June 2019: Frequency Beating on Office Desk

Table of Contents

Setup

In June 2019, first measurements have been done using the following setup in my office

• two 'DDS h=1 signals' generated using the clock generator of a timing receiver (pexaria, saft-clk-gen)
• two timing receivers for phase measurements (pexaria, lm32 firmware); one TR per signal
• one timing receiver as cbu (standalone, lm32 firwmare)
• one timine reciever for generating a 'synch signal' (pexaria, config via 'saft tools')

The following parameters have been used

• https://github.com/GSI-CS-CO/bel_projects
  • branch b2b-test_dietrich_2019-05-20
  • commit c8e1774
  • /modules/b2b-test/
• extraction: h = 1 clock 2000001 Hz, harmonic number 3
• injection h = 1 clock 3000011 Hz, harmonic number 2
• bunch (bucket) frequency ~6000000 Hz, beat frequency 9 Hz

Figure: Setup of the test setup. Two TRs serve for phase measurement of clock signals, each connected at the left most connector with 'Lemo Y' (left PC; top: extraction, bottom: injection). The DM controlling the measurement is integrated into the right PC. Another TR in a third PC serves for generating the two h = 1 signals (not shown). The standalone TR serving as CBU is positioned on top. All five WR nodes are connected using a White Rabbit switch (top).

The figure above gives an overview on the simple setup. It contains of four Timing Receivers (2 phase measurement, 1 CBU, 1 DDS (2 signals)) and one Data Master. All nodes are synchronized using White Rabbit. The TRs used for phase measurement also generate additional signals on the right most connector 'CMD_B2B_START' (top) and 'CMD_B2B_DIAGMATCH' (bottom).

Measurements

Figure: Overview on the measured signals. Signals from top to bottom are CMD_B2B_START (magenta), h=1 extraction (yellow), h=1 injection (cyan), CMD_B2B_DIAGMATCH (green).

The figure above shows an overview on the measured signals. Of interest are the rising edges of the CMD_B2B_START (magenta) and CMD_B2B_DIAGMATCH (green). The time scale is 40ms/div and the two h=1 signals are not resolved. The lower part of the figure shows a measurement of the skew ob both signals ('3->4, 68ms'). The CMD_B2B_DIAGMATCH signal jumps with respect to the CMD_B2B_START depending on the actual phases in the two ring machines upon the start of the measurement. Depending on the beat frequency (here 9Hz), there is an upper bound on the measured skew (here 111ms). This upper bound is identical to the maximum time it takes to achieve synchronization.

Figure: Closer look on the CMD_B2B_START and h=1 signals.

The figure above shows a typical situation when starting a measurement with CMD_B2B_START (magenta signal). The h=1 signals of extraction (yellow) and injection (cyan) are not phase aligned. As can bee seen, three periods of the injection signal fit into two periods of the extraction signal (simulating two rings with a ratio of circumference of 2 / 3).

Figure: Closer look on the CMD_B2B_DIAGMATCH and h=1 signals.

The figure above shows the situation when both h=1 signals are phase matched in coincidence with the CMD_B2B_DIAGMATCH signal.

Figure: Even closer look on the CMD_B2B_DIAGMATCH and h=1 signals.

The figure above shows a very close look of the two h=1 and the CMD_B2B_DIAGMATCH signals. The time scale is 5ns/div. The lower part of the figure shows the result of about 500 measurements. Shown is the skew of the h=1 signals (left, maean ~600ps, standard deviation ~500ps, max deviation 2.4ns) and the skew between the h=1 signal of the extraction machine and the CMD_B2B_DIAGMATCH signal (right, mean ~500ps, standard deviation ~500ps, max deviation 1.4 ns).

Summary

To summarize: Using the beating method and a Timing Receiver based phase measurement, a synchronization of the h=1 signals in the order of 1ns can actually be achieved.

-- DietrichBeck - 27 Nov 2020