(a) Suppose that in Figure P11.50(b) are both pure resistances, say, , respectively. A...

(a) Suppose that in Figure P11.50(b) are both pure resistances, say, , respectively. A typical value for is in the range 1 to , while a typical value for K is . Using the results of Problem 11.50(a), calculate the actual system function for this value of K and for equal to 1 and then to , and compare each resulting value to . This should give you some idea of how good the approximation of Problem 11.50(b) typically is.

(b) One of the important uses of feedback is in the reduction of system sensitivity to variations in parameters. This is particularly important for circuits involving operational amplifiers, which have high gains that may be known only approximately.

(i) Consider the circuit discussed in part (a), with . What is the percentage change in the closed-loop gain of the system if K changes from ?

(ii) How large must K be so that a 50% reduction in its value results in only a 1% reduction in the closed-loop gain? Again, take