Download Dual-mode Multiphase Sinusoidal Oscillator using CDBAs

Dual-mode Multiphase Sinusoidal
Oscillator using CDBAs
D. Pulsub
and
W. Surakampontorn
Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang (KMITL),
Ladkrabang, Bangkok 10520, THAILAND E-mail: [email protected], [email protected]
Abstract- This paper describes a multiphase sinusoidal
oscillator based on the use of Current Differencing Buffered
Amplifiers (CDBAs). The proposed oscillator provides output
signals both in voltage and current forms simultaneously. It
comprises N cascaded lossy integrators and an inverter, and
generates N+1 sinusoidal signals with 180°/N phase difference.
The SPICE simulation results obtained using AD844 macro
model are given to confirm the theoretical analysis.
I.
vn
ip
iw
in
iz
vw
vz
Figure 1. Circuit symbol of CDBA Put units in parentheses.
INTRODUCTION
The wide use of the multiphase sinusoidal oscillators
(MSOs) in power controllers, communication system and
signal processing [1-5] have stimulated the development of the
MSOs. Voltage-mode operational amplifiers (op-amps) are
widely used for realizing the multiphase sinusoidal waveforms
[6] due to their commercial availability. However, circuit
synthesis techniques in current domain using current
conveyors [7], current followers [8] and operational
transductance amplifiers [9] have gained substantial interests.
The main advantages of processing signal in current form are
wide bandwidth, high slew rate and independent gain
realization without a constant gain–bandwidth product
constraint.
Recently, a new active building block named as a current
differencing buffered amplifier (CDBA) has been introduced
[10]. Since the CDBA consists of a unity-gain differential
amplifier and a unity-gain voltage amplifier, a high frequency
operation and less parasitic can be expected. The MSO based
on CDBAs has been reported in the literature [11], however it
can produce only sinusoidal voltage output. This paper
presents a CDBAs based MSO circuit, which is possible to
provide output sinusoidal signals in both voltage and current
forms simultaneously. The oscillator structure is constructed
by cascading of N stages current domain lossy integrators and
a current inverter. Consequently, the N+1 outputs with 180°/N
phase difference are available.
II.
vp
CIRCUIT DESCRIPTION
The circuit symbol of the CDBA is shown in Fig. 1, where p
and n are the input terminals, z and w are the output terminals.
Its current and voltage characteristics can be described by the
following relations [1-2]
v p= 0 , vn = 0 , iz = ip - in and
vw = vz
.
(1)
vp
vn
ip
iw v
w
in
iz
vz
Figure 2. Circuit implementation of CDBA
using two CFOAs (AD844).
According to Eq. (1), an output current at the z-terminal iz
follows the difference of input currents through the p-terminal
and n-terminal. Then, the output current is converted into an
output voltage vw through an impedance connected at the
terminal z. Although there are numerous techniques to realize
the CDBAs, a popular one is obtained by using two
commercially available CFOAs, AD844 [12], as shown in Fig.
2 [13]. Fig. 3 shows a general block diagram of the MSO for
N+1 phase sinusoidal oscillator. It is constructed by cascading
N stages of current domain lossy integrators and a current
inverter. The output current Io,N of the last stage is fed back to
the first stage through the current inverter. Therefore, the
transfer function between Ii and Io,N can be written as:
' K $
!%
"
Ii
& 1 ( Ts #
I o, N
N
! 1,
(2)
where K is DC current gain of each stage and system time
constant (T) is 1/ c, when c is the internal-pole of the lossy
integrator. By expanding Eq. (2), the characteristic equation is
obtained as
)1 ( Ts *N ( (
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1) N (1 K N ! 0
(3)
I o, 2
I o,1
K
1 ( Ts
K
1 ( Ts
I o, N
I o,( N 1)
K
1 ( Ts
K
1 ( Ts
Ii
Figure 3. General block diagram of the multiphase oscillator
By replacing s = j 0, into Eq. (3), we can find the oscillation
frequency and oscillation condition. It can be proved that this
equation will give a realistic solution only for N 3. To solve
for K and 0, the real and imaginary parts of Eq. (3) are set to
zero. In case of N = 3, Eq. (3) yields
)1 ( j, 0 T *3 ( K 3
!0,
(4)
R1
R2
Ii
Vw
C
Io
K
1 ( Ts
R3 I o
Ii
hence,
(a)
1 3, 0 2T 2 ( K 3 ! 0 ,
(5)
Ii
and
Ii
3 j, 0T
j , 03T 3 ! 0
(6)
where 0 is the oscillation angular frequency. The oscillation
frequency f0 of this case is obtained by solving equation (6) as
f0 !
3 .
2+T
Io
Io
(b)
Figure 4. Sub-blocks and their realization using CDBAs
(a) current domain lossy integrator (b) current inverter
(7)
Substituting Eq. (7) into (5) will give the oscillation condition
that is K = 2. The conditions of the MSO for the others N can
be obtained in a similar way and will result in the MSO with
N + 1 outputs. Each output is equal in amplitude and has phase
shift by 180°/N.
III. PROPOSED CDBA-BASE MULTIPHASE
SINUSOIDAL OSCILLATOR
According to the block diagram representation of the MSO
shown in Fig. 3, the system consists of two repeated subblocks such: current domain lossy integrator and current
inverter. In this work, two new sub-blocks using the CDBA
are introduced in Fig. 4. To perform lossy integrator function ,
the proposed sub-block consisting of one CDBA, three
resistors and one capacitor is show in fig. 4(a). The current
transfer function Io/Ii can be written as
$
'
R1 R 2
%%
""
Io
K
& R1 R 2 ( R1 R3 R 2 R3 #
!
!
I i 1 ( Ts
'
R1 R 2 R3
1 ( sC %%
& R1 R 2 ( R1 R3 R 2 R3
$
""
#
. (8)
For simplicity sake, the current inverter is designed using the
CDBA as shown in figure 4(b). From Eq. (1), when the input
current at terminal p is absent, the current transfer function
(Io/Ii) is obtained equal -1.
By substituting our proposed sub-circuits into the general
block diagram of the MSO in fig. 3, the complete circuit of the
CDBA-based MSO for N = 3, which has 60° phase difference,
can be obtained as shown in fig. 5. Since our proposed
structure exploits an advantage of having both voltage and
current outputs of the CDBA, the resulting MSO will be able
to produce the sinusoidal signals in voltage and current forms
simultaneously. This gives a potential to apply this circuit in
wider range of applications. The current and voltage transfer
function between each lossy integrator stage are equivalent
and can be directly represented use by Eq. (8). For the sake of
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R1
R1
R1
R2
R2
R2
Vo,1
C
Vo,2
C
Vo,3
C
I o,1
I o, 2
I o,3
R3
R3
R3
Vo,0
I o,0
R3
Figure 5. Proposed CDBAs-base multiphase sinusoidal oscillator, which can generate 4 outputs current and 4 outputs voltage
different phase sinusoidal both voltage and current signal output each shifted in phase by 60°
design, let us select the circuit components such that R1 = R3.
Therefore, the current and voltage transfer function are
I o, N
I o, N 1
!
Vo , N
Vo , N 1
!
)R R *
K
! 2 3
1 ( Ts 1 ( sCR 2
.
(9)
The oscillation conditions and the oscillation frequency
solving from Eq. (4) of this circuit are
K!
fo !
R2 ,
R3
3 .
2+R2C
(10)
(11)
Figure 6. The simulated output voltage (Vo,0, Vo,1, Vo,2, Vo,3) and output current
(Io,0, Io,1, Io,2, Io,3) over time at frequency of 28kHz
As already determined in the previous section, the oscillation
condition is satisfied when K = 2 or R2 = 2R3. It should be
noted that, the output voltages are ready to be used since they
appear at the voltage output ports of the CDBAs. However,
the current outputs need additional ports to duplicate the
desired signals to the next stage. This configuration is easily
implemented by employing multi-output current mirrors in
many customed design CDBAs available both Bipolar and
CMOS technology [14 -15].
IV. SIMULATION RESULTS
Figure 7. Frequency spectrum of the waveform in Fig. 6.
Simulation results of the proposed circuit as depicted in
Fig. 5 are obtained using the PSPICE circuit simulator with
±18V supply voltage. To verify the proposed circuit, the dualmode MSO is designed at 27.6 kHz oscillation frequency.
Hence, the capacitor and resistors are calculated by using
Eq. (10) and (11), that are C = 1nF, R1 = R3 = 5 k! and
R2 = 10 k!. The CDBA was constructed using two AD844 as
shown in Fig. 2. In fact, there are non-zero impedances at the
input ports, p and n, that cause the current transfer error and
hence resulting in an oscillation condition violation (K < 2).
In order to compensate this error, the resistor R1 and R3 have
to be reduced to satisfy the oscillation condition (K > 2). In
this case, R1 = R3 = 4.7 k! is selected and K = 2.087 is
obtained. The simulated oscillation frequency of 28 kHz is
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observed and its output voltages (Vo,0, Vo,1, Vo,2, Vo,3) and
output currents (Io,0, Io,1, Io,2, Io,3) over time are shown in Fig. 6.
The outputs have equal amplitude of 13.3 V and 2.83 mA for
voltage and current signals, respectively. Fig. 7 shows
frequency spectrum of the output current signal, which has the
total harmonic distortion (THD) about 1.19 %. Note that the
oscillation frequency is slightly higher than the calculation.
This can be explained by considering Eq. (5). It can be seen
that increasing K will also make 0 higher.
TABLE I
FREQUENCY, AND CURRENT PHASE WHEN VARYING
THE OSCILLATION FREQUENCY
Parameters
C,
fexpected
Oscillation
frequency
Phase comparison
Io,0 - Io,1
Io,0 - Io,2
Io,0 - Io,3
266 kHz
59.38°
118.13°
179.7°
C = 1 nF
fe = 27.6 kHz
28 kHz
59.86°
119.98°
179.8°
C = 10 nF
fe = 2.76 kHz
2.8 kHz
59.66°
119.87°
179.79°
C = 0.1 uF
fe = 276 Hz
280 Hz
59.68°
120°
180°
C = 1 uF
fe = 27.6 Hz
28 Hz
59.67°
119.97°
180°
C = 0.1 nF
fe = 276 kHz
The output voltage (Vo,0, Vo,1, Vo,2, Vo,3, Vo,4) and output
current (Io,0, Io,1, Io,2, Io,3, Io,4 ) have equal amplitude of 13.3 V
and 3.5 mA, respectively.
V. CONCLUSION
A new multiphase sinusoidal oscillator based on CDBAs is
proposed. The proposed circuit can generate sinusoidal
waveforms of both voltage and current signals in the same
circuit, so it can be applied in both voltage mode and
current mode applications. The circuit can realize N+1
difference phase sinusoidal output signals by using N cascaded
lossy integrators and an inverter. This circuit possesses
another advantage of that the oscillation condition can be
always realized from resistor ratio for every chosen oscillation
frequency. The simulation results confirm the theoretical
conclusions very well.
REFERENCES
[1]
[2]
[3]
[4]
The simulation results when varying the capacitor C to
0.1 nF, 1 nF, 10nF, 0.1uF and 1uF, are summarizable in
TABLE I. The expected oscillation frequency, the simulated
oscillation frequency and the phase difference of the output
currents Io,1, Io,2, Io,3 with respect to Io,0 are given. For the
frequency of 28 kHz and lower, the frequency error and phase
shift error of less than 1.82 % and 1.7 % are observed,
respectively. These errors are larger at higher frequency due to
the limitation of the employed AD844. Therefore, for the high
frequency applications, a high performance CDBAs either
implemented in CMOS or Bipolar technology should be
properly designed to overcome this problem. Fig. 8 shows
simulation results of the MSOs for N = 4 at frequency 28 kHz.
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
A. Rahman and S. E. Haque, “A simple three-phase variable-frequency
oscillator,” Int. J. Electron., vol. 53, pp. 83–89, July 1982.
V. P. Ramamurti and B. Ramaswami, “A novel three-phase reference
sinewave generator for PWM invertors,” IEEE Trans. Ind. Electron., vol.
IE-29, pp. 235–240, Aug. 1982.
R. Rabinovici, B. Z. Kaplan, and D. Yardeni, “Fundamental topologies
of three-phase LC resonators and their applications for oscillators,” Proc.
Inst. Elect. Eng., vol. 140, pt. G, pp. 148–154, June 1993.
W. B. Mikhael and S. Tu, “Continuous and switched-capacitor
multiphase oscillators,” IEEE Trans. Circuits Syst., vol. CAS-31, pp.
280–293, Mar. 1984.
B. Z. Kaplan and S. T. Bachar, “A versatile voltage controlled three
phase oscillator,” IEEE Trans. Ind. Electron. Contr. Instrum., vol. IECI26, pp. 192–195, Aug. 1979.
J.Stephan and G.Gift, “Multiphase sinusoidal system using operational
amplifiers”, International Journal of Electronics, vol.83, no.1, pp.61- 67,
1997.
M.T.Abuelma, atti and M.A AI’Quahatani, “Low component second
generation current conveyor-based multiphase sinusoidal oscillator”,
International Journal of Electronics, vo1.84, no.1, pp.45-52, 1998.
D. Prasertsom, T. Pukkalanun, W. tangsrirat “Realization of currentmode multiphase sinusoidal oscillator based on current followers”, The
21st international Technical Conference on Circuit/Systems, Computers
and communications, pp.105-108,2006.
M.T. Abuelma’atti and M.A Ai’Quahatani, “New current controlled
multiphase sinusoidal oscillator using translinear current conveyors”,
IEEE Trans.Circuit & Sys., vol.72, pp.443-450,1992.
C. Acar, and S. Ozoguz, “A new build block: current differencing
buffered amplifier”, Microelectronics journal, 30, pp.157-160, 1999.
K. Klahan, W. Tangsrirat and W.Surakampontorn, “Realization of
multiphase sinusoidal oscillator using CDBAs”, IEEE Asia pacific on
conference on Circuits and Systems, Dec. 6-9, 2004.
AD844 Data Sheet (1992).
J.A Svoboda, l.Mcgory and S. Webb, “Applications of a commercially
available current convoyer”, Int. J. Electron,’ vol. CAS-23, pp.166-169,
1976Science,1989
V. Sawangarom, W. Tangsrirat, W. Surakampontorn, “NPN-based
current differencing buffered amplifier and its application” , SICEICASE,’Otc.18-21,2006
K. Klahan, W. Tangsrirat and W. Surakampontorn, “A low voltage
CMOS current differencing buffered amplifier”, EECON-26,’pp.13371340
Figure 8. The output voltages (Vo,0 ,Vo,1,Vo,2 ,Vo,3) and output currents
(Io,0 ,Io,1,Io,2 ,Io,3) over time at frequency 28 kHz.
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A. An Electronically and linearly tunable CMOS OTA (EOTA)
The OTA1 converts a differential input signal
voltage vin v1 ! v2 into a signal current iL to flow into an
active resistor RL, formed by the OTA2, where Z L 1 g m 2 and
gm2 represents the transconductance gain of the OTA2. Since
the current signal iL g m1Vin , the voltage drop across the active
resistor (OTA2) becomes
VDD
M4
M3
M5
M1
M2
M6
io
V1
V2
io
vin
OTA
IBB
IBB
VSS
M7
vL
M8
iL Z L
g m1vin "
1
gm2
(4)
VSS
The OTA3 will convert the voltage vL, with the transconductance
gain of gm3, into the output current iout as
Figure 1 A balanced CMOS OTA
iout
Figure 1 shows a balanced single-output CMOS OTA,
which is formed by MOS coupled pair and current mirrors,
where Vin is the differential input voltage (Vin=V1-V2), io is the
output current and IBB is the bias current. Let us assume that
M1 and M2 are perfectly matched and the current mirrors have
unity current gain. By using equation (1), the differential
output current of the circuit in Figure 1 can be given by
From equations (4) and (5), the current iout can be rewritten as
iout
KVin2
I
, for ! BB # Vin #
2 I BB
K
I BB
K
(2)
iout
The transconductance gain (gm) of the MOS coupled pair can
be derived by taking the derivative of (2) with respect to Vin,
yielding
dio
dVin
2 I BB K , for !
Vin 0
I BB
# Vin #
K
I BB
K
iout
OTA1
OTA3
iL
IBB1= IBE
vin
IBB3= IBE
vL
iout
2 I BE K1 K 3
2 I BB 2 K 2
Vin
g mT vin
(7)
where gmT represents the transconductance gain of the
proposed EOTA and can be expressed as
(3)
A CMOS-based electronically and linearly tunable OTA,
called as an EOTA [10], that realized by using three OTAs the
circuit diagram shown in figure 1.
vin
(6)
2 I BB1 K1 , g m 2
2 I BB 2 K 2 and g m3
2 I BB 3 K3 ,
if we set IBB1=IBB3=IBE, then from equation (6) we obtain
2 I BB K " Vin " 1 !
gm
g m1 g m 3
vin
gm2
Since g m1
i2 ! i1
io
(5)
g m 3 vL
g mT
2 I BE KT
(8)
and KT
K1 K3 / 2 I BB 2 K 2 , which can usually be kept to
constant. The equation (8) clearly indicted that the
transconductance gain of the proposed EOTA can be
electronically and linearly tuned by the bias current IBE.
B. The proposed electronically and linearly tunable sinusoidal
quadrature oscillator
EOTA
IBE
The proposed electronically tunable sinusoidal quadrature
oscillator is constructed by using EOTAs and OTAs
OTA2
IBB2
Figure2. An electronically and linearly tunable CMOS OTA
(EOTA)
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100000
REFERENCES
C=1nF
Frequancy, (Hz)
operation at high frequencies. Simulation results have been
employed to demonstrate the performances of the proposed
oscillator.
10000
C=10nF
1000
Predicted
C=20nF
Simulated
100
1.00E-03
1.00E-04
IBE, (A)
Figure 5. Frequency tunable range of the oscillator
Figure 5 demonstrates the oscillation frequency that
tunable with respect to the dc bias-current IBE1=IBE2=IBE,
where the bias current is varied from 100$A to 1000$A. and
for the cases of C= 20nF, C=10nF and C=1nF, respectively.
The figure shows that, for the cases of C= 20nF, C=10nF and
C=1nF, the oscillation are in the frequency ranges of 500 Hz
to 5 kHz, 1 kHz to 10 kHz and 10 kHz to 98 kHz, respectively,
with the error of less that 5%. This result demonstrates that the
maximum frequencies up to 98 kHz is achieved by reducing
the capacitance values (C1=C2=C=1nF).
IV. CONCLUSIONS
A design of CMOS-based electronically tunable quadrature
oscillator has been proposed. The oscillator is realize by using
two EOTAs, two OTAs and two grounded capacitors which is
suitable for implementing in CMOS integrated form. Its
oscillation frequency can be electronically and linearly tuned
for a wide range by the transconductance gain without
affecting the oscillation condition and the capability of
[1] M.T. Abuelma’atti, “Two new integrator active OTA-based voltage
(current) controlled oscillator”, International Journal of Electronics,
Vol.66, 1989, pp.135–138.
[2] B. Linaress-Barranco, A. Rodriguez-Vazquez, E., Sanchez-Sinencio, and
J.L. Huertas, “CMOS OTA-C high frequency sinusoidal oscillators”,
IEEE Journal of Solid-State Circuits, Vol.26, 1989, pp.160–165.
[3] M.T. Ahmed, I.A. Khan, and N. Minhaj, “On transconductance-C
quadrature oscillator”, International Journal of Electronics, Vol.83, 1997,
pp.201–207.
[4] I.A. Khan and S. Khwaja, “An integrable gm-C quadrature oscillator”,
International Journal of Electronics, Vol.87, 2000, pp.1353–1357.
[5] B. Srisuchinwong, “Fully balanced current-tunable sinusoidal quadrature
oscillator”, International Journal of Electronics, Vol.87, 2000, pp.547–
556.
[6] Sen-Iuan Liu and Tu-Hung Liao, “Current-mode quadrature sinusoidal
oscillator using single FTFN”, International Journal of Electronics,
Vol.81, 1996, pp.171–175.
[7] B. Linaress-Barranco, A. Rodriguez-Vazquez, E. Sanchez-Sinencio, and
J.L. Huertas, “10 MHz CMOS OTA-C voltage controlled quadrature
oscillators”, Electronics Letters, Vol.25, 1989, pp.765–767.
[8] Michael P. Flynn and Sverre U. Lidholm, “A 1.2-um CMOS CurrentControlled Oscillator”, IEEE J. of Solid-State Circuits, Vol. 27, no.7,
1992, pp.982-987.
[9] Antonio J. Lopez-Martin and A. Carlosena, “A tunable CMOS square-root
domain oscillator”, IEEE Symposium on Circuits and Systems, Geneva,
Switzerland, 2000, pp.V-573-V-576.
[10] K. Kaewdang, W. Tangsrirat and W. Surakampontorn, “An
Electronically and Linearly Tunable CMOS OTA,” The 2004
International Technical Conference On Circuits/Systems,Computers and
Communications (ITC CSCC 2004), Sendai, Japan, 2004, pp. 6A3L-1-1-6A3L-1-4.
[11] K. Kumwachara and W. Surakampontorn, “An Integrable TemperatureInsensitive gm-RC Quadrature Oscillator” International Journal of
Electronics, Vol. 90, no.9, 2003, pp. 599 - 605.
[12] H. O Elwan, A. M. Soliman, “Low-Voltage Low-Power CMOS Current
Conveyors,” IEEE Trans. Circuits and Systems 44 (1997) 828-835.
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Vo2
IBB3
Vo1
EOTA1
EOTA2
C1
IBE1
C2
IBE2
OTA4
g mT
C
.0
OTA3
The gm-C quadrature oscillator based on the use of
EOTAs is shown in Fig.3. The quadrature oscillator circuit
diagram is similar to the bipolar-based quadrature oscillator
circuit of the reference 11. The basic building blocks of the
oscillators consist of two integrators cascaded in a loop; an
inverting integrator (EOTA and C1) and a non-inverting
integrator (EOTA2 and C2). It should be noted that a
regenerative circuit made by the balance CMOS OTA, OTA3
and OTA4, are included in order to place the poles in the righthalf complex plane so that the circuit is unstable and selfstarting, from equation (7), the characteristic equation of the
oscillator can be express as
% g ! g m 4 & g mT 1 g mT 2
s 2 ! s ( m3
)'
C2
C 1 C2
*
+
0
(9)
Therefore, in order to initially locate the poles inside the righthalf complex frequency plane to assure self-starting operation,
the condition for the oscillation can be start as
g m3 ! g m 4 - ,
(10)
III. SIMULATION RESULTS
The performance of the proposed electronically and
linearly tunable sinusoidal quadrature oscillator of figure3 was
verified through the use of PSPICE simulation results. All the
balanced CMOS OTA and EOTAs were simulated by using
CMOS transistor parameters of the SCN2 level 2 of MOSIS
[12]. The dimensions of transistors M1 and M2 are W=50$m and
L=10$m. The dimensions of the transistor M3-M8 are W=100$m
and L=10$m. The power supply voltage were set to VDD = -VSS =
/ 5V.
Figure 4 shows the results obtained from the
electronically and linearly tunable quadrature oscillator circuit
of figure 3 in the case of C1=C2=C=20nF. IBE1=IBE2=IBE=1mA,
IBE3=1mA,
IBE4=995µA,
with
2 I BE 3 K3 ! 2 I BE 4 K 4 =1.26µA. The simulated
=
oscillation frequency with quadrature outputs of equal
magnitude of about 5 kHz is achieved. The circuit provides
the oscillation frequency with the error of less than 5%, since
the predicted oscillation frequency from the equation (13) is
about 4.8 kHz.
20nV
10nV
0V
or
I BB 3 ! I BB 4
where
is
(13)
It is obvious from (12) and (13) that the oscillation frequency
can be tuned without disturbing the oscillation. Moreover, the
frequency of oscillation .0 can be linearly controlled by
adjust the dc bias current IBE1=IBE2=IBE.
IBB4
Figure 3. The proposed electronically and linearly tunable
sinusoidal quadrature oscillator
2 I B KT
C
,
-,
(11)
-10nV
is a small positive number. The oscillating frequency
-20nV
0s
0.2ms
V(C2:1)
.0
g mT 1 g mT 2
C1C2
(12)
0.4ms
V(C1:1)
0.6ms
0.8ms
Time
Figure 4. Simulation results of the gm-C quadrature oscillator
Where gmT1=2IBE1KT and gmT2=2IBE2KT. For simplicity, if we
set C1=C2=C and gm1=gm2=2IBEKT, the frequency of
oscillation can be given by
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1.0ms