Design and Analysis: The simple high-pass and low-pass filters shown to the right have been analyzed in class. The transfer functions are H-HP(f) = j fRC / ( 1 + j fRC ) and H-LP(f) = 1 / ( 1 + j fRC ). In either case the -3dB frequencies are F-3DB = 1/ (2 f RC). These are 300 Hz for the HP and 20 Khz for the LP. To choose components you need to make some arbitrary choices. A good way is to consider the value of the resistors.
For typical analog circuits resistors shouldn't be too small because they will draw too much current, nor too large because they will cause too much noise. A value of 10 K is often a good compromise. Here we need a larger RC product for the HP so we'll use a 100 K resistor there, and 10 K for the LP.
(a) Calculate the capacitors needed. Plot the transfer functions for both circuits using the Matlab code on the web site and confirm
that your choices are correct. Make a hard copy.
(b) Calculate the transfer function for the cascade of the HP and LP (i.e. the direct connection shown above). Modify the Matlab code as indicated in the code and plot this transfer function too. You will see that it falls significantly below the idea product of the HP and LP. Make a hard copy showing two traces: the product of the HP and LP; and the transfer function of the direct connection. Save your Matlab code on a USB drive and bring it to the lab because you will want to rerun it with the actual R and C values that you use in the lab.