martedì 9 febbraio 2021

How to easily improve by a factor of 100 the measurement of the frequency difference between two reference oscillators

Recently I had the idea to improve the possibility to quick measure the frequency difference of two reference oscillators , in this case two Rubidium Oscillators : a Rhode Schwarz and an M100 that I put into a yellow rack with a power supply , as in the pictures .

The method is based on :

A) Multiplying by 100 the frequency of both oscillators ( with the use of  simple home made Comb Generators )

B) Comparing the  frequency of the two oscillators with the method of the " beats " at 1 GHz , using a selective receiver . In the test I have used a Spectrum Analyzer , but every simple receiver , even an RTL Dongle can be used with the same results .

The two Comb Generator needed was made with two EX-OR fast ports ( ACT86) , with one of the two inputs connected directly and the second through  a variable resistor that , with the input capacitor of the port ,add a small delay .




The input is so a very sharp pulse depending on the rise and fall time of the EX-OR and of the delay of the RC constant ( in the range of ns ) .

Trimming the resistor the component at 1 GHz was at a comfortably level of -50 dBm .

The output of the two Comb generator was summed simply with two capacitor and two resistors .

You can find here the images of the output of a single Comb Generator , wide band and relatively narrow band .




What can we espect from this setup while summing the signal of the two Comb Generator at 1 GHz coming from the two Rubidium ? 

The composition of the two signals will change from a maximum of +3 dB when the phase of the two oscillator is the same and to a minimum ( if the signals are exactly equal of ) zero .

In this case the spream is around 20 dB , but doesn't mattere because we have only to count the cycles .

The maximums will be always very wide , while the nulls will be always very sharp .

To check this I have tuned the Rubidium M100 as far as was possible , and you can see in the first part of the following screen with zero span ( this means that the Spectrum Analyzer acts as a receiver tuned at 1 GHz with vertical logaritmic scale ) .

Please note that the horizontal time sweep is 1000 s ( 100 second/div) .

At the beginning you can count around 10 oscillations in 100s , that means one cicle each 10 seconsd = 0,1 Hz of difference at 1 GHz .

Being 1 GHz = 10E9 Hz , this means a frequency maximun difference of 10E-10 .

While time was running , I have changed the frequency of the Rubidium M100 to approach that one of the RS Rubidium .

At the end of the screen the difference is around one cycle each ten second at 1 GHz , that means 10E-11.


Continuing the approach of the frequencies , I have increased the timebase till 6000 s because the phase change was very slow .


At the end , using sequential methof of approcimation , in the last picture ,it is not easy if impossible to see a real periodicity in the phase rotation and so in the frequency difference .

We are in the range of 10E-12 . I am pretty sure that this limit doesn't depend from the method of measurement ( being a "physical method ") , but from the limit of stability ( jitter ) of one ( if not both ) Rubidium Oscillator , and this was the scope of the experiment .

If I am right , this simple setup , that everyone can easily reproduce at low cost , can measure stability higher than that of Rubidium Oscillators .

To check this with no dubts , I need two oscillator with performance 10 times better than the rubidium oscilllator I have used .

Hope one day I can check this , if I am so crazy to invest in two Masers  , because actually I am only playing to infringe my limits .....

But I have another couple of Rubidium Oscillators from  Stanford that I can try to check in the same way ....
 


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