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Nonlinear damping of the LC circuit using antiparallel diodes
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View: Figures


Image of Fig. 1.
Fig. 1.

The nonlinear circuit obtained from antiparallel diodes (1N4148), an inductor , and capacitor . The resistor is included to account for the inherent resistance of the inductor. The voltage source is either a low frequency square wave for the transient response experiments or sinusoidal for the steady-state driven oscillator experiments.

Image of Fig. 2.
Fig. 2.

The calculated dynamic resistance (solid line) for antiparallel diodes using Eq. (7). Also shown is the inverse current approximation (dashed line). The dimensionless current is , where is the current in amperes and is the diode’s reverse saturation current.

Image of Fig. 3.
Fig. 3.

Standard push-pull driver used with the signal generator in the antiparallel diodes-LC circuit. This use is necessary because the output impedance of most signal generators is too high to drive the circuit. General purpose op amps and transistors suffice. We used LF411, 2N3904, and 2N3906. A simpler driver omits the diodes and the and resistors and connects the op amp output directly to the bases of the transistors. This simplification adds a small cross-over glitch to the signal from the signal generator.

Image of Fig. 4.
Fig. 4.

Transient response of the capacitor voltage when the square wave source makes a transition from at . The numerical result (smooth line) and measured response (noisy line) are nearly indistinguishable. Note that a transition from underdamped to overdamped behavior occurs near . As described in the text the overdamped decay to zero is comparatively slow and is not complete in the plot.

Image of Fig. 5.
Fig. 5.

The resonant frequency as a function of the source amplitude. The resonance was identified by adjusting the frequency to maximize the capacitor voltage amplitude for each source amplitude. The numerical results are lines and measured data are circles.

Image of Fig. 6.
Fig. 6.

The maximum voltage gain as a function of the source amplitude. is the ratio of the voltage amplitudes of capacitor and source at the resonant frequency. The solid line is the result using the single parameter set for the diode characteristics and the dashed line is the prediction when an additional set of diode parameters was included for high currents as described in Sec. III The dot-dashed line includes for the capacitor’s equivalent series resistance.

Image of Fig. 7.
Fig. 7.

Calculated resonant frequency (dashed line), Eq. (13), and maximum gain (solid line), Eq. (14), for the standard RLC circuit versus and . The resonant frequency drops to zero and at .

Image of Fig. 8.
Fig. 8.

The frequency response of the voltage gain for two source amplitudes: (lower) and 1.2 (upper) V. The numerical results used the two-part parametrization for the diodes corresponding to the dashed line result in Fig. 5.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonlinear damping of the LC circuit using antiparallel diodes