Electrical – Why is such amplifier configuration chosen for HB100 microwave sensor

This is basically a classic window comparator, with stuff around it to make is actually useful in the particular application.

PIR sensors report changes in IR accross the sensor area. C2 removes the DC bias, and the circuit around IC1D amplifies the result and also does some frequency filtering. This is probably in part to reduce frequencies that aren't relevant and therefore just add noise, and in part to get the response of the overall sensor+filter that is useful for detecting motion.

IC1C and IC1B are the window comparator. R7, R8, R9, and R10 are a divider chain making voltages for the output of IC1D to be compared against. Just from the topology without looking at any numbers, you can see that the threshold for IC1C is higher than that for IC1B. Also see that the input signal into the window comparator (outout of IC1D) is fed in to the two comparators (IC1C and IC1B) at opposite polarity. In the "window" region, which is the voltage range between the - input of IC1C and the + input of IC1B, both amps will be driving low. Below the window region, IC1B will drive high and IC1C low. Above the window, IC1C will drive high and IC1B low.

The two comparator outputs are averaged by R11 and R12, then the result compared to a threshold by IC1A. This threshold is set so that IC1A drives high only when both comparator amps are driving low, meaning the voltage is in the window region.

The digital signal that indicates whether the sensor output is within the window region is capacitively coupled into this HT2812 thing. I didn't look that up, so I don't know what exactly it does, but from the transistor and speaker it is probably intended to produce a beep when motion is detected.

I'm not sure what the point of the switch in series with the KEY input is. When the switch is open, the HT2812 block won't receive the motion signal. If that is the intent, then powering everything down would be the more obvious approach, so there is probably some additional feature it supports. I don't know why you'd want to only sound a beep due to motion when a button is pressed, but that appears to be what what this circuit will do.

1. Main effect of that loss of sharpness is to delay the sliced output pulse. Whether or not that's a problem depends on context we don't have.
   Secondary effect, IF the waveform doesn't reach its steady state value before the next edge, is to change the observed duty cycle. Again, we don't have the context to know if that matters. You'll observe this at about 3-4x the signal frequency you're using now.
   Ultimately, as you increase frequency, the signal won't reach the slicing point and will disappear altogether, which is a problem if it occurs at frequencies of interest.
   You can mitigate these by reducing the R-C time constant if necessary.

2. Increase the resistances too far and op-amp input bias and offset currents start to matter, and so do stray capacitances including the opamp input capacitances. These currents and capacitances will be in the IC's datasheet.
   Use Ohm's Law and calculate R-C time constants to decide for yourself if you can increase these resistances without compromising accuracy or performance.

3. The idea is that when the output switches, the positive feedback capacitor C1 should give a big enough kick to the input to cross the hysteresis. Otherwise there's a time window when input noise can still cause glitches as C2 charges to the new limit via R1. Do the math, (note R2 = 34k of course) and you'll see C1 is too small.