Using 1k resistors capacitors and ideal op amps designed a 3

Using 1k resistors, capacitors and ideal op amps, designed a 3rd order butterworth where the cutoff frequency is 500 rad/sec and the passband gain = 1. Determine the Transfer function for your design Construct the circuit diagram and label all component values.

Solution

steps. (a) Let = 0. Using our voltage divider rule, = = 50 50 + 100(15 ) = 5 (b) Set = 0, i.e. put a wire across the terminal. The voltage across the 50 resistor is now zero, meaning 2 must be zero. We are solving for = . Using KCL, 1 = , = . By KVL, 1001 = 15, 1 = 3 20 , = 3 20 . (c) Zero out the voltage source, meaning short-circuit it (replace it with a wire). From the right-hand side of the circuit, the two resistors are in parallel. Thus, = ( 1 100 + 1 50)1 = ( 3 100)1 = 100 3