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let's consider this logarithmic Amplifier:

enter image description here

I do not understand why at the terminal LOG OUTPUT there is a current which is proportional to log(Vinput). The current flowing on each diode is equal proportional to exp(-qVouti/KT), where Vouti is the output voltage of each stage.

Each stage is a limiting amplifier: it has a transfer function like this one:

enter image description here

References: https://www.analog.com/media/en/training-seminars/tutorials/MT-078.pdf

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The text appears to indicate that current output is desired, so that summing is simpler. I believe based on the text that the diodes are added to indicate a conversion to current output for the summation. Note that it specifically states that "the detectors should be current outputs (not simple diodes)" indicating a linear voltage-to-current conversion. If I'm right, I agree that it could have been explained/drawn better.

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