I have completed my lossless ladder bandpass filter 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 the 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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1\$\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\$– jramsay42Commented Dec 2, 2018 at 22:53
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2\$\begingroup\$ So you have created a ladder topology with parts values WITHOUT knowing the realized transfer function in advance? Very uncommon. \$\endgroup\$– LvWCommented Dec 3, 2018 at 8:18
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1\$\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\$– LvWCommented Dec 3, 2018 at 8:58
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\$\begingroup\$ Hence, my recommendation: Goggle for "Foster Partial Fraction" \$\endgroup\$– LvWCommented Dec 6, 2018 at 10:01
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1\$\begingroup\$ If you didn't start with a transfer function, then what were your inputs to the design process? And since there seems to be ambiguity, what do you want as a "transfer function" -- are you looking for a detailed Bode plot, a ratio of two giant polynomials in \$s\$, a list of poles and zeros, or what? \$\endgroup\$– TimWescottCommented Apr 11, 2021 at 18:25
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2 Answers
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One way you could do a system identification on the circuit. The way that this is done is either providing a step input or a sine sweep (you could also provide an impulse but this probably wouldn't work as well). If you recorded the input and the output (with an oscilloscope) you can feed this into a system identification algorithm and it can find the transfer function.
answered Dec 23, 2021 at 15:19
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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\$– steveCommented Dec 6, 2018 at 12:41
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\$\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\$ Commented Dec 7, 2018 at 15:20
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\$\begingroup\$ To get the Laplace transfer function, a function of ‘s’ like in a textbook, you can use a symbolic algebra program and evaluate the continued fraction. This is the way I have done it. You can use Maple, Mathematica, the symbolic toolbox of Matlab, probably several other programs. If you are just trying to validate your design, you can use LTSpice and look at the frequency response graph, but it will not give you the Laplace transfer function. \$\endgroup\$ Commented Apr 12, 2021 at 1:05