130 Original scientific paper  MIDEM Society Dual-Mode Sinusoidal Quadrature Oscillator with Single CCCTA and Grounded Capacitors Worapong Tangsrirat Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Ladkrabang, Bangkok, Thailand Abstract: In this work, a sinusoidal quadrature oscillator which simultaneously generates voltage and current signal outputs is proposed. It contains only a single current-controlled conveyor transconductance amplifier (CCCTA) and two grounded capacitors. The proposed oscillator has the advantage features of resistorless structure realization, electronic frequency control, availability of two explicit voltage and current quadrature outputs, and low sensitivity figure. Moreover, the parasitic elements existing at the CCCTA terminals are taken into account. The performance of the proposed oscillator circuit was verified using PSPICE simulation with acceptable results. Keywords: Current-Controlled Conveyor Transconductance Amplifier (CCCTA); Quadrature Oscillator; Resistorless circuits; Voltage- mode and current-mode circuits. Dvojni sinusni kvadrantni oscillator z enosnim CCCTA in ozemljenimi kondenzatorji Izvleček: V članku je predstavljen je kvadrantni oscilator, ki vzporedno generira napetostni in tokovni signal. Vsebuje le en tokovno krmiljeno vezje transkonduktančnega ojačevalnika in dva ozemljena kondenzatorja. Predlagano vezje je brez uporov, vsebuje elektronski nadzor frekvence, omogoča dva ločena napetostna in tokovna izhoda in izkazuje nizko občutljivost. Upoštevani so parazitni elementi na CCCTA terminalih. Lastnosti oscilatorja so bile preverjene v PSPICE okolju. Ključne besede: tokovno krmiljeno vezje transkonduktančnega ojačevalnika; brez uporovno vezje;napetostno in tokovno vezje * Corresponding Author’s e-mail: drworapong@gmail.com Journal of Microelectronics, Electronic Components and Materials Vol. 46, No. 3(2016), 130 – 135 1 Introduction Sinusoidal quadrature oscillator or two-phase sinusoi- dal oscillator is a kind of the sinusoidal oscillators that provides explicit two signal outputs with 90° phase shift from the same structure. Accordingly, it performs an essential circuit block employed a wide range of appli- cations in modern electronic and communication sys- tems, control systems, and signal processing. There are many attempts recently in designing sinusoidal quad- rature oscillators based on various types of modern ac- tive components [1-16]. However, many of them make use of at least two active components [1-12]. Only few circuits can provide both voltage and current quadra- ture signals from the same configuration [11-14]. These oscillator realizations contains an excessive number of external passive components, i.e., at least four passive components. The recent current-mode quadrature os- cillators based on single current differencing transcon- ductance amplifier (CDTA) were introduced in [15-16]. The previous work in [15] employs only one CDTA and three passive components (including two virtually grounded passive components that are floating in the non-ideal sense). In [16], a compact single CDTA-based quadrature oscillator with three external passive com- ponents was reported. This circuit requires a floating capacitor, which is not favorable for further integration. In 2008, the recently defined active circuit element, the so-called current-controlled conveyor transconduct- ance amplifier (CCCTA), was introduced [17]. This de- 131 W. Tangsrirat; Informacije Midem, Vol. 46, No. 3(2016), 130 – 135 vice is a modified conception of the current conveyor transconductance amplifier (CCTA) [18], in which its parasitic resistance seen at the x-terminal (Rx) is vari- able electronically by adjusting an external biasing current. This property provides the advantage of realiz- ing electronically controllable analog function circuits without external passive resistor requirement. Since its introduction, the CCCTA has numerous applications in a class of analog signal processing solutions and cir- cuits [17], [19-21]. This paper presents a sinusoidal oscillator with variable oscillation frequency, able to provide explicitly quadra- ture voltage and current outputs from the same circuit configuration. The proposed quadrature oscillator em- ploys only one CCCTA and two grounded capacitors. A detailed analysis shows that the oscillator circuit in- cludes low active and passive sensitivities and has good frequency stability. Moreover, the effects of the CCCTA parasitic elements on the oscillator performance are also discussed. Simulation results with PSPICE using standard 0.35-mm BiCMOS process parameters are per- formed to verify the practical utility and validity of the realized circuit. 2 Principle of the CCCTA and its realization Basically, the CCCTA can be realized through a cascade connection of second generation current-controlled conveyor (CCCII) and multi-output transconductance amplifier. Fig.1 shows the electrical symbol and equiva- lent circuit of the CCCTA. It is shown that this device consists of two input terminals (y and x) and two out- put terminals (z and o±). An ideal property of the CC- CTA is described by the following matrix :                         ± =             ±± o z y x m x o z x y v v v i g R i i v i . 000 0001 001 0000 (1) where Rx represents the parasitic serial resistance at the x-terminal, and gm denotes the effective small-signal transconductance gain of the CCCTA. As described in eq. (1), the x-terminal has a parasitic resistance Rx, where its value usually depends on an external sup- plied current. The y-terminal exhibits the high-input impedance terminal, while the z and o-terminals are two types of high-output impedance terminals. One possible realization of the CCCTA in BiCMOS technology is shown in Fig.2 [22]. The circuit is mainly composed of second-generation current-controlled conveyor (Q1-Q2, M1-M7) and dual-output transcon- ductance amplifier (Q3-Q6, M8-M14). Referring to Fig.2, the parasitic resistance Rx of the CCCTA has been de- rived as : A T x I VR 2≅ (2) where VT is the thermal voltage, whose value is approxi- mately 26 mV at 27oC. Note from eq.(2) that the value of Rx depends on the external DC bias current IA. Assum- ing transistors Q3-Q5 as well as M8-M11 are matched, the expression of gm can be given by : T B z o m V I v ig 2 == (3) Also note that the gm-value is controllable electroni- cally and linearly by changing the IB–value. (a) (b) Figure 1: The CCCTA. (a) circuit symbol (b) equivalent circuit. Figure 2: BiCMOS realization of the CCCTA. 132 3 Proposed dual-mode sinusoidal quadrature oscillator Fig.3 shows a canonic sinusoidal oscillator that produc- es voltage and current quadrature outputs explicitly. The circuit constructs from only one CCCTA and two grounded capacitors without needing any external passive resistor. The state-space equations for this con- figuration is obtained as [23]-[24] :             =      2 1 2221 1211 2 1 v v aa aa v v   (4) where 02211 == aa 1 12 C ga m−= 2 21 1 CR a x =, and (5) From the above autonomous state-space expression, the characteristic equation of the circuit can be derived as : 0)()( 2112221122112 =−++− aaaasaas (6) The condition of oscillation and the frequency of oscil- lation (wo) from eq.(6) are expressed, respectively, by 02211 =+ aa (7) and 21122211 aaaao −=ω (8) This means that the circuit will oscillate with no oscillation condition at the oscilla- tion frequency of 21CCR g x m o =ω (9) It is obvious that the wo is electronically tunable through the transconductance gain (gm) and/or parasitic resist- ance (Rx) of the CCCTA. Thus, the circuit can work as an electronically variable frequency quadrature oscillator. Considering the proposed configuration of Fig. 3, the two output voltages marked v1 and v2 are related as : 211 vjkv = (10) where k1 = woRxC2. Eq.(10) represents a 90°-phase differ- ence between both voltages, showing the quadrature property of the proposed oscillator. Furthermore, in case of k1 = 1, the amplitudes of two quadrature out- puts will also be equal. In addition, it is crucial to note that the quadrature output voltages v1 and v2 are not in low-impedance levels, hence external voltage buffers are necessary Also from Fig.3, the relation for two output currents (i1 and i2) can be given by the following matrix equation.                   − =      2 1 1 2 2 1 01 0 i i CR C g i i x m   (11) It is seen that, in this case, the relationship between two quadrature current outputs i1 and i2 can be obtain as : 122 ijki = (12) where k2 = woC2/gm. Clearly, for k2 = 1, two marked ex- plicit quadrature current outputs have equal magni- tude. It is also to be noted that the circuit provides the output current i1 from the high-impedance terminal (terminal o+) but the output current i2 can be obtained across C2. Therefore, for explicit dual-mode utilization, an external buffering unit would be required for sens- ing and taking out the current i2. According to eq. (9), the relative sensitivity of wo with respect to active and passive components can be ob- tained as : 2 1=o mg S ω 2 1−=o xR Sω 2 1 1 −=oCS ω 2 1 2 −=oCS ω, , and (13) All of which are lower than unity in magnitude. 4 Effects of the CCCTA Parasitic Elements Fig.4 shows the practical model of the CCCTA. As it is seen, there are parasitic resistances and capacitances Figure 3: Proposed dual-mode sinusoidal quadrature oscillator. W. Tangsrirat; Informacije Midem, Vol. 46, No. 3(2016), 130 – 135 133 from terminals y, z and o± to the ground (Ry //Cy , Rz //Cz and Ro //Co), and a serial parasitic resistance Rx at the x- terminal. It is further to be noted that the typical values of parasitic resistances Ry, Rz and Ro are in the range of several MW, whereas parasitic capacitances Cy, Cz and Co are within a few fFs. Consider the CCCTA parasitic ele- ments in the proposed oscillator of Fig.3. It is clear that the external grounded capacitors C1 and C2 are parallel connected at the terminals y and z, respectively. The effects of parasitic capacitances at corresponding ter- minals could be adsorbed, as they merge with external capacitance values. Hence, the total impedance at the y-terminal can be approximated to : 1)//( )//( 1 + ≅ sCRR RR Z oy oy y (14) For the working frequencies, y oy CRR ωω =>> 1)//( 1 (15) Zy can be further reduced to the value of 1/C1s, which is practically not affected by Ry//Ro. In a similar way, at the z-terminal, the influence of Rz can also be alleviated for operation at frequencies: z zCR ωω =>> 2 1 (16) As a result, it can be realized from eqs. (15) and (16) that the frequency range at low frequencies should be se- lected as [25]: { }zyL ωωω , max10×>> (17) Furthermore, it should be considered that there is a high-frequency limitation owing to the parasitic im- pedances (Ro //Co) in parallel at the terminal o+. Thus, the extra pole introduced at the terminal o+ can be expressed as : wo @ 1/(RoCo). To exhibit the ideal charac- teristic, the operating frequency range at high frequen- cies is found as : { }oH ωω min1.0 ×<< (18) Finally, combining eqs.(17) and (19), the useful frequen- cy range of the proposed oscillator can be defined as : HL ωωω <<<< (19) 5 Computer Simulation and Performance Verification The proposed dual-mode sinusoidal oscillator as de- picted in Fig.3 was simulated using PSPICE program. In simulation purpose, the CCCTA structure given in Fig.2 was employed with standard 0.35-mm BiCMOS pro- cess parameters using supply voltages of +V = -V = 1 V. The aspect ratios (W/L in mm/mm) of the MOS transis- tors were set to 7/0.7 and 8.5/0.7 for all the NMOS and PMOS transistors respectively. By choosing C1 = C2 = 0.4 nF, IA = IB = 25 mA, the proposed oscillator circuit of Fig.3 was designed to oscillate at fo = wo/2p @ 191 kHz. By performing time-domain analysis, the simulated transient waveforms for quadrature volt- age and current outputs of the proposed oscillator are shown in Figs.5 and 6, respectively. As obtained from simulation results, the frequency of oscillation (fo) was observed as 185 kHz. Fig.7 also shows the simulated fre- Figure 4: Practical model of the CCCTA including para- sitic elements. Figure 5: Simulated time-doamin responses for v1 and v2. (a) initial-stage responses, (b) steady-state responses (a) (b) W. Tangsrirat; Informacije Midem, Vol. 46, No. 3(2016), 130 – 135 134 Figure 8: Electronic tuning of fo with IO. Figure 6: Simulated time-doamin responses for i1 and i2. (a) initial-stage responses, (b) steady-state responses (a) (b) Figure 7: Simulated frequency spectrums of the pro- posed quadrature oscillator of Fig.3. (a) for v1 and v2, (b) for i1 and i2 (a) (b) quency spectrums of both voltage and current quad- rature output waveforms, and the observed values of total harmonic distortion (THD) at all the outputs were less than 2.89%. To further demonstrate the electronic frequency controllability of the oscillator, the variation of fo as a function of IO (= IA = IB) is plotted in Fig.8. 6 Concluding Remarks A generalized scheme to realize a resistorless dual- mode sinusoidal quadrature oscillator using one CC- CTA and only two grounded capacitors is presented. The presented circuit is capable of simultaneously generating two quadrature voltage outputs and two quadrature current outputs. The frequency of oscilla- tion can be made electronically tunable by external DC biasing currents of the CCCTA. 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