5.4.5 Cable electrical length control

The reference frequency is also used for a continuous control of the electrical length of the High-Q cables transporting the IF2 signal from the antennas to the correlator room in the central building. A variation $\Delta L$ in the electrical length of the High-Q cable will affect the signal phase by $360 \Delta L/\ensuremath{\lambda_\mathrm{\scriptscriptstyle IF2}}$; for a length of 500m and a temperature coefficient of 10^-5 we have a variation in length of 5mm or 17ps, which translates into a phase shift of 4 degrees at the high end of the passband: this is a very small effect.

The same length variation induces a phase shift of $360 \times 0.017 \times 1.875 = 11.5$ degrees at the LO2 frequency. This signal being multiplied by $(\ensuremath{N_\mathrm{\scriptscriptstyle H}} +1)\ensuremath{N_\mathrm{\scripts... ...ptscriptstyle USB}} / \ensuremath{\nu_\mathrm{\scriptscriptstyle LO2}}\sim 120$ for the 1.3mm receiver, we have a totally unacceptable shift of about 4 turns. The cables are buried in the ground for most of their length; however they also run up the antennas and suffer from varying torsions when the sources are tracked, and in particular when the antenna is moved from the source to a phase calibrator.

For this reason the electrical length of the cables is under permanent control. The LO2 signal is sent back to the central building in the High Q cable, and there it is mixed with the $\ensuremath{\nu_\mathrm{\scriptscriptstyle LO2}} +\ensuremath{\epsilon_\mathrm{\scriptscriptstyle 2}}$ signal from the synthesizer. The phasemeter measures every second the phase difference between the beat signal at 0.5 MHz and a reference 0.5 MHz signal.

The measured phase difference is twice the phase offset affecting the LO2, it is used by the computer to correct the LO1 phase after multiplication by $\ensuremath{\nu_\mathrm{\scriptscriptstyle LO1}} / \ensuremath{\nu_\mathrm{\scriptscriptstyle LO2}}$.