Question on Op Amp Integrator

[victordion]

In the above is a exam question asking if the input wave and output wave are given, design a circuit with op-amp to realize it.

The solution finds R1 * C2 by considering period and voltage, which I can understand.

However it says we needs R2, and must make sure R2 * C2 is 100 times of the lowest frequency which is 1/T.

I am confused as why we need R2 at all? Can somebody help?

 

[godfreyl]

In theory you don't need R2. However in practice, there's always a little bit of DC offset at the input. Without R2, that would cause the output voltage to slowly drift up (or down) until it reached it's maximum (or minimum).

 

[victordion]

Then how in detail does R2 help to eliminate DC offset on Vin?

 

[godfreyl]

DC gain = R2/R1 so DC at output = DC at input * R2/R1

So you still get some DC offset, but it's limited to a sensible value.

 

[victordion]

The solution is
R1 = 1k R2 = 390k C2 = 24 nF
this way DC will be hugely amplified??

 

[godfreyl]

So if DC offset at input is 1mV, then DC offset at output is 390mV.

 

[victordion]

I see. So if there is no R2, R2 = infinite, this offset is infinitely amplified.

 

[LvW]

I see. So if there is no R2, R2 = infinite, this offset is infinitely amplified.

No, not "infinitely" but with the open-loop opam gain Ao (which is 100 dB or even more).
Please keep in mind that each opamp designed to operate in its linear mode needs dc feedback for a stable and suitable bias point.