Transfer function of RC-filter

[Galileo]

Suppose you have two RC-filters as shown below. Ignore the #'s, they are for spacing purposes.

o---R1--------o
# # # # # | #
Ui(1) # # C1 # Uo(1)
# # # # # | #
o--------------o

o---R2--------o
# # # # # | #
Ui(2) # # C2 # Uo(2)
# # # # # | #
o--------------o

Calculating the transfer functions $H_1(\omega), H_2(\omega)$ ($H(\omega)=u_o/u_i$) using the impedance model is simple.
But what if you couple the two? By coupling the output Uo(1) of the first at the input Ui(2) of the second. Is there an easy way to calculate the resulting transfer function? It's not just the product of the two and my calculation is big and ugly. I know there is a trick or method to do it easily, by using some sort of substitution or something? Can anyone enlighten me?

 

[chromosome24]

i'm assuming that your new output is the connected nodes Uo1 and Uo2. in that case i would use the node voltage method for finding the transfer function. concerning a faster way i don't know if there is one.

 

[chromosome24]

oh wow i just noticed you post is two years old! haha. you've probably figured it out already.