Download A ELEC-353 Analogue electronics

A
ELEC-353 Analogue electronics
Assignment 3 – Deadline 2pm on 6 May 2013
1) Entanglement [10pt]
The following circuit has three input voltages, V1 , V2 , and V3 as shown. Assume that the operational amplifier has
a finite open-loop gain of A0 , but otherwise can be considered ideal.
a) What is the input impedance of this circuit?
b) Determine Vout as a function of the input voltages, the resistances and A0 .
c) What is Vout in the limit of A0 → ∞ ?
d) Based on your result, describe, in words, what one might use this circuit for.
e) Determine Vout if all resistances are chosen to be as follows: R3 = 3R, R2 = 2R, R1 = RF = R. Also the input
potentials, V1 , V2 and V3 , may take either 0 V or 1 V, independently of each other. Create a table in which you
calculate Vout for all possible combination of input potential values, i.e.
V1 V2 V3
Vout
0
0
0
0
0
1
..
..
..
.
.
.
R3
R2
V3
RF
R1
−
A0
+
V2
V1
Vout
2) Disentanglement [3pt]
Consider the following circuit, where each operational amplifier is assumed to be ideal.
a) Classify each building blocks (circled by gray dashed lines) by their configurations.
b) Calculate the output voltage when R1 = 10 kΩ, R2 = 30 kΩ, R3 = 15 kΩ, R4 = 75 kΩ, and R5 = 25 kΩ, while
the voltage sources provide V1 = 0.5 V and V2 = 0.2 V.
R2
R1
R4
R3
−
+
−
+
−
+
V1
Vout
R5
−
+
V2
3) Oscillator? [7pt]
Consider the following circuit, where each operational amplifier is assumed to be ideal.
(Hint: you may find a similar circuit on page 120 in the textbook.)
R1
A
Vin
C2
A
C1
R2
Vout
a) Derive the closed-loop gain, A(s), as a function of s. You may perhaps wish to perform this task by identifying
and individually analysing the building blocks (gray dashed boxes) appearing in the circuit, however, this
approach is not necessary.
b) Write a piece of code in your favourite mathematics software which evaluates and plot the Nyquist diagram
of A(s). Submit not only the plot, but your code as well. Label few characteristic points in the graph, e.g.
ω = 0 Hz, ω → ∞ Hz, etc. Repeat this numerical procedure for few distinct values of A, such as A =1, 1.5, 2.0,
5.0, 100. If you think it can be interesting to have a closer look around other values of A do not hesitate to do
that. Explain your reasons.
c) Based on your numerical experiments, can you qualitatively determine the stability of this circuit for different
values of A?
d) Can this circuit be driven into an oscillation by a careful choice of A? If ’yes’, then determine this characteristic
A value. If ’not’, explain the reasons why this circuit cannot produce oscillation. Check that your result can
reproduce the one published in the textbook for R1 = R2 = R and C1 = C2 = C.