Intermittency-induced criticality in a resistor-inductor-diode circuit

The current fluctuations of a driven resistor-inductor-diode circuit are investigated here looking for signatures of critical behavior monitored by the driving frequency. The experimentally obtained time series of the voltage drop across the resistor (as directly proportional to the current flowing through the circuit) were analyzed by means of the method of critical fluctuations in analogy to thermal critical systems. Intermittent criticality was revealed for a critical frequency band signifying the transition between the normal rectifier phase in the low frequencies and a full-wave conducting, capacitorlike phase in the high frequencies. The transition possesses critical characteristics with a characteristic exponent $p_l=1.65$. A fractal analysis in terms of the rescale range ($R/\phantom{RS}S$) and detrended fluctuation analysis methods yielded results fully compatible with the critical dynamics analysis. Suggestions for the interpretation of the observed behavior in terms of $p\text{−}n$ junction operation are discussed.

Figure 1

(a) Experimental setup; values of the RLD circuit components and details about the used instruments are also shown. (b) Photograph of the circuit implementation used for experimentation.

Figure 2

The three kinds of acquired $V_R\left(t\right)$ waveforms. (a) Part of the 1 kHz time series as an example of the low-frequency rectifying behavior. (b) Part of the 5 kHz time series presenting undershoots entering the negative values region. (c) Part of the 500 kHz time series in the full-wave conducting, capacitorlike operation.

Figure 3

(a) One full, arbitrarily selected period of the measured 2 kHz $V_R\left(t\right)$ time series. (b) Closeup of the lowest fluctuations of the 2 kHz $V_R\left(t\right)$ time series excerpt depicted in (a). The existence of reverse-recovery phenomenon is obvious.

Figure 4

The time series $V_{bt}\left(t\right)$ for $f=5\mathrm{kHz}$ has values in the region from $-0.55$ to 0.15 mV.

Figure 5

Normalized density of turning points for different driving frequencies.

Figure 6

(a) The time series $V_{bt}\left(t\right)$ for $f=5\mathrm{kHz}$, resulting from the original time series $V_R\left(t\right)$ after the exclusion of the positive values above the bending point. (b) The distribution of the $V_{bt}\left(t\right)$ time series values. It is characteristic of the appearance of a plateau.

Figure 7

(a) Distribution of waiting times. For very long waiting times ($700<l<900$) a very narrow distribution is observed as indicated by the arrow. (b) For waiting times $l<40$ an excellent power law appears; the fitting line is given by the Eq. (2) with $p_2=1.55$, $p_3=0.01$, and $R^2=0.999$.

Figure 8

The fitting exponents $p_2$, $p_3$ vs the width of the laminar region for the 5 kHz $V_{bt}\left(t\right)$ time series.

Figure 9

The minimum $p_3$ exponent vs frequency. Within a narrow zone from 2 to 8 kHz the minimum $p_3$ values are very close to zero, indicating critical dynamics.

Figure 10

The maximum $p_2$ exponent value vs frequency within the critical band.

Figure 11

Three segments piecewise linear approximation of the $log{\left(R/\phantom{RS}S\right)}_m-logm$ representation. The slopes, attributed to “local” Hurst exponents over the three scale ranges, are shown.

Figure 12

Three segments piecewise linear approximation of the $logF\left(m\right)-logm$ representation. The slopes, attributed to “local” $a$ exponents over the three scale ranges, are shown.