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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, E-mail: chaos@mail.cplire.ru Abstract - Chaotic signals must have specific characteristics in order to be used in certain applications. One of them is band-limited power spectrum. An approach to design of chaotic sources with band-limited feature is proposed. Realization of the approach in microwave band is demonstrated. 1. Introduction Since recently, the research direction of dynamical chaos is gradually moving from science to practice. At present, an active search for chaos applications goes. To apply dynamical chaos, it is necessary to have signal sources generating chaotic signals. As is known, chaotic oscillators play the role of the sources. Now, there is a large variety of chaotic oscillators which differ from each other by both the structure and element set and which are capable to generate chaotic oscillations from lowest frequencies up to optical bands [1-5]. On the other hand, the use of chaotic signals in some applications (for example, communications, radiolocation and so on) is possible when oscillators have specific characteristics. Band-limited power spectrum of the generated signals is one of the characteristics. Of course, to obtain band-limited signals we can use any wide-band chaotic sources and limit the bandwidth by means of a bandpass filter (passive approach). But there is another (active) approach. According to this approach, the signal with the required characteristics is formed by the chaotic oscillator itself. There are applications where the active approach is preferable especially if it can be realized by means of relatively simple and energyeffective technical decisions. Chaotic oscillators which consist of only one active element (for example, a transistor) and a few passive elements (capacitors, inductors, resistors) can play the role of such decisions. The aim of the report is to propose an approach to design of a single-transistor oscillator providing generation of band-limited chaotic oscillations in different frequency bands and to demonstrate its microwave (MW) realization. 2. The approach As is known, there are single-transistor oscillators with a simple structure capable of generating periodical oscillations of up to 2 GHz, e.g., three-point circuits on bipolar transistors [6-7]. An example of such circuit is Colpitts's oscillator [3]. A schematic diagram of the oscillator is shown in the left-hand side of Fig. 1. The oscillator contains one nonlinear active element, i.e. bipolar transistor Q. The feedback loop is formed by an inductor L with a resistor RL and a voltage divider consisting of capacitors C1 and C2. The operation point of the transistor is set by voltages VC, VE and resistor RE. Sometimes, to extend possibilities for the control of the oscillator modes, an additional capacitor C3 is introduced between the transistor collector ( С) and base ( B). If the oscillator generates periodic oscillations then the oscillation frequency is determined as

0 = L

1 C 1C 2 C1 + C
2

This expression determines the oscillation frequency in the band up to 1 MHz and is a correct enough estimation for RF and MW bands. As was shown in [3,8], the oscillator can demonstrate chaotic behavior in low-frequency band. Later [9-10], a possibility of generating RF chaotic oscillations was also reported. However, broad-band oscillations are a singularity of oscillator chaotic modes. The power spectrum is extended in both low and high frequencies. Moreover, this extension takes place around the frequency 0. In other words, this oscillator doesn't provide band-limited chaotic signals. How can the three-point circuit be modified in order to provide the generation of band-limited chaotic signals? We propose to introduce a resonant element with the band incorporating 0 into the oscillator feedback loop. Similar approach is applied to design MW transistor periodic oscillators [6]. However, in our case, the function of the resonant element is not only to provide the required frequency-selective characteristics of the feedback loop and thus to create conditions for generation of oscillations primarily within the resonant element band but also to preserve chaotic modes of the oscillator. If the above functions are realized then we can 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. 3. Simulation To verify the approach, let us take Colpitts's oscillator as a basic three-point circuit and introduce an additional resonant element (RE) consisting, in general, of a series of N parallel-serial resonant units into the feedback loop (right-hand side in Fig. 1). Parameters of the units may be different from each other. However, to simplify the situation, we will assume that the unit parameters are the same. Moreover, the parameters of both parallel and serial resonant elements inside the units (R0, L0, C0) are also the same. & C1V CE = I L - I c - I1 & C 2 V BE = V E - V BE - IL- IB RE & L I L = V C - V CE + V BE - I L R L & L 0 &&1 + R 0 I1 + ( I

2
C0

+

1
C1

) I1 =

I L - I C I L1 + I 2 + C1 C0

I1 - I 2 I & L 0 &&L1 + R 0 I L1 + L1 C = I 0 C0 3 I1 + I 3 + I L 2 - I L1 & L 0 &&2 + R 0 I 2 + I2 = I C0 C0 I 2 - I3 I & & L 0 I&L 2 + R 0 I L 2 + L 2 C0 = C 0 I 2 + I L3 - I L 2 3 & & L 0 I&3 + R 0 I 3 + I3 = C0 C0 I3 I & & L 0 I&L 3 + R 0 I L3 + L3 C = 0 C0 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 currents through the inductor, collector and base respectively. Moreover,

Figure 2. A typical power spectrum of chaotic oscillations. A schematic diagram of the modified oscillator is shown in Fig. 1. Let, N=3 for a definiteness. The oscillator is described by the following differential equations

IB=0, if V

BE



V

пор.

and

IB= (VBE-V

пор

), if VBE>Vthr,


IC= IB.
where Vthr is the threshold voltage over the p-n junction (-0.7 V), is the coefficient coupled with the backresistance of the emitter's p-n junction for a small signal and is essentially the current gain in the transistor. The next six equations are for the resonant units, where I1, I2, I3 are the currents at the inputs of the first, second and third units, respectively, while IL1 , IL2 , IL3 are the currents through the inductors in the parallel resonant elements of the corresponding units. Varying oscillator parameters (VC, VE, RL, RE, R0, L, L0, C0, C1, C2) we can select those allowing us to obtain band-limited chaotic signals. For example, Fig. 2 demonstrates the power spectrum of chaotic oscillations obtained for the following parameters: VC= 8 V, VE= -0.7 V, RE=RL= 40 Ohm, L=L0= 30 ч H, C2= 1.5 nF, C0=C1= 1 nF, R0= 10 Ohm. Note that for above parameters, the original Colpitts's oscillator (without the resonant element RE) generates periodical signals.

We made also the circuit simulation of the oscillator with the above parameters by means of "Electronics Workbench" software. It is based on PSpice simulation and allowed us to visualize signals and its characteristics with the help of virtual devices. In this connection, we used the model of the bipolar transistor 2N2222A. The results are presented in Fig. 3. The figure demonstrates voltage waveforms and its phase portrait on the screen of the virtual oscilloscope. Above results are to the case N=3. Increasing N didn't lead to any essential change of oscillator modes. On the other hand, a range of parameters values corresponding to chaotic modes was constricted when N was decreased. 4. Experiments To implement the approach in MW band, an experimental oscillator model (Fig. 4) was designed.

a

Figure 4. Microwave oscillator model. mm thickness and dielectric constant . The bipolar =10 transistor 2Т938А-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 (С) 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 additional lumped capacitor C4 (see Fig. 1). The oscillator modes are tuned by means of varying the capacitors C4, C2, C3 (4/30 pF) and voltages VE, VC. The model was realized on FLAN-10 material with 1

b Figure 3. Electronics Workbench simulation: a) waveforms of the voltages at the second resonant unit (top trace) and emitter (bottom trace); b) phase portrait of the voltages.


We made experiments with the oscillator model and found a range of parameters values (C1, C2, C3, C4, VE, VC) where the oscillator generates chaotic oscillations. Moreover really, the band and nonuniformity of chaotic signal power spectrum are determined by the resonator amplitude-frequency response. A typical power spectrum of the output chaotic signal realized for VE= -0.85 V and VC= 5.3 V is shown in Fig. 5a. The spectrum measured in 0-1500 MHz band demonstrates the absence of oscillations outside the generation band. The output power of the model was 25 mW. However, the presented chaotic mode does not exhaust the oscillator capabilities. Changing one or several parameters corresponding to the mode in Fig. 5a gives chaotic oscillations with different spectral characteristics. For example, with capacitors C4 and C3 we can change the band and nonuniformity of the oscillation power spectrum (Fig. 5b).

5. Conclusions We proposed an approach to design of singletransistor chaotic oscillators with band-limited power spectrum. Here we have presented an oscillator model in 900-1000 MHz band, however, this approach allows us to realize oscillators in the frequency bands of as high as several GHz. Acknowledgment This report is supported in part by a grant from Russian Foundation for Fundamental Research (No. 9902-18315). References [1] A. Dmitriev, V. Ivanov and M. Lebedev. "The model of single-transistor oscillator with chaotic dynamic". Radiotechnika i Elecktronika, Vol 33, ? 5 , pp. 1085-1088, 1988 (in Russian). [2] L. O. Chua, C. W. Wu et al. "A universal circuit for studying and generating chaos. Part II. Strange attractors". IEEE Trans. Circuits & Systems, CAS40, pp. 732-761, 1993. [3] M. Kennedy. Chaos in Colpitts oscillator". IEEE Transaction on Circuits and Systems - 1, Vol. 41, ? 11, pp. 771-774, 1994. [4] A. Namajunas and A. Tamasevicius . "Modified Wien-bridge oscillator for chaos". Electronics letters, 31, pp. 335-336, 1995. [5] J. Zhang, X. Chen and A. Davis. "High frequency chaotic oscillations in a transformer-coupled oscillator". Proc. of NDES'99, Ronne, Denmark, pp. 213-216, 1999. [6] O. Chelnokov. Transistor periodical oscillators. Moscow, Sov. Radio, 1975. (in Russian). [7] B. Kayrginsky. Oscillators based on bipolar transistors with different power. Elecktronnaya technika, ? 3(457), pp. 3-6, 1993 (in Russian) . [8] E. Lindberg. "Colpitts, eigenvalues and chaos". Proc. of NDES'97, Moscow, Russia, pp. 262267, 1997. [9] C. Wegene & M. Kennedy."RF chaotic Colpitts oscillator". Proc. of NDES'95, Dublin, Ireland, pp. 255-258, 1995. [10] V. Burykin & A. Panas. "Chaotic synchronization of RF generators". Proc. of NDES'97, Moscow, Russia, pp. 548-553, 1997.

a

b Figure 5. Power spectrum of chaotic oscillations.