Question 1
C
a) In the circuit of Fig.(1), consider that the Op-Amp. is ideal and VCC =
12 V;
i) Derive an expression for vo in time-domain. Show how the initial
R
VCC
vi
voltage of the capacitor is set to zero.
vo
ii) Given that R = 2.5 KΩ, C = 0.1 µF, VCC =12 V and vi is a
+
symmetrical square wave with amplitudes ± 5 V and frequency
- VCC
1 KHz;
 Draw the waveforms of vi and vo assuming that the capacitor is
Fig.(1)
initially discharged to zero voltage.
 Find peak-to-peak and the average volatge values of the output waveform.
b) The amplifier in Fig. (2) is designed to be of a voltage gain 100
and must develop output voltage of maximum 10 V when
R2
connected to a load resistance RL of minimum 1 KΩ. Assume
ideal Op-Amp.;
VCC
R1
i) Find suitable values for the resistors considering that the
‫־‬
available resistors are of minimum 1 KΩ and maximum 100
_
vo
KΩ. Then, find the condition on the output current of the
F
vs +
RL
Op-Amp.
i
- VCC
ii) If the output current of the Op-Amp. is limited to its minimum
g
value obtained in part (i);
. Fig.(2)
 Illustrate the effect on the output if RLis decreased to half
(
of its minimum value.
3
c) If the amplifier in part (b) is implemented using real Op-Amp. with open loop) gain A = 100 dB
Prove that the voltage gain 𝑨𝒗 is given by:
𝑨
𝑹𝟏
𝑨𝒗 = 𝟏+𝑨𝑩 and
Where 𝑩 = 𝑹 +𝑹
𝟏
𝟐
Then, Calculate the gain error (in %).
Question 2
a) In the circuit shown in Fig.(3), assume ideal Op-Amp.,
VCC = 12 V and the forward diode drop is 0.7 V. Consider that the
VCC
R
vi
vo1
‫־‬
input vi is a sinusoidal signal with peak voltage VP and frequency f.
vo
_
i) Find vo and vo1 for vi > 0 and for vi < 0. Then, draw the transfer
+
characteristics(vo/vi).
-VCC
ii) Draw the waveforms of vo and vo1 along with vi. Then, express
the average of vo in terms of VP.
Fig.(3)
iii) Show how to detect if the diode has fallen short circuit.
b) Consider the low-pass filter circuit shown in Fig.(4), consider that the
R2
Op-Amp. is ideal and VCC = 12 V,
i) Find the transfer function vy(s)/vx(s). Then, draw |Vy(jɷ)/Vx(jɷ)|
versus the frequency. Express the DC gain and the cut-off
R1
C
frequency fc in terms of the circuit components.
vx
ii) If the resistor R2 is open-circuited,
vy
+
 Discuss what will occur and find vy(s)/vx(s) Then, draw
|Vy(jɷ)/Vx(jɷ)| versus the frequency
Fig.(4)
c) Now, If the the circuit in Fig.(3), with RL omitted, is cascaded with the
circuit in Fig.(4);
 If the cut-off frequency fc is selected proberly, show that the output of the whole circuit is
approximately DC voltag proportional to the peak volatge,VP of the input signal vi and
express this DC voltage in terms of VP.
Question 3
a) For the astable circuit shown in Fig.(5), consider that the Op-Amp.
is ideal, VCC =12 V;
i) Draw the waveforms of vc, vo on the graphs shown below. Then,
derive an expression for TH and TL in terms of R1, R2 and C and
express the duty cycle (δ) in terms of R1, R2.
ii) Using C = 0.1 µF, find the values of R1 and R2 to obtain
frequency f = 5 KHz and duty cycle (δ) = 25%. Then, find the
average value of vo.
R2
D2
R1
D1
vc
VCC
-
vo
C
+
R
-VCC
iii) Discuss the effect on the output frequency and its duty cycle in
cases:
 If diode D2 has fallen as short circuit.
 If diode D2 has fallen as open circuit.
R
Fig.(5)
b) Draw a voltage controlled oscillator (VCO) circuit. Draw the waveforms at the different nodes in the
circuit and derive an expression for the output frequency in terms of the controlling input Vm and the
circuit components.
c) Using Log. and Anti-log circuits, implement the function 𝒁 = √𝒙𝒚 where x and y are time
varying signals. Clarify your answer by expressing the signals at the different points in the
circuit.
Question #1
a) In the amplifier shown in Fig.(1), the gain is variable in the range
10 to 100. Assuming ideal Op-Amp with supplies
± 10 V;
i. Find the value of the potentiometer P and redraw the circuit
indicating the connection of the potentiometer terminals.
ii. Find Rin and Rout of the amplifier.
iii. Find the limit on the output current of the Op-Amp.
iv. If the – ve terminal of the Op-Amp, is accidentally shortcircuited to ground;
 Does the voltage at the + ve change? Clarify your answer
and find vo.
b) In the circuit shown in Fig.(2), assume ideal Op-Amp;
i.
Find an expression for vo and suggest a function for the
I
circuit.
ii.
Find the output resistance Rout.
iii.
If the current source I has a finite internal resistance Rs, find
vo and comment.
c) For the circuit shown in Fig.(3), assuming ideal Op-Amp;
𝒗
i.
Derive an expression for the transfer function 𝒗𝒐(𝒔)
and
(𝒔)
1 KΩ
P
5 KΩ
-
vo
v
+
10 KΩ
i
Fig.(1)
R
C
C
C
C
C
+
vo
RL
Fig.(2)
R2
𝒊
𝑣 (𝑗𝜔)
sketch | 𝑣𝑜
𝑖(𝑗𝜔)
ii.
| versus frequency.
R1
C
Given that vi is a square wave with frequency 10 KHz, duty vi
vo
cycle 50% and its amplitude levels are 0 V and 5 V and
+
considering that: C = 0.1 µf, R1 = 2.5 KΩ and R2 = 5 KΩ;
 Show that the circuit operates as integrator.
Fig.(3)
 Find the DC voltage at the output.
 Draw the waveform of vo assuming that the initial voltage of the capacitor is zero.
Question #2
a) In the circuit shown in Fig.(4), assuming ideal Op-Amp;
i. Find an expression for 𝑣𝑜 as a function of 𝑣𝑖 in the
both cases: 𝑣𝑖 > 0 and 𝑣𝑖 < 0.
v
ii. For the circuit to give 𝒗𝒐 = 𝑲 |𝒗𝒊 |
 Find the condition on the resistance R1 in terms of i
RL and R and hence give expression for K.
iii. Considering that: R = 5 KΩ and RL = 10 KΩ and R1=
15 KΩ and given that 𝑣𝑖 is a sinusoidal signal with
frequency 1 KHz and its peak voltage is 9 V, draw the
waveform of 𝒗𝒐 and state the function of the circuit.
R
CC
R
R1
R
R
v
oL
R
+
1
Fig.(4)
𝒙𝒚
b) Implement a circuit to perform the function 𝑭 =
using Log & Anti-log circuits. Clarify your
𝒛
answer by expressing the signals at the different nodes in the circuit and give the conditions on the
input signals x, y, z.
R
P
Question #3
a) For the shown astable circuit, consider that VCC = 12 V,
Vz = 4.3 V at Iz = 10 mA and VD = 0.7 V;
VCC
vc
R2
vo1
i. Draw the waveforms of the signal at vc and vo and vo1.
vo
C
Derive an expression for the frequency of the output.
ii. Using C = 0.01 µf, find the values of R, R2 and the
+
R1
-VCC
potentiometer P to obtain a frequency in the range 1 KHz
to 10 KHz.
iii. Illustrate the importance of the resistor R.
R1
b) Draw a triangular waveform generator with a control voltage
Vs to control the output frequency. Draw the necessary
waveforms at the different nodes in the circuit and derive an expression for the frequency of the
output in terms of Vs and the circuit components. What is the duty cycle of the output waveform?
Question #1
R2
P
R1
a) The amplifier shown in Fig.(1) is designed to obtain a variable vs
gain in the range 10 to 100 and input resistance of 1 KΩ. The
VCC
amplifier must develop output voltage with value of at least 5 V
vo
when connected to a load resistance of minimum value 1 KΩ;
i. Find the values of R1, R2, the potentiometer P and redraw the
+
circuit indicating the connection of the potentiometer
-VCC
terminals.
Fig.(1)
ii. Find the minimum output current of the Op-Amp.
iii. Discuss the operation and find vo in the following cases:
 R1 is open-circuited.
R
vx
2R
R
 R2 is open-circuited
D2
b) In the circuit shown in Fig.(2);
R
i. Find vx and vo as function of vs for both
vo
cases: vs > 0 and vs < 0.
ii. If vs is a sinusoidal signal, draw the
+
D1
vs +
waveform of vo and suggest a function for
the circuit.
iii. If diode D1 is open-circuited, discuss the
Fig.(2)
operation and draw vo for the sinusoidal
waveform of vs.
c) In the LOG circuit shown in Fig.(3);
i. Show that vs should be positive and express vo as a function
of vs.
vs
ii. In case of vs = 0; discuss the operation and hence, find vo.
iii. Modify the circuit to operate for both vs > 0 and vs < 0.
R
-
vo
+
Question #2
Fig.(3)
a) For the circuit shown in Fig.(4), assuming ideal Op-Amp;
𝑹
i. Prove that: 𝑨𝒗 (𝒔) = − 𝑹𝟐 (
𝟏
𝟏
𝒔
𝟏+
𝟐𝝅𝒇𝒄
) and express fc.
R2
ii. Determine R1, R2, C to obtain a L.P.F with fc = 1 KHz, DC
gain
C
R1
of 20 dB and input resistance of 10 KΩ.
vi
iii. Discuss the operation and find vo in terms of vi and the circuit
vo
+
components in the following cases:
 C is open-circuited.
Fig.(4)
 C is short-circuited.
R
 R2 is open-circuited.
b) For the astable circuit, shown in Fig.(5), consider that VCC = 12 V,
VCC
i.
Draw the waveforms of vc, vo and prove that the frequency of
v
c
𝟏
the output is given by: ≅ 𝟐.𝟐 𝑹𝑪 .
vo
C
ii. The circuit is designed to oscillate at a frequency 1 KHz using
+
C = 0.1 µF. and considering that the current from the Op-Amp
R1
-VCC
output must never exceed 5 mA.
 Find the values of R, R1
R1
 If the resistors have ± 5% tolerances and the capacitors
Fig.(5)
have ± 20%, find the minimum and the maximum values
for the oscillation frequency.
iii. Show how to modify the circuit to obtain a square wave with duty cycle 75%.
Draw a voltage controlled oscillator circuit (VCO). Draw the waveforms at the circuit nodes
and derive an expression for the frequency of the output.