On Saturday, August 28, 2021 at 9:41:48 PM UTC-3, Richard Hertz wrote:
1) Cesium atomic clocks are more expensive that rubidium ones, and also has an stability about 300 times more than the
second one. Because of the cost, rubidium based AC are the most used at internet hubs where monster routers exist and ,
also, for master timing within telecom operators. Cesium AC are used in national gov. agencies to provide a reference
source for companies, and they are in the 2nd. tier of precision, related to the master site at France.
For more than 25 years, rubidium clocks use GPS based devices to adjust drifts from cesium or to resync guided by them,
in cases of network shutdowns. Every nation has a special network to distribute sync signals on its territory. These centers
interconnect between them, regionally, and with the master reference at France.
2) Without considering other factors but quantum ones, atomic clocks suffer from phase noise. it can be explained by telling
that emissions of radiation from cesium atoms due to the microwave exciting signal is NOT PERFECT, as physicists would
prefer, because cesium atoms at states A or B are not in a perfect energy state with EXACT differences Eo = h.fo
, but are
distributed in a way that they verify gaussian-like differences in the amount of atoms around such exact difference.
So, as any oscillator, a factor Q (stability) is assigned to the amounts of atoms outside of their exact (predicted) differences,
as is related to the amount of atoms at which transitions are made at fo compared to those at nearby frequencies.
Then, a quantum Q factor is measured as a quotient between fo and the noise bandwidth Δfo. Averaging the energies hf' at
every slot of the spectrum shape, sideways fo, the number of atomic transitions at every narrow bandwidth can be calculated.
The quantum Q factor is further degraded by several other perturbations within or outside the atomic clock. The approximate
value of the quantum Q factor is calculated by subtracting the effect of other known degradations that exist and that are
explained here (NIST):
3) In cesium clocks, at a chamber where atoms transitioned back from level F= 3 to level F=4 (A and B state) are guided, by a
a magnet, to a hot wire ionizer, where an electric current proportional to the number of atoms that were at F=4 is produced.
Since here, and applied to GPS atomic clocks (for instance), there are two versions:
3.1) The feedback is done entirely in the microwave region:
This current regulates a microwave oscillator, so it can excite atoms in a Ramsey cavity to maximize the output current
produced at 9,192,631,770 Hz (exact fo). And this signal (current) is amplified and scaled down to regulate an TCXO
oscillator at 10.230000 Mhz (exactly).
3.2) The feedback is done with a loop that involves a TCXO at 10.23 Mhz:
This current oscillates at 9,192,631,770 Hz, in the microwave region, and is amplified and scaled down and non-linearly
mixed with that of an TCXO (10.230000 Mhz exactly). The difference below 1000 Hz is low-pass filtered and
processed to obtain the lowest error signal possible, by fine-tuning the TCXO (using varicaps). The 10.23 Mhz output
is upscaled up to 9,192,631,770 Hz, containing by then the error compensation to maximize the current output.
At any case, the ratio between 9,192,631,770 Hz and 10.230000 Mhz is a number with many decimal places, around 898.
So, traditional digital frequency dividers or digital synthesizers can not be used, and special digital techniques are required.
According to NIST page, the noise bandwidth Δfo for commercial products is narrowed to the range of 600 to 1000 Hz. Probably,
more stable and costly cesium clocks are available for space and military applications.
In GPS systems, the reference OCXO oscillates at 10.230000 Mhz (exactly), which is multiplied by 154 to obtain the L1 band carrier
frequency of 1575.42 Mhz (exactly). But the ratio of cesium fo to OCXO 10.230000 Mhz makes the downscaling factor a non-integer
number which is, exactly, 898.595480938416 (exactly), so special frequency synthesizers are required.
Fractional-N systems have been used in commercial signal generators since 1989, with initial 0.1 Hz frequency resolution. Such
devices had to be evolved across several generations to offer much greater decimal resolution as a multiplier.
Between other advanced techniques, in DDS (Digital Direct Synthesis), chips with accumulative phase (digital counters with very
large modulus (64/128 bits counters) generate a continuous signal with slow phase increase, which output is transformed in an
analog signal, using DAC (Digital to Analog Converters) with accurate precision on its frequency.