# Sine oscillator at extremely high frequencies

I would like to make a "good" (doesn't need to be perfect) sine wave oscillator from 50 GHz to 1 THz, if possible with two outputs: one is $$\\sin(2 \pi f t)\$$, the other one would be $$\\cos(2 \pi f t)\$$.

Maybe I already asked for a lot, but if possible, the system would reach 2 V where the output impedance is basically a capacitance around 100 pF, which at 50 GHz is around 30 mΩ (but if required the capacitance could be lowered to ~ 1 pF).

As far as I understand, working at these frequencies is extremely difficult where even the wire distance is extremely important, specially to get the cosine.

I thought about using an SDR and just generate a perfect sine wave, but most SDR only go up to ~ 6 GHz. The cosine maybe could be reached with just using a cable and the length alone would be sufficient to generate the phase difference.

I tried at ~100 MHz and it did a reasonable job (checked with an oscilloscope). But at 50+ GHz it's a completely different matter.

Edit: I realize now that my question lead many people in a different direction than intended: when I said from 50 GHz to 1 THz what I actually mean is that my expectation is for a single circuit should work at a specific frequency. That is, I do not expect that the same circuit can work at 50 GHz and that (e.g. by changing a resistor) it could work at 1 THz.

Given the (understandable) limitations at 1 THz, could you please consider relaxing the frequency to the interval [5 GHz ; 50 GHz] - again, I only expect a circuit to work at one specific frequency and not in the whole range. But please still consider the 2 V and ~100 pF load.

Edit 2 I understand now that my question is foolish. In order not to edit anymore, I posted a new question (https://electronics.stackexchange.com/questions/700406/oscillator-at-5ghz-to-50ghz) with refined parameters so as to try and make it feasible. Thank you for all your help

Edit 3 Apologies but my lack of knowledge on this subject seems to have requested the impossible (high freq/V/F) and I don't know how to pose the question (or pose 100s of questions with different combinations of freq/V/F to try to find some that is feasible) in order to not offend people. It seems the exact parameters of my experiment are required but I don't know them. So again, apologies for wasting your time and thank you for your effort. I will try to look at the waveguides to understand how an oscillator could be made from them, thank you for the suggestion.

• at 50GHz, a quarter wavelength is around 1.5mm. You are asking to multiply that frequency by 20, which means geometries of much less than 1mm will become significant. This does not seem to me to be possible with conventional PCB technology and electronics packages. There seems to be a good reason why electronics running at 1THz is not commonly available. A search on "1THz oscillator" does throw up some results, so they exist, but the tech is highly specialised. Commented Feb 5 at 9:30
• Here is some application at this frequency hangroup.mit.edu/wp-content/uploads/2018/04/… See oscillator. Commented Feb 5 at 10:03
• @danmcb already at around 50 GHz, you try to avoid electronics that deal with these frequencies ever "touch" the PCB, for loss and precision reasons. There's nice automotive radar ICs that integrate all the 72 GHz stuff on the usually prohibitively expensive silicon die's top layer - including the antennas. But it's still mostly based on the "electronics" idea that the signal travels where I put a conductor, and not on the more THz/Photonic idea that I need to build wave guides in chip technology. Commented Feb 5 at 10:50
• For these kinds of applications, you usually start with a lower frequency clock (say, 100 MHz) that is relatively easy to generate and, using PLL's you multiply that up to whatever frequency you need. You easily go from 100 MHz up to several GHz using readily available ICs such as the LMX2615. Commented Feb 5 at 13:14

You're still way off in your technological estimate of what's doable.

At 50 GHz, a 10 pF load is pretty much impossible to drive: |X|=|1/(j2πfC)|, for f=5×10¹⁰ Hz and C=1/10¹⁰ F, is |X|=1/31.4 Ω. At 2 V, that leads to an apparent power, and thus a power flow, of P = U²/R = 4 V² × 31.4 / Ω = 120 W. The most powerful millimeter wave oscillators we can build directly in semiconductor technology barely scratch the Milliwatt range (also, they are built as interviewed circuits on chips. You can't just solder a transistor, a capacitor and a coil to a board at 50 GHz); so you'd either need to couple this out into a waveguide and feed an amplifier with it (and quite an impressive one - this is military radar material), or you directly go for traveling wave tubes or Klystron technology for the oscillator or resonator. Again, that looks nothing like the electronics you're used to.

So, again, whatever you think you're solving with this, it'll need a different solution.

One cannot build such an oscillator. You need different technologies to find something that electronically oscillates at 50 GHz, which is still RF, possible to work with in semiconductor electronics, and 1 THz, which isn't RF, and needs different kinds of approaches to circuitry, which might more reminiscent of photonics than electronics.

The enormous 20x difference in frequency is an additional challenge.

So, whatever you want to solve by building that oscillator, your problem either is impossible to solve, or you will have to use different oscillators for different frequency ranges, or, and that is in my humble experience the most likely case, you might have misunderstood a technical problem.

I say that, because the very same problems that lead to technology not working for both 50 GHz and 1 THz stem from the fact that the same things, exposed to 50 GHz and 1 THz, react with different "physics", if you will. So, whatever you do with that oscillation is unlikely to actually make sense in a technological way to span this huge range.

The frequency classes you are interested in are SHF and EHF and range from 3GHz to 300GHz. To create something that works in such frequency bands, new knowledge such as microwave engineering with extensive use of Maxwell's equations is required. The electromagnetic energy is conveyed into waveguides, sized based on the working frequency and can be very small in size, so it is necessary to use mechanical lathes and milling to create a microwave circuit. As you can see, things have all changed. A substantial difference compared to the circuit techniques used in the lower frequency bands is that we are no longer dealing with concentrated constant devices but rather distributed constant devices.Here is an old photo of some microwave components:

• mabeco, your edit reveals you have misunderstood this answer: Franc doesn't say it's the waveguide that is used to make the oscillation, but to get the generated RF power anywhere. That's a difference! Commented Feb 6 at 22:29

For the frequency range you speak of, we don't really have good solid dielectrics. So you'll need waveguides and related hardware just to get the output of the oscillator to wherever the load is.

I don't know if you know how much waveguides cost, but essentially if you don't have tens of thousands of USD just for the interconnects, and some more for instrumentation, you won't even be able to measure whether it works at all.

And we haven't even touched how you'd generate such signals.

So, I'd say the first problem to overcome is the budget for such experimentation. Once you have a carrier, there are passive elements that will do phase shifting all right.

doesn't need to be perfect

With RF it's somewhat easier, since carrier harmonics are not a big problem - they are easy to filter out. So the oscillator will indeed output a beautiful, almost perfect sine wave, because the harmonics will be attenuated even just by the waveguides, and additional filtering is also relatively easy to set up - just costs a lot due to mechanical precision required.

Let's break down you problem a little bit:

We start at 50 GHz. 50 GHz is already an extreme frequency to work at. However, it is possible and there is measurement equipment commercially available to work with frequencies < 64 GHz. Searching for components at manufacturers like AD will give you actually buyable results. So in that frequency range a pure oscillator is mainly a challenge of finding the right IC. Semiconductor technologies in both bipolar and today even CMOS technologies are available in that frequency range.

Making a PCB for that IC, however, is another question. You need a very low loss high frequency PCB substrate (like rogers or other Teflon based PCB materials.) This is expensive but doable. A 90° phase shift can be achieved by building a 90° hybrid on the PCB or searching for a ready built one. Note, tat every millimeter of trace and every connector will create noticeable power loss of you signal. And good components like connectors for ~64 GHz are very expensive. In that frequency range it already makes sense to use hollow waveguides as conductors as they show lower losses than coax connectors. However, cables and connectors are still available at this frequency.

Now we look at you other extreme. 1THz. Terahertz is tricky as this approaches the so called “terahertz-gap”. This is the frequency gap at low terahertz frequencies 1-10 THz in which electronics stop working and optics are not yet working very well. I used to develop microwave ASICs at ~300 GHz in an GaAs mHEMT technology. See the image (taken from: https://web.archive.org/web/20180710095445/https://www.terapan.de/) At 300 GHz waveguides become the only viable solution to wiring these signals. In the image you can see an asic in the middle. It is fed a low frequency )several GHz) over the thick waveguide. The energy is received by a patch antenna and fed to the ASIC. The ASIC now multiplies the frequency to 300 GHz. On the other side, you see a thinner waveguide. This is used for a 300 GHz signal. For 1 THz the design would look very similar but is even trickier. You would have to take a semiconductor technology capable of a fmax > 1THz (there are only a few) and build a frequency multiplier in it. Which is usually only a few trasnsistros in a non-linear operating point and some filters made of transmission lines. After multiplying the frequency for e.g. 64 Ghz to ~1THz you can couple it to a waveguide. Power levels at these frequencies are usually very low and losses are huge. Furthermore, yields at these frequencies are low. You will basically produce 1 or more whole wafers of chips to get even 1 working chip off of them.