Linear circuit complexity classes

The class $textrm{NC}^i$ is the class functions computable by circuits families of bounded fan-in, $n^{O(1)}$ size and $O(log^i(n))$ depth.
The $textrm{NC}$-hierarchy is the union of those classes.

Is there any study of the linear-size variant of this hierarchy? That is circuits families of bounded fan-in, polylog depth and linear size?

I know their exists some work with linear-$textrm{AC}^0$ but nothing else. Remark that at least linear-$textrm{NC}^1$ is nontrivial since it contains regular languages (and thus some $textrm{NC}^1$-complete languages).

Designing a constant current pulse circuit

I’m looking for help designing a constant current pulse through a variable load impedance of 10-100k (R4). The ideal response is shown here:
Ideal circuit response

My current design results in a circuit response as shown below (not ideal):

Circuit response

I’m hoping for my circuit response to more closely match that of the response shown above. What modifications could be made in order to square out the waveform?

Circuit schematic

RC circuit frequency response

I am developing a project where I must analyze an incoming signal that was acquired from a microcontroller. The objective is to obtain the main frequency of the incoming signal.

At first, I’m analyzing an RC step response signal. So, basically, I want to obtain the frequency response, from the characteristic charging curve of an RC circuit.

My mentor told me that I could achieve this with the FFT. He told me that if I applied it twice at the incoming signal, I would obtain the frequency response curve. I think I did, but my only issue is the frequency axis. They’re completely messed up. Even when I apply the method to obtain the frequencies, it goes bad. (I know it’s wrong because my cut-off frequency is around 11 Hz)

https://drive.google.com/file/d/1-ppjp6qE8J8O96Lj4uaJx36o2pt3KMSG/view?usp=sharing

So, what I’m asking is:

  1. Why is it that applying the FFT twice to the signal give the frequency response?

  2. Does anyone know how I can obtain the correct frequency axis?

Waveguide equivalent circuit applicaiton limitations

I’m trying to simulate connection of two 2-port RF devises via waveguide. All calculations are in the notebooks.

Connection is through the magnetic field and looks like so:

enter image description here

Its equivalent T-circuit:

waveguide equivalent circuit

Where
$$
Z_1 = Z_2 = Z n^2 tanh{frac{Lgamma}{2}} \
Z_3 = frac{Z n^2}{sinh{Lgamma}}
$$

When I try to simulate connection of two devices using this circuit, results do not match those obtained using FEM software. I used sympy for my math so equation transformation error is unlikely. Is there a conceptual error limiting the application of the waveguide equivalent circuit?

How to implement OCV(open circuit voltage) method for battery using Look-up table?Li-ion battery

I have gone through a ocv method using look-up table,they have given below steps.can anyone suggest how to implement using any controller or circuits?

  1. Charge the cell to the full point.
  2. Discharge the cell to the 0% point to learn the capacity of the cell, which should be recorded in mAh.
    Page 1 of 5
  3. Charge the cell to the full point.
  4. Allow the cell to relax for 60 minutes.
  5. Record the open-circuit voltage for the 100% point.
  6. Discharge the cell 5% (based on the capacity of the cell from Step 2) at a rate of approximately 0.2C.
  7. Allow the cell to relax for 60 minutes.
  8. Record the open-circuit voltage for the 95% point.
  9. Repeat Steps 6–8 19 times until the capacity reaches 0%.

Or

You have any idea to implement this?

How do I set up a lumped element equivalent circuit?

In the treatment of metamaterials, optical problems and antennas, very often a simplified model is extracted by considering only lumped elements. In some cases this is fairly obvious, for example in this paper, which shows a split-ring resonator with its equivalent circuit.

enter image description here

The straight wires act like inductors, and the capacitor-shaped element in the middle acts like a .. capacitor. So far so good.

But how do I approach this in other cases, for example for this coplanar waveguide?

enter image description here

Is there a cookbook-style, systematic recipe how to set up the equivalent circuit of such a system? Where do I start? It seems to me there are loads of capacitances and inductances everywhere – when should I stop including them? And where do the geometric and electric parameters of the original structure come in when evaluating the final circuit (surely I would like to calculate the inductance from the crosssection and length of the wire)?

An answer would be either an explanation how it works in general, insightful examples of different cases or some guidelines as to where I can read about it in detail. At the moment, these equivalent circuits seem to fall out of the sky for me and it’s not clear to me, how authors arrive at them.

Automatic Self-Test Circuit in GFCI outlet

What kind of Self-Test circuits or method do they used in the GFCI outlets generally? Is it just firmware or is there a physical addition (and what it is usually?)

This is because after 2015. It is required by UL. But there were many old stocks without it and the physical appearance of the product is the same. So is there any way to recognize or test the function if I buy a product which both has the function and not (depending on whether manufactured after or before 2015 which they don’t specify?)

Note: This isn’t about the manual test button, but a circuit inside… see

“New Self-Test Requirements:
n Underwriters Laboratories (UL) made new revisions to the UL 943 (GFCI) standard that will take effect on
June 29th, 2015.
n UL REVISION 943 STATES:
1. All GFCI receptacles must have an auto-monitoring (self-testing) feature.
2. If auto-monitoring determines the GFCI can no longer offer protection, one or more of the following will happen:
(1) Unit is no longer able to reset and denies power.
(2) Unit can reset and is subject to
the next auto-monitoring test
cycle within 5 seconds of power
to the device.
(3) All GFCIs must provide audible or visual indication if it does NOT
go into power denial.
3. Provisions to ensure receptacle will not reset if miswired during installation as
well as reinstallation.

Self-Test Circuit in GFCI outlet

What kind of Self-Test circuits or method do they used in the GFCI outlets generally? Is it just firmware or is there a physical addition (and what it is usually?)

This is because after 2015. It is required by UL. But there were many old stocks without it and the physical appearance of the product is the same. So is there any way to recognize or test the function if I buy a product which both has the function and not (depending on whether manufactured after or before 2015 which they don’t specify?)

Flashing LED circuit using Flyback Topology Flickering Problems

Background: Design an LED circuit that alternatively flashes 40W LED strings approximately 45 times per minute.

Approach: I began by getting my hands on Linear Technology’s LT3799-1 – Offline Isolated Flyback LED Controller with Active PFC Demo Board DC1947A for initial testing. The circuit for that demo board great when lights are in steady state. The strings consist of 14 LEDs with a Vf~42V, being driven at 900mA, this I assume I good starting point for my project.

I prototyped a simple flashing circuit by adding two external BUK9616-75BN Channel FETs with the LEDs, the circuit below shows just one, but it would be the same for two strings:

enter image description here

The BUK9616 receives sufficient Vgs~10V from the function generator, therefore it operates in full saturation. The flashing circuit works well when not connected to the demo board.

Problem: When the flashing circuit is added to the demo board and I vary the duty cycle of the wave, just as I did without the demo board, as the LEDs transition from Off to On, there is a slight noticeable flicker. I suspect the issue may be in the ‘Open Circuit Protection’ of the board as I see a slight hiccup in the gate of Q1 on the demo board (10V), corresponding to the light flicker that looks like this:

enter image description here

I believe this suggests that the voltage divider formed by R3 and R4 have reached a voltage > 1.25 triggering an open circuit fault and essentially stopping all the switching in Q1, entering hiccup mode to clear the fault once a load is “detected”, and this very same hiccup is causing the flicker.

I would like to essentially de-activate this open circuit protection, however, these boards are very expensive and I’d hate to damage one. Here are the possible approaches to solving this issue:

1) Remove R3: This “cuts” the feedback from the third winding and forces FB to be 0V, therefore FB will never reach 1.25V and Q1 will never stop switching.

2) Increase the value of C7: This capacitor also charges up to 1.25V when there is an open in the secondary, both the CT and FB pins must be at 1.25 for switching to stop.

3) Using a Triac dimmable LED driver, like the 3799, although I think the flickering associated with triacs in LED drivers is not the issue here. Could the PFC circuitry be causing this as well?

Suggestions/feedback on the three proposed approaches is highly appreciated!