Q.With the circuit diagram show how to obtain an output which is multiplication of two input signals.

Two signals are multiplied by taking the logarithm of each, adding the logs, and then taking the anti-logarithm of the sum — since adding logarithms is equivalent to multiplying. …

[!TLDR]

Multiplication is done with log-add-antilog: log-amplify $V_1$ and $V_2$, add the two logs, then anti-log the sum, giving $V_O \propto V_1\times V_2$.

Principle: Since $\log_e(V_1) + \log_e(V_2) = \log_e(V_1 \times V_2)$, two signals can be multiplied by adding their logarithms and then taking the anti-logarithm of the result. Logarithmic and anti-logarithmic amplifiers are therefore used together to multiply two input signals.

Circuit (Fig 5.7.3): The circuit uses four op-amp stages:

1. Two logarithmic amplifiers — $V_1$ is applied to the first log amplifier and $V_2$ to the second, giving outputs

2. An inverting adder — the two log outputs are summed:

3. An anti-logarithmic amplifier — it takes the anti-log of the adder output:

$\boxed{V_O \propto V_1 \times V_2}$ …