I recently acquired a GPSDO (a BG7TBL design)

– its capable of producing a 10MHz reference sine wave signal accurate to 10E-14

– when stabilized over a prolonged period of time

– not moved or touched in any way in an isolated position (because of its high time accuracy

– we can ‘see’ gravitational influence by nearby objects and movement of the device.

For now

– in the few days I have been running it

– it is most likely accurate to at least 10E-12

– but how can you measure this device

– unless you have some reference with even ‘better’ accuracy.

This is the beginning of the ‘time standard or GPSDO and Rubidium’ rabbit hole –

BE WARNED!

There is no end – so for now I simply accept that the GPSDO I have is accurate to at least 10E-11

Great!

**So what can we do with it?**Well, I have a really good RF signal Generator which I am reviewing – the Rigol DSG815 – it ALSO has an accurate frequency generation mechanism – after all this is VERY important for a RF Signal Generator.

So why not compare the 10MHz signal – a pure sine wave – to the GPSDO’s 10MHz pure sine wave – which we assume is (it most likely is) accurate to 10E-11

So how do we do this – I don’t have a frequency counter – capable of 10E-11 accuracy @ 10MHz – but I do have a MSO5000 capable of plotting x-y for respective CH1 and CH2 inputs.

X-Y plotting on a Oscilloscope – generates interesting Lissajous figures – and if you understand how these are generated – then it’s VERY easy to ‘compare’ any two frequencies to determine how many Hz they are apart – or if indeed they are totally in-synch.

Here is how you do your measurements / testing;-

Connect your oscilloscope’s CH1 to your KNOW (the accurate reference frequency) frequency.

Connect your oscilloscope’s CH2 to the source of the frequency you are trying to measure – the deviation from the KNOWN source.

If you trigger your scope on the CH1 sine wave, you will see a rock steady sine wave (CH1) and a ‘moving’ sine wave on CH2.

The rate – or speed of the CH2 sine wave as it moves out of phase and repeats this continuously – is in essence the time period of the frequency deviation from the CH1 frequency.

Bu simply ‘looking’ at the moving waveform – we cannot tell how much the frequency of CH2 is deviated from the reference Frequency of CH1

BUT

If we now enable X-Y mode – we will see a spinning circle – our Lissajous figure.

The spinning circle represents the phase difference of the two sine waves.

¼ of a ‘spin’ of the circle represents 90 degrees,

½ of a ‘spin’ of the circle represents 180 degrees,

¾ of a ‘spin’ of a circle represents 270 degrees,

1 full ‘spin’ of a circle represents 360 degrees.

Remember because we see the circle in 2 dimensions – when it spins onto itself – it actually has made ½ of a revolution, so it needs to spin onto itself TWO times for a full revolution.

To understand this is very important.

NOW, if we assume that CH1 frequency is rock solid (the time reference) – then any deviation will be in the frequency we are testing – CH2 in our case.

The Rigol DSG815 – was set to be ‘spot-on’ its internal 10.000 000 00 MHz

Its capable of displaying 8 significant digits – this means it can be programmed to produce .01 Hz resolution.

The GPSDO is capable to producing ACCURATE resolution to 10.000 000 00000 MHz

So let’s look at this side-by-side

10.000 000

**00**10.000 000

**00000**So we can now resolve

**0.00001 Hz** – that’s incredible for a $100 device!

Back to the ‘spinning circle’ – the rate of the ‘spin’ is an indication of how much deviation in Hz there is between the two frequencies.

So, we nor go to the control panel on the DSG815 – and simply vary the least significant figure – to adjust the output frequency.

As we ‘turn the know’ we are either increasing or decreasing (your choice) the signal generators output frequency – to try to match it as close as possible to the GPSDO reference frequency.

As if you increase the frequency and the circle starts to spin faster – then we are going the wrong way – the sig gen frequency is already too high – we must reduce it.

So if we now reduce the frequency the circle should start to slow down – we keep decreasing the frequency until we can ‘stop’ the spinning circle COMPLETELY.

Unfortunately you will not be able to stop the spin completely – the Rigol DSG815 simply does not have such an accurate clock that it can match the GPSDO.

BUT

We can virtually stop the ‘spin’

You will be able to go down to 0.01Hz increment on the DSG815 and you will find that if you step this ‘up’ by 1 or ‘down’ by 1 this will be your final limit.

When the DSG815 has been ‘warmed-up’ so its internal frequency source becomes stable – you will reach a point where the circle will still spin but VERY slowly – either left or right – depending on the last significant digit you dial.

**Now what?**When you reach this stage – get your stop watch out and get ready.

Now we are going to calculate the exact frequency ‘drift’ from the GPSDO reference frequency.

Look at the circle – and wait until it becomes a ‘straight line’ – start your stopwatch.

Wait until the ‘circle’ spins an entire revolution and becomes a ‘line’ again – remember this is only ½ turn because we are viewing in 2D – then wait for another revolution until it becomes a ‘line’ again – now STOP the stopwatch!

**VOILÀ!**We have completed the measurements – congratulate yourself if you are still with me

WARNING – the above ‘stop watch process could take a long time – especially if your signal generator is very close to the 10MHz frequency.

To calculate how much ‘off frequency in Hz’ we are from the reference frequency we do the following;-

In my case with the Rigol DSG815 – it took 172 seconds to make a FULL 360 degree turn of the circle.

If we divide 1 by 172 – we will get the frequency offset

In my case this was 1/172 which is 0.0051813953 Hz

If we round this off to the GPSDO resolution it then becomes;-

**0.00581 Hz**Pretty Good frequency accuracy for the Rigol DSG815

(I am looking forward to performing same test on the Siglent SSG2032X soon)

So what does this mean in relation to the DSG815’s ability to set ‘exact’ frequency?

My offset for the 815 was 0.071 Hz

I could only change the last significant figure

So, can dial either 0.072 – circle still spinning

OR

I can dial 0.070 – circle still spinning – in opposite direction

Because I need to ‘dial’ 0.71581

But since I cannot – because I only have 0.00 Hz resolution and not the required 0.00000 Hz resolution offered by the GPSDO – this is why with the use of the GPSDO reference frequency – I can calculate the ‘exact’ difference needed to have a precise ‘lock’ to the 10MHz.

In my case the Rigol DSG815 was 0.71581 Hz ‘higher’ in frequency than the exact 10.000 000 00 MHz dialed on the control panel.

Interesting that the Rigol DSG800 series specification states a ‘frequency stability’ and not ‘frequency accuracy’

– I don’t think manufacturers like to specify accuracy

– because it can be way off.

*See detailed specifications / data sheet on the DSG800 series here*http://telonic.co.uk/v/pdf/rigol/Rigol-DSG800-Signal-Generator-Datasheet.pdfWe just measured – frequency

accuracy – something NOT specified in the data – but good to know.

The STABILITY of the frequency – is specified in the data – referenced to 25 deg Celsius

Within the range of 0 to 50 degrees Celsius.

So if the instrument has ‘warmed-up’ and the room temperature where the instrument is operating is within the 0 to 50 degrees Celsius, Rigol specifies that the deviation in frequency will be less than 2ppm

To understand this better

– visually it can be seen as this

Either

**09.999 999 90** OR

**10.000 000 10**Remember – Rigol only specifies STABILITY – not accuracy

So we determined the

accuracy to be within 0.71581 HzAnd the

STABILITY within 0.2 Hz – at least around my room temp which was 21 degrees Celsius.

The frequency did not drift more than

**0.00581Hz** for over 10 minutes – when instrument was warmed up.

**These are certainly impressive figures for a ‘cheap’ (non Agilent or Keysight) instrument.**I did not stress the temperature stability to the entire range from 0 to 50 degrees Celsius unfortunately.

**Conclusion**I have demonstrated how a GPSDO is a very useful instrument to have in your laboratory.

With this device and a simple oscilloscope – capable of X-Y plot – we can measure the frequency accuracy of an instrument under test, and consequently its stability with respect to temperature.

The Rigol DGS815 RF Signal Generator proved to be well within its published specifications.

See attached screen captures.It’s not possible to ‘see’ spinning circle in the screen shots – so I tried to ‘capture’ as it was moving from straight line – to indicate its movement.

*Hope the above – rather detailed explanation of this simple testing process is useful for application to other devices under test.*