A decadent band plan

2026-10-05 · Electronics/RF Clock

I didn't know what exactly I was getting into when I came up with the idea to split 6 signals across the 4-20kHz range. Turns out I am getting into trouble, but that would be a spoiler since my writing is running behind the actual design work... Yes, I am setting up a cliffhanger for stuff that is not even in this "episode" 🤣

So, let's start from the beginning.

The objective

The first module to build for the wonder clock is the digit signal filters, because I identified it as mission critical - if I can't reliably tell apart 6 digit signals, then there is no time to show. So the objective is to run calculations/simulations and prove that such a filter array can be constructed. And I really have no idea if that can be done or not, as the last time I tried to build an electronic device was 25 years ago!

Constraints

We need the signals to fit into the sound card range. Even without much experience I can say that low frequencies will require some serious iron, so let's randomly pick something a bit higher than 50Hz:

To be honest, this is not completely random. I have already done all my calculations, but the range didn't change much; I think my first pick was 2-18kHz.

The carrier is going to sit at ~94.5kHz. It doesn't require any licensing, and it brings its own batch of problems. In particular, some stuff is still active in that range, e.g. the DCF77^[1] time signal (yep, this is how it is done properly), and even some old navigation systems might still transmit, e.g. Chayka^[2]. Claude called my design decadent and said that a true 50s engineer would never spread their signal like that, all over the band, leaving no option to squeeze in somewhere between these monsters. What did I say? I said I'll spread my signals any way I want, and it's a problem for later me. I have to protect my brain from cognitive overload!

So, that's all about the setup. The signal range and the carrier are set.

Band allocation

There are 6 signals overall, one for every digit in the 00:00:00 time format. Each signal is FM and encodes one of the digit places: H₁, H₀, M₁, M₀, S₁, S₀. This approach is, I think, the most straightforward one: each channel has 10 states at most (the tens digits get away with 3 or 6) and maps nicely to some voltage -> display driver device.

Filter log graphs are totally going to try to trick you by showing beautiful linear(ish) responses, but in reality that's not true - to keep the same bandwidth in Hz while increasing the center frequency, we have to add more filter poles and/or tweak input/output impedance and coil Q. So while it is tempting to split the range equally between signals, this is going to create a lot of work, with progressively increasing demands on Q in the upper bands. Not to mention all the calculations would have to be done separately for every filter. And on top of that, driving FtV (frequency to voltage) stages becomes harder due to decreasing accuracy: telling apart 100Hz at 2kHz is an easier job than at 16kHz, where 100Hz is basically within error margins. Therefore the right move is to allocate bands proportionally to their frequency:

With this ratio the bands will be as follows:

The bands map pretty nicely from H₁ -> N₁ to S₀ -> N₆, with H₀ being the tightest one because it needs 10 states in 1.61kHz of BW.

Coming back from the future, I can say the attenuation on the filters is not great! So, a bit of padding makes filter design survivable. Without padding, 3 poles are a must; with padding, 2 poles might be enough? My oscilloscope will tell me later! Continuing with the same theme of scaling to frequency, we can pad as follows:

Where 𝛼 controls the amount, which I set to 0.2. Why that value? Nothing here is heavily optimized, I am just vibing, going with gut feeling and tweaking numbers till they somewhat make sense. I totally could up my Julia game and run a full optimization on this, but then I could just pick up any filter design package and let it spit out numbers for me. It is home made, ok!

So, here are the final padded bands. That took a good bite off the BW, but we are totally saving some caps/coils on those extra filter poles, trust me!

Digit allocation

FtV converters give a linear response, therefore digit bins will be allocated linearly for every channel. As mentioned before, H₀ clearly demonstrates how bad it is, sitting at only 100Hz step per digit.

Bandpass filters

Well, you know what? I am hungry. My writing is lagging behind this series quite a bit, to the point that I think if I try to push through this log in one go, I'll starve myself to death 🤣

I spent my last weekend picking ferrite pots and caps for this monstrosity. Even that part was exhausting when you do it for the first time. Designing your own electronics is kinda hard: all the parts move, every decision is on you, this is so much not like following a schematic. Who could have guessed, right? 🫩 So, I'm off to have lunch instead!

See you in the next installment of this series, where we stare at some filter charts from Practical Electronics for Inventors^[3].

The current progress is roughly at filter design tag.