a) Using the circuits you designed in Experiment 1 for the second-order, third-order, and fourth-order filter circuits, analyze the circuits for the following issues (assume the op amps in your circuit are 741):
1) Gain Bandwidth Product
2) Slew Rate
3) Vos
4) Ios
5) Only for the second-order LP filter, look at Thermal Noise (Assume E^2 = 4 k T R f, f assumed to be the bandwidth for your second-order LP filter for these calculations)
Would any of these cause an issue in the operation of your circuits? Would any of the other issues discussed in the notes cause an issue in the circuits that cannot be considered negligible?
b) Next, using a Tustin transformation, convert the filter transfer functions you designed in Experiment 1 to the Z domain (assume a sampling period T = 0.000033 seconds). Now convert the Z domain transfer functions to difference equations for the output y(k). Look at the frequency responses in Matlab for each filter (G(z)) (Hint: use freqz command).
Finally, write two programs in C:
1) One program to implement the difference equation for the 3rd-order HP filter output y.
2) One program to implement the difference equation for the 4th-order LP filter output y.
What conclusions can you make about the filter implementation as a difference equation for y(k)? Are your filters stable? Are they considered FIR or are they considered IIR filters? Why or why not?
