Understanding this op amp circuit

[XaviPacheco]

Looking into the circuit attached:

When the input signal is negative, D1 is forward biased, and D2 reverse biased. In this case the circuit is an inverting low pass filter with unity gain R3/R1 and cutoff frequency defined by R3 and C1.

When the input signal is positive, D1 is reverse-biased and D2 is forward-biased. The op amp becomes a non-inverting low pass filter, right? My question is: If D1 is reversed-biased, the op amp doesn't see R1.  How does the amplifier keep unity gain?

[Ian.M]

It doesn't need to see R1.  Although a unit gain buffer usually has in- directly connected to out, neglecting input bias current and stray capacitance to ground, it can have any resistance for feedback and will still be unit gain, as long as there are no other connections to in- (except other two terminal components in parallel to the feedback resistor).

If in doubt have a play with the attached LTspice sim!

[SiliconWizard]

My question is: If D1 is reversed-biased, the op amp doesn't see R1.  How does the amplifier keep unity gain?

As Ian said.

Note that the cut-off frequency of the low-pass filter will be much higher when the input signal is positive than when it's negative.