| Summary: | Design and some performance results of the pulsed digital low level radio frequency (LLRF) for the radio frequency quadrupole (RFQ) systems of Rutherford Appleton Laboratory–front end test stand and the future European Spallation Source Bilbao linac are presented. For rf field regulation, the design is based on direct rf-to-baseband conversion using an analog in-phase quadrature (IQ) demodulator, high-speed sampling of the I/Q components, baseband signal processing in a field-programmable gate array (FPGA), conversion to analog, and IQ modulation. This concept leads to a simple and versatile LLRF system which can be used for a large variety of rf frequencies and virtually any LLRF application including cw, ramping, and pulsed. In order to improve the accuracy of the probe voltage measurement, errors associated with the use of analog IQ demodulators have been identified and corrected by FPGA algorithms and proper setting of the feedback loop parameters. Furthermore, a baseband-equivalent model for the rf plant is developed in MATLAB-Simulink to study the RFQ transient response under beam loading in the presence of phase and delay errors. The effect of the unwanted resonant modes on the feedback loop stability and the LLRF considerations to avoid such instabilities are discussed and compared to some other machines such as the ILC and the European free electron laser . The practical results obtained from tests with a mock-up cavity and an RFQ cold model verify that amplitude and phase stabilities down to a fraction of one percent and one degree and phase margins larger than ±50° can be achieved with this method preserving the linearity and bandwidth of the feedback loops.
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