You’re cutting yourself a single slice of cake. You grab a butter knife out of the drawer, hack off a moist wedge, and munch away to your mouth’s delight. The next day, you’re cutting forty slices of cake for the whole office. You grab a large chef’s knife, warm it with hot water, and cube out the sheet cake without causing too much trauma to the icing. Next week, you’re starting at your cousin’s bakery. You’re supposed to cut a few thousand slices of cake, week in, week out. You suspect your haggardly knifework won’t do.

In the home kitchen, any old knife will do the job when it comes to slicing cakes, pies, and pastries. When it comes to commercial kitchens, though, presentation is everything and perfection is the bare minimum. Thankfully, there’s a better grade of cutting tool out there—and it’s more high tech than you might think.

Shake It

Knives are very good at cutting food into distinct separate pieces. However, they have one major problem—food is sticky, and so are they. If you’ve ever cut through a cheesecake, you’ve seen this in action. Unless you’re very careful and deft with your slicing, the cake tends to grip the blade of the knife as it comes through. Try as you might, you’re almost always going to leave some marred edges unless you work very slowly.

While most home chefs and cafes can turn a blind eye to these sorts of things, that’s not the case in the processed food industry. For one thing, consumers expect each individually-packed morsel of food to be as cosmetically perfect as the last. For another, cutting processes have to be robust to work at speed. A human can compensate as they cut, freeing the blade from sticking and fettling the final product to hide their mistakes. Contrast that to a production line that slices ice cream bars from a sheet all day. All it takes is one stuck piece to completely mess up the production line and ruin the product.

This is where ultrasonic food processing comes in. Ultrasonic cutting blades exist for one primary reason—they enable the cutting of all kinds of different foods without sticking, squashing, or otherwise marring the food. These blades most commonly find themselves used in processed food production lines, where a bulk material must be cut into individual bars or slices for later preparation or packaging.

It’s quite something to watch these blades in action. Companies like Dukane and MeiShun have demo videos that show the uncanny ability of their products to slice through even the stickiest foods without issue. You can watch cheesecakes get evenly sectored into perfect triangular slices, or a soft brie cheese being sliced without any material being left on the blade. The technique works on drier materials too—it’s possible to cut perfectly nice slices of bread with less squishing and distortion using ultrasonic blades. Even complex cakes, like the vanilla slice, with layers of stiff pastry and smooth custard, can be cut into neat polygons with appropriate ultrasonic tooling.

The mechanism of action is well-understood. An ultrasonic cutting blade is formally known as a sonotrode, and is still sharpened to an edge to do its job. However, where it varies from a regular blade is that it does not use mere pressure to slice through the target material. Instead, transducers in the sonotrode vibrate it at an ultrasonic frequency—beyond the range of human hearing, typically from 20 kHz to 40 kHz. When the sonotrode comes into contact with the material, the high-frequency vibrations allow it to slice through the material without sticking to it. Since the entire blade is vibrating, it continues to not stick as it slides downwards, allowing for an exceptionally clean cut.

Generally, the ultrasonic sonotrode is paired with a motion platform to move the food precisely through the cutting process, and an actuator to perform the cutting action itself. However, there are also handheld ultrasonic knives that can be purchased for those looking to use the same technique manually.

The technique isn’t solely applied to the food industry. The same techniques work for many other difficult-to-cut materials, like rubber. The technique can also be applied to various textiles or plastic materials, too. In some cases, the sonotrode can generate enough heat as it cuts through the materials to melt and seal the edges of the material it’s cutting through.

If you’re simply looking to cut some cake at home, this technique might be a little overly advanced for you. At the same time, there’s nothing stopping you from rigging up some transducers with a blade and a DIY CNC platform seeing what you can achieve. If you want the most perfectly cubed sheet cake at your next office party, this might just be the technology you’re looking for.

If you’re the sort who finds beauty in symmetry – and I’m not talking about your latest PCB layout – then you’ll appreciate this clever take on the long-tailed pair. [Kevin]’s video on this topic explores boosting common mode rejection by swapping out the old-school tail resistor for a current mirror. Yes, the humble current mirror – long underestimated in DIY analog circles – steps up here, giving his differential amplifier a much-needed backbone.

So why does this matter? Well, in Kevin’s bench tests, this hack more than doubles the common mode rejection, leaping from a decent 35 dB to a noise-crushing 93 dB. That’s not just tweaking for tweaking’s sake; that’s taking a breadboard standard and making it ready for sensitive, low-level signal work. Instead of wrestling with mismatched transistors or praying to the gods of temperature stability, he opts for a practical approach. A couple of matched NPNs, a pair of emitter resistors, and a back-of-the-envelope resistor calculation – and boom, clean differential gain without the common mode muck.

If you want the nitty-gritty details, schematics of the demo circuits are on his project GitHub. Kevin’s explanation is equal parts history lesson and practical engineering, and it’s worth the watch. Keep tinkering, and do share your thoughts on this.

Pi Day is here! We bet that you know that famous constant to a few decimal points, and you could probably explain what it really means: the ratio of a circle’s circumference to its diameter. But what about the constant e? Sure, you might know it is a transcendental number around 2.72 or so. You probably know it is the base used for natural logarithms. But what does it mean?

The poor number probably needed a better agent. After all, pi is a fun name, easy to remember, with a distinctive Greek letter and lots of pun potential. On the other hand, e is just a letter. Sometimes it is known as Euler’s number, but Leonhard Euler was so prolific that there is also Euler’s constant and a set of Euler numbers, none of which are the same thing. Sometimes, you hear it called Napier’s constant, and it is known that Jacob Bernoulli discovered the number, too. So, even the history of this number is confusing.

But back to math, the number e is the base rate of growth for any continually growing process. That didn’t help? Well, consider that many things grow or decay through growth. For example, a bacteria culture might double every 72 hours. Or a radioactive sample might decay a certain amount per century.

Classic

The classic example is compound interest. Suppose you have $100, and you put it in the bank for a 10% per year return (please tell us where we can find that, by the way). So at the end of the year, we have $110, right? But what if you compound it every six months?

To figure that out, you look at the $100 after six months. The annual interest on the money is still $10, but we are only at 6 months, so prorated, that $5. Therefore, after six months, we have $105. At the end of the year, we look at the 10% of $105 ($10.50). That’s still for a year, so we need to halve it ($5.25) and add it in ($105+105.25=110.25). So, compounding every six months means we get an extra quarter compared to simple interest.

What if it was compounded monthly? Now, we divide our interest by 12, but we have a little more money every month. After the first month, we have $100.83 ($100.00 + 10/12). The second month’s net is $101.67. By the end of the year, you have $110.47. Not quite twice as much extra as you had before.

So what if you could compound weekly? Or daily? Or hourly? Generally, you’ll get more, at least up to a point. Eventually, the interest will be split up so much that it will balance the increase and, at that point, you won’t make any more. There is an upper limit to how much money we can have at the end of the year at 10%, no matter how often you compound the interest.

So Where’s e?

Assume you could get a 100% return on your money (definitely let us know how to do that). That means if you go for a year, that’s a return of 2 — you double your money. But if you split the year in half and compound, you get 2.25 times the original amount. You can try a few more splits, and you’ll find the equation for growth is (1+1/n)n. That is, if you only compute it once (n=1), you get double (1+1). If you compute interest twice, you get 2.25 (that is, (1+1/2)2).

If you set n to 1,000, the return will be 2.7169. That’s even better than 2.25. So 100,000 should be wildly better, right? Not so much. At 100,000 you get a 2.71814 return. At 10,000,000 the rate is 2.71828 (or so).

Look at those numbers. Going from 1,000 to 10,000,000 only increases yield by about 0.001. If you know calculus, you might know how to take the limit of the growth equation. If not, you can still see it is going to top off at around 2.718. Those are the first digits of e.

Of course, e is like pi — transcendental — so you can’t ever get all the digits. You just keep getting closer and closer to the actual value. But 2.718 is pretty close for practical purposes.

Scaling

We can scale e to whatever problem we have at hand. We just have to be mindful of the starting amount, the rate, and what a time period means. For example, to work with our 10% rate (instead of 100%) we have to consider the rate e^0.10 or about 1.105. Then, to scale for amounts, we have to multiply by the rate. So remember our $100 at 10% example? Our maximum return is 100 x 1.105 = 110.50. Why did we only get $110.47? Because we compounded 12 times. The $110.50 result is the maximum.

More Years

You can also multiply the rate by the number of periods. So if we left the money in for five years: 100 x e^{(0.10 x 5)}.  If you think about it, then, making 50% for one year has the same maximum as making 10% for 5 years (or 25% for 2 years).

Negative Growth?

Suppose you have 120 grams of some radioactive material that decays at a rate of 50% per year. How much will be left after three years? Simplistically, it seems like the answer is that it will be depleted after two years. But that’s not true.

Just as compounding adds more money, a decay rate removes some of the radioactive material, meaning the absolute decay rate gets slower and slower with time because it is a percentage of the radioactive material’s mass.

Just for the sake of an example, suppose at some imaginary small period, the sample is at 100 grams and, thus, the decay rate is 50 grams/year. Later, the sample is at 80 grams. The decay rate is 40 grams/year, so it will take longer to go from 80 to 60 than it did to go from 100 to 80.

In this case, the rate is negative, so the formula will be 120 x e(-0.5 x 3). That means you will have about 26.8 grams of radioactive material left in three years.

Modeling

Consider the classic equation for an RC circuit: Vc=Vs(1-e(-t/(RC))). Here, Vc is the capacitor voltage, Vs is the supply voltage, t is in seconds, and RC is the product of the resistance in ohms and the capacitance in farads.

What can we infer from this? Well, you could also write this as: Vc=Vs-Vs x e(-t/(RC)). Looking at our earlier model for money, it is plain that Vs is the voltage we start with, t is the time, and rate is -1/RC (time can’t be negative, after all). That makes sense because RC is the time constant in seconds, so 1/RC is the rate per second. The formula tells us how much voltage is charged in the capacitor, and subtracting that from Vs gives us the voltage drop across the capacitor.

Think about this circuit:

At t=0, we have Vs(1-e⁰), which is 0. At t=0.5, the voltage should be about 7.86V; at t=1, it should be up to 10.57V. As you can see, the simulation matches the math well enough.

Discharging is nearly the same: Vc=V0 x e(-t/(RC)). Obviously, V0 is the voltage you started with and, again -1/RC is the rate.

So Now You Know!

There’s a common rule of thumb that after a time period (RC) a capacitor will charge to about 63% or discharge to about 37%. Now that you know the math, you can see that e-1=0.37 and 1-e-1=0.63. If you want to do the actual math, you can always set up a spreadsheet.

Anything that grows or shrinks exponentially is a candidate for using an equation involving e. That’s why it is a common base for logarithms. Of course, most slide rules use logarithms, but not all of them do.

(Title image showing e living in pi’s shadow adapted from “Pi” by [Taso Katsionis] via Unsplash.)

Have you seen Severance? Chances are good that you have; the TV series has become wildly popular in its second season, to the point where the fandom’s dedication is difficult to distinguish from the in-universe cult of [Kier]. Part of the show’s appeal comes from its overall aesthetic, which is captured in this description of the building of one of the show’s props.

A detailed recap of the show is impossible, but for the uninitiated, a mega-corporation called Lumon has developed a chip that certain workers have implanted in their brains to sever their personalities and memories into work and non-work halves. The working “Innies” have no memory of what their “Outies” do when they aren’t at work, which sounds a lot better than it actually ends up being. It’s as weird as it sounds, and then some.

The prop featured here is the “WoeMeter” from episode seven of season two, used to quantify the amount of woe in a severed worker — told you it was weird. The prop was built by design house [make3] on a short timeline and after seeing only some sketches and rough renders from the production designers, and had to echo the not-quite-midcentury modern look of the whole series. The builders took inspiration from, among other things, a classic Nagra tape recorder, going so far as to harvest its knobs and switches to use in the build. The controls are all functional and laid out in a sensible way, allowing the actors to use the device in a convincing way. For visual feedback, the prop has two servo-operated meters and a string of seven-segment LED displays, all controlled by an ESP-32 mounted to a custom PCB. Adding the Lumon logo to the silkscreen was a nice touch.

The prop maker’s art is fascinating, and the ability to let your imagination run wild while making something that looks good and works for the production has got to be a blast. [make3] really nailed it with this one.

Thanks to [Aaron’s Outie] for the tip.

SD cards & the much smaller microSD cards are found on many devices, with the card often accessible from outside the enclosure. Unfortunately there’s a solid chance that especially small microSD cards will find their way past the microSD card reader slot and into the enclosure. This is what happened to [Rob] of the SevenFortyOne Radios and Repairs channel on YouTube with a NanoVNA unit. While shaking the unit, you can clearly hear the microSD card rattling inside, courtesy of the rather large gap above the card slot.

After a quick teardown and extracting the lost microSD card, the solution to prevent this is a simple bit of foam stuck on top of the microSD card slot, so that the too large opening in the enclosure is now fully blocked. It’s clearly a bit of a design fail in this particular NanoVNA unit, worsened by the tiny size of the card and having to use a fingernail to push the card into the slot as it’s so far inside the enclosure.

While [Rob] seems to blame himself for this event, we’d chalk it mostly up to poor design. It’s an issue that’s seen with certain SBC enclosures and various gadgets too, where losing a microSD card is pretty much a matter of time, and hugely fiddly at the best of times. That said, what is your preferred way of handling microSD card insertion & removal in devices like these?

[Hope This Works] wants to someday build a tiny factory line in the garage, with the intent of producing some simple widget down the line. But what is a tiny factory without tiny conveyor belts? Not a very productive one, that’s for sure.

As you may have noticed, this is designed after the transporter belts from the game Factorio. [Hope This Works] ultimately wants something functional that’s small enough to fit in one hand and has that transporter belt aesthetic going. He also saw this as a way to level up his CAD skills from approximately 1, and as you’ll see in the comprehensive video after the break, that definitely happened.

And so [Hope This Works] started by designing the all-important sprockets. He found a little eight-toothed number on McMaster-Carr and used the drawing for reference. From there, he designed the rest of the parts around the sprockets, adding a base so that it can sit on the desk or be held in the hand.

For now, this proof-of-concept is hand-cranked. We especially love that [Hope This Works] included a square hole for the crank handle to stand in when not in use. Be sure to check out the design/build video after the break to see it in action.

How happy would you be to see Factorio come up in a job interview?

Thanks for the tip, [foamyguy]!

When it comes to the majority of sports broadcasting, it’s all about the visual. The commentators call the plays, of course, but everything you’re being shown at home is on a screen. Similarly, if you’re in the stadium, it’s all about getting the best possible view from the best seats in the house.

Ultimately, the action can be a little harder to follow for the vision impaired. However, one company is working hard to make sports more accessible to everyone. Enter OneCourt, and their haptic sports display technology.

Haptic, Fantastic

If you can see, following just about any sport is relatively straightforward. Your eyes pick out the players and the lines on the field, and you can follow the ball or puck wherever it may land. Basically, interpreting a sport is just taking in a ton of positional data—the state of the game is represented by the position of the people and the fundamental game piece involved.

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But how do you represent the state of a game to somebody who can’t see? Audio helps, but it’s hard for even the fastest commentator to explain the entire state of the game all at once. As it turns out, touch can be a great tool in this regard. Imagine if you could place your hands down on a football field, and instinctively feel the position of all the players and the ball. That would be impractical, of course, because the field is too big. But if there was a small surface that represented the field in a touchable manner, that might just work.

This is precisely what OneCourt has created. The company realized that many modern professional sports already had high-quality data streams that represented the positions of players and the ball in real time. With the data on hand, they just needed a way to “display” it in a touchable, feelable form. To that end, they created a range of haptic displays that use vibrations to represent the action on the field in a compact tablet-like device. They receive game data over a 5G or WiFi link, and translate it into vibrations across a miniature replica of the playing surface.

OneCourt created a range of devices to suit different sports. A basketball version is marked out with raised lines matching those on the court, and trackable vibrations on the surface tell the user where the ball is going. The company has teamed up to offer devices to spectators going to see the Sacramento Kings and the Portland Trail Blazers at their home games throughout the season.  Those visiting the stadium can request to use one of the devices during the game via guest services, and get a greater insight into the play.

The company has also demonstrated a similar device for use at baseball games, with the characteristic diamond laid out on the haptic surface. The devices were demoted at Dallas’s Glove Life Field last year.

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On a technological level, the hardware appears relatively straightforward. The OneCourt devices just pack an array of vibration motors into a rectangular surface, and they’re controlled based on a feed of gamestate data already collected by the professional leagues. However, for the vision impaired, it’s a gamechanger—allowing them to independently “watch” the game in far greater detail than before.

For now, the devices are very much in a pilot rollout phase. OneCourt is running activations with individual sports teams to offer the devices to vision impaired spectators at their stadiums. However, the intention is that this technology could also be just as useful for fans tuning into a sports broadcast at home. The company hopes to start pre-orders for individual customers in the near future. 

Accessible technology doesn’t always have to be highly advanced or complicated to be useful—or, indeed, fun! Devices like these can open up a whole new world of perception to those that otherwise might find sports difficult or frustrating to follow. Ultimately, that’s a good thing—and something we hope to see more of in future!