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I am trying to figure out how this filter circuit works:

enter image description here

The filter is part of a mini color organ from Forrest Mims Engineer's Mini-handbook. I know it is a high pass active filter which will only illuminate the green LED at certain frequencies, but every other high pass active filter I've looked at has the cap and resistor in series both going to the inverting input. Can somebody please help me undertstand how this filter works? Thank you!

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  • \$\begingroup\$ Out of curiosity, what's the input signal? \$\endgroup\$ – BeB00 Dec 12 '17 at 3:49
  • \$\begingroup\$ @BeB00, pdf page 24 ... book page 45 .... archive.org/details/… \$\endgroup\$ – jsotola Dec 12 '17 at 4:32
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It's probably best to think of it as a normal differential amplifier, but with a complex impedance on the non-inverting input resistor (R2 in the following diagram):

enter image description here

The derivation of the equation is shown here, but it simplifies down to:

enter image description here

Now replace R2 with the capacitor impedance R2=Xc=1/(2*pi*f*C). We can see that as the frequency increases, this term decreases. This means that the V2 term increases as the frequency decreases, making the output increase and making the circuit act as a high pass filter.

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  • \$\begingroup\$ Np, it is a slightly unusual design choice, I suppose it's because it's directly driving the LED and doesn't have any negative rails \$\endgroup\$ – BeB00 Dec 12 '17 at 3:39
  • \$\begingroup\$ You can also see that as the impedance tends to 0, the output becomes equal to the input \$\endgroup\$ – BeB00 Dec 12 '17 at 3:45

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