and are shaped to resonate at specific frequencies. When particles pass through the electric field in a cavity, some of the energy from the radio waves is transferred to the particles. To maintain the RF field in the cavities, both amplitude and phase control loops are required.
Low-level RF (LLRF) control loops are normally implemented on digital FPGA boards. Nutaq’s Perseus 601X advanced mezzanine card (AMC), for example, is based on the Virtex-6 FPGA and offers high-performance, high-bandwidth, low-latency processing and its uTCA software tools are highly suitable for developing Linac and other high-energy applications.
Phase modulation is often used to switch from the I/Q domain into the phase domain . This is done with a Coordinate Rotation Digital Computer (CORDIC), an algorithm that converts the Cartesian I/Q vectors to Polar (phase and amplitude) coordinates in order to simplify the phase controllers. The CORDIC IP by Xilinx can be used to target the Nutaq Perseus601x uTCA FPGA board . Alternative implementations can also be realised using Nutaq’s Model-Based Design Kit (MBDK) or Board Support Development Kit (BSDK), which provide enable you to benefit from the FPGA’s capabilities.
The improved flexibility offered by digital control systems enables the creation of more complex control loops . For example, the FPGA board can be programmed with different algorithms for comparison. Digital solutions enable the use of redundant diagnostic channels to display the parameters of the control loop. Nutaq’s Real-Time Data Exchange (RTDEx) supports a real-time readout of digital signals from within the FPGA. Reading and writing from custom registers is also easy, which is useful for control loop optimization, tuning, and diagnostics.
The FGPA mezzanine cards (FMCs) inserted between the RF board and the uTCA digital board are used to digitize RF signals at sampling rates ranging anywhere from 1 MHz to thousands of MHz. Nutaq’s MI125, for example, provides 16 or 32 channels and offers 125 Mega Samples Per Second (MSPS) analog-digital conversion (14-bit width per channel). It is common to use FMCs with additional analog channels to provide interfaces for standard equipment like oscilloscopes for LLRF control loop diagnostic and monitoring. Moreover, the analog channels can be used to receive readings from sensors. State machines, for example, are used to drive the interlocks accordingly to ensure safe operation of the Linac.
System for cavity LLRF digital control loop
 http://home.web.cern.ch/abouthttp://www.nutaq.comgineering/radiofrequency-cavities  http://accelconf.web.cern.ch/Accelconf/SRF2009/papers/thppo048.pdf  http://www.xilinx.com/products/intellectual-property/CORDIC.htm