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Design of a Chaotic Balanced Colpitts Oscillator
O. TSAKIRIDIS, E. ZERVAS , M. KOUTSIOUMPOS and J. STONHAM
Dept. of Computer and Electronics, Brunel University, Uxbridge, Middx UB8 3PH, United Kingdom.
Dept. of Electronics, TEI of Athens, Athens, Egaleo 12210, Athens, Greece.
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Abstract: - A differential bipolar Chaotic Colpitts Oscillator is presented. Compared to the classical Colpitts oscillator the
Differential Chaos Colpitts Oscillator (DCCO) produces anti-phase dual output chaotic carriers and the circuit is insensitive to
any extra parasitic components. Pspice simulations performed up to 1 GHz, demonstrate the effectiveness of DCCO.
Key-words: Chaos, Colpitts Oscillator, Parasitic Capacitances, Bipolar Transistor.
1 Introduction
Chaos in the Colpitts oscillator, first reported in [1], has
recently attracted a lot of interest due to its applications in
encryption and modulation methods applied to
communication systems. In this paper we propose a
balanced version of the chaotic Colpitts oscillator. The
proposed circuit adds functionality to the classical Colpitts
oscillator in the sense that it produces anti-phase signals,
which is often a difficult task to achieve. Several proposed
chaos-based modulation schemes, including DCSK [2],[3]
and DNSK [4], require the generation of a chaotic
waveform and its inverted signal. Traditionally, balanced
signals are obtained by the use of passive or active baluns,
with the latter being often more complex and sensitive to
the operating conditions. Balanced oscillators providing
anti-phase outputs can eliminate the need of baluns. The
differential topology is insensitive to any extra parasitic
inductance and capacitance [5] due to the distributed metal
lines, components, and power supply. On the other hand
this topology increases the power consumption by a factor
of two. Nevertheless, the power transfer efficiency remains
constant. This is because the output voltage swing, of this
differential topology, is doubled but the overall
capacitances are half than that of the single-ended Colpitts
oscillator. Single ended Colpitts oscillators are rarely used
in today’s integrated circuits due to their higher required
gain for reliable start up and single-ended nature that
makes them more sensitive to parameter’s variations. The
proposed circuit diminishes some of the aforementioned
problems rendering the use of the Colpitts oscillator more
attractive. The outline of the paper is as follows. Section 2
describes the circuit design whereas simulation results are
presented in Section 3. Finally Section 4 concludes the
paper.
This work and its dissemination efforts have been supported by the
Hellenic Ministry of Education under grant “Archimedes 2003”
2 Circuit Design
The single ended Colpitts oscillator is shown in Fig. 1. The
Colpitts oscillator is a combination of a transistor amplifier
consisting of a single bipolar junction transistor (BJT), and
an LC circuit used to feedback the output signal as it is
depicted in Fig. 1. The fundamental oscillation frequency
is given by:
1
f 
2 L1
C1C 2
C1  C 2
The Colpitts oscillator exhibits a complex dynamic
behavior and for a set of element parameters the system’s
attractor is as in Fig. 2. The Lyapunov exponent for this
dynamic system is positive, an indication of the chaotic
behavior of the Colpitts oscillator.
R1
L1
V1
Q1
C1
Q2N2222
V2
C2
R2
Fig 1. Circuit Layout of the Single Ended Chaos Colpitts
Oscillator.
Fig. 2. Colpitts oscillator’s attractor.
The proposed Differential Chaos Colpitts Oscillator
(DCCO) is shown in Fig.3. The fundamental frequency of
the proposed DCCO can be calculated as:
f 
1
C 2C
2 L1 3 1
C 3  2C1
With r being small signal ON resistance of the emitter base
junction and Vth the break point voltage (approximately
0.7 Volt).
A differential output can be produced by coupling two
identical Colpitts oscillators and sharing their emitter to
ground capacitors. Since the center node, where both
capacitors are connected together, is a differential virtual
ground, the original operation of the oscillators remains
unchanged when the two sides oscillate 1800 out of phase.
The differential operation will be guaranteed if the center
node is left floating and not grounded. Noting that the
current through the main transistors, Q1 and Q2, in each of
the Colpitts oscillators flows for less than the half of the
oscillation period, it is possible and favorable to replace
the emitter-to-ground dc current sources by one dc current
source and a timed switch which alternates the current
between the two sides of the oscillator. The switching must
take place in a synchronized manner and can be achieved
by using a pair of bipolar transistors to switch the current
from one side to the other.
R1
R2
V3
L1
L2
Q1
Q2
The system in Fig. 3. is described by the following set of
equations:
C3
dVCE
 I L1  I C1
dt
L1
dI L1
 V3  R1 I L1  VCE  VBE  VQ4 on
dt
C1 / 2
dVBE
 I L1  I C1  I E1 (VCE , Q1 )  I1
dt
The collector current
current:
Ic is proportional to the emitter
I c1  I e1
The non-linear current-voltage characteristic of the
emitter-base junction can be approximated by a piecewise
linear function as follows:
  VBE1  Vth
,VBE1  Vth

I E1 (VBE )  
r
0,VBE1  Vth
C3
C4
C1
Q4
Q3
I1
Fig 3. Circuit Layout of the Differential Chaos Colpitts
Oscillator.
The currents through Q1 and Q2 controlled by the
corresponding ones Q4 and Q3 respectively (same type of
transistors). Moreover, the negative resistance of this tail
cross-coupled pair provides a very effective means to
enhance the signal loop gain, improving the start-up
condition. The Q3 and Q4 switching coupled transistors
operate mostly between ohmic and cut-off regions and
hence they have smaller noise contribution to the main
oscillator transistors. The use of one current source
facilitates the circuit implementation and provides the
same current flow to the output transistors, thus enhancing
the quality of the output signals.
3 Simulation Results
We assess the behaviour of the chaotic oscillator via
simulations performed by a p-spice based simulator. The
main transistors that produce the chaotic carriers are Q1
and Q2 (Type BFR 96 N-Trans.UHF-A/Tr 5GHz).
Table 1. contains the parameters values used throughout
the simulations. Fig. 4 depicts the anti-phase outputs of the
simulated DCCO circuit. As it is observed the outputs
from the collectors of Q1 and Q2 are 180 0 out of phase. In
Fig. 5. we plot the output power spectrum for one output
signal. Clearly, the flatness of the spectrum reveals the
chaotic nature of the signal output.
Circuit
Elements
V3
I1
R1/R2
L1/L2
C3/C4
C1
Elements’
values
12
V
25
mA
22
Ω
10
nH
4.7
pF
2.2
pF
Table 1. Circuit Parameters Values used in Simulation.
Fig. 5. Output Spectrum of the Differential Chaos Colpitts
Oscillator.
4 Conclusions
A Differential Balanced Chaos Oscillator (DCCO) has
been proposed capable of producing anti-phase signals.
The presented circuit design has numerous advantages
such as insensitivity to parasitic capacitances and
improved of the start-up condition due to the enhance loop
gain obtained by the negative resistance of the tail crosscoupled pair.
References:
Fig 4. (a) Time domain output of non inverting output
[1] M. P. Kennedy, “Chaos in the colpitts oscillator”, IEEE Trans.
Circuits and Systems, vol. 41, pp. 771–774, Nov. 1994.
[2] G. Kolumban, M. P .Kennedy and Leon O. Chua, “The Role of
Synchronization in Digital Communications Using Chaos—Part II:
Chaotic Modulation and Chaotic Synchronization”, IEEE Trans. Circuits
and Systems, vol. 45, pp. 1129–1140, Nov. 1998.
[3] Z. Galias and G. M. Maggio, “Quadrature Chaos-Shift Keying:
Theory and Performance Analysis”, IEEE Trans. Circuits and Systems,
vol. 48, pp. 1510–1519, Dec. 2001.
[4] T. Shimming and M. Hasler, “Optimal Detection of Differential
Chaos Shift Keying”, IEEE Trans. Circuits and Systems, vol. 47, pp.
1712–1719, Dec. 2000.
[5] O. Tsakiridis, D. Syvridis, E. Zervas and J. Stonham, “Chaotic
Operation of a Colpitts Oscillator in the Presence of Parasitic
Capacitances”, in Proc. EHAC’03, Salzburg, Austria, pp. 240-245, 2004.
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Fig 4. (b) Time domain output of inverting output.