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Ultra-high-frequency chaos in a time-delay electronic device with band-limited feedback
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10.1063/1.2335814
/content/aip/journal/chaos/16/3/10.1063/1.2335814
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/3/10.1063/1.2335814
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Transistor-based nonlinearity. (a) Picture of the modified ERA-SM test board (modifications highlighted by the white box). (b) Details of the implementation of the nonlinearity, which consists of a bias-T (Mini-Circuits ZFBT 6GW, 0.1 MHz–6 GHz bandwidth) and a modified ERA-SM test board (Mini-Circuits ERA-TB). The component values on the ERA-TB are: ; ; ; ; ; ; ; L1 is a rf choke (MCL Model AdcH-80A); D1 is a Zener diode; and T1 is an NPN wideband transistor BFG520. (c) Measured nonlinearity (dots) and fit of Eq. (1) (line).

Image of FIG. 2.
FIG. 2.

An electronic generator of rf chaos. (a) Schematic of the device. (b) Transfer function for the case of a capacitor in the feedback loop (●: data; — fit) and without capacitor (×: data; - - -: fit). (c) Linear-scale plot of for the case of a capacitor in the feedback loop (●: data; —: fit).

Image of FIG. 3.
FIG. 3.

Characterization of the Hopf bifurcations for a setup with a capacitor. (a) Supercritical Hopf bifurcation: oscillation amplitude as a function of the attenuator control voltage for . Increased corresponds to increased (negative) feedback gain. (b) The measured dependence of the Hopf frequency on the time delay is shown (●). The dashed lines are the approximate scaling. The solid line is from theory (see text).

Image of FIG. 4.
FIG. 4.

Stability boundary of the steady state. (a) Experiment: measured attenuator control voltage vs the feedback-delay . (b) Comparison of experiment and theory: values of from panel (a) are mapped onto the effective slope (●). The line indicates the theoretical prediction.

Image of FIG. 5.
FIG. 5.

Experimentally measured time series as well as the corresponding power spectra and Poincaré sections are shown for (a)–(c) , (d)–(f) , and (g)–(i) . The feedback loop contained a capacitor, , and .

Image of FIG. 6.
FIG. 6.

Numerical time series, power spectra, and Poincaré sections are shown for (a)–(c) , (d)–(f) , (g)–(i) .

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/content/aip/journal/chaos/16/3/10.1063/1.2335814
2006-08-30
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Ultra-high-frequency chaos in a time-delay electronic device with band-limited feedback
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/3/10.1063/1.2335814
10.1063/1.2335814
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