How to Calculate the Coupled Transfer Function of Two RC-Filters?

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SUMMARY

The discussion focuses on calculating the coupled transfer function of two RC filters, specifically H_1(ω) and H_2(ω), where the output of the first filter (Uo(1)) is connected to the input of the second filter (Ui(2)). The impedance model is used for individual transfer function calculations, but the challenge arises in determining the overall transfer function when the filters are coupled. The node voltage method is suggested as a viable approach for finding the resulting transfer function, although the discussion notes that there may be simpler methods or substitutions available.

PREREQUISITES
  • Understanding of RC filter design and behavior
  • Familiarity with transfer functions and their calculations
  • Knowledge of the impedance model in circuit analysis
  • Proficiency in the node voltage method for circuit analysis
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  • Research the application of the node voltage method in coupled circuits
  • Explore alternative methods for calculating transfer functions of coupled filters
  • Study the impact of coupling on the frequency response of RC filters
  • Learn about advanced circuit analysis techniques for complex filter designs
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Electrical engineers, circuit designers, and students studying filter design and analysis will benefit from this discussion, particularly those interested in understanding the complexities of coupled RC filters.

Galileo
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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 [itex]H_1(\omega), H_2(\omega)[/itex] ([itex]H(\omega)=u_o/u_i[/itex]) 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?
 
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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.
 
oh wow i just noticed you post is two years old! haha. you've probably figured it out already.
 

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