Download A Novel Current-Mode Alternative Topology for Oscillator

A Novel Current-Mode Alternative Topology for
Realization of Universal Filter and Quadrature
Oscillator
Winai Jaikla * and Montree Siripruchyanun **
* Electric and Electronic Program, Faculty of Industrial Technology,
Suan Sunandha Rajabhat University, Dusit, Bangkok, 10300, THAILAND Email: [email protected]
** Department of Teacher Training in Electrical Engineering, Faculty of Technical Education,
King Mongkut’s Institute of Technology North Bangkok, Bangkok, 10800, THAILAND Email: [email protected]
Abstract- In this article, a new topology which can function
both as quadrature oscillator and universal biquad filter is
introduced. Working as quadrature oscillator, the oscillation
condition and oscillation frequency can be adjusted independently.
Functioning as universal biquad filter, it can provide 3 standard
functions (Highpass, Lowpass, Bandpass), the quality factor and
cutoff frequency can be tuned orthogonally. It comprises 2 voltage
to current converters, 2 grounded capacitors, 1 positive grounded
and 1 negative grounded resistors. The proposed topology can
work as either quadrature oscillator or biquad filter without
changing circuit topology. In addition, it can provide output
signal both in current-mode and voltage-mode simultaneously.
The current-mode universal filter and quadrature oscillator using
OTAs being active elements as an example are proposed to shown
the usefulness of proposed topology and the PSPICE simulation
results are depicted. The given results agree well with the
theoretical anticipations.
Index Terms- universal filter, OTA, current-mode, quadrature
oscillator, topology
I.
INTRODUCTION
An oscillator and a filter are 2 basic important building
blocks which are frequently employed. A quadrature oscillator
is widely used because the circuit provides two sinusoids with
90o phase difference, as for example in telecommunications for
quadrature mixers and single-sideband generators or for
measurement purposes in vector generators or selective
voltmeters. Therefore, the quadrature oscillator constitutes an
important unit in many communication and instrumentation
systems [1-5]. In similar, nowadays, the applications and
advantages in the realization of various active transfer
functions, called as universal biquad filters, have received
considerable attention. A universal filter may be used in phase
locked loop FM stereo demodulators, touch tone telephone and
crossover networks used in three-way high fidelity
loudspeakers [6].
In the last decade, there has been much effort to reduce the
supply voltage of analog systems. This is due to the command
for portable and battery-powered equipment. Since a lowvoltage operating circuit becomes necessary, the current–mode
technique is ideally suited for this purpose more than the
voltage-mode one. Presently, there is a growing interest in
synthesizing the current-mode circuits because of more their
potential advantages such as larger dynamic range, higher
signal bandwidth, greater linearity, simpler circuitry and lower
power consumption [7-8].
The purpose of this paper is to introduce a new topology to
implement current-mode universal biquad filter and quadrature
oscillator. The features of proposed topology are that:
It can work as universal filter and quadrature
oscillator without changing the circuit topology.
When it works as universal filter, it can provide 3
functions (lowpass, highpass and bandpass) in the
same time. In addition, the natural frequency can
be adjusted independently from the quality factor.
When it works as quadrature oscillator, the
proposed topology can provide quadrature
sinusoidal signals in both voltage-mode and
current-mode simultaneously. Moreover, the
oscillation
condition
can
be
adjusted
independently from the oscillation frequency.
The topology requires only grounded capacitors
(beneficial to an IC implementation [9]).
It can be implemented by employing any active
building blocks to serve as voltage to current
converters and positive/negative resistors, such as
current conveyor, Operational Transconductance
Amplifier (OTA), current feedback op-amp, etc.
Due to commercial availability, the bipolar OTAs are used
as the main active elements to be an example and to investigate
the performances of proposed topology. The PSPICE
simulation results are also shown, which are in correspondence
with the theoretical analysis.
II. PROPOSED TOPOLOGY
A. Proposed topology as a current-mode universal filter
The block diagram of the proposed topology is shown in Fig.
1. It consists of inverting/non-inverting voltage-to-current
converters, positive/negative grounded resistors and two
grounded capacitors. Straightforwardly analyzing the block
diagram in Fig.1, the transfer functions at different terminals of
this network can be obtained as
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s2
I HP
!
I in
I BP
I in
,
(1)
1 " 1
1 # KK
s $s & % '$ 1 2
C1 ( R1 R2 ) C1C2
sK1
C1
,
!
1 " 1
1 # KK
s2 $ s & % ' $ 1 2
C1 ( R1 R2 ) C1C2
I LP
!
I in
S RBW
!
1
and
2
(2)
1
1
.
!%
; S RBW
2
1 % ( R1 / R2 )
( R2 / R1 ) % 1
C. Proposed topology as a quadrature oscillator
If no input current applied to the topology as shown in Fig. 2,
system characteristic equation can be expressed as
s2 $ s
K1 K 2
C1C2
.
1 " 1
1 # K1 K 2
2
s $s & % '$
C1 ( R1 R2 ) C1C2
(3)
1 " 1
1 # K1 K 2
!0.
& % '$
C1 ( R1 R2 ) C1C2
V to I
(K1)
I HP
C1
R1
V to I
(-K2)
I BP
R2
C2
Q0 ! *0
IO 2
C1
From Eqns. (1)-(3), the natural frequency *0 and quality
factor Q0 of each filter response can be expressed as
and
VO 2
I O1
Figure 1. Proposed circuit topology
K1 K 2
,
C1C2
(4)
C1
.
1/ R1 % 1/ R2
(5)
*0 !
(12)
VO1
I LP
R1
R2
We found that the bandwidth can be controlled by R1, R2 or
C1. Moreover, the quality factor can be much high by
controlling 1/R2 to be much less than 1/R1.
B. Topology Sensitivities
The sensitivities of the proposed topology are low and can
be found as
1
1
(7)
S K*10 ! S K*20 ! ; SC*10 ! SC*20 ! % ,
2
2
1
1
1
(8)
S KQ10 ! S KQ20 ! ; SCQ10 ! ; SCQ20 ! % ,
2
2
2
1
1
,
(9)
S RQ10 !
; S RQ20 ! %
1 % ( R1 / R2 )
( R2 / R1 ) % 1
C2
Figure 2. Proposed quadrature oscillator
Eqn. (12) is called as condition of oscillation, then the
characteristic equation of the system is changed to
s2 $
From Eqns. (4) and (5), it can be seen that the quality factor
can be adjusted by varying R1 or R2 without affecting the
natural frequency. On the other hand, the natural frequency can
be adjusted by varying K1 , K 2 , C1 or C2 . Thus bandwidth
( BW ) is given by
* 1/ R1 % 1/ R2
.
(6)
BW ! 0 !
Q0
C1
(11)
From Eqn. (11), it can obviously seen that the proposed
topology can be set to be an oscillator if
R1 ! R2 .
I in
(10)
K1 K 2
! 0.
C1C2
(13)
From Eqn. (13), the oscillation frequency of this system can
be obtained as
*0 !
K1 K 2
.
C1C2
(14)
It can be seen, from Eqns. (12) and (14), that the oscillation
condition can be adjusted independently from the oscillation
frequency by varying R1 or R2, while the oscillation frequency
can be adjusted by varying K1 , K 2 , C1 or C2 .
Furthermore, the quadrature sinusoidal signals can be
obtained both in current-mode and voltage-mode at I O1 and
I O 2 or VO1 and VO 2 of Fig. 2, respectively, with the same time.
III. APPLICATION EXAMPLES
A. Current-Mode Universal Filter Using OTAs
Fig. 3 demonstrates the circuit scheme of the current-mode
universal filter using OTAs. The OTAs are employed as
voltage to current converters and positive/negative resistance
simulators. The depicted bias currents I B1 , I B 2 , I B 3 and I B 4
are the input bias currents of OTA1, OTA2, OTA3 and OTA4,
respectively. From routine analysis, the following current
transfer functions are obtained
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circuit can be obtained by setting I B 4 close to I B 3 , which
differs from conventional universal filters in such that the
maximum Q0 is limited by component values.
$
OTA
% 4
B. Circuit Sensitivities due to element variations
The sensitivities of the OTAs-based circuit are low and can
be found as
1
1
(23)
S g*m01 ! S g*m0 2 ! ; SC*10 ! SC*20 ! % ,
2
2
1
1
1
(24)
S gQm01 ! S gQm02 ! ; SCQ10 ! ; SCQ20 ! % ,
2
2
2
1
1
,
(25)
; S gQm04 ! %
S gQm03 !
1 % ( g m 4 / g m3 )
( g m3 / g m 4 ) % 1
1
1
and
.
(26)
S gBW
!
!%
; S gBW
m3
m4
1 % ( g m 4 / g m3 )
( g m3 / g m 4 ) % 1
%
OTA3
$
I in
I HP
C1
$
OTA1
%
C2
I BP
%
OTA2
I LP
$
Figure 3. Current-mode universal filter using OTAs
I HP
!
I in
I BP
I in
I LP
I in
s2
,
g g
1
+ g m3 % g m 4 , $ m1 m 2
C1
C1C2
sg m1
C1
,
!
g g
1
s 2 $ s + g m 3 % g m 4 , $ m1 m 2
C1
C1C2
g m1 g m 2
C1C2
.
!
g g
1
s 2 $ s + g m3 % g m 4 , $ m1 m 2
C1
C1C2
(15)
s2 $ s
If no input current applied to the circuit in Fig. 3 as shown in
Fig. 4, system characteristic equation can be expressed as
(16)
(17)
and
s2 $ s
g g
1
+ g m3 % g m 4 , $ m1 m 2 ! 0 .
C1
C1C2
IB
,
(20)
2VT C
IB
and
Q0 !
.
(21)
I B3 % I B 4
From Eqns. (20) and (21), it should be observed that the
quality factor can be adjusted independently from the natural
frequency, as explained in section II.B, by varying I B 3 or I B 4 . In
addition, the natural frequency can be adjusted by I B or C.
Thus bandwidth ( BW ) is given by
*
I %I
(22)
BW ! 0 ! B 3 B 4 .
Q0
2VT C
In the same view, the bandwidth can be linearly tuned by I B 3 .
Another advantage of the proposed circuit is that the high Q0
(28)
Eqn. (28) is called as condition of oscillation, this is achieved
by I B 3 ! I B 4 , then the characteristic equation of the system
becomes
s2 $
(19)
Where g mi ! I Bi / 2VT . VT is the thermal voltage. For simple
consideration, and we assign that I B1 ! I B 2 ! I B and
C1 ! C2 ! C , it yields
(27)
From Eqn. (27), it can obviously seen that the proposed circuit
can be set to be an oscillator if
g m3 ! g m 4 .
From Eqns. (15), (16) and (17), the parameters *0 and Q0
can be expressed as
g m1 g m 2
*0 !
,
(18)
C1C2
C1
Q0 ! *0
.
+ g m3 % g m 4 ,
C. Quadrature Oscillator Using OTAs
g m1 g m 2
! 0.
C1C2
(29)
From Eqn. (29), the oscillation frequency of this system can be
obtained as
*0 !
*0 !
g m1 g m 2
.
C1C2
(30)
$
OTA
% 4
%
OTA3
$
VO1
I O1
C1
$
OTA1
%
VO 2
C2
IO 2
%
OTA2
$
Figure 4. Quadrature oscillator using OTAs
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Q6
Q7
Q8
Q1
V$
Q10
Q11
Q2
To investigate and verify the performances of proposed
topology, the current-mode universal filter and quadrature
oscillator based on OTAs have been proposed. The PSPICE
simulation results are well agreed with the theoretical anticipations.
Gain (dB)
VCC
Q9
IO
V%
Q5
IB
Q3
Q4
Q13
Q12
Q14
VEE
Figure 7. Bandpass responses at different values of IB4
Figure 5. Internal construction of OTA
Gain (dB)
10
0
VO1
VO2
IB1=IB2=400 A
IB3=100 A
IB4=103 A
-10
2.00
IV. CONCLUSIONS
The new circuit topology has been presented. The
advantages of the proposed topology are that: it can function
both as quadrature oscillator and current-mode universal filter
(lowpass, highpass and bandpass) without changing a circuit
topology: when it works as the universal filter, the quality
factor and the natural frequency can be orthogonally controlled
by using input bias currents of the OTAs, this is easily
modified to use in control systems using a microcontroller [7]:
when it functions as quadrature oscillator, its oscillation
condition and oscillation frequency can be adjusted independently.
2.04
2.06
Time (ms)
2.08
2.10
Figure 8. Transient responses in voltage-mode outpuyt signals
Io( A)
Figure 6. Gain responses of universal filter
D. Simulation Results
To prove the performances of the proposed circuits, the
PSPICE simulation program was used for the examination. The
PNP and NPN transistors employed in the proposed circuits
were simulated by respectively using the parameters of the
PR200N and NR200N bipolar transistors of ALA400 transistor
array from AT&T [10]. Fig. 5 depicts schematic description of
the OTA used in the simulations. All OTAs were biased with
±2V power supplies and C1 ! C2 ! 10nF . The results shown in
Fig. 6 are the gain responses of the universal filter obtained
from Fig. 3. There are clearly seen that the universal filter
circuit can provide low-pass, high-pass and band-pass
functions, simultaneously.
Fig. 7 display gain responses of bandpass, with different I B 4
values. They are shown that the quality factor can be adjusted
by the input bias current I B 4 as depicted in Eqn. (21) without
affecting the natural frequency. Figs. 8 and 9 show the
responses when operation as quadrature oscillator. The
maximum oscillation frequency is about 11.23MHz.
2.02
Figure 9. Transient responses in current-mode output signals
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