Suppose I have a circuit below:
simulate this circuit – Schematic created using CircuitLab
I know the the transfer function of a negative feedback loop is:
$$H(s)=\frac{H_1(s)}{1+H_1(s)H_2(s)}$$
But this applies only if all resistors are equal in the summing amplifier and the input voltage is inverted. The equation for the summing amplifier is:
$$V_3(s) = \frac{-R_3}{R_1} V_{in}(s) + \frac{-R_3}{R_2} V_2(s)$$
Where \$V_3(s)\$ is the resulting voltage of the summing amplifier, based on its two inputs, \$V_{in}(s)\$ and \$V_2(s)\$.
My question is how to correctly put both formulas together to get the overall transfer function of the above circuit?
Best Answer
I can redraw the block diagram as follows:
Where $$H_3(s) = \frac{R_3}{R_2}$$ and $$H_4(s) = \frac{R_3}{R_1}$$
From this, $$\frac{V_o}{V_{in}} = \frac{-H_1(s)\times H_4(s)}{1+H_1(s)H_2(s)H_3(s)}$$