Resistorless Current-mode Quadrature Sinusoidal Oscillator Using CDTAs

Abstract

APSIPA ASC 2009: Asia-Pacific Signal and Information Processing Association, 2009 Annual Summit and Conference. 4-7 October 2009. Sapporo, Japan. Poster session: Advanced Circuits and Systems/VLSI (5 October 2009). A circuit technique for realizing a current-mode quadrature sinusoidal oscillator using current differencing transconductance amplifiers (CDTAs) as active components is presented in this paper. The proposed circuit employing only three CDTAs and two grounded capacitors can provide two quadrature sinusoidal current outputs with 90° phase difference. The oscillation condition and the oscillation frequency (ωo) of the proposed circuit can be electronically and orthogonally tuned. Simulation results with PSPICE are used to confirm the presented theory.

Full text

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Instructions for use
Title
Resistorless Current-mode Quadrature Sinusoidal Oscillator
Using CDTAs
Author(s)Tanjaroen, Wason; Tangsrirat, Worapong
Citation
Proceedings : APSIPA ASC 2009 : Asia-Pacific Signal and
Information Processing Association, 2009 Annual Summit and
Conference: 307-310
Issue Date2009-10-04
Doc URLhttp://hdl.handle.net/2115/39698
Right
Typeproceedings
Additional
Information
Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP

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Resistorless Current-mode Quadrature Sinusoidal
Oscillator Using CDTAs
Wason Tanjaroen and Worapong Tangsrirat

Faculty of Engineering and
Research Center for Communications and Information Technology (ReCCIT),
King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bangkok 10520, Thailand
E-mail : t-wason@src.ku.ac.th and ktworapo@kmitl.ac.th



Abstract- A circuit technique for realizing a current-mode
quadrature sinusoidal oscillator using current differencing
transconductance amplifiers (CDTAs) as active components is
presented in this paper. The proposed circuit employing only
three CDTAs and two grounded capacitors can provide two
quadrature sinusoidal current outputs with 90o phase difference.
The oscillation condition and the oscillation frequency (ω ωo) of the
proposed circuit can be electronically and orthogonally tuned.
Simulation results with PSPICE are used to confirm the
presented theory.
Keywords: Current differencing transconductance amplifier
(CDTA), Quadrature oscillator, Current-mode circuit

I.
INTRODUCTION
The quadrature sinusoidal oscillator is widely used in analog
signal-processing and communication. The quadrature
oscillator is employed because it can generate two sinusoidal
outputs of identical frequency but of 90° phase shift, as for
examples in telecommunications for quadrature mixers and
single-sideband generators or for measurement purposes in
vector generator or selective volmiters [1]. Several
synthesizes of quadrature oscillator circuits have received
considerable attention [2]-[4]. However, these earlier
quadrature oscillators operate in voltage-mode. Current-mode
quadrature sinusoidal oscillator circuits are receiving much
attention because of their potential advantages such as wider
bandwidth, wider dynamic range, simpler circuitry, and lower
power consumption. Considering this fact, a number of
current-mode quadrature sinusoidal oscillator realizations
using CDTAs were reported in the literature [5]-[8]. all of
these quadrature oscillators suffer from the following
disadvantages: (i) the oscillation condition and the oscillation
frequency are interdependent [7]; (ii) the use of some external
passive resistors [5]-[7]; (iii) the use of a large number of
CDTAs in circuit realization, namely four CDTAs [8].
In this paper, the resistorless realization of an electronically
tunable current-mode quadrature sinusoidal oscillator using
only three CDTAs and two grounded capacitors is proposed.
Comparing to the recently realization available in [5]-[8], the
proposed circuit offers the following advantages: (i) two
quadrature sinusoidal output waveforms of 90o phase shift are
obtained simultaneously without
configuration; (ii) the oscillation condition and the oscillation
frequency are independently tunable; (iii) the use of only
grounded capacitor, which makes the circuit attractive for
integration; (iv) low sensitivity. Simulation results verifying
the theoretical analysis are also included.

changing circuit
II.
CIRCUIT DESCRIPTION
The circuit representation of the CDTA is shown in Fig.1,
where p and n are input terminals, z and x are output
terminals. The terminal relation of the CDTA can be
expressed by the following matrix [9]-[10]:

⎡
−
⎥
⎢
v
00

where gm is the transconductance gain of the CDTA, and Zz is
an impedance connected at the terminal z. From equation (1),
the current through the terminal z (iz) follows the difference of
the currents through the terminals p and n (ip-in), and flows
from the terminal z into an outside impedance Zz. The voltage
drop at the terminal z is transferred to a current at the terminal
x (ix) by a transconductance gain (gm), which is generally
controllable by electronic means.


⎥
⎦
⎥
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎢
⎡
⎥
⎦
⎥
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎢
=
⎥
⎦
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎡
x
z
n
p
m
n
p
x
z
v
v
i
i
g
v
i
i
00
0000
000
0011
(1)
vp
vn
vx
ix
ix
vx
ip
in
n
x
x
p
CDTA
z
IB
vz

iz

Fig 1 Symbol of the CDTA.
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IB /2
Q5
Q2n
n
in
IA
Q1n
Q4n
Q3n
+V
-V

Q2p
p
ip
IA
Q1p
Q4p
Q3p
z
iz
IB
IB /2
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q14
Q13
Q16
Q19
x
ix
Q15
Q17
Q18
Q20
x
ix

Fig.2 Possible bipolar implementation of the CDTA.

IB2
C2
CDTA2
z
p
n
x
x
io2
CDTA1
z
p
n
x
x
x
IB1
io1
IB3
C1
CDTA3
z
n
p
x
x


Fig.3 Proposed current-mode quadrature oscillator.

Fig.2 shows the possible bipolar implementation of the
CDTA circuit used in this work [11]. It mainly consists of a
current subtractor formed by current followers Q1p-Q4p and
Q1n-Q4n, and a multiple-output transconductance amplifier Q8-
Q20 that converts the voltage drop at the terminal z (vz) to its
corresponding differential output currents ix. In this case, the
transconductance gain gm is directly proportional to the
external bias current IB, which can be written by:


T
B
m
V
I
g
2
=
(2)
where VT ≅ 26 mV at 27οC is the thermal voltage

III. PROPOSED CIRCUIT
The proposed current-mode quuadrature oscillator is shown
in Fig.3, which is based on the use of three CDTAs and two
grounded capacitors. From routine calculations for the
proposed quadrature oscillator, the characteristic equation of
the circuit can be written by:

⎛
−
+
C

0
21
21
1
132
=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
⎟⎟
⎠
⎞
⎜⎜
⎝
CC
gggg
ss
mmmm
(3)

From equation (3), the oscillation condition and the
oscillation frequency (ωo) can also be obtained as:


1
m
g
=

g
=ω
3
m
g
(4)
and
21
21
0
CC
g
mm
(5)

Further, if we setting C1 = C2 = C and by substituting
equation (2) into equation (4) and (5), the oscillation
condition and oscillation frequency can now be rewritten as

I
=
31
BB
I
(6)

and
210
2
1
BB
T
II
CV
=ω
(7)

It is interesting to note that the oscillation condition can be
electronically controlled by adjusting IB3 without taking an
effect to ωo, that is adjusted by IB2 and/or C. Therefore, both
the oscillation condition and ωo of the proposed oscillation are
orthogonally controlled. From Fig.3, the current transfer
function between quadrature outputs io2 and io1 can be
expressed as:

308

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2
2
1
2
sC
g
i
i
m
o
o
=
(8)

Equation (8) shows that the phase difference (φ) between io2
and io1 is 90o. This recommends that the currents io1 and io2 are
in quadrature.

IV. NON-IDEAL EFFECTS
By taking into consideration of the non-ideal CDTAs, the
relationship of the terminal current and voltage given in
equation (1) can be rewritten as:

⎡
−
⎥
⎢
v
00
⎥
⎦
⎥
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎢
⎡
⎥
⎦
⎥
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎢
=
⎥
⎦
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎡
x
z
n
p
m
np
n
p
x
z
v
v
i
i
g
0
v
i
i
00
000
000
00
β
αα
(9)

where αp = 1- εp and εp (|εp| << 1) is the current tracking
errors from p to z terminals, αn = 1- εn and εn (|εn| << 1) is the
current tracking errors from n to z terminals, and β = 1 – εv
and εv (|εv| << 1) is the transconductance inaccuracy factor
from z to x terminals, respectively. Reanalysis the proposed
oscillator circuit of Fig.3 using equation (9) yields the
modified characteristic equation as follows:

⎞
⎜⎜
⎝
C

where αpi, αni and βi are the parameters αp, αn and β of i-th
CDTA (i = 1, 2, 3), respectively. In this case, the modified
oscillation condition and oscillation frequency are:

g
βα

βαα
ω =
0
21
212121
1
111333
2
=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
⎟⎟
⎠
⎛
−
+
CC
gggg
ss
mmpnmpmn
ββααβαβα
(10)
333111
mnmp
g
βα=
(11)
and
21
212121
0
CC
gg
mmpn
β
(12)

The sensitivities with respect to the active and passive of the
oscillation can be written as:


2
1
0
2
, 1
C
0
m
2
, 1
=−=
ωω
gC
m
g
SS
(13)


2
1
0
, 1
n
2, 1
β
, 2
p
=
ω
αβα
S
(14)

and
0
0
p
3, 3
n
,
2 , 3
p
, 1
=
ω
αβααα
n
S
(15)

It is important to note that the active and passive
sensitivities are within unity in magnitude. Thus, the proposed
circuit exhibits a low sensitivity performance.

V.
SIMULATION RESULTS
The proposed CDTA-based current-mode quadrature
oscillator configuration of Fig.3 has been simulated with
PSPICE simulation program. In simulations, the CDTA was
performed with the transistor model of PR100N (PNP) and
NP100N (NPN) of the bipolar arrays ALA400 from AT&T
[12]. The power supply voltages were set equal to ±V = ±3V,
and the bias current was IA = 200 µA.
To obtain the quadrature output waveforms with the
oscillation frequency of fo = ωo/2π ≅ 478 kHz, the active and
passive components were chosen as: IB1 = IB2 = IB3 = IB = 150
µA and C1 = C2 = 1 nF. Fig.4(a) shows the simulated
quadrature output responses io1 and io2, where the simulated
frequency of the oscillation is found to be 470 kHz. Fig.4(b)
represents the simulated frequency spectrums of the proposed
circuit. In addition, the total harmonic distortion (THD) of the
output responses io1 and io2 is approximated to 2.5%.


200
io2
io1
Time (µs)
(a)

646648 650652 654656658 660
-200
-100
0
100
Output current (µA)

Frequency (kHz)
(b)

400440480520 600
0
100
200
Currents
io1
io2
(µA)
560

Fig.4 Simulated quadrature output responses io1 and io2 of the proposed
oscillator.
(a) output waveforms (b) output spectrums
309

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Oscillation frequency (kHz)
0
800
1200
1600
0
100200
300
400
500
400
Simulation
Theory
Bias current, IB (µA)


Fig.5 Theory and simulation results of the oscillation frequency (f0) by
varying the bias current IB


The tunability of the oscillation frequency (f0) by varying
the bias current IB is shown in Fig.5. It is obvious that the
simulated responses are found to be in good agreement with
the theoretically predicted behaviour. The deviation between
the theoretical calculated with equation (7) and simulated
values are less than 2.5%, 5.6% and 8.8% for IB within the
ranges of 100-200 µA, 200-400 µA and 400-500 µA,
respectively. However, this influence can easily be minimized
by simply adjusting IB of the CDTAs.

VI. CONCLUSIONS
The resistorless realization of current-mode quadrature
oscillator using three CDTAs and two grounded capacitors
has been proposed in this paper. The proposed quadrature
oscillator circuit offers the following advantages:
(i) Realization of two quadrature sinusoidal output
waveforms of 90o phase shift is obtained simultaneously,
without changing circuit configuration.
(ii) Independent current-control
condition and the oscillation frequency.
(iii) Using only grounded capacitors for its realization,
which is suitable for integration.
(iv) Low passive and active sensitivities.
PSPICE simulations are given to verify the theoretical
analysis.

of the oscillation
ACKNOWLEDGEMENT
This work is funded by the Commission on Higher
Education & ASEAN University Network / Southeast Asia
Engineering Education Development Network (CHE &
AUN/SEED-Net).





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International Journal of
Signal Processing
amplifier and its
current differencing
310