# Recommendation for sine wave of 100kHz with 1ppm stable amplitude

I need to design a 100 kHz sine wave with 1 ppm stable amplitude. I mean the noise of the amplitude should be lower than 1 ppm RMS and also the thermal stability should be < 1 pmm/K. I was thinking of a Colpitts circuit with a crystal oscillator.

• You should use a DDS oscillator for this circuit ... Then use a good filter ... Commented Apr 17 at 12:47
• OK, you're asking for conflicting things: noise being amplitude < 1 ppm is a different problem than stable signal amplitude. Do you count distortion of your sine wave from its theoretical perfect sinusoidal form into noise? Commented Apr 17 at 13:18
• That sounds rather challenging. How will you measure the amplitude? Can you just compensate for variations in some way? Are you talking about RMS amplitude noise/drift or peak to peak or what? Commented Apr 17 at 13:26
• Thanks for the replies. For the noise I mean the rms of the amplitude over 10kHz side bands around 100kHz. Compensation is an alternative that can indeed be considered, but first I want to see if it can work without. Commented Apr 21 at 1:46
• Can you explain why a digital generated waveform works better than a crystal ? Commented Apr 21 at 2:58

Setting aside the fact that your specifications are not very complete, here's how I would go about quickly getting something stable enough to start experimenting with.

There's a little-known circuit for shaping single tones from a higher frequency logic clock, that generates exact amplitudes, rather than the approximate ones that a general DDS would.

The following diagram shows its implementation with a 6 stage shift register performing a divide by 12, though by using suitable resistor values, you can use any larger number of stages to get a higher division ratio.

simulate this circuit – Schematic created using CircuitLab

The resistors are simply the inverse (that is, have conductance) of the sines of angles 30 to 180 in 30 degree steps. I've shown R6 for completeness, even though it computes to zero conductance, or open circuit. If for some reason you wanted to shift the phase of the sinewave (to make 3 phases, or sine/cosine pairs) then it would have a finite value.

The output can be used as is, as a rail2rail voltage output of a few kΩs output resistance, or be driven into a small value resistor, like 50 Ω to drive a coax, or into a virtual ground amplifier.

Starting from here, you have an amplitude that's nearly as stable as your Vdd supply to the shift register. With the right technology shift register (I'd use 74AC, for speed and low output resistance), it won't add much noise to the supply. You would use a crystal-derived master clock. It's cheap enough, and the less noise you invite in from other sources, the better.

With many outputs in parallel, the output resistance is low, their noise is averaged, and individual resistors are much higher than the shift register output resistances. You can scale all the resistor values with a constant term, but these values seem reasonable. You need to keep them dominating the IC output resistances, which can be voltage and temperature dependent. There is no scaling that allows all the resistances for 30 degrees to be single values from the E24 series, so if you are using those, at least one has to be made from several resistors (11k + 560). I have not checked for whether all three are available as single resistors in the finer families (E48/96/192)

The design of this type of dividing clock to sine converter means that it has very low harmonics up to the 11th (for /12 division), so your low pass filter can be very low Q. When the resistors are exactly sine conductances, the harmonics are zero, but tolerances and allowances for shift register resistance means they will just be low, you could expect -40dB or better for 1% resistors.

One area of long term amplitude instability would be a shift of the corner frequency of your low pass filter with respect to the signal. A low order filter can be more stable than a high order one in this respect. If you wanted to increase the signal to corner frequency ratio, then divide by more than 12 (must be even), and choose resistors accordingly.

Your 1ppm aspiration is challenging, your test gear and test methods will be as difficult as your source. I would suggest you throw the above together, and experiment to see what you've got, and what you can measure, before embarking on further refinement, especially refinement of your specifications. I have found that I always learn something I didn't expect when doing a quick initial real experiment. One refinement that may be worth testing is to use CMOS switches instead of gate outputs to drive the resistors - they may be better, or worse, for noise and stability.

• I mean, this is a DDS; but as you say, it's a synchronous one, not a general one, and hence low in jitter, but not in harmonics unless I'm missing something - you still have a rectangular "pulse shape" so to speak, and hence harmonics Commented Apr 17 at 18:39
• @MarcusMüller Have you read what I've said about no or low harmonics, ideally zero, practically -40 dB, until the 11th harmonic, to allow a low order filter? Part of the OP having only partial specs is that the harmonic purity is up for grabs. -40 dB might be quite good for the OP's suggested Colpitts as well. Anyway, what do you think of my suggestion to throw something together and experiment, to learn something? Commented Apr 18 at 5:38
• Absolutely love the idea of learning something! That's one of the reasons I'm here. Yep, read that paragraph saying there's low harmonics up to the 11th, that's why I commented: I didn't understand how this excellent spectral purity arises, so I asked :) It is as you say an intriguing design – a non-uniformly quantized discrete time sine wave generator – and I hoped you had some information on how you (or someone else) invented that. Commented Apr 18 at 9:36
• @MarcusMüller I'll refer you to this Q/A which has several links. Unfortunately Sphero's link to the original paper is broken. It's easy enough to analyse what the circuit does and demonstrate no harmonics up to the (N-1)th. Being synchronous, there are no spurious tones, which is more useful in some applications than others. Where it shines is its ability to generate multiple waveforms of precisely different phases, so 3 phase, or quadrature Commented Apr 18 at 11:16
• Thank you, Neil! Commented Apr 18 at 11:42