The Worlds Most Accurate 1Hz Oscillator

You may have heard, or seen the challenge to construct the fastest circuit possible on a breadboard. However, this is not trivial to achieve, let alone measure as specialized and expensive equipment is required to do so. Hence, we have proposed quite literally the opposite- the world's "slowest oscillator". Now, one may be tempted to shoot for the slowest oscillation speed to satisfy the criteria at a cursory glance, but I predict one of you out there will be a smartass and hit me with something like: "0 Hz is the slowest ". Piss off. To this extent, a precise frequency would be enforced to mitigate any tomfoolery.

The frequency chosen shall be 1 Hz. Seems like a nice round number.

The details of how the design will be directed and evaluated will be outlined in the following sections. Specifications will clearly outline the requirements. This will be what the circuit is expected to do, behave like, perform as, etc. Constraints are what adds some spice (pun not intended) to the challenge. It should be noted that if any of the constraints are invalidated, then the associated submission that had violated the constraints would then be considered as an invalid submission (i.e. don't cheat, probably difficult for some of you fuckers). The evaluation and figure of merit section outline the weighting and evaluation formula. This is published to keep judging fair and for you to get an idea of how your circuit does (or doesn't) perform.

Anyway, I shall leave some parting words of advice for this, and any following challenge. However, I lack the originality to synthesize profound statements, therefore I shall take inspiration (read: steal) from a famous electrical engineer: 

"Note that the design requirements are very open; there are many solutions to the problem (which makes this a good engineering exercise), some good, some not so good. The same can be said about the requirements to the report. It is left for the students to judge what makes up a good design, good supporting simulations, and a convincing report, keeping the following in mind: the report must answer all questions asked and implied in the project description, it must document the work done, and it must show that the authors understand the material. Also, note that any illegible material will be considered incorrect." - TL

Specifications

• 1 Hz +- 0 Hz.
• The circuit must be able to drive 1 Vrms into a 50-ohm resistive load. 
• The output waveform can be any shape you want, just as long as it has a clearly defined periodic signal.
• Hint: you should probably be sure that the oscillator is both supply and temperature invariant. Read: Yes. We will test it over temperature and supply variation.

Constraints

• No signal inputs to the circuit. No direct or radiated coupling into the circuit from an external source. No E or H fields.
• Power supplies are obviously allowed. One 5V positive rail and one -5V negative rail. These must be DC. No intentional injection of signals on the rails is allowed.
• The circuit must be constructed on a standard breadboard. No, you can't just dead bug solder it and sticky tape it to a breadboard, or anything else to that effect. You are allowed to use breakout boards (TH to SMD). Note that this means you could potentially use elements that are not on the breadboard as your main source of oscillation.
• No "single-chip" off-the-shelf solutions. Do some design. No PLL IC's either.

Evaluation and Figure of Merit

• Tested at a nominal 25 degrees C to even see if it works.
• Tested between -20 and +40 degrees C to see if it stays at 1 Hz. 
• Tools used for evaluation: DP832, RTM3000, DN2.445-02, a thermal chamber that I can't remember the brand.
• Figure of Merit:
  \begin{equation} \mathrm{FoM} = \left( 1 - \mathrm{exp} \left[ - \frac{(f_o - 1)^2}{0.1} \right] \right) \sigma_y^2 (\tau) V_\mathrm{ps} I_\mathrm{ps} \end{equation}
• Where the Figure of Merit (FoM) is dictated by the oscillator frequency  \(f_o\) , the differential supply voltage \(V_{\mathrm{ps}}\) , the supply current \(I_{\mathrm{ps}}\) and the Allan deviation \(\sigma_y^2 (\tau)\) . You want to minimise this. 
• A substantial portion of the score will be subjectively judged based upon the creativity and absurdness of the implemenetion. The wackier it is, the better.

Applicants & Submissions

The challenge begins as of 9/01/2023. Submissions close on 9/04/2023.

EOI (Expression of Interest) and submissions (design report) should be made to [email protected].

Be aware that it is assumed that the applicant will be able to provide the breadboard circuit for testing in-person (i.e. be at UNSW Sydney, Kensington NSW 2052, Australia when the testing occurs).

Challenge Details Major Update History

v1.3 - 14/01/2022 - Leon - Added some submission details.

v1.2 - 10/01/2022 - Julian - Added Prize

v1.1 - 10/01/2022 - Julian - Added Figure of Merit

v1 - 08/01/2022 - Julian - Created Challenge Specification

Results

TBA

Prize

• $50 AUD.
• Celebratory tart (not a euphemism).