Location of input for negative feeback bandpass filter
In thinking thru such circuits, one approach is to have the INPUT be still, unmoving. Then examine the &quot;noise&quot; response.
In this opamp circuit, if the Vin is unmoving (Vin+), then the opamp strives to make the other input also be unmoving.
If Vin- is unmoving, then the networks around Vin- are DECOUPLED,
and you can examine them separately.
The network to Ground is a high_pass filter. This is easy to see, if you realize DC impedance is infinite, making the total gain be Feedback/infinity.
The Feedback network is a low_pass filter, and at very high frequencies the impedance IS zero, so the total gain is Zero/Input_network_impedance = zero.
If you properly set the two corner frequencies, you have a well-controlled passband with gain set by Rfeedback/Rin. In this case, gain is R5/R6.
For accurate gain in the &quot;passband&quot; (accurate within a few percent), you need a passband width of several decades (such as 100Hz to 10,000Hz, not quite adequate for audio signals).
Here the low_frequency time_constant (as someone tries to SLOWLY SLOWLY move thru the field_of_view of the PIR, is 33uF * 40Kohm. This is 1.3 second time_constant, thus by moving VERY SLOWLY, you can trespass at will.
The upper end is 100pF and 15Meg ohm. Given 1pF and 1MegOhm is 1 uS, we easily compute a 1.5 millisecond time_constant, or about 100Hz upper corner (F3dB, 45 degree phase shift). Note this DOES NOT attenuate 60Hz energy, thus electro_static power line interference may be a problem; some thinking about shielding might be useful to prevent surprises, or false triggers.