MEC4126F: Integrating Embedded Systems
Due: 17:00 March 28, 2025
MEC4126F Problem Set 1
(61 marks)
Transistors
1. Consider the following circuit:
[11]
Assume the NPN transistor has a minimum β of 50 and a maximum β of 150.
Assume Vce(saturated) = 0.2 V and Rload = 1 Ω.
(a) Calculate the minimum and maximum Vce when Rb = 100 Ω and:
• Vin = 0 V
• Vin = 6 V
• Vin = 12 V
(b) In which of these conditions do(es) saturation occur?
(c) What is the effective β in the case(s) of saturation? Can the effective β be smaller than the
specified β?
(d) When 𝛽 =
!!"# "!!$%
#
(2)
(2)
(2)
(1)
(2)
, and Vin = 6 V, calculate the power dissipated in the transistor and the load.
(2)
MEC4126F: Integrating Embedded Systems
Due: 17:00 March 28, 2025
MEC4126F: Integrating Embedded Systems
2. Transistor circuit design.
Due: 17:00 March 28, 2025
[8]
(a) Design an emitter follower circuit which dims a 24 V 60 W halogen light bulb. The input to the
dimmer is a 10 𝑘Ω potentiometer. Use a TIP 122 as the transistor and consider what might be
required between the potentiometer and the transistor.
(4)
(b) Model the light bulb of 2(a) as a resistor. Calculate its resistance by calculating that at 24 V it
dissipates 60 W. What is the maximum power dissipated by the transistor during any mode of
operation of this circuit? TIP: You may use the simplified equation for transistor power.
(4)
MEC4126F: Integrating Embedded Systems
Due: 17:00 March 28, 2025
Amplifiers and comparators
3.
Design a non-inverting op-amp based circuit which takes in a voltage in the range of -3 V to
+3 V and amplifies it by a factor of 4.5. Use the E12 resistor values. You may use up to 4
resistors. Show all power supply rails and component values.
[4]
MEC4126F: Integrating Embedded Systems
4.
Due: 17:00 March 28, 2025
Design a comparator-based circuit which detects when a voltage is between 1 V and 2 V.
When the input is in this range the output must swing up to 5 V, if not the output must be at 0
V. You can assume the availability of a +5 V DC power supply. Use the E12 resistor values.
Show all power supply rails and component values.
[6]
MEC4126F: Integrating Embedded Systems
5.
Due: 17:00 March 28, 2025
Design a circuit that takes in a voltage from 1 V to 2.5 V and gives an output of 0 V to 9 V.
Use the E12 resistor values. Show all power supply rails and component values. You may
use a maximum of 6 resistors.
[7]
MEC4126F: Integrating Embedded Systems
Due: 17:00 March 28, 2025
Filters
6.
Consider the following circuit
[25]
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(a) Prove that the transfer function & (𝑠) = (
=
(
1
'
)& )' *' *(
'
'
'
'
'
'
'
( (
'
&
'
' ( (
&
'
- ( "-2* ) "* 3) ") 45"* * ) 3) ") 4
.
(4)
(b) What order and type of filter is this?
(2)
(c) What is the DC gain and gain at very high frequency?
(2)
(d) Design the filter to have a |DC gain| of 7.0, a cutoff frequency of 65 Hz and 𝜁 = 1.1. Use only 5
components (resistors and capacitors), all selected from the E12 series.
(10)
(e) Calculate the percentage error, including the sign, for DC gain, cutoff frequency and the damping
ratio.
(3)
(f) What do the cutoff frequency, and the damping ratio represent?
(4)
MEC4126F: Integrating Embedded Systems
Due: 17:00 March 28, 2025
MEC4126F: Integrating Embedded Systems
Due: 17:00 March 28, 2025
MEC4126F: Integrating Embedded Systems
Due: 17:00 March 28, 2025