Precision rectifier - gain ??

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Hello, everybody. I didn't know where to post that topic and 'line level' forum seemed the most logical place, since the precision rectifier is used to feed a level meter. For a number of reasons, I chose this circuit:
An externally hosted image should be here but it was not working when we last tested it.
However, the specifics of my project requires the rectified signal to be amplified, but it's not possible to add another opamp in order to introduce gain. Can I change R3 to, let's say, 10K, in order to obtain a higher gain, or that will lead to distortion? Is the opamp on the right amplifying the whole rectified signal, or just parts of it?
 
If you change R3 to 10K you will amplify every other output pulse ( 10V followed by a 1V pulse). It's hard to get perfect symmetry with standard resistor values but if you change R3 to 11K and add a 1.2K resistor from the negative input of the input opamp to gnd you will have a gain of 11 with the output pulses within 10mv of each other with an 11V output.
 

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