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I am trying to understand & implement simple toy AGC system . Few questions while reading about it,

1) How POWER metric came into picture, why not other metric like absolute value to control amplitude of input signal?

2) What's the role of LPF(Low Pass Filter) in AGC? LPF is an attenuator or blocker to high frequency components. How such filtering effect can control input amplitudes?

Any reading references will be helpful.

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Either power or rms value is typically used for AGC as a peak value would be much more variable given it is an instantaneous measurement. The low pass filter typically refers to the Loop Filter (and if so, would be better described as such as it more typically done as an integrator) which is a core part of the control loop design. A band pass filter prior to the power detector is also important since any signals within the bandwidth of the filter/detector would control the AGC level.

Below are example block diagrams depicting typical AGC implementations in the analog and digital domain. The log and alog interfaces for the digital implementation provide consistent loop bandwidth over the operational range of the AGC due to using multipliers for the gain adjust.

AGC

digital AGC

Further AGC considerations for digital implementation are covered in this post: How to adjust receiver gains to avoid saturation and quantization noise to optimise post digital processing?

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1) Dan's answer has already given a clear idea about this. I just want to add that, typically you adjust the gain at the RF Front end depending on the amplitude of sampled signal (assuming you are sampling the signal and then computing the power). But even if you compute the amplitude in terms of unit like volt, ultimately you will need to adjust gain at the front end in terms of dB. So naturally, you will need to convert amplitude to dB, and then perform the AGC algorithm on it to come up with gains.

2)My take - the adjacent channel power (signals or interference just outside your wanted BW) plays a huge role in AGC algorithm. If the adjacent channel power is high, you will have to de-sensitize your AGC so that it does not end up setting high gain, and saturating ADC. You may wonder, why not the adjacent channel is blocked by LPF? Well you do not have an ideal filter and there will spectral leakage due to aliasing into your band. You do not want this to saturate the ADC just because AGC set high gain.

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