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====== Phase Servo Loop Setup ======

===== Block Diagram =====

Let's start from the block diagram of the phase servo loop.

{{ :dim:appnotes:phase_servo.svg |}}

iGp12 averages ADC input for 500(nbsp)ms (number of samples is dependent on the RF frequency). Input offset (due to the non-zero mixer offset) is subtracted from that average producing the error signal. The error signal is multiplied by the loop gain and loop sign (+/-1). Resulting value is integrated, producing the delta signal. Delta is added to the longitudinal phase shifter setpoint, thus adjusting the local oscillator phase. The goal is to keep the beam signal and the local oscillator in quadrature, resulting in a phase detector output. Signal flow in blue on the block diagram is RF and analog, while the EPICS phase servo loop running at 2(nbsp)Hz is shown in red.

==== Applicability ====

It's important to understand that the phase servo loop, as currently implemented, only works in the multibunch regime, where a significant number of RF buckets are filled. With a single bunch, the change in the mean value is small and can be swamped by parasitic effects, resulting in loop runaway. The same can happen if the offset is not set right or if the total beam current is very small
(ADC input signal is $I_b \sin(\phi)$, so if $I_b$ is small, there might not be enough range to adjust the mean).

===== Setup Procedure =====

Start from performing single-bunch front end setup, including ADC timing and LO phasing. Once single-bunch configuration is established, fill the ring in the normal operating fill pattern to a moderate current with the phase servo loop open. Adjust LO phase manually to achieve well centered phase detection (it is helpful to have a fill pattern with a gap or multiple gaps). Once the signal is centered, note the ADC mean signal value on the front/back-end control panel. Set the phase servo offset to that value. Then set loop gain to a low value (0.05 or so) and close the loop. Loop sign is still to be determined. In order to figure out the loop sign, move phase servo setpoint by 100 counts in the positive direction. This should create some error signal and the phase servo loop will adjust the phase shifter setting. If the adjustment moves in the negative direction, bringing the phase shifter back to the original setting, we have negative feedback. If, however, closed-loop action moves the phase shifter further in the positive direction, loop sign needs to be inverted. Once you determine the proper loop sign, return the phase servo setpoint to the original value.

Once you have negative feedback established, you can proceed to fill the ring to the design current and adjust overall loop gain. Since loop gain is proportional to current, we need to make sure the gain is not excessive at the highest beam current. In order to optimize the loop gain it is helpful to perform step response measurements. Moving the phase servo setpoint positive or negative by 50-100 counts will create a setup. Loop response (CIC mean and phase shifter setting) can be monitored on a stripchart. At low loop gains settling can take tens of seconds. Increase the loop gain in 6(nbsp)dB steps (doubling the gain at each step) and check the response. Settling time should decrease with each step. At some point the response will start showing overshoot. Once you observe overshoot, reduce the gain by a factor of 2 --- that is your optimized gain setting.