Is there a buck-boost converter with I2C digital control from a microcontroller?

O

OppaYA

I want to build a portable pocket power supply with a digital voltage/current control (controlled by Arduino).

After doing research I realized that there is no simple way to do it with simple buck/boost converters since digital potentiometers are designed for low voltage and can't be used to control DC/DC converters.

Are there buck-boost converters with I2C control? I mean ones that are popular and available to buy, ideally ready to use (soldered schematic on boards).
 

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Analytic continuation to the upper-half plane

Let $A= \left\{ z \in \mathbb{C}: \mbox{Im}(z)>0 \right\}$. I know that the following property is true and I am looking for an elementary proof of it. I want to show that for $\alpha \in (0,1)$, we have $$|e^{iz}| \leq \Big| 1 + \alpha \int_{0}^{1} \frac{1-e^{itz}}{t^{\alpha+1}} dt \Big|$$ for all $z \in A$. This must be true because the LHS/RHS is the analytic continuation of some random variable's characteristic function.

Does fiber product defines for rational map, projectivity stable under base change via a rational map?

I was reading Professor Kollár's paper Moishezon morphism. In the definition of Moishezon morphism:

Definition 10. Assume $S$ be reduced, we call a proper morphism of analytic space $g:X\to S$ is Moishezon if there is a projective morphism of algebraic varieties $G:\mathbf{X}\to \mathbf{S}$ and a meromorphic $\phi_S:S \dashrightarrow \mathbf{S}$ such that $X$ is bimeromorphic to $\mathbf{X}\times_{\mathbf{S}} S$.
Click to expand...

Here are 2 questions about the definition:

(1) In the definition, it seems $\mathbf{X}\times_{\mathbf{S}}S$ is the fiber product for a rational map $S \dashrightarrow \mathbf{S}$, I am not sure how is it defined? (I try to define it as the base change on the domain of definition of the rational map $S \dashrightarrow \mathbf{S}$. I am not sure is my interpretation correct)

(2) The second question is does the projectivity of the morphism being preserved by the base change via a rational map? I mean $\mathbf{X}\times_{\mathbf{S}}S \to S$ is projective? (if using the interpretation of (1) that the fiber product is defined over the domain of definition of $S \dashrightarrow \mathbf{S}$ then it's clearly projective).

Is the derivative of a $C^1$ function nonzero almost everywhere on almost every level set?

Note: Here $\mathcal H^k$ denotes the $k$-dimensional Hausdorff measure.

Let $f \in C^1 (\mathbb \Omega)$ for some open, connected, bounded subset $\Omega$ of $\mathbb R^n$. We consider for each $t \in \mathbb R$ the level set $E_t := \{x \in \Omega \, | \, f(x) = t\}$.

Question: Is it true that for Lebesgue almost every $t \in \mathbb R$, we have $Df(x) \neq 0$ for $\mathcal H^{n-1}$-almost every $x \in \partial E_t$?

Comments: It is interesting to contrast the desired result to the fact that we have $Df = 0$, $\mathcal H^n$-a.e. on every level set $E_t$.

Kasparov's descent homomorphism for higher KK groups

I am currently trying to understand equivariant $KK$-theory. I think I roughly get the idea of Kasparov's descent homomorphism $$KK^G(A,B) \rightarrow KK(A \rtimes G,B \rtimes G).$$ but what still confuses me are higher $KK$ groups defined by $KK_n^G(A, B):=KK^G(A \hat{\otimes} Cl_n)$ where $Cl_n$ is the $n$-th Clifford-Algebra with trivial $G$-action and $\hat{\otimes}$ is the spatial graded tensor product. How do I get a descent homomorphism $$KK_n^G(A,B) \rightarrow KK_n(A \rtimes G,B \rtimes G)?$$

Thanks.

Chain slipping on middle chainring

  • Art Gertner
  • Physics
  • Replies: 0
I have recently replaced the chain and the cassette. Previous chain never slipped. I never had any problems with it at all. But I have made about 10 000 km on it and the wear was beyound any limits, so friends and guys in the bike service recommended replacing both chain and the cassette. I did a lot of reading and I know that chain and the cassette wear together.

So I got chain and the cassette replaced. It is a 9 speed cassette. I have asked to replace it with a little lower gear ratio. Guys in the workshop also indexed the derailleur for me.

Since I collected my bike the chain slips terribly every time I stand up on the pedals. Sometimes it also slips when I apply enough pressure even while seated. But standing up is a definite slip. I already have few bruises from falling down on the frame.

I had assumption about chain being too long, but is seems to be just about ok.

I have also figured out that the chain never slips if it is on the lowest or the highest chainring. It only happens with the middle chainring. As I have said before - it never happened before with the old chain/cassette. Now I have tried to stand up and pedal very hard in all gears on low and high chainrings. Never got a single slip in about half an hour of trying. Changed back to the middle chainring - it slips in every gear from 1 to 9 when enough torque is applied.

So the question is: can it be that chain is slipping at the chainring? Do chains ever slip at the chainring at all? I have never heard of anything like that. Is there a simple way to test it in order to be sure that the chainring is the root cause?

I really don't want to blame it on the chainring and get it replaced just to figure out that the problem never went away.

Do you put a ferrite bead on both the positive voltage and GND trace?

  • Rydberg
  • Physics
  • Replies: 0
I'm designing some basic DC power filtering for a very simple PCB. Do ferrite beads go on BOTH the positive voltage trace AND the GND trace, or should GND be completely free?

ferrite circuit

Which type of motor use in oil-free air compressor? And how to detect stall?

  • M lab
  • Physics
  • Replies: 0
I got 220V AC single-phase air compressor which labeled "Oil-free" and it look like this. enter image description here

Some time the motor fail to start and got smoke out. (Some people says that happen when start motor with high air pressure in tank. Maybe start torque is too low to pump the air into pressurized tank.)

I called this situation as "Stall".

So my questions are.

  1. Which type of motor used in that compressor? There are four wires, two for line and neutral, two for capacitor. I measure current about 3 A for L-N and 2.5 A for capacitor.
  2. Any ideas how to detect or prevent stall? Can I just detect over-current using fuse or detect phase shift between 2-coil?
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