Electronic – How to derive the transfer function for this Texas Instruments Application note narrowband pass filter

Let \$g_1 = {10 \over s+1}, g_2 = {1 \over s}\$, and let \$w\$ be the output of the \$g_1\$ block.

You get \$w = g_1 (u - 2 w -g_2 w)\$, which gives \$w = {g_1 \over1 + 2 g_1 + g_1 g_2} u\$, and so \$y = {g_2 g_1 \over1 + 2 g_1 + g_1 g_2} u\$, or \$y = {1 \over 1+{2 \over g_2}+{1 \over g_1 g_2}} u\$ if you would prefer.

Substituting in the values for \$g_1, g_2\$ gives the transfer function you wanted.

For anyone interested how I derived the transfer function, here is the solution:

(This is the derivation for the schematic as shown in the question. If you have more inputs, just do the same procedure for each one.)

So, the solution was to have as many transfer functions as your inputs, and then the derivation is the same as an Inverting Amplifier.