Current mode quadrature oscillator using current
differencing transconductance amplifiers (CDTA)
A.Ü. Keskin and D. Biolek
Abstract: A CDTA-based quadrature oscillator circuit is proposed. The circuit employs two
current-mode allpass sections in a loop, and provides high-frequency sinusoidal oscillations in
quadrature at high impedance output terminals of the CDTAs. The circuit has no floating
capacitors, which is advantageous from the integrated circuit manufacturing point of view.
Moreover, the oscillation frequency of this configuration can be made adjustable by using voltage
controlled elements (MOSFETs), since the resistors in the circuit are either grounded or virtually
grounded.
1
Introduction
In the last decade, various new current-mode (CM) active
building blocks have received considerable attention owing
to their larger dynamic range and wider bandwidth with
respect to operational amplifier (opamp)-based circuits. As
a result, current-mode active components have been
increasingly used to realise high-speed and high-bandwidth
circuits operating in the current or the voltage mode.
The term quadrature oscillator (QO) is used because such
a circuit provides two sinusoids with 901 phase difference.
Various types of QOs are reported in the literature. In [1],
an active RC integrator and a passive RC integrator are
combined with a negative resistance to yield a QO. Another
QO using active-R circuits is described in [2]. The study
in [3] presents an operational transconductance amplifier
(OTA)-based current-mode integrator and an all-pass
section and their application to design of a dual-mode
QO. Operational transresistance amplifier (OTRA)-based
QOs using virtually grounded passive components have
been introduced in [4]. Maheshwari [5] reports a QO using
three current-controlled current conveyors of negative type
(CCCII-) and floating passive components, generating
relatively low-amplitude and unequal sinusoidal output
signals. The QO described by Toker et al. [6] uses two
positive second-generation current conveyors, but a voltage
buffer is also required to avoid the loading problem.
Alternatively, Horng [7] introduces a QO consisting of two
current differencing buffered amplifiers (CDBAs), however
this circuit does not exploit the full capacity of the CDBA,
since the positive input terminal of one active element is
unconnected. Another earlier work on building a QO using
the CDBAs is reported in [8].
In this paper, we propose new first-order current-mode
allpass sections using the current differencing transcon-
ductance amplifier (CDTA). Based on these canonic
sub-sections, a quadrature oscillator is designed. Simulation
results verifying the theoretical analysis are also included.
2 Current differencing transconductance
amplifiers
The CDTA element [9–11] with its schematic symbol in
Fig. 1 has a pair of low-impedance current inputs p and n,
and an auxiliary terminal z, whose outgoing current is the
difference of input currents. Here, output terminal currents
are equal in magnitude, but they flow in opposite directions,
and the product of transconductance (gm) and the voltage at
In
Vn
Ix−
x−
n
CDTA
Vp
x+
P
z
Ip
Ix+
Iz
a
gmVz
Vz
p
x+
ip
z
Z
− gmVz
r The Institution of Engineering and Technology 2006
IEE Proceedings online no. 20050304
doi:10.1049/ip-cds:20050304
Paper first received 28th July 2005 and in final revised form 22nd January 2006
A.Ü. Keskin is with the Department of Biomedical Engineering, Yeditepe
University, Kayisdagi 34755, Istanbul, Turkey
D. Biolek is with the Department of Microelectronics, Brno University of
Technology, Udolni 53, Brno, Czech Republic
E-mail: dalibor.biolek@unob.cz
214
ip-in
n
x−
in
b
Fig. 1
Symbol and ideal model of CDTA
a Symbol for the CDTA
b Ideal model of CDTA. Here, Z is externally connected impedance
IEE Proc.-Circuits Devices Syst., Vol. 153, No. 3, June 2006
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Vdd
M8
M10
M17
M16
M15
M18
M19
M20
IB1
I+
M3
M5
Vp
M1
n
p
M6
M4
IB2
Vn
z
M2
I−
M14
M13
M11
IB3
M12
M21
M7
M9
M22
M24
M23
Vss
Fig. 2
CMOS-based CDTA
IB1 ¼ IB2 ¼ 85 mA, IB3 ¼ 200 mA, bandwidth ¼ 400 MHz, VDD ¼ VSS ¼ 2.5 V
the z terminal gives their magnitudes. Therefore, this active
element can be characterised by the following equations
R1
p
lin
Vp ¼ Vn ¼ 0; Iz ¼ Ip In ; Ixþ ¼ gm Vz ; Ix ¼ gm Vz ð1Þ
where Vz ¼ Iz Zz and Zz is the external impedance
connected to the z terminal of the CDTA. CDTA can be
thought of as a combination of a current differencing unit
followed by a dual-output operational transconductance
amplifier, DO-OTA. Ideally, the OTA is assumed as an
ideal voltage-controlled current source and can be described
by Ix ¼ gm(V+ – V), where Ix is the output current, and
V+ and V denote the non-inverting and the inverting
input voltage of the OTA, respectively. Note that gm is a
function of the bias current. When this element is used
in CDTA, one of its input terminals is grounded
(e.g., V ¼ 0 V). With dual output availability, Ix+ ¼ Ix
condition is assumed.
A possible CMOS-based CDTA circuit realisation
suitable for the monolithic IC fabrication is displayed in
Fig. 2. In this circuit, transistors from M1 to M12 perform
the current differencing operation while transistors from
M13 to M24 convert the voltage at the z-terminal to output
currents at the two outputs of the DO-OTA section.
DO-OTA’s transconductance (gm) is controllable via its bias
current IB3. Also, a resistor (Rz) connected at the z-terminal
can be used to adjust the gain of CDTA, while the voltage
at the input of DO-OTA is Vz ¼ Iz Rz.
The gate terminals of the output transistors M11 and
M12 in current-differencing section are connected to biasvoltages to provide drain output and high impedance at z
terminal (ideal current controlled current source, CCCS).
Since an external resistor with relatively low resistance value
(at the order of few kO) is connected to the z-terminal, the
use of diode-connected transistors M11 and M12 becomes
advantageous from IC manufacturing point of view. This is
due to the fact that the need for two additional bias-voltages
is eliminated by using diode-connected transistors.
3
CDTA–based quadrature oscillator
Allpass (AP) filters are widely used in analogue signal
processing in order to shift the phase while keeping the
amplitude constant, to produce various types of filter
characteristics and to implement high-Q frequency selective
circuits. Many AP filter circuits are described in the
literature using various types of CM active elements
[12–23]. However, only few of these AP filter circuits are
suitable for QO realisation.
IEE Proc.-Circuits Devices Syst., Vol. 153, No. 3, June 2006
lin
Iout
n
C1
p
C2
CDTA x
Iout
CDTA x
n
z
R2
z
R4
R3
a
Fig. 3
b
Two variants of CDTA-based current-mode allpass filters
x
p
x
p
R1
CDTA 2
n
CDTA 1
n
C1
C2
R2
z
z
x−
Io2
x−
Io1
R4
R3
Fig. 4
Current-mode quadrature oscillator using CDBAs
Sinusoidal signals at x terminals of both CDTA elements have 901
phase difference
The CDTA-based QO is constructed by using the
AP sections of Fig. 3 cascaded in a loop as shown in
Fig. 4.
The current transfer function for the AP filter of
Fig. 3a is
1
s
Iout ðsÞ
R1 C1
¼ gm R3
ð2Þ
H ðsÞ ¼
1
Iin ðsÞ
sþ
R1 C1
This circuit provides a phase shift of
jðoÞ ¼ 2 arctanðoR1 C1 Þ
ð3Þ
The second allpass circuit yields a similar form of current
transfer function (2), but with a sign difference. This second
AP circuit in Fig. 3b provides a phase shift
jðoÞ ¼ 180 2 arctanðoR2 C2 Þ
ð4Þ
For the sake of circuit uniformity and ease in practical
implementation, it is convenient to set R ¼ R1 ¼ R2 and
215
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C ¼ C1 ¼ C2 in the quadrature oscillator circuit of Fig. 4.
We then obtain the oscillation frequency of the oscillator as
1
ð5Þ
RC
Therefore, the frequency of the proposed circuit is
insensitive to variations in CDTA transconductances and
R3 and R4.
However, the amplitude oscillation condition must be
fulfilled
oosc ¼
gm1 gm2 R3 R4 ¼ 1
ð6Þ
where gm1 and gm2 are transconductances of CDTAs 1 and 2.
Note that this condition can be adjusted without affecting
the oscillation frequency.
During the steady-state oscillation, condition (6) must
be dynamically fulfilled. During the initial transients, the
left-hand term of (6) must be greater than 1 to assure the
soft-start of the oscillator. There are more possibilities how
to provide it by controlling the left-hand parameters by
the oscillation amplitude.
4
Non-ideal effects
In a non-ideal case, the CDTA can be characterised by
Vp ¼ Vn ¼ 0; Iz ¼ ap Ip an In ; Ixþ ¼ gm Vz ; Ix ¼ gm Vz
ð7Þ
where ap, an are the parasitic current gains between the pz,
nz terminals of the CDTA, respectively, which are
generally deflected from their ideal unity values by the
current-tracking errors, those absolute values being much
less than one.
In non-ideal case, assuming that the tracking errors of
both CDTA elements of the proposed QO have the same
values, the frequency of oscillations for the QO can be easily
shown to be independent of the tracking errors of the
CDTA, and still described by (5).
However, the amplitude oscillation condition is modified
to
a2p
þ
216
This effect can be significant for relatively high input
resistances of CDTAs.
The effect of non-zero input impedances of the p and n
terminals can be reduced – if possible - by choosing R1 and
1/(ooscC1) much greater than Rp and Rn, or by considering
R1 reduced by Rp during the oscillator design stage. A more
general method consists in decreasing the input resistance
by negative feedback as shown in Figs. 5a and b. It can be
proved easily that in the ideal case, the current transfer
functions of the filters in Fig. 3 and Fig. 5 are identical.
However, there are more benefits of circuits in Fig. 5: We
save the resistors R3 and R4, and parasitic input resistances
are decreased owing to negative feedback. A drawback is
that we need an additional copy of output current as the
feedback signal.
feedback
Iout
R1
p
lin
Iout
CDTA x
n
C1
p
lin
C2
R2
R3
a
Fig. 5
Iout
CDTA x
n
z
a2n
¼1
ð8Þ
2
Note that this condition can also be adjusted without
affecting the oscillation frequency.
The z terminal of CDTA has high impedance, and a
small parasitic capacitance exists between this terminal and
ground in the non-ideal CDTA model. Therefore, one may
expect to see a pole at the angular frequency which is
equivalent to o ¼ 1/(Rz Cz), where Rz and Cz are the
internal parasitic resistance and capacitance of CMOS
CDTA at this terminal. Since Rz value is at the order of
megaohms, when a resistor of value RooRz is connected
at this terminal, Rz77RER.
Another non-ideal effect is caused by the non-zero input
impedances of terminals p and n. If input resistances Rp/Rn
between the p/n terminal and the ground are taken into
consideration, then ideal transfer functions (2) and (3) of
allpass sections of Figs. 3a and b are modified. For example,
the resistance between the input and the p terminal of the
section in Fig. 3a is increased by Rp, and the capacitive
reactance between the input and the n terminal is modified
by real part Rn. As a result, both the magnitude and phase
responses are modified. The phase response is shifted
towards the lower frequencies. Similar consequence is also
valid for the alternative allpass section in Fig. 3b. Note that
the amplitude oscillation condition can be again adjusted by
gm1 gm2 R3 R4
auxiliary circuitry, but the oscillation frequency is now
decreased.
For simplicity, consider the identical values of
R3 ¼ R4 ¼ Rz, gm1 ¼ gm2 ¼ gm, and identical parasitic resistances Rp ¼ Rn ¼ Rin of both CDTA elements in the
oscillator. Then the analysis leads to the modified amplitude
oscillation condition
Rin
ð9Þ
ðgm Rz Þ2 ¼ 1 þ 2
R
In contrast to the ideal case, to maintain steady-state
oscillations, it is necessary to increase current gains gmRz of
both allpass sections.
Then the oscillation frequency will be decreased from the
ideal value (5) as follows
oosc
o0osc ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð10Þ
Rin
1þ2
R
Iout
z
R4
feedback
b
Modifications of the sections in Fig. 3
Absorption by negative feedback of resistances
a R3 ¼ 1/gm,
b R4 ¼ 1/gm
Detailed analysis of the oscillator containing such
modified allpass sections shows a further essential feature.
Consider the oscillator of Fig. 4 with the first and the
second sections are modified according to Figs. 5a and b,
respectively. The analysis will be again performed on the
assumption that R3 ¼ R4 ¼ Rz and gm1 ¼ gm2 ¼ gm. However, let us distinguish different parasitic input resistances
Rp and Rn of CDTAs. The analysis leads to some interesting
conclusions. The amplitude oscillation condition is now
fulfilled automatically owing to the local negative feedback
in both allpass sections. To ensure reliable soft-start of the
oscillation, some of the classical methods of amplitude
stabilisation should be used.
The oscillation frequency is now changed according to
the formula
oosc
ð11Þ
o0osc ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
Rp Rn
1
R
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As shown in Section 5, the frequency deviation from the
ideal case can be now considerably less than for the classical
topology in Fig. 4. In the case of identical resistances Rp and
Rn, the influence of parasitic input resistances on the
oscillation frequency is totally cancelled.
It should be noted here that, one might combine the
analysis of non-idealities alpha and Rin together, and modify
the study by adding frequency dependence of alpha rather
than assuming it a constant term.
5
Simulation results
The quadrature oscillator configuration presented in this
study is simulated using the CMOS-based CDTA circuit
given in Fig. 2. For this purpose, the parameters of the
0.5 mm MIETEC real transistor model are implemented for
all MOSFETs in the circuit. Transistor aspect ratios are
indicated in Table 1.
Owing to the quadrature character of currents Io1 and Io2,
IQ is a constant value, equal to the amplitude of generated
waveforms. In (12 a, b), this amplitude is set to be 100 mA.
For concrete values of Rp, Rn, and R, (11) gives an
estimation of oscillation frequency to 1.05 MHz. It can be
concluded that the effect of parasitic input resistances is
practically supressed.
The simulation results are shown in Fig. 6. The steadystate oscillations are achieved within 4 ms. The oscillation
frequency is 1 MHz and the amplitude 100 mA, which can
be adjusted by a circuitry, operating on the basis of (12).
The THD factor is about 1%. It can be further decreased
by improving the loop gain stabilisation circuitry.
100 µA
0A
Table 1: Transistor W/L ratios used in CDTA circuit
simulations
Transistor
W/L (mm)
−100 µA
5 µs
I (V × 1)
I (V × 2)
10 µs
time
M1–M6
8/1
M7–M10
5/1
Fig. 6
M11–M12
20/2
Sinusoidal signals at the x terminals of CDTAs in the oscillator shown
in Fig. 4 with feedback current injection as indicated in Fig. 5
M13–M14
16/1
M15–M20
6/1
M21–M24
4/1
CDTA transconductance is controlled by IB3. SPICE
simulations have verified that for IB3 in the range from 20
to 700 mA, gm is proportional to the logarithm of IB3. For
200 mA, gm ¼ 479 mA/V. As follows from condition (6), for
steady-state oscillation, the corresponding external resistance connected to the z terminal is 2.88 kO.
The input resistances Rp and Rn are rather high for this
topology. Small-signal analysis leads to approximate values
of Rp ¼ 7 kO and Rn ¼ 2 kO. With respect to values of
resistors R1 and R2 mentioned below, one may expect
indispensable influence of input resistances on the oscillation frequency.
In the first step, a 1 MHz oscillator (Fig. 4) was designed
with the following element parameters: R1 ¼ R2 ¼ 15.9 kO,
C1 ¼ C2 ¼ 10 pF, IB3 ¼ 200 mA. To ensure soft-start oscillation, R3 and R4 were set to 3.2 kO. PSpice simulation led
to the following results. The steady-state oscillations were
reached within 25 ms after turning the supply sources on.
The amplitudes of output currents Io1 and Io2 are
approximately 130 mA. Owing to the absence of auxiliary
circuitry for loop gain control, the THD of generated
waveforms exceeds 7%.
The oscillation frequency is 779 kHz instead of 1 MHz
owing to the effect described in Section 4. According to (10),
this drop-off would be caused by parasitic input resistance
of 5 kO on the simple assumption that Rp ¼ Rn.
Finally, the principle of feedback current injection
(Fig. 5) was applied. Resistors R3 and R4 were removed.
Currents Ip1 and In2, injected into the p terminal of CDTA1
and the n terminal of CDTA2, were controlled as follows
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
IQ
IQ
2 þ I2
; In2 ¼ Io2
; IQ ¼ Io1
Ip1 ¼ Io1
o2
100 mA
100 mA
(12a, b, c)
IEE Proc.-Circuits Devices Syst., Vol. 153, No. 3, June 2006
6
PSpice simulation
Conclusion
In this study, a CDTA-based canonic quadrature oscillator
circuit is proposed. The proposed configuration is attractive,
because a) it can provide high frequency sinusoidal
oscillations in quadrature and at high impedance output
terminals of the CDTAs, b) the circuit has only virtually
grounded capacitors, which is advantageous from the
integrated circuit manufacturing point of view, and c) the
oscillation frequency of this configuration can be made
adjustable by using voltage-controlled elements (MOSFETs) [24–26], since the resistors in the circuit are either
grounded or virtually grounded. A special modification of
allpass sections is proposed which effectively supresses the
influence of parasitic input resistances of CDTAs on the
oscillation frequency.
It is expected that the proposed circuit will be useful
in various current-mode analogue signal processing
applications.
7
Acknowledgments
This work is supported by the Grant Agency of the Czech
Republic under grants No. 102/04/0442 and 102/05/0277,
and by the research programmes of Brno University of
Technology MSM0021630503 and MSM0021630513.
8
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