1. For each of the circuits in Figures , derive the expressions for the voltage transfer
function T (s) = Vo(s)/Vi(s) and the cutoff frequency f3dB.
2. Consider the switched-capacitor filter in Figure. Design the circuit for a lowfrequency gain of −10 and a cutoff frequency of 10 kHz. The clock frequency
must be 10 times the cutoff frequency and the largest capacitance is to be 30 pF.
Find the required values of C1, C2, and CF
3. In the phase-shift oscillator in Figure, the capacitor at the noninverting terminal of
op-amp A1 is replaced by a variable capacitor CV . (a) Derive the expression for
the frequency of oscillation. (b) If C = 10 pF, R = 10 kΩ, and CV is variable
between 10 and 50 pF, determine the range of oscillation frequency
4. Consider the Schmitt trigger in Figure. Assume the saturated output voltages are
±VP . (a) Derive the expression for the crossover voltages VTH and VTL . (b) Let
RA = 10 kΩ, RB = 20 kΩ, R1 = 5 kΩ, R2 = 20 kΩ, VP = 10 V, and VREF = 2V. (a)
Find VTH and VTL . (b) Sketch the voltage transfer characteristics.
5. Consider the Schmitt trigger in Figure. The saturated output voltages of the opamp are VH = +10 V and VL = −10 V. Assume the diode turn-on voltage is 0.7 V.
The range of the input voltage is −2 ≤ vI ≤ +2 V. (a) Determine the crossover
voltages. (b) Sketch the voltage transfer characteristics. (c) Determine ID1, ID2, IR3,
and IR2 for (i) vI = 2 V and (ii) vI = −2 V.
6. Consider the circuit in Figure. The saturated output voltages of the Schmitt trigger
comparator are ±10 V. Assume that at t = 0, output vo1 switches from its low state
to its high state and CY is uncharged. Plot vo1 and vo versus time over two periods
of oscillation.
7. Fig. shows a circuit that performs the high-pass transfer function.
(1) Derive the transfer function of this circuit and identify its high-frequency
gain and 3-dB frequency.
(2) Determine the values of R1, R2, and C to obtain a high-frequency input
resistance of 5 kΩ, a high-frequency gain of 60 dB, and a 3-dB frequency of
1000 Hz.
(3) At what frequency does the magnitude of the transfer function reduce to
unity?
8. The figure shows a two-stage amp, the 1st saturates owing to the large input
voltage, where Isat=0.4mA and C=200uF.
(a) Find the slew-rate.
(b) If the ideal output is a square wave shown below, plot the real output
waveform which is distorted by the slew rate.
9. A phase-shift oscillator is shown in Figure where R= 10 kΩ, C = 20nF
(1) Find the loop gain by breaking the circuit at node X .
(2) Calculate the oscillation frequency fO, and the minimum required value of Rf
for oscillation to start in this circuit.
10. For the circuit in Fig.
(a) Find the loop gain L(s), and the oscillation frequency fo
(b) The ratio of R2/R1 for oscillation.