An Active-only High-output Impedance Currentmode Quadrature Oscillator Using CCCCTA Basedlossless Differentiators Supawat Lawanwisut
Montree Siripruchyanun
Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mong-kut’s University of Technology North Bangkok, Bangkok, Thailand E-mail:
[email protected]
Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mong-kut’s University of Technology North Bangkok, Bangkok, Thailand E-mail:
[email protected]
Abstract— This article presents a high-output impedance current-mode quadrature sinusoidal oscillator, providing sinusoidal signals, which differ of 90◦ in phase. The features of the proposed circuit are that; oscillation frequency can be electronically controlled; it can provide the quadrature signal, which is free from the preset of oscillation condition. In addition, since the proposed circuit comprises only active elements, which are 2 CCCCTAs and 2 operational amplifiers, it is very suitable to further develop into an integrated circuit. The PSPICE simulation results are depicted.
technique makes circuit becoming smaller chip area, lower power consumption, wider frequency range of operation and programmability [8-11]. The applications can be easily seen in many literatures, for example filter [12], oscillator [13], inductance simulator [14] and etc. Most of oscillators based on integrator block using different active elements [15-18] have been proposed in the literature. But it is well known that the stage-gain of integrator is declined at high frequency. Consequently, these oscillators cannot oscillate as low frequency because the loop gain is decreased. This means that the re-adjusting of oscillation condition is required at high frequency. To solve the mentioned problem, the oscillator based on differentiator is used to achieve the stability of stage-gain at high frequency [19].
Keywords-Quadrature oscillator; CCCCTA; Differentiator; Operational amplifier; Active-only
I.
INTRODUCTION
An oscillator is an important basic building block, which is frequently employed in electrical engineering applications. Among the several kinds of oscillators, a quadrature oscillator is widely used because it can offer sinusoidal signals with 90° phase difference, for example, in telecommunications for quadrature mixers and single-sideband sytems [1]. Presently, the current-mode technique has been more popular than the voltage-mode type. This is due to requirements in low-voltage environments such as in portable and battery-powered equipment. Since a low-voltage operating circuit becomes necessary, the current–mode technique is ideally suited for this purpose, more so than the voltage-mode one. Presently, there is a growing interest in synthesizing current-mode circuits because of their many potential advantages, such as larger dynamic range, higher signal bandwidth, greater linearity, simpler circuitry, and lower power consumption [2].
A reported 5-terminals active element, namely Current Conveyor Transconductance Amplifier (CCTA) [20] has been firstly proposed in 2005, it seems to be a versatile component in the realization of a class of analog signal processing circuits, especially analog frequency filters. In addition, its output gain can be adjusted by input bias current. However, the CCTA cannot be controlled by the parasitic resistances at current input port. Recently, Siripruchyanun and Jaikla have proposed the modified-version CCTA, whose parasitic resistances at current input port can be controlled by an input bias current. It is newly named Current Controlled Current Conveyor Transconductance Amplifier (CCCCTA) [21]. It seems to be a useful building block, since many circuits and systems can be implemented by employing only single CCCCTA. The purpose of this paper is to introduce an active-only current-mode quadrature oscillator using CCCCTA-based differentiators. The oscillation frequency can be electronically adjusted without any oscillation condition. The circuit construction consists of 2 CCCCTAs and 2 opamps without any external passive element. Moreover, the output currents have high impedance, which facilitates cascading in currentmode configurations. The PSPICE simulation results are also shown, which are in correspondence with the theoretical analysis.
The high-output impedance of current-mode oscillators are of great interest because it makes easily able to drive loads and they facilitate cascading without using a buffering device [3-5]. Moreover, circuits that employ only grounded capacitors are advantageous from the point of view of integrated circuit implementation [5-7]. The synthesis and design of analog signal processing circuits using only active elements without any passive element are important in fully integrated circuit (IC) technology. This
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TENCON 2009
II.
where A0 is open-loop DC gain, ω p1 is the first pole frequency
PRINCIPLE OF OPERATION
and B(= Aoω p1 ) is the gain-bandwidth product of the operational amplifier. For the frequencies ω ω p1 , (4) is approximately given by [23]
A. Basic Concept of CCCCTA Since the proposed circuit is based on CCCCTA, a brief review of CCCCTA is given in this section. Generally, CCCCTA properties are similar to the conventional CCTA, except that input voltages of CCCCTA are not zero and the CCCCTA has finite input resistance at the x input terminal. This parasitic resistance can be controlled by the bias current: IB1 as shown in the following equation [21] ⎡ I y ⎤ ⎡0 ⎢ ⎥ ⎢ ⎢Vx ⎥ = ⎢ Rx ⎢ I ⎥ ⎢1 ⎢ z⎥ ⎢ ⎣⎢ I o ⎦⎥ ⎣0
0 0 0 ⎤ ⎡Ix ⎤ ⎢ ⎥ 1 0 0 ⎥⎥ ⎢Vy ⎥ . 0 0 0 ⎥ ⎢Vz ⎥ ⎢ ⎥ ⎥ 0 g m 0 ⎦ ⎣⎢Vo ⎦⎥
A( s) ≅
(5)
C. Principle of Oscillator The oscillator is designed by cascading the inverting and non-inverting lossless differentiators as systematically shown in Fig. 2. From the block diagram in Fig. 2, the current transfer function can be expressed as
(1)
IO (s) = T1 ( s )T2 ( s ) = − s 2τ 1τ 2 . I in ( s )
For the CCCCTA implemented by the CMOS technology, the parasitic resistance Rx and transconductance gm can be expressed as
Rx =
B . s
(6)
At oscillation situation, the system loop gain is equal to unity. Thus (6) is written to be
1 8β n I B1
,
(2)
s 2τ 1τ 2 + 1 = 0 .
and
(7)
From (7), the oscillation frequency is as follows: gm = βn I B2 .
(3)
ωosc =
Here β = μ Cox (W / L ) is the physical parameter of CMOS transistor. In general, CCCCTA can contain an arbitrary number of o terminals, providing currents Io of both directions. The symbol and the equivalent circuit of the CCCCTA are illustrated in Figs. 1(a) and (b), respectively. I B1
Vy i y
Vx ix
IB2
y
o
CCCCTA x
z
io Vo
iz Vz
(a)
y
x
τ 1τ 2
.
(8)
It can be seen from (8) that the oscillation frequency can be controlled by τ 1 or τ 2 , which is free from the preset of oscillation condition.
± g mVZ
1 ix Rx
1
T1 ( s) = sτ 1
T2 (s) = − sτ 2
o
ix
z I in ( s)
(b)
I out ( s)
Figure 2. Systematic diagram of oscillator.
Figure 1. CCCCTA (a) schematic symbol, (b) equivalent circuit.
I B1
B. Operational Amplifier The open-loop gain of a practical internally compensated operational amplifier (OA) is represented by following transfer function
A( s ) =
A0ω p1 s + ω p1
IB2
−o CCCCTA1 y z
x
I B4
o x CCCCTA2 y z
IO
I in
A1 ( s )
B = . s + ω p1
I B3
IO
I in
A2 ( s )
(4) (a)
(b)
Figure 3. Active-only Differentiators for (a) inverting type, (b) non-inverting type.
2
I o 2 ( jω ) Rx 2 g m 2 j 90 = e . I o1 ( jω ) B2
D. Proposed Current-mode Quadrature Oscillator As mentioned in the above section, the proposed oscillator is based on the inverting and non-inverting lossless active-only differentiators. The implementations of the active-only inverting and non-inverting lossless differentiators are shown in Figs. 3(a) and (b), respectively. The current transfer functions can be respectively written as follows: sRx1 g m1 , B1
(9)
sRx 2 g m 2 . B2
(10)
T1 ( s ) = −
The phase difference φ between Io1 and Io2 is
φ = 90°,
I B3
III. SIMULATION RESULTS AND DISCUSSION To prove the performances of the proposed circuit, the PSPICE simulation program was used. The PMOS and NMOS transistors were simulated by using the parameters of a 0.35µm TSMC CMOS technology [22]. Fig. 5 depicts the schematic description of the CCCCTA used in the simulations. The aspect
o x CCCCTA2 o y z
transistor ratios of PMOS and NMOS transistors are listed in Table 1. The circuit was biased with ±5V supply voltages,
I B1
I B4
IO 2
(15)
ensuring that the currents Io2 and Io1 are in quadrature.
and T2 ( s ) =
(14)
−o x CCCCTA1 −o y z
A2 ( s )
IB1=IB3=300µA, IB2=IB4=50µA. LM741 opamp with the gainbandwidth product of B=2π(1.0027)×106 rad.s-1 is used. This yields oscillation frequency of 570kHz.
IB2
IO 1 VDD
A1 ( s )
IO
IO
− IO I B2
I B1
Figure 4. Completely proposed current-mode quadrature oscillator.
VSS
The completed active-only high-output impedance currentmode quadrature oscillator is shown in Fig. 4. The oscillation frequency (ωosc) can be concluded as
Figure 5. Internal construction of CCCCTA.
TABLE I.
ωosc =
B1 B2 . Rx1 Rx 2 g m1 g m 2
− IO
DIMENSIONS OF CMOS TRANSISTORS
W ( μ m) / L( μ m)
CMOS Transistors
(11)
M1-M4 M5-M8,M10-M12 M9 M13-M14 M15-M16 M17-M18,M20-M21,M23 M19,M22 M24-M29
Substituting the parasitic resistance Rx and transconductance gm as respectively shown in (2) and (3) into (11), the oscillation frequency (ωosc) is given by
15/0.5 6/1 5.4/1 0.5/0.5 1.5/1 5/0.5 1/0.5 2/1
1
B1 B2 ⎛ I B1 I B 3 ⎞ 2 ⎜ ⎟ . 8 ⎝ IB2 IB4 ⎠
(12)
40
It is obviously found that from (12), the oscillation frequency can be electronically adjusted by setting IB1, IB2, IB3 or IB4. From the oscillator in Fig. 4, the current transfer function from Io1 to Io2 is
0
ωosc =
I o 2 ( s ) sRx 2 g m 2 . = I o1 ( s ) B2
-40
0
10
20
30
40
50 Time (µs)
60
70
80
90
100
Figure 6. The simulation results of output waveforms during initial state.
(13)
Figs. 6 and 7 show simulated quadrature output waveforms. Fig. 7 confirms that the output currents are in quadrature as analyzed in (14). Fig. 8 shows the simulated output spectrum, where the total harmonic distortion (THD) is about 6.68%. Fig.
For sinusoidal steady state, (13) becomes
3
9 depicts the plots of the simulated oscillation frequencies relative to the bias currents, IB1 and IB3, where IB2=IB4 are identical values of 50μA, 100μA and 200μA.
[2] [3]
Io (µA)
[4]
[5] [6]
Figure 7. The simulation results of output waveforms during steady state. [7] IO (A)
[8]
[9]
[10] Figure 8. The simulation result of output spectrum. [11] 103 IB2=IB4=50μΑ
[12]
IB2=IB4=100μΑ
Frequency(kHz)
IB2=IB4=200μΑ
[13] [14] 102
[15]
[16] 101 1
10
100
300
IB1,IB3(μA)
[17]
Figure 9. Oscillation frequencies against bias currents.
IV.
[18]
CONCLUSSION
A current-mode quadrature oscillator based on active-only differentiators has been presented. The proposed circuit consists of only active-elements, which are 2 CCCCTAs and 2 op amps. The oscillation frequency can be electronically tuned via input bias currents, which is free from the preset of oscillation condition. Due to high-output impedances, it enables easy cascading in a current-mode architecture. As mentioned advantages, the proposed oscillator is appropriate to fabricate into integrated circuit (IC). The PSPICE simulation results agree well with the theoretical anticipation.
[19]
[20]
[21]
[22]
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