2002 Spring [1]: In the op-amp circuit shown below, each of the impedances is made up of a resistance and a capacitor in parallel (i.e. Z1 R1 // C1; Z2 R2 // C2). Answer the following questions:
70 60 50
Phase (deg); Magnitude (dB)
40 30 20 100 80 To: Y(1) 60 40 20 0 10-1
100
101
102
103
Frequency (rad/sec)
(1) Show that
Eo ( s ) as + 1 =K . Derive K, a and b in terms of R1, R2, R3, R4, C1, and C2. Ei ( s ) bs + 1
Eo ( s ) Eo ( s ) E ( s ) R4 Z 2 ( s ) 1 + Ri Ci s 1 1 = = - - = + Ci s = , where R and C are in parallel, ( Ei s ) E ( s ) Ei ( s ) R3 Z1 ( s ) Z i Ri Ri Eo ( s ) R4 R2 1 + C1 R1 s R4 R2 = , a = C1 R1 , and b = C2 R2 where K = Ei ( s ) R3 R1 1 + C2 R2 s R3 R1 (2) If the input voltage is ei (t ) = A sin t , what is the output at steady state?
R R 1 + ( C1 R1 ) eo (t ) = A G ( j ) sin(t + ) where G ( j ) =...