It is shown that a nonlinear microwave circuit can easily be represented by a feedback model. This formalistic identity with nonlinear control systems suggests that methods and results can be borrowed from nonlinear control theory. The describing function technique, a concept that has been developed to a high degree of sophistication in control theory, is applied to the problem of phase-locking of microwave oscillators. The use of describing functions in the study of nonlinear microwave circuits may give a simple conceptual understanding of locking phenomena, for example, and thereby reduce computational efforts.

On the Use of Describing Functions in the Study of Nonlinear Active Microwave Circuits

A method is presented for increasing the accuracy of position and velocity detecting systems which make use of pattern recognition principles. The basic limitation of these systems is due to the binary nature of receptor elements which causes the receptor to have a nonlinear transfer characteristic.

Improvement of Position and Velocity Detecting Accuracy by Signal Perturbation

It is shown that a triangular perturbation signal provides increased position-detection accuracy over that provided by a sinusoidal perturbation signal [1]. Triangular perturbation is applied to a two-element photosensor receptor, resulting in perfect position detection within the dimensions of the receptor. It is also shown that perfect position detection can be obtained over as large a range as desired by using a many-element zero-deadband one-dimensional receptor subjected to triangular perturbation.

On the Improvement of Position-Detection Accuracy Using Signal Perturbation Theory

Small-signal impedance-based analysis can effectively predict the frequency and damping of resonance modes in power electronic systems. However, it cannot predict the magnitude of resonance or explain resonance-generated distortions in the absence of an external disturbance at the resonance frequency. This paper presents an impedance-based theory for the prediction of the magnitude of resonance or resonance-generated distortions in grid-connected converters. It is discovered that the impedance response of a converter starts changing with the magnitude of resonance at its terminals. The changing converter impedance response may stabilize an unstable growing resonance mode beyond a certain magnitude, at which point the converter enters a limit cycle mode of sustained oscillations. The proposed theory uses large-signal impedance for the prediction of resonance-generated distortions; the large-signal impedance of an electrical equipment represents its impedance response for different magnitudes of perturbation injected at its terminals. Large-signal impedance-based prediction of resonance-generated distortions is demonstrated for a three-phase grid-connected voltage-source converter.

Impedance-Based Prediction of Distortions Generated by Resonance in Grid-Connected Converters

This paper introduces large-signal impedance for the modeling and analysis of sustained resonance in grid-connected converters. The large-signal impedance captures the converter impedance response for different amplitudes of the injected perturbation. Large-signal impedance based calculation of the sustained resonance amplitude (interharmonics) is presented for a grid-connected three-phase voltage source converter (VSC). The paper shows that hard nonlinearities, such as PWM saturation, dominate the sensitivity of the impedance response to the perturbation amplitude. The paper also presents modeling of the large-signal impedance for VSC; modeling challenges in the absence of the small-signal approximation and their solutions are discussed.

Large-signal impedance for the analysis of sustained resonance in grid-connected converters

A new general DIDF (dual input describing function) has been analytically derived for single-valued nonlinearities subjected to two arbitrary noncommensurate sine waves. The development corroborates a previous approximate development for two sine waves widely separated in frequency. The new DIDF is applied to the problem of the stability of nonlinear systems subjected to sinusoidal forcing. It is shown that the conventional DF (describing function) cannot be used for nonautonomous systems without additional safeguards. After it has been shown by the DIDF that no auto-oscillations exist for given input conditions it is proper to employ the conventional DF in any of the methods suggested in the literature to obtain the closed-loop frequency response under those conditions.

R. Sridhar

Papers

A New Dual-Input Describing Function and an Application to the Stability of Forced Nonlinear Systems