that can be controlled by the bias current [53].Identical z-copy terminal can be obtained using current-mirrors [13] and connecting transconductance amplifiers in parallels connection are available [54], [55].Thus, MCCFCTA is an active building block that provides the possibility for utilizing its resistance simulating element and its transconductance gains that can be electronically controlled through adjusting the bias currents.Therefore we have input parasitic resistance and transconductance gains (TAs) into a single MCCFTA for realizing a third-order QO with orthogonal control of the CO and FO.The proposed structure provides four quadrature current outputs and two quadrature voltage outputs.PSPICE simulation results are given to confirm the performance of the proposed structure.The comparison between the proposed third-order QO and previously third-order QOs is expressed as Tab. 1.

Proposed Circuit
The circuit symbol and the equivalent circuit of the MCCFTA are shown in Fig. 1 and CMOS implementation of MCCFTA is shown Fig. 2. The ideal port relations of Fig. 1 can be expressed by where R f is the parasitic resistance at f-terminal and g m1 and g m2 are two TAs.The z 1 -, x 1 -terminals and g m1 are existing terminals and TA of conventional CCFTA [50].The z 2and z c -terminals are the z-copy terminals [13] of CCFTA that can be obtained by adding current mirrors in conventional CCFTA.By cascading g m2 in parallel connection, x 2terminal in CCFTA can be obtained and hence the name MCCFTA.It should be noted that connecting n TAs in parallel connection of MCCFTA is also possible.From the CMOS implementation of MCCFTA in Fig. 2, assuming that transistors M 1 to M 4 are matched and operated in saturation regions, the parasitic resistance at f-terminal (R f ) can be given as where μ is the carrier mobility, C ox is the gate oxide capacitance per unit area, W and L are the channel width and length, respectively, of MOS transistor.From (2) and Fig. 2, the parasitic resistance R f can be controlled by adjusting the bias current I b1 .This property makes it different from a conventional CFTA [13].
The third-order oscillator can be realized from the third-order polynomial equation as Letting N(s) = 0 and s = jω, (5) becomes the third-order oscillator characteristic as Considering the coefficient of real and imaginary parts, we have: From ( 7) and ( 8), the CO and FO can be given respectively [30] by The proposed mixed-mode third-order QO is shown in Fig. 3.It is continuously developed from the circuit proposed in [56] by expanding text, simulation results and adding experimental results.The circuit is consisted of only one MCCFTA and three grounded capacitors.The use of grounded capacitors makes the proposed circuit ideal for IC implementation [57].The characteristic equation of proposed circuit can be expressed using Fig. 3(b).To easy following, the proposed QO can be shown as block diagram in Fig. 3(c).Considering currents I A and I C , current transfer function between I C and I A can be given by In addition, considering currents I B and I A , current transfer function can be given by Letting I B /I A = 1 (nodes A and B are closed), the characteristic equation of proposed QO in Fig. 3 can be expressed as Compared with (5), the coefficients can be expressed as: According to ( 9) and ( 10), the CO and FO are obtained, respectively, by It is evident from ( 14) and ( 15) that the CO can be controlled using g m2 by keeping C 1 = C 3 and g m1 constant and the FO can be controlled by R f by keeping and g m1 constant.Therefore, the CO and FO can be orthogonally controlled.From Fig. 3, the relationship between I 2 and I 1 can be expressed by  (16) while the relationship between voltages V 1 and V 2 can be expressed as where the phase difference is  = /2.This guarantees that the proposed QO provides the quadrature output currents I 1 and I 2 and quadrature output voltages V 1 and V 2 .Also the uses of multiple-output MCCFTA that provides inversion of the output currents, thus it leads to I 3 = -I 1 and Moreover, all current output terminals are at high impedance of MCCFTA, thus ensuring insensitive current outputs that require no additional current followers to be sensed.However, if quadrature output voltages V 1 and V 2 are used, loads cannot be connected directly, the buffer circuit is needed.This problem can be solved easily using voltage follower circuit.

Non-Ideal Analysis
To consider the non-ideal effect of a MCCFTA by taking the non-idealities of the MCCFTA into account, the relationship of the terminal voltages and currents can be rewritten as where  1 = 1 - i1 and  i1 ( i1 << 1) is the current tracking error from f-terminal to z 1 -terminal,  2 = 1 - i2 and  i2 ( i2 << 1) is the current tracking error from f-terminal to z 2 -terminal and  c = 1 - ic and  ic ( ic << 1) is the current tracking error from f-terminal to z c -terminal, R f is the parasitic resistances at f-terminal.At high-frequency operating, Taking into account the non-ideal MCCFTA characteristics, current transfer function between I B and I A can be rewritten as a a a a a a a (19) where The modified characteristic equation of Fig. 3 can be rewritten as a a a a a a a a a a a a a a a a a a a a .( 20) Letting, parasitic parameters R z , R c , R x are very high resistance values and C z , C c , C c are very low capacitance value, (20) can be approximated as In this case, the CO and FO are modified, respectively, as: The various passive sensitivities of ω o of the proposed QO can be obtained as Thus, the proposed QO has low active and passive sensitivities.

Simulation Results
To verify the theoretical prediction of the proposed third-order QO, the circuit in Fig. 3 was simulated using PSPICE simulators and the MCCFTA in Fig. 2 was used.The model parameters for nMOS and pMOS transistors are taken from 0.25 m CMOS process from TSMC.The power supply was given as 1 V. From Fig. 2, I b1 was initially designed for 100 A while I b2 and I b3 were initially designed for 150 A.Transistors around trans-linear loop (M 1 to M 4 ) were designed to obtain g m(nMOS) = g m(pMOS) and differential transistor pairs (M 5 -M 6 and M 7 -M 8 ) were designed to obtain g m(total) = (g m(M5) + g m(M6) )/2 or g m(total) = (g m(M7) + g m(M8) )/2.For 0.25 m CMOS process used in this case, (µ o C ox ) nMOS = 242.2A/V 2 and (µ o C ox ) pMOS = 51.8A/V 2 , V th0(nMOS) = 0.37 V and V th0(pMOS) = -0.49V were given.Therefore, the aspect ratios of MOS transistors for MCCFTA in Fig. 3 were W/L = 5 m/0.5 m for M 1 -M 2 , W/L = 15 m/0.5 m for M 3 -M 4 , W/L = 5 m/0.5 m for M 5 -M 8 , W/L = 5 m/0.5 m for all M n transistors and W/L = 15 m/0.5 m for all M p transistors.PSPICE simulations have verified that when I b1 was varied from 1 to 100 µA, achieved R f was in the range of 12 to 2.19 k as shown in Fig. 5 whereas I b2 and I b3 were varied from 5 to 150 µA, achieved g m1 and g m2 were in the range of 107 to 472 A/V as shown in Fig. 6.Both simulated R f -and g mvalue were compared with ( 2) and ( 3), respectively.Simulated performances of MCCFTA were summarized in Tab. 2.
The voltage outputs and current outputs were shown respectively in Figs.7 and 8, when Fig. 3 was designed with the following values: C 1 = C 2 = C 3 = 20 pF, I b1 = 20 A, I b2 = 80 A and I b3 = 75 A.The I b3 -value was varied for g m2 so as to satisfy the CO in (14).In this case, (R f ≈ 1/g m1 ), each current output and each voltage output were almost equal of magnitude.The magnitudes of the quadrature signals will not be equaled in case of R f was varied (R f  1/g m1 ) in (15).For applications requiring equal magnitude quadrature outputs, additional amplifying circuits were needed.From Fig. 7, the simulated THD of V 1 and V 2 were about 0.26 % and 0.17 %, respectively, the FO was 2.7 MHz. From Fig. 8, the simulated the FO was found to be 2.7 MHz, the results of the I 1 , I 2 , I 3 and I 4 total harmonic distortion (THD) analysis were obtained as 0.56 %, 0.37 %, 0.85 % and 0.38 %, respectively, and the power consumption was about 1.43 mW.This low THD was obtained for the output signals  66 A P-P , respectively.THD will be increased if output signal level was increased which can be obtained by increased CO.However, increasing CO may be increased nonlinear behavior of the system which is results in high THD output signal that should be avoided.
The electronic tuning of the oscillator was shown in Fig. 9.The result gives a variation of the FO from 1.1 to 3.25 MHz with I b1 in the range of 1 to 50 µA that was confirmed by (15).This FO was achieved without adjusting the CO.It shows that the simulated FO was consistent with the theoretical values.At I b1 = 50 µA, the error of FO between the simulated and theoretical values was 4.9 %.The bias current I b1 can be continuously varied high up to 100 µA, but the g m2 must be adjusted via I b3 to satisfy the CO.However, it was also found that there was a deviation between the theoretical and simulated values in large bias current value region over the value of 50 µA.From Fig. 9, output signal levels of V 1 , V 2 , I 1 , I 2 , I 3 , and I 4 versus f o have been obtained as shown in Fig. 10.It should be noted that the output signal level is not equal and constant when I b1 was varied.This problem can be solved by using automatic gain control (AGC) circuit.There are oscillators with AGC available in literature [58][59][60][61].These techniques use AGC circuit including into the loop of the system for controlling the amplitude of signal.Usually, AGC is suitable for applying to linear control of CO and FO oscillator, if nonlinear control of CO and FO such as this work (adjusting CO and FO in square-root domain), current squaring circuits [62], [63] are required to compensate the square-root form to obtain linear current control of CO and FO.Total harmonic distortion (THD) and phase error were shown in Figs 11 and 12, respectively.From Fig. 11, THD was increased when I b1 (R f ) was varied far from satisfying condition.

Experimental Results
The proposed oscillator was experimentally tested wherein the functionality of the MCCFTA was implemented using CFOA AD844 and OTA LM13600 as shown in Fig. 13.The supply voltage 10 V was used.The noninstrument of oscilloscope as measurable currents is available to the authors.However, for sake of experimental results, the current outputs, I 1 , I 2, I 3 and I 4 , can be obtained by connecting the external resistors.In this experiment, current outputs I 1 , I 2, I 3 and I 4 were connected to the resistors 50 k and voltage across these resistors will be measured.To obtain the experimental results, Tektronix MSO  were given as 1 k.The variable resistor was used to obtain the effect of variable g m and R f .
To control the output amplitude of signals to be constant, the amplitude-automatic gain control (AGC) circuit in Fig. 14 was used.This circuit was adopted from [61].From our pretest on the proposed circuit, it was found that V 1 (I 1 and I 3 ) was dependent on tuning of FO, thus V 1 will be used for the input of AGC circuit (V in(AGC) ).CFOA AD844 and R p2 were used to work as voltage-to-current converter (V-I converter).The current output I out(AGC) of AGC circuit will be supplied additionally to bias current I b3 for compensating CO.The active device and passive-value used in Fig. 14 were tabulated in Tab.Compared between the simulation and experimental results, setting of FO-value and working capacitor-value were different.Actually, this work focuses on the QO which should be implemented as IC form.Unfortunately, the obstruction for fabricating was the cost.Although, higher FO for experimental results was possible, but our test was investigated the circuit which builds on perfboard.Using printed circuit board and high quality active devices the operation band of the circuit [59][60][61] will be increased.Therefore, this experimental result was used only to confirm the workability of the proposed structure.

Conclusions
In this paper, a mixed-mode third-order QO based on new MCCFTA has been presented.The proposed circuit uses only one MCCFTA and three grounded capacitors.The use of grounded capacitors is ideally interesting from an integration point of view.The proposed structure provides four high output impedance current sources with 90 phase difference, thus these output terminals can be directly connected to the loads without additional follower circuits.In addition, voltage with 90° phase difference can be obtained without changing any topology.Also the CO and FO can be controlled orthogonally and electronically by adjusting the bias currents of MCCFTA.The active and passive sensitivities are no more than unity of magnitude.Simulation and experimental results, which confirm the theoretical analysis, are included.
Montree KUMNGERN received the B.S.Ind.Ed.degree from King Mongkut's University of Technology Thonburi (KMUTT), Bangkok, Thailand, in 1998, the M.Eng.and D.Eng.degrees from King Mongkut's Institute of Technology Ladkrabang (KMITL), Bangkok, Thailand, in 2002 and2006, respectively, all in major of electrical engineering.He is currently an Assistant Professor at Faculty of Engineering, KMITL.His research interests include analog electronics, analog and digital VLSI circuits and nonlinear electronic circuits.He is author or co-author of more than 150 publications in journals and proceedings of international conferences.He is an author or co-author of more than 100 publications in journals and proceedings of international conferences.He is an Associate Editor for Circuits, Systems and Signal Processing and International Journal of Electronics.He is a member of the Editorial Board of IET Circuits, Devices & Systems and Microelectronics Journal.He holds four Czech national patents.

Fig. 4 .
Fig. 4. Non-ideal of MCCFTA at high operating frequency.non-ideal model of MCCFTA can be shown in Fig. 4. R z1 , R z2 and R zc are respectively the high parasitic resistances at z 1 -, z 2 -and z c -terminals, R x1 and R x2 are respectively the high parasitic resistances at x 1 -and x 2 -terminals, C z1 , C z2 and C zc are respectively the low parasitic capacitances at z 1 -, z 2 -and z c -terminals and C x1 and C x2 are respectively the low parasitic capacitances at x 1 -and x 2 -terminals.

3 .
The quadrature sinusoidal voltage and current output waveforms with resistor R f = 500 , bias currents I b2 = 50 A (g m2 = 1 mA/V) and I b3 = 61.8A were shown in Fig.15, (a) and (b), respectively.It should be noted that the quadrature sinusoidal signal was almost equal of amplitude.The FO was found as 53 kHz.From Fig.15, the THDs for V 1 , V 2 , I 1 , I 2 , I 3 and I 4 were about 1.2, 0.9, 1.2, 1.1, 1.3 and 1.1 %, respectively.The quadrature relationship was further verified through the X-Y plots of the two output forms in Fig.15as shown in Fig.16, (a) and (b), respectively.

Figure 17 shows
Figure 17 shows the experimental results of the FO by changing the value of the resistor R f with C 1 = C 2 = C 3 = 5 nF, I b1 = 50 A and I b3 = 61.8A.The tuning of the oscillator gives a variation of the FO from 2.9 to 90 kHz when R f -value was decreased from 50 to 0.15 k.In this case, FO was obtained by adjusting CO via AGC.The plots for theoretical value were also included for comparison.

Fig. 22 .
Fig. 22. Measured phase error versus f o .From Fig. 17, output signal level of V 1 and V 2 versus f o and output signal level of I 1 , I 2 , I 3 and I 4 versus f o were shown in Fig. 18 and 19, respectively.It should be noted that the amplitude was not fluctuated; thanks to AGC for obtaining this result.THDs for voltage outputs and current outputs versus f o were measured and shown in Figs.20 and 21.Finally, phase errors versus f o were also measured and shown in Fig. 22.
, output signal level of V 1 and V 2 versus f o and output signal level of I 1 , I 2 , I 3 and I 4 versus f o were shown in Fig. 18 and 19, respectively.It should be noted that the amplitude was not fluctuated; thanks to AGC for obtaining this result.THDs for voltage outputs and current outputs versus f o were measured and shown in Figs.20 and 21.Finally, phase errors versus f o were also measured and shown in Fig. 22.

Fabian
KHATEB was born in 1976.He received the Ing. and Ph.D. degrees in Electrical Engineering and Communication and also in Business and Management from Brno University of Technology (BUT), Czech Republic in 2002, 2005, 2003 and 2007, respectively.He is currently working as an Associate Professor at the Dept. of Microelectronics BUT and also at the Czech Technical University in Prague, Faculty of Biomedical Engineering, Joint Centre for Biomedical Engineering of the Czech Technical University and Charles University in Prague.He has expertise in new principles of designing low-voltage low-power analog circuits, particularly biomedical applications.He has acted as a reviewer for numerous scientific international journals.