# How does one get ticks of a clock from an atomic clock's microwave signal?

I understand that in an atomic clock there is a microwave signal that is locked to the frequency of the atomic rotation. However, if one wants to extract time ticks from the microwave signal (shown below):

$$v(t)=V_0[1+\alpha(t)]\cos[2\pi \nu_0 t+\phi(t)]$$

it would seem that we need to assign a tick of our clock as either when the signal crosses some threshold or when the signal reaches a peak (dv/dt=0). However, in choosing one of these, your ticks will be susceptible to amplitude or phase fluctuations respectively. So, what is the standard that is used in atomic clocks (or more generally if there is a more general standard), and why (i.e. maybe amplitude fluctuations are smaller than phase fluctuations or vice-versa)?

• And this is problem because? – Bruce Abbott Apr 4 '20 at 0:16

Looking online, it seems you lock to the microwave signal the same way as you lock to any other external clock, by using a phase locked loop:

https://tf.nist.gov/seminars/WSTS/PDFs/1-1_Qulsar_Shenoi_tutorial.pdf

Since a PLL averages out phase errors, so long as the atomic clock is very stable, the PLL can lock to it very accurately.

it would seem that we need to assign a tick of our clock as either when the signal crosses some threshold or when the signal reaches a peak (dvdt=0).

The input to a PLL is a phase comparator, which is a device that generates a signal in proportion to the phase difference between the input and the PLL clock. The PLL then minimizes that phase signal. This signal can be low pass filtered to reduce the effect of instantaneous errors (effectively averaging over many cycles), and you aren't restricted to looking at just one point per cycle of the input clock. An analog phase detector for instance is basically a pair of balanced mixers that demodulates and subtracts the phase difference over the entire cycle of the input.

• Atomic clocks are NOT PLLs. Take a closer look at the paper you referenced (p. 58-59). – Dave Tweed Apr 4 '20 at 14:21

it would seem that we need to assign a tick of our clock as either when the signal crosses some threshold or when the signal reaches a peak (dvdt=0).

But that would be wrong – the way you build the PLL's mentioned in user1850479's excellent answer is essentially an integrating one – so that you basically rely on the $$\\mathcal L^2\$$ inner product (which is an integral) of the reference signal (here: your amplified atomic oscillation) and a lower-frequency generated signal that you lock to the reference by multiplying the two, and then integrating.

This all works in continuous time (the presentation linked to in the mentioned answer is a bit discrete-time-heavy), and thus, jitter gets smoothed away.

• Atomic clocks are NOT PLLs. – Dave Tweed Apr 4 '20 at 14:21
• @DaveTweed that is correct, but the clocks we derive from them most likely are. – Marcus Müller Apr 4 '20 at 16:12

Atomic clocks are NOT based on PLLs, as suggested by some of the other answers. Take a look at pages 58 and 59 of this presentation (the same one referenced by user1850479). There is no phase detector in either of these diagrams.

Instead, you have a quartz oscillator that you use as your master reference signal. As it happens, quartz oscillators have excellent short-term stability, which is an asset in this application. You then synthesize the required microwave frequency from that reference frequency, pass it through the atomic cell, and measure its response. A very narrow peak (or dip) in that response provides feedback that you're on the correct frequency, but it provides no phase information at all. Therefore, this is properly called a frequency-locked loop, or FLL.

A servo circuit adjusts the quartz oscillator frequency to keep the cell response at its maximum (or minimum). The output "ticks" are then derived directly from the output of the quartz oscillator, using ordinary digital counters, etc.

• Yes. Except, possibly, if the OP was thinking of a hydrogen maser, which does amplify an atomic signal and probably needs a PLL. – tomnexus Apr 4 '20 at 18:44