Compensation and Emulation of Output Impedance in Ultra-High Bandwidth Class-D Power Amplifiers

Abstract

The stability limits for an ultra-high bandwidth class-D power amplifier (100kHz, 800V DC-link, 10kW) are derived and characterized for two different use cases and for a given inductance of the line that connects the output of the converter to the load. In the first use case, the additional impedance due to the line is compensated and in the second use case, a controlled inner ohmic-inductive impedance is emulated by the converter. General stability analyses are conducted for simplified representations of the two control concepts, i.e., for compensating the line impedance and emulating an inner impedance. A detailed linearized model of the investigated power amplifier is used to evaluate the effectivenesses of both control concepts and to identify the stability boundaries that apply to the investigated converter system. By way of example, the compensation of the line impedance can decrease the total output impedance of the converter system due to a line inductance of 10µH from 1.3Ω to 0.37Ω at 20kHz. Furthermore, the compensation of the line impedance is found to be less prone to instability than the emulation of a defined inner impedance. With regard to the inner impedance emulation, the stability analysis discloses the dependency between the maximum allowable values of emulated inner inductance and inner resistance such that the system remains stable, which facilitates the evaluation of the implications of specific modifications of the converter hardware or changes of the structure of the control system on the stability boundaries. Without external inductance, a maximum inner inductance of 430µH at the stability limit is achieved if the bandwidth of the impedance emulation is limited to 30kHz. A detailed circuit simulation of the power stage and the digital control unit is used to verify the results of the analysis.