# Logarithmic Multi - Stage Amplifier

let's consider this logarithmic multi - stage amplifier:

Each stage is an amplifier with this mechanism: if the input signal is small (under a certain threshold), it is amplified with high gain A; if it is large (over the previous threshold), it is amplified with unitary gain.

The purpose of this multi - stage amplifier is that of getting a Voutput - Vinput curve like that in the previous picture. But I do not understand the presence of the Adder circuit. I think that simply the cascade of the previous amplifier will generate a curve like that, in which small signals are amplified a lot, and high signal are amplified less.

Can you help me on understanding the presence of the adder?

This circuit is analyzed here.

• are you asking about a Relative Signal Strength Indicator RSSI? Commented Sep 9, 2019 at 16:56
• Yes, I wanted to use it for power measurement Commented Sep 9, 2019 at 16:58
• the NXP NE504 has one, if I recall correctly. Commented Sep 10, 2019 at 2:00

If you take only the output from the final amplifier, then the transfer function is:

At some value of input, the output stage will saturate and not increase any further.

If we then add the other outputs, we will get (not to scale):

As each amplifier saturates, then the slope reduces until the next amplifier in the chain saturates until all 4 amplifiers are in saturation. As each amplifier output is lower then the following devices the output slope from the addition reduces.

By adding these outputs together we get a log amp shown (not complete and also not to scale) by the purple line.

This is simplistic, but it is the fundamental principle of operation.

The output slope is for a setup where all the amplifiers have a gain of A:

All amplifier still active: 10A (4+3+2+1)

4th amplifier saturated: 6A (3+2+1)

3rd and 4th amplifier saturated: 3A (2+1)

2nd, 3rd and 4th amplifier saturated: A

So the output slope reduces as the level of input is raised.

• Perfect, thank you very much Commented Sep 10, 2019 at 4:39