A Sinusoidal Oscillator Using Translinear Current Conveyors

Montree Kumngern and Somyot Junnapiya Department of Telecommunications Engineering, Faculty of Engineering,

King Mongkut’s Institute of Technology Ladkrabang (KMITL) Bangkok 10520, THAILAND

E-mail: {montree, somyot}@telecom.kmitl.ac.th

Abstract—This paper presents a new single-element-controlled current-controlled sinusoidal oscillator. The proposed oscillator is composed of one translinear current conveyor (CCCII), one CCCII with controlled current gain and two grounded capacitors. The oscillator is beneficial to monolithic integrated circuit implementation by the use of grounded capacitors. The oscillation condition and the oscillation frequency can be controlled electronically and independently through the bias current of the CCCII. PSPICE simulation results are given to confirm the operation of the proposed oscillator. Keywords—Sinusoidal oscillator, CCCII, grounded capacitor

I. INTRODUCTION In the last decade, second generation current conveyor

(CCII)-based analog signal processing circuits have received significant attention because of their inherent wide bandwidth, greater linearity, wider dynamic range, simple circuitry and low power consumption [1]–[2]. A variety of CCII-based sinusoidal oscillator circuits have been proposed in [3]–[8]. However, CCII-based oscillators do not offer electronic adjustment properties, since the input port of a CCII can not be electronically tuned. In order to alleviate this problem, Fabre et al. [9] introduced second generation current-controlled conveyors (CCCIIs), and many applications of this new element have been reported in the literature [10]–[13].

Current-controlled sinusoidal oscillator circuits have been proposed in [14]–[18] using CCCIIs. The CCCII-based sinusoidal oscillator circuits have the capability of electronic tuning of the oscillation frequency (ωo). However, these reported circuits suffer from one or more of following weaknesses: (i) excessive use of the active and/or passive components [15]–[17], (ii) not provides non-interactive frequency control [18], (iii) use of floating capacitors [15].

Recently, two CCCII-based single-element-controlled oscillators using only two CCCIIs and two grounded capacitors were suggested by Horng [19] as well as by Fongsamut et al. [20]. However, its oscillation condition is controlled by adjusting the value of two external passive capacitors, i.e. 1.28C1=1.68C2 [19] or C1=1.1C2 [20], which is not well controlled. For integrated circuits, controlling the circuit parameters electronically is much easier to realize that changing the value of the capacitor.

In this paper, single-element-controlled current-controlled sinusoidal oscillator circuit using only two CCCIIs and grounded capacitors is presented. The proposed circuit provides the attractive feature of independent electronic control of the oscillation frequency and the oscillation condition by varying the bias current of the CCCII. The oscillator also exhibits low active and passive sensitivities and is very suitable for integration. PSPICE simulation results that confirm the theoretical prediction are given.

II. PROPOSED CIRCUIT The well-known schematic implementation for CCCII,

implemented with bipolar junction transistors is shown in Fig. 1 [9]. The multiple-output plus/minus CCCII can be obtained by adding additional current mirrors and cross-coupled current mirrors to obtain the required plus and minus type outputs [21]. According to Fig. 1, can be seen component of that CCCII has an unity voltage gain between terminal Y and X, then has an unity current gain between terminal X and Z, and also has an high impedance level of terminals Y and Z that in ideal is equal to infinite, whereas the X terminal has a RX and its can be obtained as [9]

o

TX 2I

VR = (1)

The RX is an inner resistance of a translinear mixed loop (Q1 to Q4) with grounded resistor equivalent controlled by dc bias current Io, where VT is the thermal voltage (≅26mV at 27°C).

The translinear current conveyor with controlled current gain can be obtained by modifying the original circuit of the CCCII and by adding additional current mirror with adjustable gain to obtain the required current gain at Z terminal [22], which is shown in Fig. 2. In this figure, a CCCII with controlled current gain has a unity voltage gain between terminals Y and X and tunable k current gain between terminals X and Z. The latter property makes it different from a current conveyor. The schematic of the CCCII with controlled current gain is characterized by the relationship

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⎠

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VIV

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978-1-4244-7456-1/10/$26.00 ©2010 IEEE 740

Fig. 1. Bipolar implementation of CCCII.

Fig. 2. Bipolar implementation of CCCII with controlled current gain.

The current gain k of the current conveyor can be given by

b

a

IIk = (3)

It can note that the output current is amplified by the factor k and this factor can be varied linearly controlled by adjusting the current ratio Ia / Ib.

The proposed sinusoidal oscillator circuit employing two CCCIIs and two grounded capacitors is shown in Fig. 3. The characteristic equation of Fig. 3 can be expressed as

( ) 01CkCsRRRCCs 112X1X2X1212 =+−+ (4)

The oscillation condition and the oscillation frequency can be obtained, respectively, as

112 CkC = (5)

X2X121o RRCC

1ω = (6)

Using (3) and letting C1=C2, (5) can be simplified as

b1

a1

II1 = (7)

Using (1), (6) can be rewritten as

o2o1

21T

o

IICCV

2ω = (8)

It can be seen from equations (7) and (8) that the oscillation condition can be adjusted by tuning the current ratio Ia1/Ib1 and the oscillation frequency can be controlled by adjusting the bias currents Io1 and Io2. Note that the oscillation condition is independent from temperature effect. Also, due to the employment of grounded capacitors, this oscillator provides a suitable advantage for monolithic integrated circuit (IC) implementation [23].

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Fig. 3. Proposed CCCII-based oscillator.

III. NON-IDEAL EFFECTS The previous realization has been based on the assumptions

that the CCCIIs have ideal characteristics. However, in a practical realization, the non-ideal current transfer and voltage transfer that contribute to error from the ideal performance are present. Taking the non-idealities of the CCCIIs into account, the relationship of the terminal voltage and current can be rewritten as

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X

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VIV

0βk00Rα000

IVI

(9)

where α=1-ε, |ε|«1 represents the voltage tracking error and β=1-δ, |δ|«1 represents the current tracking error.

Using equation (9), the characteristic equation of Fig. 3 becomes

( ) 0ββαCkβαCsRRRCCs 21111222X1X2X1212 =+−+ (10)

The modified oscillation condition and the modified oscillation frequency, respectively, are

11222 CkβαC = (11)

X2X121

211o RRCC

ββαω = (12)

From equations (11) and (12), the tracking errors slightly change the oscillation frequency and it will affect to the oscillation condition. However, this affectation can be easily improved by increasing the current gain of CCCII. Also, the oscillation condition and oscillation frequency still can be orthogonally controllable. The active and passive sensitivities of ωo are analysed and found within 0.5 in magnitude, thus ensuring a good sensitivity performance of the circuit.

IV. SIMULATION RESULTS The proposed oscillator was simulated using PSPICE

simulation program. The CCCII was performed with the transistor model of NR100N and PR100N of the bipolar arrays ALA400 from AT&T [24]. The voltage supply was taken as VCC=1.5V, VEE= –1.5V, C1=C2=1nF, Ia1=55μA and Ib1=50μA where Ia1 was designed to be larger than Ib1 to ensure the oscillations will start. Fig. 4 shows the sinusoidal output waveforms for Io1=Io1=50μA. The design frequency using these values is 616kHz. The results obtained simulations show a frequency of 600kHz. The oscillation frequency is 600kHz instead of 616kHz owing the effect described in Section III. According to (12), this drop-off would be caused by voltage and current tracking errors of CCCIIs. In this case, the power consumption of Fig. 3 is simulated to be about 3.5mW. Fig. 5 shows the plots of the oscillation frequency of varying the value of resistor Io2 from 1 to 500μA with Io1=50μA. The plots for theoretical value are also included for comparing. Finally, the total harmonic distortion is shown in Fig. 6.

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tput

volta

ge (m

V)

Fig. 4. The simulated output waveform.

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500

Bias current Io2 ( A)

SimulationTheory

Fig. 5. Frequency tuning with bias current Io2.

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0.0

2.0

4.0

6.0

8.0

0.0 0.5 1.0 1.5 2.0

Fig. 6. Total harmonic distortion at various the oscillation frequency.

V. CONCLUSIONS In this paper, a new current-controlled sinusoidal oscillator

using CCCIIs is presented. The proposed circuit employs one CCCII, one CCCII with controlled current gain and two grounded capacitors. The oscillation condition and the oscillation frequency can be controlled electronically and independently through the bias current of the CCCII. The used of grounded capacitors is beneficial to IC implementation [23]. The simulation results obtained were found to be in good agreement with the theory. With respect to the CCCII-based oscillators in [19] and [20], the proposed structure can easier control the oscillation condition.

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