Analog and Digital Electronics: Exam IIB Due Monday, May 9 at 10:00 a.m.
Take Home Exam: You may use your class notes, handouts, your lab notebook, and your General Physics text, but do not consult other people or materials. Be neat and show your work! Put each question on a separate sheet of paper.
Assume all op amps are ideal (zero offset voltage, infinite open loop gain and zero input or bias current) and all diodes are silicon diodes unless stated otherwise. Also assume the output voltages for op amps can go from -10V to + 10V.
1. Consider the op amp at the right. R1 = 1kW and R2 = 7kW. The input is a triangle wave going from -4V to +6V. Sketch the output for one cycle of the input, showing both on the same graph. Show important points and explain how you determined them.2. You have a signal given by the expression below, where the frequencies are in rad/s.
V(t) = 3.0V + 0.50V cos(600pt/s) + 2.0V cos(620 pt/s)
You want to measure the amplitude of the 600 p rad/s signal. To do this you multiply the entire V(t) by cos(600 pt/s) and filter it with a second order low pass filter (two non-interacting, cascaded RC filters that each have the same cutoff angular frequency of p rad/s.)
a) What frequencies, in Hz, are present in the original signal, V(t), and what are their amplitudes? (Make a table!)
b) What frequencies, in Hz, are present in the signal after the multiplication and filtering and what are their amplitudes? (Make a table!)
3. You have a signal given by the expression below, where the frequencies are in rad/s. If you have an input signal to this filter of
V(t) = 3.0V + 0.50V cos(600pt/s) + 2.0V cos(620 pt/s),
Again, like the question above, you want to measure the amplitude of the 600 p/s signal. This time you a band pass filter that has a Q of 10 and a center frequency or resonant frequency of 600 p rad/s. Assume the band pass filter is an LCR filter, although you would normally use an op amp circuit at these frequencies.
a) What frequencies, in Hz, are present in the original signal, V(t), and what are their amplitudes? (Make a table!)
b) What frequencies, in Hz, are present in the signal after the filtering and what are their amplitudes? (Make a table!)
c) Compare the final results in these two questions, 3 & 4 − which one reduces the 620 p rad/s signal (noise) the most?
4. Consider the circuit at the right. The input is a triangle wave of 4V peak to peak. Sketch the output for one cycle of the input shown below. You must explain your reasoning and justify your choices, including any calculations. Label important points!
Hint: use Kirchoff’s rules for the two cases. When the diode is off and when it is on. (Of course its trivial when it’s off.) Then find Vout in terms of Vin. What happens to the slope of Vout vs. Vin?