Why capacitor in opamp feedback?

[fubar3]

what is the purpose of C2 in the following example (b)
.... (snip from https://www.nutsvolts.com/magazine/article/op-amp-cookbook)

 

[rayma]

Reduces the gain at DC to unity.

 

[fubar3]

@rayma replied .. Reduces the gain at DC to unity.

Thanks. So gain is (0+ R2)/R2. How would this benefit an audio amplifier or some other application.

 

[MarcelvdG]

Any practical op-amp has a so-called offset voltage. That is, when you apply feedback around it, it regulates to some small DC voltage difference between its inputs. If the op-amp circuit has a large gain, the amplified offset may reduce headroom, or burn out your woofer if the path from the op-amp to the woofer is completely DC coupled. Reducing the DC gain to a small enough value prevents that.

 

[rayma]

At DC, the circuits are both followers, with the positive input connected to ground, so the output is 0VDC.
Except for any DC offset due to imperfections in the op amp.

The capacitors serve to block incoming DC voltage, and to avoid amplifying the inherent DC offset in the op amps.
Also they can reject incoming low frequency disturbances.

 

[ejp]

So gain is (0+ R2)/R2.

No. The diagram is mislabelled, and the gain shown is incorrect. If the top resistor is taken as R2, the gain (to simplify) is 1+R2/(Z(C2)+R3). At DC, Z(C2) is infinite, so the gain is 1.

 

[egellings]

Reduces the gain at DC to unity.

That way the input DC offset voltage does not get amplified by the stage gain.

 

[fubar3]

Here is headphone amp project113 which has blocking cap in the feedback. It is flat for 10hz to 100khz

https://sound-au.com/project113.htm

The unity gain mod would be useful for random generators in audio test gear.

 

[nigelwright7557]

The same method is used in power amps in the feedback to give AC gain but not DC.

 

[Boden]

How is the value of C2 calculated?

 

[mondogenerator]

what is the purpose of C2 in the following example (b)
.... (snip from https://www.nutsvolts.com/magazine/article/op-amp-cookbook)

View attachment 1287298

There's also a typo in (b) where R2 in (a) becomes R3

 

[ejp]

How is the value of C2 calculated?

Choose it such that Z(C2) = R3 at the desired turnover frequency.

 

[Boden]

Suppose the turnover frequency is 3 Hz, and R3 = 10KOhms, how do we take it from there?

 

[Boden]

Z should then be 10 KOhms at 3 Hz?

 

[lcsaszar]

Z or rather Xc = 1/(2*pi*f*C)
Dimensions are Ohm, Hz, Farad.

 

[Mark Tillotson]

Units are ohm, Hz, farad. Dimensions are resistance, frequency and capacitance...

 

[MarcelvdG]

If you want to be precise, |Z| = 1/(2πfC), but X = -1/(2πfC), and Z = -j/(2πfC). I doubt if that helps fubar3, though.

 

[fubar3]

Thanks for the replies. I like to put these results in a spreadsheet which I can resuse in future. Else I forget and have to reinvent. Here is an example of 3db cutoff.
B8 = 15000 .... R
B9 = 2 .... C
B10 = 1E+06 .... as in 2uf
B11 = 6.28 * B8 * B9 ... calculation #1
B12 = 1/(B11/B10) ... answer = 5.307 ; same as online calculator

I would like to do something similiar for the gain capacitor mystery.

 

[ejp]

5.31uF is correct for C2 if R3=10k and Ft=3Hz. What mystery?

 

[fubar3]

Choose it such that Z(C2) = R3 at the desired turnover frequency. .... 5.31uF is correct for C2 if R3=10k and Ft=3Hz. What mystery?

I am wondering what this gain-capacitor thing is called so I can look for it on the web. And how is the cap value determined.

Here is a snippet from Rod Elliot Project-11. The gain capacitor (C7) is not discussed on the project page ...
https://sound-au.com/project11.htm