If you have network N1 with transfer function H1 and network N2 with transfer function H2, is there a way to find the transfer function H3 for the network produced when cascading N1 and N2 (and assuming you cant see inside N1 or N2)?
At first I thought you could just multiply H1 and H2, but that doesn't seem to give me a right answer.
If we consider a simple LPF:
The transfer function is: \$ H(s) = \left(\dfrac{1}{sC_{1}R_{1} + 1}\right) \$
Then if we cascade it with another LPF:
The transfer function is: \$ H(s) = \left(\dfrac{1}{s^2C_{1}R_{1}C_{2}R_{2} + sC_{1}R_{1} + sC_{2}R_{2} + sC_{2}R_{1} +1}\right) \$
which is not the same as \$ \left(\dfrac{1}{sC_{1}R_{1} + 1}\right) \$\$ \left(\dfrac{1}{sC_{2}R_{2} + 1}\right) \$
Is there a shortcut to get to H3 from H1 and H2 or would I just have to calculate H3 the long way using KCL or KVL? What about if I know \$R_1=R_2\$ and \$C_1=C_2\$?