Find the following circuit, obtain the transfer functions Ed(s)/Ei(x). Express a

Question

Find the following circuit, obtain the transfer functions Ed(s)/Ei(x). Express as a ratio of polynomials in s. Also fill in the blanks on the block

Explanation / Answer

L -> jL         jbeing the imaginary number      sqrt(-1) = j C -> 1/(jC) input voltage = voltage at first resistor output voltage: use voltage divider rule to get : Vo = Vin *jL/( jL + R) you can reduce this expression by multiplying top and bottom by (1/(jL)) and noting that 1/j = -j this gives Vo / Vi = 1/ (1+R/( jL))   =  1/(1-jR/( L)) where Vi = Ei(S);   Vo = Eo(s) so final answer is Eo(s) / Ei(S = 1/(1-jR/( L)) NOITE THAT IF THE LOAD CHANGE IN eo, THE OUTPUT VOLTAGE WILLCHANGE. FOR THIS REASON IT IS CONVENIENT TO USE OPAMPS AS VOLTAGEFOLLOWERS AT THE OUTPUT

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