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The frequency range for this circuit will depend on how accurately you want the circuit to correct the gain. The gain correction charge times will be based on the RC values of R3 and CH for the positive charge time and R1, R2, and CH for the negative charge time. Based on the given ratios, the positive charge time will be 25 times faster than the negative charge time. Setting the reference voltage (VR) equal to the desired output peak voltage would correspond to a positive charging duty cycle of about 3.85%. This is about 25 times less than the negative charging duty cycle which would result in an equal charge and discharge voltage for the gain control.
A 100kHz input (10us period), will result in a positive charge time of 10us/25 = 400ns, which corresponds to a 1-e^(-400ns/(1kΩ*0.1uF)) = 0.38% overshoot on the gain control voltage (Vc). As you decrease the frequency, the overshoot will increase and the abiltity to accurately track the output will decrease which will also cause the output to look noisier. To keep the same overshoot at 10kHz, you can change your value of CH = [-1/(25*10kHz)]/ [ln(1-0.038)*1kΩ] = 1uF, but the current setup should be ok at 10kHz. If you increase the frequency, this reduces the amount of overshoot, but it takes longer for the output to settle to the final value so there will be a tradeoff there.
