Single-transistor microwave chaotic oscillator
Andrey Panas, Boris Kyarginsky, Nikolay Maximov
Institute of RadioEngineering and Electronics, Russian Academy of Sciences,
Mokhovaya St. 11, GSP-3, 103907, Moscow, Russia,
Abstract - Chaotic signals must have specific oscillations of up to 2 GHz, e.g., three-point circuits on
characteristics in order to be used in certain applications. bipolar transistors [6-7]. An example of such circuit is
One of them is band-limited power spectrum. An Colpitts's oscillator . A schematic diagram of the
approach to design of chaotic sources with band-limited oscillator is shown in the left-hand side of Fig. 1. The
feature is proposed. Realization of the approach in oscillator contains one nonlinear active element, i.e.
microwave band is demonstrated. bipolar transistor Q. The feedback loop is formed by an
inductor L with a resistor RL and a voltage divider
1. Introduction consisting of capacitors C1 and C2. The operation point
of the transistor is set by voltages VC, VE and resistor RE.
Since recently, the research direction of dynamical Sometimes, to extend possibilities for the control of the
chaos is gradually moving from science to practice. At oscillator modes, an additional capacitor C3 is introduced
present, an active search for chaos applications goes. To between the transistor collector (Ñ) and base (B).
apply dynamical chaos, it is necessary to have signal If the oscillator generates periodic oscillations then
sources generating chaotic signals. As is known, chaotic the oscillation frequency is determined as
oscillators play the role of the sources. Now, there is a
large variety of chaotic oscillators which differ from 1
each other by both the structure and element set and ω0 =
C 1C 2
which are capable to generate chaotic oscillations from L⋅
lowest frequencies up to optical bands [1-5]. C1 + C 2
On the other hand, the use of chaotic signals in some
applications (for example, communications, radio-
This expression determines the oscillation
location and so on) is possible when oscillators have
frequency in the band up to 1 MHz and is a correct
specific characteristics. Band-limited power spectrum of
enough estimation for RF and MW bands.
the generated signals is one of the characteristics. Of
As was shown in [3,8], the oscillator can demonstrate
course, to obtain band-limited signals we can use any
chaotic behavior in low-frequency band. Later [9-10], a
wide-band chaotic sources and limit the bandwidth by
possibility of generating RF chaotic oscillations was also
means of a bandpass filter (passive approach). But there
reported. However, broad-band oscillations are a
is another (active) approach. According to this approach,
singularity of oscillator chaotic modes. The power
the signal with the required characteristics is formed by
spectrum is extended in both low and high frequencies.
the chaotic oscillator itself. There are applications where
Moreover, this extension takes place around the
the active approach is preferable especially if it can be
realized by means of relatively simple and energy- frequency ω 0. In other words, this oscillator doesn't
effective technical decisions. Chaotic oscillators which provide band-limited chaotic signals.
consist of only one active element (for example, a How can the three-point circuit be modified in order
transistor) and a few passive elements (capacitors, to provide the generation of band-limited chaotic
inductors, resistors) can play the role of such decisions. signals? We propose to introduce a resonant element
The aim of the report is to propose an approach to with the band incorporating ω 0 into the oscillator
design of a single-transistor oscillator providing feedback loop. Similar approach is applied to design MW
generation of band-limited chaotic oscillations in transistor periodic oscillators . However, in our case,
different frequency bands and to demonstrate its the function of the resonant element is not only to
microwave (MW) realization. provide the required frequency-selective characteristics
of the feedback loop and thus to create conditions for
2. The approach generation of oscillations primarily within the resonant
element band but also to preserve chaotic modes of the
As is known, there are single-transistor oscillators oscillator. If the above functions are realized then we can
with a simple structure capable of generating periodical expect that the bandwidth and nonuniformity of the power
spectrum will be defined by the corresponding
characteristics of the resonant element.
Figure 1. Schematic diagram of the single-transistor chaotic oscillator.
To verify the approach, let us take Colpitts's C1V CE = I L − I c − I1
oscillator as a basic three-point circuit and introduce an V E − V BE
additional resonant element (RE) consisting, in general, C 2 V BE =
& − IL− IB
of a series of N parallel-serial resonant units into the RE
feedback loop (right-hand side in Fig. 1). Parameters of L I L = V C − V CE + V BE − I L R L
the units may be different from each other. However, to
2 1 I L − I C I L1 + I 2
simplify the situation, we will assume that the unit L 0 &&1 + R 0 I1 + (
I & + ) I1 = +
parameters are the same. Moreover, the parameters of C0 C1 C1 C0
both parallel and serial resonant elements inside the units
I I1 − I 2
(R0, L0, C0) are also the same. L 0 &&L1 + R 0 I L1 + L1 C =
3 I1 + I 3 + I L 2 − I L1
L 0 &&2 + R 0 I 2 +
I & I2 =
I I 2 − I3
L0 I L2 + R0 I L2 + L2
C0 = C
3 I 2 + I L3 − I L 2
L0 I 3 + R0 I 3 +
&& & I3 =
L 0 I L 3 + R 0 I L3 + L3 C =
Here, the first three equations describe Colpitts's
oscillator, where VCE and VBE are the collector-emitter
and base-emitter voltages, respectively; IL, IC, IB are the
Figure 2. A typical power spectrum of chaotic currents through the inductor, collector and base
oscillations. respectively. Moreover,
A schematic diagram of the modified oscillator is IB=0, if VBE≤ Vïîð. and
shown in Fig. 1. Let, N=3 for a definiteness. The
oscillator is described by the following differential IB=α (VBE-Vïîð), if VBE>Vthr,
We made also the circuit simulation of the oscillator
where Vthr is the threshold voltage over the p-n junction with the above parameters by means of "Electronics
(-0.7 V), α is the coefficient coupled with the back- Workbench" software. It is based on PSpice simulation
resistance of the emitter's p-n junction for a small signal and allowed us to visualize signals and its characteristics
and β is essentially the current gain in the transistor. with the help of virtual devices. In this connection, we
The next six equations are for the resonant units, used the model of the bipolar transistor 2N2222A. The
where I1, I2, I3 are the currents at the inputs of the first, results are presented in Fig. 3. The figure demonstrates
second and third units, respectively, while IL1 , IL2 , IL3 are voltage waveforms and its phase portrait on the screen of
the currents through the inductors in the parallel resonant the virtual oscilloscope.
elements of the corresponding units. Above results are to the case N=3. Increasing N
Varying oscillator parameters (VC, VE, RL, RE, R0, L, didn't lead to any essential change of oscillator modes.
L0, C0, C1, C2) we can select those allowing us to obtain On the other hand, a range of parameters values
band-limited chaotic signals. For example, Fig. 2 corresponding to chaotic modes was constricted when N
demonstrates the power spectrum of chaotic oscillations was decreased.
obtained for the following parameters: VC= 8 V, VE= -0.7
V, RE=RL= 40 Ohm, L=L0= 30 µH, C2= 1.5 nF, C0=C1= 1 4. Experiments
nF, R0= 10 Ohm. Note that for above parameters, the
original Colpitts's oscillator (without the resonant To implement the approach in MW band, an
element RE) generates periodical signals. experimental oscillator model (Fig. 4) was designed.
Figure 4. Microwave oscillator model.
The model was realized on FLAN-10 material with 1
mm thickness and dielectric constant ε =10. The bipolar
transistor 2Ò938À-2 is used as the active element (Q).
The MW oscillator contains lumped elements C1, C2,
RE, L which play the same role as in Fig. 1. According to
Fig. 1, the resonant element (RE) was introduced
between the collector (Ñ) and emitter (E) of the
transistor. A resonator based on coupled microstrip lines
realized the function of RE. As is known, a microstrip
line is a resonant element with distributed parameters. An
equivalent circuit of the line may be represented as
infinitely long chain of parallel-serial resonant units
similar to described above (see Fig. 1). The resonator
characteristics are modified by means of varying
Figure 3. Electronics Workbench simulation: a)
additional lumped capacitor C4 (see Fig. 1). The
waveforms of the voltages at the second resonant unit
oscillator modes are tuned by means of varying the
(top trace) and emitter (bottom trace); b) phase portrait
capacitors C4, C2, C3 (4/30 pF) and voltages VE, VC.
of the voltages.
We made experiments with the oscillator model and 5. Conclusions
found a range of parameters values (C1, C2, C3, C4, VE,
VC) where the oscillator generates chaotic oscillations. We proposed an approach to design of single-
Moreover really, the band and nonuniformity of chaotic transistor chaotic oscillators with band-limited power
signal power spectrum are determined by the resonator spectrum. Here we have presented an oscillator model in
amplitude-frequency response. A typical power spectrum 900-1000 MHz band, however, this approach allows us to
of the output chaotic signal realized for VE= -0.85 V and realize oscillators in the frequency bands of as high as
VC= 5.3 V is shown in Fig. 5a. The spectrum measured in several GHz.
0-1500 MHz band demonstrates the absence of
oscillations outside the generation band. The output Acknowledgment
power of the model was 25 mW. However, the presented
chaotic mode does not exhaust the oscillator capabilities. This report is supported in part by a grant from
Changing one or several parameters corresponding to the Russian Foundation for Fundamental Research (No. 99-
mode in Fig. 5a gives chaotic oscillations with different 02-18315).
spectral characteristics. For example, with capacitors C4
and C3 we can change the band and nonuniformity of the References
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Figure 5. Power spectrum of chaotic oscillations.