Microelectronics Journal 44 (2013) 216–224

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Microelectronics Journal

0026-26

http://d

n Corr

E-m

jmw@n

journal homepage: www.elsevier.com/locate/mejo

Dual-mode resistorless sinusoidal oscillator using single CCCDTA

Hung-Chun Chien a,n, Jian-Min Wang b

a Department of Electronic Engineering, Jinwen University of Science and Technology, No. 99, Anzhong Rd., Xindian Dist., New Taipei City 23154, Taiwanb Department of Vehicle Engineering, National Formosa University, Huwei Township, Yunlin County 63201, Taiwan

a r t i c l e i n f o

Article history:

Received 18 June 2012

Received in revised form

9 December 2012

Accepted 13 December 2012Available online 16 January 2013

Keywords:

Current-controlled current-differencing

transconductance amplifier (CCCDTA)

Dual-mode circuit

Resistorless circuit

Sinusoidal oscillator

92/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.mejo.2012.12.007

esponding author. Tel.: þ886 2 82122000x6842

ail addresses: hcchien@just.edu.tw (H.-C. Chie

fu.edu.tw (J.-M. Wang).

a b s t r a c t

This study proposes a new design for a resistorless second-order sinusoidal oscillator. The proposed

circuit uses a single current-controlled current-differencing transconductance amplifier (CCCDTA) and

two capacitors to perform the functions of a resistorless sinusoidal oscillator. The proposed oscillator

provides a voltage output and a current output simultaneously, and can independently control the

oscillation condition and oscillation frequency by using the separate bias currents of the CCCDTA. This

study first introduces the CCCDTA and the related formulations of the proposed oscillator circuit, and

then presents the non-ideal effects, sensitivity analyses, and design considerations of the proposed

circuit. The proposed oscillator features a compact topology and dual-mode operation, including low

active and passive sensitivities, and has high potential for integration because it is composed of a single

CCCDTA and two capacitors. The HSPICE simulation results in this study confirm the feasibility of the

new resistorless oscillator circuit.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Sinusoidal oscillators have numerous applications in commu-nication, instrumentation, measurement, control, and signal-processing systems [1]. For decades, operational amplifiers (OPAs)have been widely used in various electronic circuit systems andused to construct various sinusoidal oscillators [2]. Operationalamplifier-based sinusoidal oscillators first appeared in the1980s [3]. However, the main disadvantage of these OPA-basedconstructions is that they require excessive active devices andpassive components. Furthermore, OPAs are characterized by aconstant gain-bandwidth product and low slew rate, which limitsthe high-frequency operations of oscillator circuits. The current-mode circuit technique for signal processing has attractedincreasing attention from analog circuit designers in the pastfew years because it shows wider bandwidth, better linearity,higher dynamic operation range and slew rate, functional versa-tility, and simple implementation [4]. The current-mode circuittechnique has become a popular method for designing newactive-RC circuits using recent active devices, which offer severaladvantages over traditional operational amplifiers [5–8]. Previousstudies have presented several typical realizations of active-RCsinusoidal oscillators using various active devices [9–14].In addition to the active-RC topologies, researchers have developed

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n),

several implementations of resistorless sinusoidal oscillators (oractive-C sinusoidal oscillators) using various active devices[15–20] One study [15] proposed six OTA-C-based voltage-mode(VM) sinusoidal oscillators. Each presented circuit was con-structed using three differential-input single-output operationaltransconductance amplifiers (DISO-OTA) and two external capa-citors. The oscillation condition and oscillation frequency for thereported sinusoidal oscillators can be adjusted non-interactivelyto control the bias currents of the DISO-OTAs. Abuelma’attiintroduced a current conveyor (CC) combined with an OTA-based scheme employing a second-generation current conveyor(CCII), three DISO-OTAs, and two capacitors [16]. This circuit wasbased on a 3Rþ2C CCII-based oscillator topology that replacedthe three external linear resistors with DISO-OTA-based activeresistance simulators to achieve a resistorless design. However,the oscillation condition and oscillation frequency of this circuitare interactive control parameters. Another study [17] reportedseveral dual-output operational transconductance amplifier (DO-OTA)-based current-mode (CM) topologies using three to six DO-OTAs with two capacitors. Another feasible approach employing acurrent-controlled current conveyor (CCCII) appears in [19]. Thepresented circuits were implemented using three CCCIIs with twocapacitors. However, the main problem with these circuits is thatthey require a larger number of active devices. Therefore, recentresearch has introduced a current-controlled current-differencingbuffer amplifier (CCCDBA)-based topology consisting of a singleCCCDBA and two capacitors to reduce the number of activedevices [18]. However, this type of circuit does not normally oscillatebecause of the limitation of its oscillation conditions [18].

H.-C. Chien, J.-M. Wang / Microelectronics Journal 44 (2013) 216–224 217

Therefore, an extra resistor is often required to start the oscilla-tion operation. This approach deviates from the classification ofresistorless oscillators. A recent study presented an electronicallytunable dual-mode (DM) resistorless sinusoidal oscillator [20].This circuit exhibits a compact design, which uses one current-controlled current-backward transconductance amplifier (CC-CBTA)and two capacitors. However, the main drawback of this circuit isthat the manner of adjustment for the oscillation condition andoscillation frequency is not independent, thus indicating that thereported oscillator cannot easily tune its oscillation frequencywithout affecting its oscillation condition. The concept of thecurrent-controlled current-differencing transconductance ampli-fier (CCCDTA), which is based on the current-differencing trans-conductance amplifier (CDTA) [21], was first appeared in 2006 [22].Previous studies on this topic have used CCCDTA in variousapplications, including active filters, analog multiplier/dividers,square-rooting circuits, Schmitt triggers, square/triangular wavegenerators, monostable multivibrators, quadrature oscillators,and four-phase quadrature oscillator [23–28]. However, thereare no reports in the open literature of adopting a single CCCDTAwith minimum passive components to develop a dual-moderesistorless sinusoidal oscillator. In view of this, the main objec-tive of this paper is to present a novel CCCDTA-based circuitconfiguration. Based on literature review, this is the first reporteddual-mode resistorless sinusoidal oscillator built by using a singleCCCDTA. The proposed topology requires only one CCCDTA andtwo external capacitors. The circuit configuration is simple andcan operate under dual-mode operation (i.e., voltage and currentoutputs). Because CCCDTA-based application circuits have gainedconsiderable attention in recent years, the presented circuit ispreferable to existing designs for applications in CCCDTA-basedcircuit systems. Compared to previous solutions (active-RC andactive-C oscillators in [9–20]), the proposed circuit features thefollowing benefits: (1) use of the minimum number of activedevices and passive components (except for [20]); (2) a resistor-less design, which is substantially better than the active-RCschemes because of the easier IC manufacture process; (3) dual-mode operation (current- and voltage-mode outputs at a parti-cular time); (4) the oscillation condition and oscillation frequencyare non-interactive control parameters and feature electronicallytunable properties; (5) desirable active and passive sensitivityperformance and less power consumption because only a singleactive device is required; and (6) high impedance current output,which enables the use of cascading applications without the needof supplementary buffer circuits. Table 1 shows the novelty of theproposed circuit by comparing it with previous designs. The restof this paper is arranged as follows: Section 2 presents a modifiedversion of a CCCDTA, including the proposed dual-mode resistor-less sinusoidal oscillator and related governing equations. Section 3introduces the non-ideality analysis and design considerations.Section 4 provides a feasible design procedure for the oscillationcondition and oscillation frequency of the proposed oscillator.This section also presents computer simulations to demonstratethe feasibility of the theoretical analysis; and finally, Section 5offers a conclusion.

2. Proposed CCCDTA and dual-mode resistorless sinusoidaloscillator

The CCCDTA design concept originated from the CDTA [21].The CCCDTA is a versatile current-mode active device and hasproperties similar to the CDTA introduced in [22], except that theCCCDTA has finite input resistances rather than zero inputresistances at the p and n terminals, respectively. The parasiticp and n terminal resistances of CCCDTA simulate resistors,

thereby avoiding any use of external resistors. However, basedon our investigations, these intrinsic input resistances are equaland are tuned by the same bias current of the reported CCCDTA[22]; thus they limit the flexibility and performance of theCCCDTA in some applications. This section presents a modifiedtopology in which the input resistances at the two current inputterminals (p and n terminals) can be directly controlled by thediverse bias currents of the CCCDTA. In addition, the proposeddual-mode resistorless sinusoidal oscillator is introduced. Fig. 1shows the circuit symbol and the equivalent circuit of theproposed CCCDTA. The terminals p and n represent the twocurrent inputs, and the xþ , x� , and z terminals are the high-impedance current outputs. Using these notations, the terminalrelationships of an ideal CCCDTA can be defined by (1), where Rp

and Rn represent the intrinsic resistances at the p and n inputterminals, respectively. These intrinsic resistances can be con-trolled by the bias currents, IB1 and IB3, of the CCCDTA. Eq. (1)shows that the current in the z terminal is the difference of thetwo input currents Ip and In. The voltage at the z terminal isconverted to the output currents, Ixþ and Ix� , by a transconduc-tance gain (gm), which can be controlled by the bias current IB2 ofthe CCCDTA. Fig. 2 shows the internal circuit construction of theproposed CCCDTA, which consists of two principle blocks: acurrent-controlled current differencing circuit (Q1–Q42) and amulti-output transconductance amplifier circuit (Q43–Q56). Forthe BJT CCCDTA (Fig. 2), Eqs. (2)–(4) show the formulations of Rp,Rn, and gm related to the bias currents, indicating that Rp, Rn, andgm can be controlled by using the diverse bias currents. In general,CCCDTA can contain an arbitrary number of x terminals, thusproviding currents Ix in both directions.

Vp

Vn

Iz

Ixþ

Ix�

26666664

37777775¼

Rp 0 0 0 0

0 Rn 0 0 0

1 �1 0 0 0

0 0 0 0 gm

0 0 0 0 �gm

26666664

37777775

Ip

In

Vxþ

Vx�

Vz

26666664

37777775

ð1Þ

Rp ¼VT

2IB1ð2Þ

Rn ¼VT

2IB3ð3Þ

gm ¼IB2

2VTð4Þ

In Eqs. (2)–(4), VT¼BT/q is the thermal voltage, where B is theBoltzmann constant (1.38�10�23 J/K), T is the temperature in K,and q is the electrical charge on the electron (1.602�10�19 C).At room temperature (27 1C), VT is about 26 mV. Fig. 3 shows acircuit diagram of the proposed dual-mode resistorless sinusoidaloscillator, which uses one CCCDTA and two capacitors to meet theminimum requirements of a resistorless oscillator. The proposedcircuit provides voltage and current outputs to achieve dual-mode operation. The presented topology is simple and has a highpotential for IC implementation because it is resistorless and usesonly one active device. It is crucial to note that the x terminalimpedance of the CCCDTA has a high impedance current outputproperty that is cascadable without requiring buffer elements fora current-mode output. However, an external voltage buffer isrequired to use the voltage across the output Vo and avoid theloading effect on this terminal for cascading applications. Ingeneral, such an overhead cost is inevitable in any CCCDTA-based voltage-mode design, because CCCDTAs do not offer anybuffered terminals for voltage outputs used.

Assuming an ideal CCCDTA characterized by (1), routine circuitanalysis yields the characteristic equation of the circuit expressed

Table 1Comparisons of the proposed sinusoidal oscillator to other designs.

Topology (classification) Active device numbers

and passive component

types

Electronically

operation/ Independent

control of oscillation condition

and oscillation frequency

Signal output mode/

Insensitive to temperature

Measured highest operating

frequency/ Implement technology

CDBA-based [9] (Active-RC) CDBA�1 No/Yes VM/No Hundreds of kHz/ Commercial ICs

Resistor�3

(At least one floating)

Capacitor�2

(Floating)

OTRA-based [10] (Active-RC) OTRA�1 No/No VM/Yes Several MHz/ CMOS realization

Resistor�3

(Only one grounded)

Capacitor�2

(Floating)

VF/CF-based [11] (Active-RC) VF/CF�2 No/Yes VM/Yes Several MHz/ CMOS realization

Resistor�3

(At least two floating)

Capacitor�2

(At least one grounded)

DDCCC-based [12] (Active-RC) DDCCC�1 No/Yes CM/Yes Several MHz/ CMOS realization

Resistor�3

(At least one floating)

Capacitor�2

(At least one grounded)

CDTA-based [13] (Active-RC) CDTA�1 Yes/Yes VM/No Hundreds of kHz/ Commercial ICs

Resistor�2

(Floating)

Capacitor�2

(At least one grounded)

CFOA-based [14] (Active-RC) CFOA�2 No/Yes CM/No Several MHz/ Commercial ICs

Resistor�3

(Only one grounded)

Capacitor�2

(Grounded)

DISO-OTA –based [15] (Active-RC) DISO-OTA�3 Yes/Yes VM/No Hundreds of kHz/ Commercial ICs

Resistor�0

Capacitor�2

(Grounded)

CC/OTA -based [16] (Active-RC) CCII�1 Yes/No VM/No Hundreds of kHz/ Commercial ICs

DISO-OTA�3

Resistor�0

Capacitor�2

(At least one grounded)

DO-OTA-based [17] (Active-C) DO-OTA�3 Yes/Yes CM/Yes Several MHz/ CMOS realization

Resistor�0

Capacitor�2

(Grounded)

CCCDBA-based [18] (Active-RC) CCCDBA�1 Yes/No VM/No Hundreds of kHz/ Commercial ICs

Resistor�1

(Floating)

Capacitor�2

(At least one grounded)

CCCII-based [19] (Active-C) CCCII�3 Yes/Yes VM/Yes Hundreds of kHz/ CMOS realization

Resistor�0

Capacitor�2

(Grounded)

CCCBTA-based [20] (Active-C) CCCBTA�1 Yes/No DM/Yes Several MHz/ CMOS realization

Resistor�0

Capacitor�2

(Grounded)

CCCDTA-based (Proposed) (Active-RC) CCCDTA�1 Yes/Yes DM/No Several MHz/ BJT realization

Resistor�0

Capacitor�2

(At least one grounded)

H.-C. Chien, J.-M. Wang / Microelectronics Journal 44 (2013) 216–224218

in (5). Based on (5), the proposed oscillator can produce oscilla-tion if the oscillation condition expressed in (6) is fulfilled.

s2 RpRnC1C2

� �þsRp 2C1þ2C2�gmRnC2

� �þ2¼ 0 ð5Þ

gmRn ¼ 2 1þC1

C2

� �ð6Þ

And, the oscillation frequency of the oscillator is expressed as

oo ¼ 2pf o ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

RpRnC1C2

sð7Þ

By substituting the formulations of the intrinsic resistancesand transconductance gain, as depicted in Eqs. (2)–(4), into

I p

Vp

I n

Vn

Vz

Vx+

Vx_

I z

I x+

xI _CCCDTA

p

n z

x+

x_

IB1 IB2

x+ Vx+

I x+

IB3

xI _

I x+Rp

Rn

_I p I n

gmVz

gmVz

gmVz

I x+

I z

I p

Vp

I n

Vn

Vz

Vx_

Vx+

Vx+

Fig. 1. (a) CCCDTA circuit symbol and (b) its equivalent circuit.

Fig. 2. Internal circuit construction of CCCDTA.

CCCDTA

p

nz x +

x _

x +

IB1 IB2 IB3

C1

I o C2

Vo

Fig. 3. Circuit diagram of the proposed CCCDTA-based dual-mode resistorless

sinusoidal oscillator.

H.-C. Chien, J.-M. Wang / Microelectronics Journal 44 (2013) 216–224 219

Eqs. (6) and (7), the oscillation condition and oscillation frequencyrelated to the bias currents of the CCCDTA are derived by using(8) and (9), respectively.

IB2

IB3¼ 8 1þ

C1

C2

� �ð8Þ

oo ¼ 2pf o ¼1

VT

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi8IB1IB3

C1C2

sð9Þ

Eqs. (8) and (9) show that the oscillation condition is inde-pendently controllable by using the bias current IB2 of the CCCDTAwithout affecting the oscillation frequency, whereas the oscilla-tion frequency can be adjusted by varying the bias current IB1.Both the oscillation condition and oscillation frequency have non-interactive adjustment manners and feature dual electronic con-trols for tuning. Because the oscillation frequency is controllableby using the bias current IB1 of the CCCDTA, a current-controlledsinusoidal oscillator is feasible. Section 4 presents a feasibledesign procedure for the oscillation condition and oscillationfrequency of the proposed oscillator. Compared to the resistorless

oscillators reported in [15–17,19], the proposed scheme usesfewer active devices to realize an electronically tunable non-interactive control resistorless sinusoidal oscillator, and featuresdual-mode operation. Because CCCDTA-based application circuitshave been widely studied, the proposed circuit can serve as apractical design for application in CCCDTA circuit systems.

3. Non-ideality analysis and design considerations

This section considers several non-ideal issues to determinethe influences of non-ideal effects on the proposed circuit.A practical CCCDTA device can be modeled as an ideal CCCDTAwith finite parasitic resistances and capacitances, as well as non-ideal current transfer gains and a transconductance inaccuracyfactor of the CCCDTA [29]. Fig. 4 shows a more sophisticatedcircuit model to represent the non-ideal CCCDTA device, whereRp, Rn, Rx, and Rz are the terminal parasitic resistances. Rp and Rn

are the current-controllable parasitic resistances expressed in(2) and (3), whereas the typical values of the parasitic resistancesRx and Rz connected to the terminals x and z, respectively, arein the range of several mega-ohms. Cx and Cz are the terminalparasitic capacitances from terminals x and z to the ground.Normally, these parasitic capacitances are in the order of severalpFs. In Fig. 4, ap represents the non-ideal current transfer gainfrom the p terminal to the z terminal of the CCCDTA, an denotesthe non-ideal current transfer gain from the n terminal to thez terminal of the CCCDTA, and b is the transconductance inaccuracyfactor from the z terminal to the x terminal of the CCCDTA. Thetypical values of the non-ideal current transfer gains and thetransconductance inaccuracy factor an, ap, and b range from 0.9 to1, with an ideal value of 1. After applying the non-ideal equivalentcircuit mode of the CCCDTA to the proposed circuit (Fig. 3),tedious derivations lead to the following modified character-istic equation, oscillation condition, and oscillation frequency.

H.-C. Chien, J.-M. Wang / Microelectronics Journal 44 (2013) 216–224220

The characteristic equation of Fig. 3 becomes

s2 RpRnC1C2

� �þsRp½ 1þanð Þ C1þC2ð Þ�bgmRnC2�þ 1þanð Þ ¼ 0 ð10Þ

The modified oscillation condition and oscillation frequencywere determined as

bgmRn ¼ 1þanð Þ 1þC1

C2

� �ð11Þ

oo ¼ 2pf o ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þan

RpRnC1C2

sð12Þ

Eqs. (10)–(12) apply the following conditions: Rp5Rx, Rn5Rx,Rp5Rz, Rn5Rz, C1bCx, C1bCz, C2bCx, and ap¼1. By substitutingEqs. (2)–(4) into (11) and (12), the oscillation condition andoscillation frequency are modified as

IB2

IB3¼

4 1þanð Þ

b1þ

C1

C2

� �ð13Þ

oo ¼ 2pf o ¼1

VT

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4ð1þanÞIB1IB3

C1C2

sð14Þ

Eq. (13) shows that the non-ideal current transfer gain an andthe transconductance inaccuracy factor b influence the oscillationconditions. However, this problem can be overcome by slightlyreadjusting the bias current IB2 because an and b are close tounity. The non-ideal current transfer gain an also slightly changesthe oscillation frequency of this circuit. This slight deviation canbe compensated by retuning the bias current IB1 of the CCCDTA tominimize the influence on the frequency of oscillation. Using (12),the active and passive sensitivities of the proposed CCCDTA-basedresistorless oscillator circuit can be derived in (15).

Soo

Rp¼ Soo

Rn¼ Soo

C1¼ Soo

C2¼� 1

2

Sooan¼

1

2

an

1þan

� �ð15Þ

z'

Ideal CCCDTA

p'

n'

x+'

x_

x+'

α I pp α I nn−

VzI z

Rz

Cz

I n

Vn

I p

Vp

Vx_

xI _

I x+

Vx+

Rx

Cx

Vx+

Rx

Cx

Rx

Cx

β gmVz

β gmVz

β gmVz

I x+

IB1 IB2 IB3

Rp

Rn

'

Fig. 4. Non-ideal equivalent circuit model of the CCCDTA.

Table 2Key design formulations for the proposed sinusoidal oscillator.

Configuration

Ideal proposed circuit (formulated by the circuit parameters)

Ideal proposed circuit (formulated by the bias currents)

Non-ideal proposed circuit (formulated by the circuit parameters)

Non-ideal proposed circuit (formulated by the bias currents)

Eq. (15) shows that the proposed circuit achieves goodsensitivity performance because all active and passive sensitiv-ities do not exceed 50% in magnitude. Therefore, the designprocedure must satisfy the conditions Rp5Rx, Rn5Rx, Rp5Rz,Rn5Rz, C1bCx, C1bCz, C2bCx, and ap¼1 to minimize theinfluence of the non-ideal effects and sensitivity factors on theproposed circuit. Because the proposed oscillator (Fig. 3) employsthe minimum active device and passive components, one capa-citor is arranged as a floating connection design. In consideringthe integration aspects, the proposed oscillator circuit with afloating capacitor may render it difficult to implement this circuitin an integrated circuit. However, an advanced layout technology(double ploy layers) can be applied to overcome this obstacle [30].Based on Eq. (9), the oscillation frequency is related to thethermal voltage VT, which is a dependence of the temperatureparameter. The influence of the temperature on the proposedcircuit is reported in the next section, based on simulation tests.Because the resulting circuit uses a single CCCDTA and twocapacitors, the realization is compact and suitable to be imple-mented in standard BJT or CMOS technology. However, if theCCCDTA is realized using CMOS technology, the temperatureproblem of the proposed circuit can be improved. In addition,the dependence on the temperature can also be reduced if thebias current is made by using the proportional to absolutetemperature (PTAT) circuit technology [31]. The BJT CCCDTAshown in Fig. 2 is used to depict the examination of this work(not perfect but sufficient for experiments). Furthermore, theoscillation frequency depends on the temperature variation andcan be easily compensated by slightly readjusting the bias currentIB1; thus, it should not be considered as an unsolved problemin this circuit. Finally, Table 2 summarizes the key designformulations for the proposed dual-mode resistorless sinusoidaloscillator.

4. Design examples and simulation results

This study presents some simulation examples to demonstratethe validity of the theoretical analysis. The proposed circuit(Fig. 3) was simulated with HSPICE circuit simulation softwareusing the bipolar implementation of CCCDTA (Fig. 2). The NPNand PNP in the circuit were simulated using the process para-meters of the NR200N and PR200N bipolar transistors of theALA400 transistor array from AT&T [32] with a71.2 V voltagesupply. Eqs. (2)–(4), (6) and (7) were used to facilitate a feasibledesign procedure for the oscillation condition and oscillationfrequency of the proposed oscillator (Fig. 3). C1 and C2 were firstassigned. By using Eq. (6), gm can be determined when anarbitrarily Rn is chosen. The bias currents IB2 and IB3 can then becalculated using Eqs. (3) and (4), respectively. The oscillationfrequency fo is then specified, and the values of Rp can bedetermined using (7). The value of the bias current IB1 is subse-quently calculated by using (2). For example, the circuit isdesigned for the oscillation frequency of fo¼100 kHz and is

Oscillation condition Oscillation frequency

gmRn ¼ 2 1þ C1C2

� �oo ¼ 2pf o ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

RpRnC1 C2

qIB2IB3¼ 8 1þ C1

C2

� �oo ¼ 2pf o ¼

1VT

ffiffiffiffiffiffiffiffiffiffiffi8IB1 IB3C1 C2

qbgmRn ¼ 1þanð Þ 1þ C1

C2

� �oo ¼ 2pf o ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þan

Rp Rn C1C2

qIB2IB3¼

4 1þanð Þ

b 1þ C1C2

� �oo ¼ 2pf o ¼

1VT

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4ð1þan ÞIB1 IB3

C1 C2

q

Fig. 5. Simulation results of the voltage output Vo for the circuit (Fig. 3): (a) output waveform in the steady state and (b) corresponding frequency spectrum.

H.-C. Chien, J.-M. Wang / Microelectronics Journal 44 (2013) 216–224 221

operated at room temperature 27 1C, and C1¼C2¼10 nF wasselected. The following component values were determined basedon the design procedures: Rp¼Rn¼0.225 kO (IB1¼ IB3¼57.78 mA),and gm¼17.77 mS (IB2¼924.04 mA). In practice, the value ofgm was designed slightly larger than the theoretical value(gm¼17.77 mS) to start the oscillations. It was necessary tochange the value of gm to 17.98 mS (IB2¼934.96 mA) to start theoscillations. The oscillations were built up in the steady-statewaveforms, and Figs. 5 and 6a show the corresponding outputwaveforms for the voltage and current outputs (Vo and Io),respectively. Simulation results show an oscillation frequency offo¼97.08 kHz, which is 2.92% in disagreement with the designedvalue. This slight frequency deviation was caused by the non-ideal current transfer gain an which is similar to the anticipationdescribed in (12). However, this deviation can be overcome byslightly retuning the bias current IB1 of the CCCDTA. Figs. 5 and 6bshow the output frequency spectrums of Vo and Io, respectively.The percent total harmonic distortion (THD%) for the voltageoutput was 2.94%, whereas the percent total harmonic distortionfor the current output was 3.51%. The power consumption wasfounded to be 9.06 mW. The value of the total harmonic distor-tion for the performed experiment may not be acceptable forsome applications. The high precision of a sinusoidal oscillatorshould have a THD lower than 1%. Thus, an additional auxiliaryamplitude control circuit and technology can be used to yield alower total harmonic distortion of the generated output signalsthrough external means. [2]. However, such a circuit and technol-ogy were beyond the scope of this study. Fig. 7 shows the

transient response of the proposed oscillator when buildingthe oscillations for the component values of Rp¼Rn¼0.225 kO(IB1¼ IB3¼57.78 mA), C1¼C2¼10 nF, and gm¼17.88 mS (IB2¼

929.76 mA). With regard to strengthening the start-up processfor oscillation, an external automatic gain control circuit shouldbe used to ensure a smooth start-up process [2]. To attain thehighest applicable operating frequency of the proposed circuit,the fastest and most convenient way is to employ a lowercapacitance value. By adopting Rp¼0.086 kO (IB1¼150 mA), Rn¼

0.197 kO (IB3¼65.9 mA), gm¼11.34 mS (IB2¼590 mA), C1¼0.1 nF,and C2¼1 nF, Fig. 8a shows the simulation results for the voltageoutput and current output waveforms of the proposed circuit inthe steady state with fo¼4.52 MHz. Under this condition, thepercentage of total harmonic distortions was determined to be2.93% for Vo and 4.56% for Io. Fig. 8b shows a start-up case for thehighest frequency of oscillation by adopting Rp¼0.086 kO (IB1¼

150 mA), Rn¼0.197 kO (IB3¼65.9 mA), gm¼11.15 mS (IB2¼580 mA),C1¼0.1 nF, and C2¼1 nF. Because of the limitation of the max-imum slew rate of the proposed CCCDTA (Fig. 2), the highestfrequency of the proposed oscillator was only demonstrated atapproximately several MHz. However, it is concluded that ahigher slew rate of the CCCDTA can be applied to accelerate theoscillation frequency for the proposed oscillator. To demonstratethe influence of the oscillation frequency dependence on thetemperature variation of the circuit (Fig. 3), a test with a designspecification of fo¼100 kHz was executed to explore this char-acteristic. In this experiment, Rp¼Rn¼0.225 kO (IB1¼ IB3¼

57.78 mA), C1¼C2¼10 nF, and gm¼17.98 mS (IB2¼934.96 mA)

Fig. 6. Simulation results of the current output Io for the circuit (Fig. 3): (a) output waveform in the steady state and (b) corresponding frequency spectrum.

Fig. 7. Simulation results of the start-up oscillations of the circuit (Fig. 3).

H.-C. Chien, J.-M. Wang / Microelectronics Journal 44 (2013) 216–224222

were first decided based on the previous design example. Thetemperature was then varied from 0 1C to 70 1C in 10 1C stepsto investigate the oscillation frequency changed. Fig. 9 showsthe test results for the variation of the oscillation frequency underdifferent temperature conditions. Fig. 9 shows that higher tem-perature conditions result in lower oscillation frequency, as

anticipated by using (9). The oscillation deviations between thetheoretical value (fo¼100 kHz) and the test results ranged from2.69% to 11.51%, and the temperatures varied from 0 1C to 70 1C.One feature of the presented circuit is its electronically tunablefunction. To investigate this characteristic, the following valueswere first applied: Rn¼0.197 kO (IB3¼65.9 mA), gm¼11.34 mS

Fig. 8. Simulation results of the highest applicable oscillations of the circuit (Fig. 3): (a) output waveform in the steady state; and (b) the start-up of the oscillations.

0 10 20 30 40 50 60 70

88

90

92

94

96

98

100

102

104

Temperature (oC)

Osc

illat

ion

freq

uenc

y(k

Hz)

Fig. 9. Variation of the oscillation frequency under different temperature condi-

tions of the circuit (Fig. 3).

20 30 40 50 60 70 80 90 100 110 120 130 140 150150

200

250

300

350

400

450

500

550TheoreticalSimulation

IB1 (μA)

Osc

illat

ion

freq

uenc

y(k

Hz)

Fig. 10. Oscillation frequency against the bias current IB1 of the circuit (Fig. 3).

H.-C. Chien, J.-M. Wang / Microelectronics Journal 44 (2013) 216–224 223

(IB2¼590 mA), C1¼1 nF, and C2¼10 nF. IB1 was then changed from20 mA to 150 mA in 10 mA steps to inspect the variation of theoscillation frequency. Fig. 10 shows the theoretical and simulatedresults of the electronic tuning of the oscillation frequency withthe bias current IB1. These simulations results are close to thetheoretical prediction and confirm the feasibility of the proposedconfiguration. The proposed sinusoidal oscillator has a simpletopology and provides dual-mode operation with electronicallytunable properties.

5. Conclusions

This study presents a sinusoidal oscillator that uses a recentlyreported active-device CCCDTA, which has not appeared in theprevious studies. The proposed circuit consists of a single activedevice with only two external capacitors, and is capable of dual-mode operation. This paper describes the related governingequations of the proposed oscillator, and presents a discussionon the non-ideality analysis and design considerations of the

H.-C. Chien, J.-M. Wang / Microelectronics Journal 44 (2013) 216–224224

circuit. The computer simulations in this study show goodagreement with the theoretical analyses. The proposed circuitprovides a novel application for CCCDTA devices. Because of itssimplicity and versatility, the proposed oscillator provides a newpossibility for circuit designers and will have wide applications ininstrumentation, measurement, and communication systems.

References

[1] S. Franco, Design with Operation Amplifiers and Analog Integrated Circuits,3rd ed., McGraw-Hall, New York, 2002.

[2] G. Gonzalez, Foundations of Oscillator Circuit Design, Artech House Publish-ers, Boston, 2007.

[3] B.B. Bhattacharyya, M.T. Darkani, A unified approach to realization of canonicRC-active, single as well as variable, frequency oscillators using operationalamplifiers, J. Franklin Inst. 317 (6) (1984) 413–419.

[4] C. Toumazou, F.J. Lidegy, D. Haigh, Analog IC Design: The Current-ModeApproach, Peter Peregrinus Press, U.K., 1990.

[5] B. Almashary, H. Alhokail, Current-mode triangular wave generator usingCCIIs, Microelectron. J. 31 (4) (2000) 239–243.

[6] Y.H. Ghallab, W. Badawy, Karan V.I.S. Kaler, B.J. Maundy, A novel current-mode instrumentation amplifier based on operational floating current con-veyor, IEEE Trans. Instrum. Meas. 54 (5) (2005) 1941–1948.

[7] Y.K. Lo, H.C. Chien, H.J. Chiu, Current-input OTRA Schmitt trigger with dualhysteresis modes, Int. J. Circuit Theory Appl. 38 (7) (2010) 739–746.

[8] H.C. Chien, Y.K. Lo, Design and implementation of monostable multivibratorsemploying differential voltage current conveyors, Microelectron. J. 42 (10)(2011) 1107–1115.

[9] S. Ozcan, A. Toker, C. Acar, H. Huntman, O. Cicekoglu, Single resistance-controlled sinusoidal oscillators employing current differencing bufferedamplifier, Microelectron. J. 31 (3) (2000) 169–174.

[10] U. Cam, A novel single-resistance-controlled sinusoidal oscillator employingsingle operational transresistance amplifier, Analog Integrated Circuits SignalProcess. 32 (2) (2002) 183–186.

[11] S.S. Gupta, R. Senani, New single resistance controlled oscillators employing areduced number of unity-gain cells, IEICE Electron. Express 1 (16) (2004)507–512.

[12] S. Kilinc, V. Jain, V. Aggarwal, U. Cam, Catalogue of variable frequency andsingle-resistance-controlled oscillators employing a single differential differ-ence complementary current conveyor, Frequenz 60 (7–8) (2006) 142–146.

[13] D. Prasad, D.R. Bhaskar, A.K. Singh, Realisation of single-resistance-controlledsinusoidal oscillator: new application of the CDTA, WSEAS Trans. Electron.5 (6) (2008) 257–259.

[14] A. Lahiri, W. Jaikla, M. Siripruchyanun, Explicit-current-output second-ordersinusoidal oscillators using two CFOAs and grounded capacitors, Int. J.Electron. Commun. 65 (7) (2011) 669–672.

[15] R. Senani, M.P. Tripathi, B.A. Kumar, Systematic generation of OTA-Csinusoidal oscillators, Electron. Lett. 26 (18) (1990) 1457–1458.

[16] M.T. Abuelma’atti, A new electronically tunable integrable CCII-OTA-based

active-C oscillator, Eur. Trans. Telecommun. 2 (3) (1991) 353–355.[17] H. Kuntman, A. Ozpinar, On the realization of DO-OTA-C oscillators, Micro-

electron. J. 29 (12) (1998) 991–997.[18] M. Koksal, M. Sagbas, H. Sedef, An electronically tunable oscillator using a

single active device and two capacitors, J. Circuits Syst. Comput. 17 (5) (2008)885–891.

[19] A. Lahiri, Deriving (MO)(I)CCCII based second-order sinusoidal oscillatorswith non-interactive tuning laws using state variable method, Radioengi-neering 20 (1) (2011) 349–353.

[20] U.E. Ayten, M. Sagbas, H. Sedef, Electronically tunable sinusoidal oscillatorcircuit with current and voltage outputs, Int. J. Electron. 99 (8) (2012)

1133–1144.[21] D. Biolek, CDTA-building block for current-mode analog signal processing, in:

Proceedings of the International Conference on ECCTD’03, 2003, pp. 397–400.[22] W. Jaikla, M. Siripruchyanun, Current controlled current differencing trans-

conductance amplifier (CCCDTA): a new building block and its applications,in: Proceedings of ECTI Conference 2006, 2006, pp. 348–351.

[23] M. Siripruchyanun, W. Jaikla, A current-mode analog multiplier/divider basedon CCCDTA, Int. J. Electron. Commun. 62 (3) (2008) 223–227.

[24] A. Lahiri, A. Chowdhury, Current-mode square rooting circuit using CCCDTA,Int. J. Recent Trends Eng. 1 (3) (2009) 280–282.

[25] M. Siripruchyanun, W. Jaikla, Current-controllable current differencing trans-conductance amplifier and applications in continuous-time signal processingcircuits, Analog Integrated Circuits Signal Process. 61 (3) (2009) 247–257.

[26] P. Silapan, M. Siripruchyanun, Full and electronically controllable current-mode Schmitt triggers employing only single MO-CCCDTA and their applica-

tions, Analog Integrated Circuits Signal Process. 68 (1) (2011) 111–128.[27] C. Sakul, W. Jaikla, K. Dejhan, New resistorless current-mode quadrature

oscillators using two CCCDTAs and grounded capacitors, Radioengineering20 (4) (2011) 890–897.

[28] W. Jaikla, A. Lahiri, Resistor-less current-mode four-phase quadrature oscil-lator using CCCDTAs and grounded capacitors, Int. J. Electron. Commun.66 (3) (2012) 214–218.

[29] W. Tangsrirat, T. Pukkalanun, W. Surakampontorn, Resistorless realization ofcurrent-mode first-order allpass filter using current differencing transcon-

ductance amplifiers, Microelectron. J. 41 (2–3) (2010) 178–183.[30] A. Hastings, The Art of Analog Layout, Prentice-Hall, New Jersey, 2001.[31] A. Lahiri, New CMOS-based resistor-less current-mode first-order all-pass

filter using only ten transistors and one external capacitor, Radioengineering20 (3) (2011) 638–644.

[32] D.R. Frey, Log-domain filtering: an approach to current-mode filterin, IETCircuits Devices Syst. 140 (6) (1993) 406–416.