I have completed my Lossless Ladder BPF design, but I don't know how to find the transfer function of the resulting circuit without going through the slow and rigorous process of getting resistances of capacitors, inductors, and resistors in s-domain and working backwards from the end of the circuit until I have an equation relating the output to the input and then solving for Vout/Vin. Is there a faster way?

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    \$\begingroup\$ Unless I am mistaken, you find the values required to implement a particular transfer function or power loss ratio. At least that is the usual approach of the insertion loss method. \$\endgroup\$ – jramsay42 Dec 2 '18 at 22:53
  • \$\begingroup\$ So you have created a ladder topology with parts values WITHOUT knowing the realized transfer function in advance? Very uncommon. \$\endgroup\$ – LvW Dec 3 '18 at 8:18
  • \$\begingroup\$ There is a method invented by FOSTER which shows how such a ladder structure can be described in form of "continued fraction" (the denominator contains a fraction with a denominator which agian contains.....) \$\endgroup\$ – LvW Dec 3 '18 at 8:58
  • \$\begingroup\$ Hence, my recommendation: Goggle for "Foster Partial Fraction" \$\endgroup\$ – LvW Dec 6 '18 at 10:01
  • \$\begingroup\$ One useful tool is Sapwin wherein you can just draw your circuit and it spits out analyses such as transfer functions, pole-zero maps and other plots. These can also be exported to matlab. \$\endgroup\$ – BB ON Aug 2 '19 at 20:16

Since you clearly stated that you had already completed the design, and only need "to determine the transfer function after the design process has finished", I suggest you use Spice, free from TI (called TINA) and linear Tech (called LTspice). Spice will get you the transfer function from your already designed filter. I suggest you change the first line of your question since it implies you are looking for how to design the filter, but the second line clears up that you are only looking for getting the transfer function from the already designed filter.

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  • \$\begingroup\$ I have updated the question. Could you please, in a step-by-step process, explain how can I get the transfer function from LTSpice? Please do not refer me to another site, but state the steps explicitly here. \$\endgroup\$ – Connor Dec 6 '18 at 12:41
  • \$\begingroup\$ The term "transfer function" can mean many things. To some it is an equation, to others a frequency and phase graph, to others a set of S21 parameters. Which are you looking for? \$\endgroup\$ – skeptonomicon Dec 7 '18 at 15:20

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