Download A Novel Single-Resistance-Controlled CFOA-Based

A Novel Single-Element- Controlled CFOA-Based Square Wave
Oscillator
Mashhour Bani Amer and Mohammad Ibbini,
Department of Biomedical Engineering,Jordan University of Science and Technology,
P.O. Box 3030, Irbid 22110, Jordan
Abstract
A novel square wave oscillator circuit using the current-feedback operational amplifier
(CFOA) is presented. The circuit uses one CFOA, three resistors and one capacitor. The
main advantages of this oscillator are that it enjoys independent control of the frequency of
oscillation and the condition of oscillation; and the frequency of oscillation is controlled by
one passive element The experimental results that support the theoretical expectations are
also included.
I.
Introduction
The current-feedback operational amplifiers (CFOA) are getting popularity as alternative
building blocks for analog signal processing [1]–[4]. This is because the CFOA has wide
bandwidth, very high slew rate and ease of realizing various functions with least possible
number of external passive components compared with the conventional voltage feedback
operational amplifier (VFOA). Consequently, there is a growing interest in employing
CFOA’s to the realization of active filters [5]–[7], analogue divider [8], R-L and C-D
impedances, single frequency [10], [12], as well as single-element-controlled sinusoidal
oscillators [13] and square wave oscillators [14].
To the author’s knowledge, the oscillator proposed by [14] is the only CFOA-based
square wave oscillator that has been reported in the literature so far. It uses four passive
elements and one CFOA. However, its frequency of oscillation (FO) cannot be controlled
without disturbing the condition of oscillation (CO). Thus, it can be used in practice as a
single frequency square wave oscillator. Moreover, the experimental evaluation of this
oscillator showed that it could not oscillate square wave with low (fraction of Hz)
frequencies.
The purpose of this paper is to propose a novel square wave oscillator that utilizes one
CFOA and four passive elements. Its major advantage is the feasibility of obtaining
independent control of the frequency and condition of oscillation. Furthermore, single
passive element can realize the control of frequency of oscillation. In addition, the
proposed oscillator can oscillate square waves with very small frequency (fraction of
Hertz).
II.
Proposed Circuit
The general structure of the proposed oscillator is shown in Fig.1. The equivalent circuit
of this oscillator structure is shown in Fig.2 where the dotted box represents a simplified
equivalent circuit for the CFOA [2]. In this equivalent circuit, R IN and RO
represent the output resistances of unity-gain buffers B1 and B2 respectively; Zt(s) is the
CFOA transimpedance and can be expressed as:
1
Zt ( s) 
Rt
.............................................................................. (1)
1  sRt Ct
where Rt and Ct are transresistance and transcapacitance of the CFOA, respectively.
Fig.1. The proposed oscillator circuit.
Fig.2. Equivalent circuit of the oscillator structure of Fig.1. The circuit inside the
dotted box is a simplified equivalent circuit for the CFOA.
A resistor or a capacitor can realize each of Z1, Z2 and Z3. Therefore, several oscillator
circuits can be derived. In deriving these oscillator circuits it must be noted that pure
capacitive feedback between the output and the inverting input of the CFOA is not allowed
[1]. Thus, a resistive feedback (Z4 = R4) path must exist in order to ensure predictable
operation of the oscillator circuit. Each circuit derived from Fig.1 was then analyzed by
determination the characteristic equation assuming ideal CFOA with R IN = RO = 0 Ω.
2
The analysis results showed that only two oscillator circuits could be used as a square
wave oscillator. These two circuits are shown in Fig.3 while the frequency (ωO) and the
condition of oscillation of these circuits are presented in Table 1.
(a)
(b)
Fig.3. The oscillator circuits derived from Fig.1.
Table 1. Frequency and condition of oscillation for the circuits of Fig.3
Circuit
Frequency of Oscillation
(a)
1
 O2 
R1 R3 CCt
(b)
 O2 
R1  Rt
CCt R1 R3 Rt
Condition of Oscillation
Control element
R1C ( Rt  R2 )  R2 Rt Ct
R4
R2 Ct Rt  CR3 ( R2  Rt )
R1
From Table 1, it can be concluded that the frequency of oscillation of the circuit of Fig.3 (a)
can be adjusted by tuning the resistor R3 without disturbing the condition of oscillation.
From Table 1, it can be also concluded that the frequency of oscillation of the circuit of
Fig.3 (b) can be adjusted by tuning the control element R 1 without disturbing the condition
of oscillation. Thus, the circuits of Fig.3 (a) and (b) enjoy the attractive feature of
independent control of the frequency and the condition of oscillation. Moreover, single
resistor realizes the control of the frequency of oscillation.
From Table 1 it is easy to see that the FO and CO is function of the CFOA transimpedance
Zt(s) parameters Rt and Ct. The Zt(s) has a pole at  P  1 Rt Ct .
Although the CFOA does not have a constant gain-bandwidth product [4], it shows some
dependence of  P on the gain. This is attributed to the fact that the R IN and RO of the
buffers B1 and B2 are not exactly zero. Thus  P is not constant and it changes with the
change of the gain. However, the variation of with gain in CFOA is a small second-order
effect, where in VFOA it is a first-order effect [15]. This second-order effect may result in a
slight deviation performance from the theoretically predicted.
3
III.
Experimental Results
The proposed oscillator circuits of Fig.3 were experimentally tested utilizing the AD844
which has an Rt = 3 MΩ and Ct = 4.5 pF [4]. For the oscillator circuit of Fig.3 (a), the
passive elements were selected to be Z1 =R1 = 100 Ω, Z2 = C = 100 pF, Z3 = R2 = 1 MΩ
and Z4 = R4 = 1 MΩ potentiometer. For the circuit of Fig.3 (b), Z1 = R1 = 100 Ω, Z2 = R2 =
100 kΩ, Z3 = C = 68 nF and Z4 = R4 = 10 kΩ potentiometer. A sample of the square waves
obtained from oscillator circuit of Fig.3 (a) are shown in Fig.4
F = 10 kHz, R3 = 0.678 kΩ. VP-P = 2.6 V
(b)
F = 0.1 Hz, R3 = 9.81 kΩ. VP-P = 6.3 V
(a)
F = 100 kHz, R3 = 0.035 kΩ. VP-P = 450 mV
(c)
Fig.4. The output of oscillator circuit of Fig.3 (a) for R1 = 100 Ω, R2 = 100 kΩ, C = 100 pF
and (a) R3 = 9.81 kΩ, (b) R3 = 0.678 kΩ and (c) R3 = 0.035 kΩ.
The results shown in Fig.4 were obtained by tuning only R 3 while the other elements were
use constant along all experiments. From these results it is easy to see that changing R 3
from 0.035 to 9.81 kΩ the frequency increased from 0.1 Hz to 100 kΩ, respectively. The
variation of the frequency of oscillation of Fig.3 (a) with R3 is shown in Fig.5.
During the experimental tuning of R3 for the oscillator circuits of Fig.3 from 0.035 kΩ to
9.81 kΩ, it was observed that the frequency was changed from 0.1 Hz up to about 1 MHz
with a peak-to-peak voltage of 500 mV to 7 V.
4
FO [kHz]
o Theoretical
* Experimental
R3 [kΩ]
Fig.5. Variation of the frequency of oscillation of Fig.3 (a) with resistance R 3.
IV.
Conclusions
In this paper, two novel CFOA-based square wave oscillators have been presented.
Each circuit uses one CFOA three resistors and one capacitor. The main advantages of
these oscillators in comparison with the published in [14] square wave oscillator are:
 They enjoy independent control of the frequency of oscillation and
condition of oscillation.
 The frequency of oscillation is controlled by single-resistive-element.
Thus, they can be used to realize single-element controlled
oscillators.
 They can be used to realize very low frequency oscillators
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