1. The transfer function of a circuit is given by
H(s)= 2s+4/4s^2+2s+2
a. Express the transfer function in a form in which the coefficients of the highest power of s are unity in both numerator and denominator.
b. What is the characteristic equation of the system? (Hint: see this week%u2019s lecture for a definition of characteristic equation.)
c. Determine the order of the transfer function.
d. Determine where the poles and zeroes of the system are located.
2. The transfer function of a circuit is of the form
H(s) = (s+4)(2s+1)/(s+1+j1)(s+1-j1)
a. Express the transfer function in descending powers of s with the coefficients of the highest power ofs unity in both the numerator and denominator.
b. Determine where the poles and zeroes of the transfer function are located.
c. Is this the transfer function of a causal system? Justify your answer.
3. Determine the location of the poles and zeroes and the stability of the following two transfer functions. Express the location of the poles and zeroes in both rectangular and polar form.
a) H(s) = s^2-sqr(2s)+1/s^2+sqr(2s)+1
b) H(s) = s^2+sqr(2s)+1/s^2-sqr(2s)+1
Using MATLAB, plot the pole zero map and the Bode plot of the two transfer functions and paste the graphs below. Identify and briefly discuss the differences between the Bode plot of the two transfer functions.
c) Which of the two is a stable system and why?