Hung-Chun Chien* Indian Journal of Engineering & Materials Sciences Vol. 23, February 2016, pp. 7-19

Transcription

1 ndian Journal of Engineering & Materials Sciences Vol. 3, February 016, pp Current-mode resistorless sinusoidal oscillators and a dual-phase square-wave generator using current-controlled current-differencing transconductance amplifiers and grounded capacitors Hung-Chun Chien* Department of Electronic Engineering, Jinwen University of Science and Technology, No 99, Anzhong Rd, Xindian Dist, New Taipei City, 3154, Taiwan Received 3 February 015; accepted 8 December 015 n this paper, two new designs r current-mode (CM) resistorless sinusoidal oscillators based on current-controlled current-differencing transconductance amplifiers (CCCDTAs) are presented. Each of the proposed oscillators employs a single CCCDTA along with two grounded capacitors, and the oscillation condition and frequency can be orthogonally controlled using the bias currents of the CCCDTA. This paper also presents a CCCDTA-based CM resistorless dual-phase square-wave generator derived from the proposed oscillator. This paper first presents a literature review of previous designs and then describes the applied CCCDTA as well as the relevant rmulations of the proposed circuits llowed by non-ideal problems, sensitivity analyses, and computer simulation examples and results. Simulation tests of the proposed circuits were conducted using the HSPCE program. Simulation results confirmed the theoretical analyses and validated the proposed circuits. Keywords: Current-controlled current-differencing transconductance amplifier (CCCDTA), Current-mode (CM) circuit, Resistorless circuit, Sinusoidal oscillator, Square-wave generator n electronic and electrical engineering, sinusoidal oscillators are crucial circuits and have numerous applications in communication modules, instrumentation equipment, measurement interfaces, power conversion feedback control circuits, and portable medical devices. n early active-rc sinusoidal oscillator designs, the operational amplifier (OA)-based sinusoidal oscillator was the dominant topology and these well-known topologies were applied widely in numerous electronic circuit systems 1. However, OA-based sinusoidal oscillators still do not satisfy the strict demands r current sinusoidal oscillator designs because they exhibit complex circuitry, cannot be operated at high frequencies, and lack electronic tuning properties required r circuit outputs. To realise optimal current sinusoidal oscillators, ur main design criteria must be met: (1) orthogonal control of the oscillation condition and frequency; () an electronic tuning law r controlling the oscillation condition and frequency; (3) a resistorless circuit configuration containing grounded capacitors; and (4) no extra buffer circuits r cascading applications. n early * hcchien@just.edu.tw designs, operational transconductance amplifier (OTA)-based sinusoidal oscillators were widely considered to have achieved the demand r the electronic tuning of the oscillation condition and frequency. n 003, an active device called the currentdifferencing transconductance amplifier (CDTA) was introduced 3, and a modified version called the currentcontrolled current-differencing transconductance amplifier (CCCDTA) was subsequently reported 4. CDTAs and CCCDTAs are preferred to OTAs in CM circuit designs because they are current input and current output active devices, whereas OTAs are voltage input and current output active devices. Previous studies have presented various types of CDTA- and CCCDTA-based sinusoidal oscillator, including single-phase, quadrature, and multiphase sinusoidal oscillators. A CDTA-based CM quadrature sinusoidal oscillator was constructed using two CDTA-based CM allpass filters cascaded in a closed loop 5. n 009, another CDTA-based design was implemented using two CTDAs, a resistor, and two capacitors to realise a dual-mode (DM) (voltage and current output modes) quadrature sinusoidal oscillator 6. Tangsrirat and Tanjaroen introduced a CM

2 8 NDAN J. ENG. MATER. SC., FEBRUARY 016 resistorless CDTA-based quadrature sinusoidal oscillator constructed using three CDTAs and two capacitors 7. Three CM resistorless schemes were also suggested, combining two CCCDTAs and two capacitors 8. Furthermore, a study presented a DM resistorless third-order quadrature sinusoidal oscillator that consisted of three CCCDTAs along with three capacitors 9. n addition to resistorless realisations 7-9, several CDTA- and CCCDTA-based solutions r reducing the number of active devices used have been presented Studies have reported results regarding CDTA- and CCCDTA-based multiphase sinusoidal oscillator designs. A study proposed three CM CDTAbased three-phase sinusoidal oscillators 14. n 007, three CDTAs and two capacitors were used to create a CM ur-phase sinusoidal oscillator 15. An additional approach involved employing two CCCDTAs and two capacitors 16. Furthermore, two studies have proposed CDTA- and CCCDTA-based CM multiphase sinusoidal oscillators n addition to quadrature and multiphase oscillators 5-18, studies have reported several CDTA- and CCCDTA-based single-phase sinusoidal oscillators Amongst them, the first single-phase sinusoidal oscillator to adopt a single CDTA was introduced in a VM topology 19. Biolek et al. 0 reported a CM solution. Both of the presented circuits perrm favourably well and enable the oscillation condition and frequency to be controlled orthogonally by tuning diverse circuit parameters, but they contain excessive floating passive components and lack an electronic manner r tuning the oscillation frequency Consequently, a recent study 1 presented an improved design, which contains a single CCCDTA and two capacitors and enables the oscillation condition and frequency to be orthogonally controlled using the bias currents of the CCCDTA. However, this circuit still includes a capacitor in a floating connection. Although several configurations of CDTA- and CCCDTA-based single-phase sinusoidal oscillators exist 19-1, two new configurations r CM resistorless single-phase sinusoidal oscillators are proposed in this paper to augment the catalogue of CDTA- and CCCDTAbased sinusoidal oscillators. A review of the relevant literature indicated that no oscillator topology presented in this paper was previously published. This study also presents a CCCDTA-based CM resistorless dual-phase square-wave generator derived from the proposed oscillator as an extended design. Table 1 shows a comparison of the designs in this study and the previous CDTA- and CCCDTA-based designs, accentuating the novelty of the proposed sinusoidal oscillators. Compared with previously reported CDTA- and CCCDTA-based single-phase sinusoidal oscillators 19-1, the proposed designs provide the llowing advantages: (1) a resistorless and allgrounded capacitor configuration, which is advantageous from the standpoint of integrated circuit implementation; () all-grounded capacitor designs r reducing parasitic capacitance effects on the circuit; (3) an explicit current output from a highoutput impedance terminal, which facilitates cascading applications with other CM circuits not requiring external buffer circuits; (4) orthogonal control of the oscillation condition and frequency, with electronic tuning perrmed by varying the bias currents of the CCCDTA; (5) adequate active and passive sensitivity perrmance levels. Proposed Current-Mode Resistorless Sinusoidal Oscillators and Square-wave Generator The CCCDTA is a versatile CM active device and its design concept originated from the CDTA. Compared with the CDTA 3, the most crucial feature of the CCCDTA is that its intrinsic input resistances can be adjusted by using its bias current. However, these intrinsic resistances are equal and are controlled by the same bias current of the CCCDTA 4 ; thus, they limit the flexibility of the CCCDTA in some circuit applications. Consequently, an improved topology in which the intrinsic resistances at the two current input terminals (p and n terminals) can be independently adjusted by tuning the diverse bias currents of the CCCDTA was introduced to overcome this problem 1. The circuit symbol and equivalent circuit model of the CCCDTA in this study are shown in Fig. 1. The terminals p and n represent the two current inputs with finite intrinsic input resistances (R p and R n ), and the x+, x-, z, and z c terminals are the high-impedance current outputs. The terminal characteristics of an ideal CCCDTA are described in Eq. (1). Using this notation, Eq. (1) shows that the currents in the z and z c terminals are the difference between the two input currents p and n and that the voltage at the z terminal is converted to the output currents, x + and x -, by a transconductance gain (g m ), which can be controlled by the bias current B of the CCCDTA. The intrinsic input resistances, R p and R n, of the CCCDTA (Fig. 1) are controllable by using the bias currents, B1 and B3,

3 CHEN: CURRENT-CONTROLLED CURRENT-DFFERENCNG TRANSCONDUCTANCE AMPLFERS 9 Topology (Published year) CDTA-based 5 (006) CDTA-based 6 (009) CDTA-based 7 (010) CCCDTAbased(Topology b in Fig. 3) 8 (011) CDTA-based 9 (010) CDTA-based 10 (008) CCCDTA-based 11 (011) CDTA-based 1 (01) CDTA-based 13 (010) CDTA-based 14 (014) CDTA-based 15 (007) Table 1 Comparison of the proposed sinusoidal oscillators with other CDTA- and CCCDTA-based solutions Active devices and passive components CDTA Resistor 4 (Two grounded) Capacitor CDTA Resistor 1 Capacitor CDTA 3 Capacitor CCCDTA Capacitor CDTA 3 Capacitor 3 CDTA 1 Resistor 1 CCCDTA 1 Resistor 1 CDTA 1 Resistor 1 CDTA 1 CDTA CDTA 3 Classification of oscillator/ Orthogonal control of OC and OF/ Type of OC and OF control/ QSO/Yes/ OC: by R and g m OF: by R QSO/Yes/ OC: by R QSO/Yes/ QSO/Yes/ OC: by R n QSO/Yes/ QSO/No/ OC: NA OF: NA QSO/Yes/ OC: by R QSO/No/ OC: NA OF: NA QSO/No/ OC: NA OF: NA MSO/Yes/ MSO/Yes/ Circuit order/ Signal output mode/ Electronically tunable/ Resistorless topology/ Need of buffer circuits Yes (Only of the oscillation condition)/ No/No Second-order/DM/ Yes (Only of the oscillation frequency)/ No/Yes (r voltage output) Yes/Yes/No Yes/Yes/No Third-order/DM/ Yes/Yes/Yes (r voltage output) Yes (Only of the oscillation frequency)/no/yes No/Yes/No Yes/Yes/No Yes/Yes/No mplement technology/ Supply voltages/ Measured highest operating frequency/ Power consumption/ Total harmonic distortion CMOS realization (METEC 0.5-µm CMOS process technology)/ ±.5 V/1 MHz/NA/1% CMOS realization (METEC 0.5-µm CMOS process technology)/ NA/985.6 khz/na/na (NP100N and PR100N ±3 V/1.4 MHz/NA/.5% ±.5 V/1.3 MHz/9.5 mw/1.59% CMOS realization (TSMC µm CMOS process technology)/ ±1.5 V/800 khz/.87 mw/10.39% CMOS realization (0.7-µm CMOS process technology)/ NA/96 khz/na/0.16% CMOS realization (METEC 0.5-µm CMOS process technology)/ ±1 V/114.4 khz/na/0.6% CMOS realization (NA)/ NA/1.73 MHz/NA/3% (NA)/ ±1.5 V/ khz/na/3.16% CMOS realization (TSMC µm CMOS process technology)/ ±1.5 V/68.88 khz/na/1.94% (AD844 and CA3080)/ ±1 V/31.65 khz/na/4.45% (Contd.)

4 10 NDAN J. ENG. MATER. SC., FEBRUARY 016 Table 1 Comparison of the proposed sinusoidal oscillators with other CDTA- and CCCDTA-based solutions (Contd.) CCCDTA-based 16 (01) CDTA-based 17 (009) CCCDTA-based (Fig. 6) 18 (011) CDTA-based 19 (008) CDTA-based 0 (009) CCCDTA-based 1 (013) CCCDTA-based (Proposed in Fig. 3a) CCCDTA-based (Proposed in Fig. 3b) CCCDTA CDTA (N +) Capacitor N CCCDTA N Resistor N Capacitor N CDTA 1 Resistor CDTA 1 Resistor CCCDTA 1 CCCDTA 1 CCCDTA 1 OC: oscillation condition. OF: oscillation frequency. SSO: single-phase sinusoidal oscillator. QSO: quadrature sinusoidal oscillator. MSO: multiphase sinusoidal oscillator. NA: not available, not possible, or not tested. R: external resistor. g m : transconductance gain of the CCCDTA. R p and R n : intrinsic input resistances of the CCCDTA. N: n-phase output. MSO/Yes/ and R n and R n MSO/Yes/ MSO/Yes/ and R OF: by R n SSO/Yes/ OF: by R SSO/Yes/ OF: by R SSO/Yes/ OF: by R p SSO/Yes/ OC: by R n SSO/Yes/ OF: by R p Yes/Yes/No Yes/Yes/No Yes/No/No Second-order/VM/ Yes (Only of the oscillation condition)/no/yes Yes (Only of the oscillation condition)/no/no Secondorder/DM/Yes/Yes/Yes (r voltage output) Secondorder/CM/Yes/Yes/No Secondorder/CM/Yes/Yes/No ±.5 V/.15 MHz/1.1 mw/1.14% (NP100N and PR100N ±3 V/180 khz/na/1.4% CMOS realization (TSMC 0.5-µm CMOS process technology)/ ±1.5 V/1.03 MHz/NA/0.5% (AD844 and LM3080)/ ±6 V/110 khz/na/na CMOS realization (0.7-µm CMOS process technology)/ ±.5 V/53.89 khz/na/1.17% ±1. V/4.5 MHz/9.06 mw/3.51% ±1. V/4.93 MHz/4.94 mw/3.75% ±1. V/.9 MHz/7.8 mw/4.96% Fig. 1 (a) Circuit symbol of the CCCDTA and (b) its equivalent circuit model

5 CHEN: CURRENT-CONTROLLED CURRENT-DFFERENCNG TRANSCONDUCTANCE AMPLFERS 11 of the CCCDTA, respectively. Figure shows the internal circuit configuration of the CCCDTA (Fig. 1), as modified from the circuit 1. n this circuit, (Q 1 Q 46 ) simulates a current-controlled current-differencing circuit to generate the currents z and zc as the difference between the p and n currents. To generate the output currents x + and x -, which are a function of the transconductance gain (g m ) with respect to the voltage V z, a multipleoutput transconductance circuit (Q 47 Q 58 ) was applied and connected at the z node of the circuit. A typical CCCDTA can contain an arbitrary number of current output terminals (x+ and x-), providing output currents, x + and x -, in both directions. However, the use of multiple output terminal of the CCCDTA may degrade the circuit perrmance especially the tracking error and output impedance. However, additional tracking error compensator and buffer circuit can be added to overcome this problem. Equations ()-(4) show the rmulas of the R p, R n, and g m related to the bias currents of the CCCDTA (Fig. ), indicating that these circuit parameters can be controlled using the currents of the CCCDTA. n Eqs (), (3), and (4), V T is the thermal voltage, where V T = 6 mv at room temperature (7ºC). Vp Rp p V n 0 Rn n z, zc = Vx g V x+ m x x g m V z R V Fig. nternal circuit construction of the CCCDTA 1... (1) T p =... () B1 V T R n =... (3) B3 Fig. 3 Circuit diagrams of the proposed CCCDTA-based CM resistorless sinusoidal oscillators g B m =... (4) VT Figure 3 shows circuit diagrams of the proposed CM resistorless sinusoidal oscillators, which consist of a single CCCDTA and two capacitors. The x+ and x- output terminals of the CCCDTA have highimpedance current output properties that are cascadable, requiring no additional buffer circuits r current outputs in CM circuit applications. Assuming an ideal CCCDTA characterised by Eq. (1) and using routine circuit analysis yields the characteristic equation of the circuit in Fig. 3a, as expressed in Eq. (5): Rp s ( RpC1C ) + s C1 C + gm = 0 Rn... (5) From Eq. (5), it can be und that the circuit can produce oscillation if the oscillation condition expressed in Eq. (6) is fulfilled, and the oscillation frequency of the circuit is then determined, as expressed in Eq. (7): R R C =... (6) C p n 1 g m =... (7) RpC1C

6 1 NDAN J. ENG. MATER. SC., FEBRUARY 016 By substituting the rmulas of the intrinsic resistances (R p and R n ) and transconductance gain (g m ) expressed in Eqs () - (4) into Eqs (6) and (7), the expressions of the oscillation condition and frequency related to the bias currents of the CCCDTA r the circuit, respectively, are determined in Eqs (8) and (9), as llows: C =...(8) C B3 B1 1 1 B1 B =... (9) VT C1C Equations (8) and (9) show that the oscillation condition and frequency of the circuit can be adjusted in an orthogonal manner by controlling the bias currents of the CCCDTA. Through routine circuit analysis, the characteristic equation, oscillation condition, and oscillation frequency of the circuit in Fig. 3b are derived as llows: ( ) s ( R R C C ) + sr C 3 g R + = 0... (10) p n 1 p m n gmr n = 3... (11) o = π =... (1) R R C C p n 1 By substituting Eqs () - (4) into Eqs (11) and (1), the oscillation condition and frequency can then be expressed, respectively, in Eqs (13) and (14), as llows: B B3 = 1... (13) 1 8 B1 B3 =... (14) VT C1C Equations (13) and (14) show that the tuning procedures of the oscillation condition and frequency of the circuit can be orthogonally controlled by using the bias currents of the CCCDTA. Compared with previous designs (e.g., CDTA- and CCCDTA-based single-phase sinusoidal oscillators) 19-1, the proposed designs (Fig. 3) use only a single CCCDTA and two grounded capacitors to realise the CM sinusoidal oscillators. n addition to previous studies on sinusoidal oscillators, designing a square-wave generator containing various active devices has attracted increasing attention from circuit designers over the past few years. A literature survey revealed an electronically tunable scheme in which a single OTA was connected to ur resistors and a capacitor to construct a VM square-wave generator. Furthermore, a current conveyor (CC)-based VM topology was realised by combining one CC with two resistors and a capacitor 3 but has an oscillation frequency that is difficult to adjust because the tuning law of its oscillation frequency is directly dependent on the parasitic resistance of the CC. To solve these problems, Srinivasulu 4 and Marcellis et al. 5 suggested improved topologies. n 005, another VM design consisting of a single operational transresistance amplifier (OTRA) and three external passive components was presented 6. A differential voltage CC (DVCC) along with a few passive components was used to create a VM square-wave generator 7. n addition to VM topologies -7, a CM square-wave generator consisting of one CCCDTA, a resistor, and a capacitor was developed 8. Although several configurations of square-wave generators exist, this study presents a completely new configuration to enrich the field of square-wave generator design. Figure 4 shows a circuit diagram of the proposed CCCDTA-based CM resistorless dualphase square-wave generator, which is an extend design derived from the circuit in Fig. 3a. The proposed CM square-wave generator consists of two Fig. 4 Circuit diagram of the proposed CCCDTA-based CM resistorless dual-phase square-wave generator

7 CHEN: CURRENT-CONTROLLED CURRENT-DFFERENCNG TRANSCONDUCTANCE AMPLFERS 13 Table Comparison of the proposed square-wave generator with other designs Topology (Published year) OTA-based (199) CC-based 3 (1998) CC-based 4 (011) CC-based 5 (013) OTRA-based (Fig. a) 6 (005) DVCC-based (Fig. 3a) 7 (013) CCCDTA-based (Fig. 4) 8 (011) CCCDTA-based (Proposed in Fig. 4) Active devices and passive components OTA 1 Resistor 4 Capacitor 1 CC 1 Resistor Capacitor 1 CC 3 Resistor 6 (Four grounded) Capacitor 1 CC Resistor 6 (Five grounded) Capacitor 1 OTRA 1 Resistor Capacitor 1 DVCC 1 Resistor Capacitor 1 CCCDTA 1 Resistor 1 Capacitor 1 CCCDTA Resistorless topology/ Electronically operation/ Amplitude tunable No/Yes/Yes No/Yes/Yes Yes/Yes/Yes Signal output mode/ Dual-phase operation/ Need of buffer circuits/ VM/No/Yes VM/No/Yes VM/No/Yes VM/No/Yes VM/No/No VM/No/Yes CM/No/No CM/Yes/No mplement technology/ Supply voltages/ Measured highest operating frequency (CA3080)/ ±6 V/3.34 khz (AD844)/ ±10 V/1 MHz (AD844)/ ±6 V/31.5 khz CMOS realization (AMS 0.35-µm CMOS process technology)/ ±1 V/737 khz (AD844)/ ±15 V/800 khz (AD844)/ ±15 V/400 khz ±1.5 V/100 khz ±1. V/ 1.18 MHz CCCDTAs and two grounded capacitors, and the connection of the second CCCDTA rms a current comparator. Once an input current signal, p, is input into the p terminal of the second CCCDTA and the input current, n, is set to zero, the outputs ( o1 and o ) of the second CCCDTA can be described as o1 = B5 if p > n, o1 = - B5 if n > p, o = - B5 if p > n, and o = B5 if n > p. Thus, if the oscillation condition described in Eq. (8) is satisfied, then this circuit can produce two inverting phase output squarewave signals at o1 and o with an oscillation frequency given by Eq. (9). Table shows a comparison of various solutions r illustrating the novelty of the proposed topology. Non-ideal and Parasitic Effect Analyses A practical CCCDTA can be modelled by including non-ideal transfer gains and finite parasitic elements. Figure 5 shows a sophisticated circuit model of the CCCDTA that is used to present the non-ideal CCCDTA, where α p represents a non-ideal current transfer gain from the p terminal to the z and z c

8 14 NDAN J. ENG. MATER. SC., FEBRUARY 016 Fig. 5 Non-ideal equivalent circuit model of the CCCDTA terminals of the CCCDTA, α n denotes a non-ideal current transfer gain from the n terminal to the z and z c terminals of the CCCDTA, and β is a non-ideal transconductance transfer gain from the z terminal to the x+ and x- terminals of the CCCDTA. Typical values of the non-ideal transfer gains α p, α n, and β range from 0.9 to 1, with the ideal value being 1. As shown in Fig. 5, R p and R n are the current-controlled intrinsic input resistances expressed in Eqs () and (3). R x and R z represent the finite parasitic resistances, which approach infinity in an ideal case, and C x and C z denote the finite parasitic capacitances of the CCCDTA. Typical values of the parasitic resistances R x and R z are in the order of several hundreds of kiloohms to several mega-ohms, and the parasitic capacitances C x and C z are in the range of several picofarads to several tens of picofarads. After the non-ideal equivalent circuit model (Fig. 5) is applied to the proposed circuit in Fig. 3a, the derivations yield the modified characteristic equation expressed in Eq. (15). Rp s ( RpC1C ) + s C1 C + β gm = 0 Rn... (15) Based on Eq. (15), the oscillation condition has the rmula expressed in Eq. (6), and the modified oscillation frequency is determined using Eq. (16). βg m =...(16) RpC1C After the substitution of Eqs () and (4) into Eq. (16), the oscillation frequency can be expressed as: 1 β B1 B =... (17) VT C1C Equations (15) and (16) apply the llowing conditions: R p << R x, R p << R z, R n << R z, C 1 >> C x, C 1 >> C z, C >> C z, and α p = α n = 1. As indicated in Eq. (17), the non-ideal transconductance transfer gain, β, influences the oscillation frequency, which deviates from the ideal scenario. However, this problem can be addressed by slightly retuning the bias current B of the CCCDTA to minimise the influence of the nonideal transconductance transfer gain, β, on the circuit. Using Eq. (16), the active and passive sensitivities of the circuit are determined in Eq. (18): o o 1 o SR = S p C = S 1 C =...(18) 1 o o Sβ = Sg = m After the non-ideal equivalent circuit model of the CCCDTA (Fig. 5) and the conditions R p << R z, R n << R x, R n << R z, C 1 >> C x, C 1 >> C z, C >> C z, and α p = 1 are applied to the circuit in Fig. 3b, the modified characteristic equation expressed in Eq. (19) can be derived through a tedious analysis. The modified oscillation condition and frequency can then be determined from Eq. (19) and expressed in Eqs (0) and (1), respectively. (( ) ) s ( R R C C ) + sr C α + 1 βg R + α = 0 p n 1 p n m n n...(19) βgmr n = αn (0) α n =... (1) RpRnC1C After the substitution of Eqs ()-(4) into Eqs (0) and (1), the oscillation condition and frequency can be expressed as shown in Eqs () and (3), respectively. Equation () shows that the non-ideal transfer gains, α n and β, influence the oscillation condition, which deviates from the ideal scenario. This problem can be overcome by retuning the bias current B of the CCCDTA to start the oscillation process. Eq. (3) indicates that the non-ideal current transfer gain, α n, changes the oscillation frequency, which deviates from the ideal scenario. However, this frequency deviation can be addressed by slightly retuning the bias current B3 of the CCCDTA. B B3 ( + ) 4 αn 1 =... () β 1 8α n B1 B3 =... (3) VT C1C

9 CHEN: CURRENT-CONTROLLED CURRENT-DFFERENCNG TRANSCONDUCTANCE AMPLFERS 15 Based on Eq. (1), the active and passive sensitivities of the circuit can be derived using Eq. (4). o o o 1 o SR = S p R = S n C = S 1 C =... (4) 1 o Sα = n Equations (18) and (4) indicate that the values of all of the active and passive sensitivities are low and do not exceed 50% in magnitude; thus, the circuits exhibit adequate active and passive sensitivity perrmance levels. Keep in mind that to minimize the influence of the parasitic elements on the proposed circuits, the llowing conditions must be satisfied in the design procedures: R p << R x, R p << R z, R n << R x, R n << R z, C 1 >> C x, C 1 >> C z, and C >> C z. Computer Simulation Examples and Results This section presents computer simulations perrmed using the HSPCE program to verify the validity of the proposed circuits (Figs 3 and 4). The CCCDTA was employed in a bipolar implementation (Fig. ) by using the process parameters of the NR00N and PR00N bipolar transistors of the AT&T ALA400 transistor array 9 with the llowing supply voltages: V CC = V EE = 1. V. For examples, the circuit in Fig. 3a was designed to have an oscillation frequency of f o = 100 khz using the llowing component values R p = kω ( B1 = 10 µa), R n = 0.1 kω ( B3 = µa), g m = 4.8 ms ( B =.39 µa), and C 1 = C = 10 nf. The simulation results of the time waverm in a steady state and its corresponding frequency spectrum r the output o are shown in Fig. 6. The simulation results show that the oscillation frequency was f o = khz and had a 1.96% deviation with respect to the designed value. This slight frequency deviation was caused by the non-ideal transconductance transfer gain, β, as anticipated in Eq. (16). The total harmonic distortion (THD) percentage and the power consumption were und to be.81% and 5.18 mw, respectively. To reduce the total harmonic distortion on the circuit, an additional auxiliary amplitude control circuit can be used to yield a lower total harmonic distortion of the generated output signal 1. However, such circuit was beyond the scope of this study. To demonstrate the feasibility of the proposed circuit in Fig. 3b, the llowing simulation tests were conducted. After an oscillation frequency of f o = 100 khz was specified, the component values R p = 0. kω ( B1 = µa), R n = 0.3 kω ( B3 = µa), g m = ms ( B = µa), and C 1 = C = 10 nf were determined. The oscillation developed into steady-state waverms; the corresponding frequency spectrum of output o is shown in Fig. 7. The oscillation frequency of the simulation results was determined to be f o = 97.1 khz, representing a.88% deviation from the designed value. This deviation originated from the non-ideal current transfer gain, α n, Fig. 6 Simulation results r the output o of the oscillator (Fig. 3a): output waverm in the steady state and its corresponding frequency spectrum

10 16 NDAN J. ENG. MATER. SC., FEBRUARY 016 as anticipated in Eq. (1). The THD was 3.81% r the current output, and the power consumption was 7.95 mw. Because of the limitation of the CCCDTA maximal slew rate, the highest oscillation frequency of the circuits was limited; the llowing component values were used r the circuit in Fig. 3a: R p = kω ( B1 = 10 µa), R n = 0.1 kω ( B3 = µa), g m = 1.15 ms ( B = µa), and C 1 = C = 0.1 nf. Figure 8a shows the simulation results r the output waverm of the circuit. The oscillation frequency was recorded as f o = 4.93 MHz, indicating a 5.01% frequency deviation from the theoretical calculation. n consideration of the highest oscillation frequency of the circuit in Fig. 3b, a specific simulation was conducted using the component values R p = 0.09 kω ( B1 = 145 µa), R n = 0.3 kω ( B3 = µa), g m = ms ( B = µa), and C 1 = C = 0.5 nf. The output waverm is shown in Fig. 8b. The oscillation frequency was determined to be f o =.9 MHz, deviating from the theoretical value by 6.41%. The simulation results (Fig. 8) indicated that the highest oscillation frequency of the circuits occurred at several megahertz. Fig. 7 Simulation results r the output o of the oscillator (Fig. 3b): output waverm in the steady state and its corresponding frequency spectrum Fig. 8 Simulation results r the highest applicable oscillations of the (a) oscillator in Fig. 3a and (b) oscillator in Fig. 3b

11 CHEN: CURRENT-CONTROLLED CURRENT-DFFERENCNG TRANSCONDUCTANCE AMPLFERS 17 Two simulation examples were conducted to demonstrate the property used to control the oscillation frequency of the proposed circuits (Fig. 3) by using the bias currents of the CCCDTA. For the circuit in Fig. 3a, the bias current B of the CCCDTA was varied from 00 µa to 900 µa in 100-µA steps, and the llowing component values were applied: R p = kω ( B1 = 10 µa), R n = 0.1 kω ( B3 = µa), and C 1 = C = 10 nf. Figure 9 shows the theoretical and simulated results r the variation in the oscillation frequency, indicating that the oscillation frequency of the circuit can be controlled using the bias current B of the CCCDTA. To investigate the ability to tune the oscillation frequency of the circuit in Fig. 3b, the llowing component values were used: R n = 0.3 kω ( B3 = µa), g m = ms ( B = µa), and C 1 = C = 10 nf. B1 was varied from 00 µa to 600 µa in 50-µA steps to examine the variation in oscillation frequency. Figure 10 shows the theoretical and simulated results r the tuning of the oscillation frequency by using the bias current B1 of the CCCDTA. To verify the validity of the circuit in Fig. 4, a test with a design specification of f o = 100 khz was conducted using the component values R p = kω ( B1 = 10 µa), R n = 0.1 kω ( B3 = µa), g m = 4.8 ms ( B =.39 µa), B4 = B6 = 710 µa, B5 = 400 µa, and C 1 = C = 10 nf. As shown in Fig. 11, the simulation results indicated that the oscillation frequency f o = khz and verified that the circuit provided dual-phase square waverm current outputs. The frequency deviation between the designed and simulated values was 1.35%. The power consumption of the circuit was mw. Fig. 9 Oscillation frequency against the bias current B of the CCCDTA r the oscillator in Fig. 3a Fig. 10 Oscillation frequency against the bias current B1 of the CCCDTA r the oscillator in Fig. 3b Fig. 11 Simulation results r the current output waverms of the proposed square-wave generator

12 18 NDAN J. ENG. MATER. SC., FEBRUARY 016 To demonstrate that the oscillation frequency could be tuned by varying the bias current B r the circuit in Fig. 4, the llowing component values were used: R p = kω ( B1 = 10 µa), R n = 0.1 kω ( B3 = µa), B4 = B6 = 710 µa, B5 = 400 µa, and C 1 = C = 10 nf. B was varied from 00 µa to 900 µa in 100-µA steps to examine the variation in the oscillation frequency. As shown in Fig. 1, the theoretical and simulated results indicated that the oscillation frequency of the circuit can be adjusted using the current tuning procedures. To investigate the influence of oscillation frequency dependence on the variation in the temperature of the proposed circuits, a test with a design specification of f o = 100 khz over a 0 70 ºC temperature range was executed. On the basis of the previous design examples, the llowing component values were applied to test the Fig. 1 Oscillation frequency against the bias current B of the CCCDTA r the proposed square-wave generator Fig. 13 Variation of the oscillation frequency of the circuits under different temperature conditions circuits in Figs. 3a and 4: R p = kω ( B1 = 10 µa), R n = 0.1 kω ( B3 = µa), g m = 4.8 ms ( B =.39 µa), B4 = B6 = 710 µa, B5 = 400 µa, and C 1 = C = 10 nf, and the llowing component values were applied to test the circuit in Fig. 3b: R p = 0. kω ( B1 = µa), R n = 0.3 kω ( B3 = µa), g m = ms ( B = µa), and C 1 = C = 10 nf. Figure 13 shows the simulation results r the variation in the oscillation frequency under different temperature conditions. The simulation results showed that the frequency deviations between the theoretical values and the simulated results ranged from 4.39% to 14.53% r the circuit in Fig. 3a,.7% to 1.8% r the circuit in Fig. 3b, and 6.1% to 13.85% r the circuit in Fig. 4, respectively. Conclusions This paper presents two new CM resistorless sinusoidal oscillators consisting of a single CCCDTA and two grounded capacitors. The oscillation condition and frequency of the proposed sinusoidal oscillators can be orthogonally controlled using the bias currents of the CCCDTA. This study also proposes a CCCDTA-based CM resistorless dualphase square-wave generator as an extended design. This paper describes the related governing equations of the proposed circuits, an investigation of non-ideal problems conducted using a sophisticated circuit model of the CCCDTA, and sensitivity analyses. The effectiveness of the proposed circuits was verified through computer simulations by using the HSPCE program, and the results exhibited satisfactory agreement with the theoretical predictions. References 1 Gonzalez G, Foundations of oscillator circuit design, (Artech House Publishers), 007. Martinez P A & Mongesanz B M, nt J Electron, 9 (005) Biolek D, CDTA-building block r current-mode analog signal processing, Proc nte Conf on ECCTD 03, 003, Jaikla W & Siripruchyanun M, Current controlled current differencing transconductance amplifier (CCCDTA): a new building block and its applications, Proc ECT Conf, 006, Keskin A U & Biolek D, ET Circuits Devices Syst, 153 (006) Lahiri A, Analog ntegr Circuits Signal Process, 61 (009) Tangsrirat W & Tanjaroen W, ndian J Pure Appl Phys, 48 (010)

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