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无代写-ELEC2133
时间：2022-06-16
THE UNIVERSITY OF NEW SOUTH WALES
School of Electrical Engineering and Telecommunication
Assignment I
2022
ELEC2133
Analogue Electronics
This assignment contributes to 5% of the total assessment of this course
The due date is on Friday June 17, 2022 11:59pm. Assignments are to be
submitted on Moodle before the due date and time. Any submission after the
due date will attract a penalty of 5% per day.
The assignment contains one problem with four parts. Each part contains one or
more questions related to the various topics covered related to op-amp. Each
question has been labelled with P, C, D or HD that indicates the level of
difficulty. P means that the question could be attempted by all students and
students who answer the question correctly are at the level of “pass”. C means
the question could be attempted by students who are at the level of “credit” in
the course. D and HD indicate the question could be attempted by students who
are at the level of “Distinction” and “High Distinction”, respectively.
What does this mean?
If you are targeting to pass or get credit in the course, you may only attempt
those P or C types of questions.
If you are happy or targeting to get distinction, you can attempt those P, C, and
D types of questions.
If you are targeting to get high distinction, you should attempt all the questions
including HD type of questions
2
QUESTION 1 [100 marks]
The circuit in Fig. 1(a) is a sensor readout circuit developed by MEMS/NEMS research group
(simple but effective) at EE&T UNSW for amplifying a small charge (voltage) generated by
a PZT thin film in a micro-lens actuator when the actuator resonates. A PZT stands for lead
zirconium titanate. It is a piezoelectric material that transduces strain into an electrical charge
(voltage) and conversely applied voltage (charge) into strain. Hence, the material is used to
build actuators, which are devices that produce mechanical energy (force, moment and etc)
from electrical energy (applied voltage) – the most precise nanoscale movements in advanced
equipment, robotics, automobile, energy harvesters, and others are enabled by piezoelectric
actuators. The same material is also used to build sensors to detect tiny movements, pressure,
and forces such as touch screens, pressure sensors, accelerometers, gyroscopes and etc.
Fig. 1(b) shows the sensor readout circuit with the PZT actuator replaced by its electrical
equivalent circuit that consists of a voltage source (VPZT) in series with a capacitor (CPZT).
When the actuator is excited (driven) by Vin, it resonates and generates small VPZT. Hence,
VPZT is in phase with Vin.
(a)
(b)
C2
VPZT CPZT
Vin
R1
R2
C1
R5
R3
R4
+V
-V
+V
-V
-V
+V
Vo
PZT Actuator
R1
R2
C1
C2
R5
R3
R4
PZT Actuator
+V
-V
+V
-V
-V
+V
Vo
V
in
3
PART 1 (Gain calculation and op-amp applications) [30 marks]
(a) [P,C] Obtain the expression for the output voltage (Vo) of the amplifier when the
actuator is driven (excited) by an AC source Vin operating at a frequency ω. [Hint:
apply superposition principle and express the sources and the capacitor in complex
frequency]. [10 marks]
(b) [D] The purpose the readout circuit is to amplify the VPZT and reject any output due
to Vin (Vo due to Vin is to be zero). How can the purpose of the amplifier circuit be
achieved based on your expression in (a)?
[5 marks]
(c) [P,C] Assuming R1 = R2 , C1 = C2 = CPZT and R5 ≫
1
2
, obtain the expression for
the gain of the amplifier (Vo/VPZT). [10 marks]
(d) [HD] Could you suggest a modification to the readout circuit (or new altogether) that
improves the gain of the amplifier and better achieve the purpose of the circuit. [5
marks]
PART 2 (Frequency response) [25 marks]
In reference to Fig. 1(a), the op-amps have large signal limitations and other characteristics as
provided in table 1.
Large signal limitations
Output voltage saturation ±10V
Output current limits ±20mA
Slew rate 0.5V/µs
Other characteristics
Internal compensation capacitor 30pF
Open loop voltage gain 100dB
Open loop bandwidth 6Hz
Table 1: The non-ideal op-amp characteristics
(a) [P,C] Assuming the bandwidth of the readout circuit is limited by the non-inverting
amplifier stage (the last stage) and R4 = 1K and R3 = 280K, estimate the
bandwidth of the readout circuit assuming that the internal compensation capacitor
creates the dominant pole in the frequency response of the op-amps? [8 marks]
(b) [P, C] With Vin = VAcos(ωt) and VA=1V and assuming VPZT = 0.005Vin, will there be
a frequency at which the output (Vo) will be distorted? If so, what is that frequency?
[8 marks]
4
(c) [D] With Vin = VAcos(2π*900t) and assuming R5 = 0.5M, R4 = 1K, R3 = 280K,
R1=1K, R2=1K, C1 = C2 = CPZT = 10nf, what is the constrain on the VA if the
output is to be undistorted? [7 marks]
PART 3 (DC imperfection) [30 marks]
(a) [HD] In the non-ideal case, all op-amps in Fig. 1 have the following DC imperfections
Input bias current: IB = 40nA at room temperature
Input offset current: Iio = ±2nA at room temperature
Input offset voltage: Vio = ±2mV at room temperature
Calculate the worst-case output offset voltage at room temperature assuming R5 =
0.5M, R4 = 1K, R3 = 280K, R1=1K, R2=1K, C1 = C2 = CPZT = 10nf.
[Hint: Consider the DC imperfections in all of the op-maps. In DC, capacitor can be
regarded as open] [20 marks]
(b) [D] Propose a method by modifying the readout circuit to reduce the output offset
voltage and explain why the modification may be able to reduce the output offset
voltage. [10 marks]
PART 4 (Simulation) [15 marks]
[P,C] Using LTspice or Pspice simulation, confirm your answer for part 1(c), part 2(a), part 3
(a) and (b). You may use LM301 op-amp and its model for the simulation. The op-amp will
be used in the first lab and there is Pspice manual included in the lab manual you may want to
refer. [15 marks]
School of Electrical Engineering and Telecommunication
Assignment I
2022
ELEC2133
Analogue Electronics
This assignment contributes to 5% of the total assessment of this course
The due date is on Friday June 17, 2022 11:59pm. Assignments are to be
submitted on Moodle before the due date and time. Any submission after the
due date will attract a penalty of 5% per day.
The assignment contains one problem with four parts. Each part contains one or
more questions related to the various topics covered related to op-amp. Each
question has been labelled with P, C, D or HD that indicates the level of
difficulty. P means that the question could be attempted by all students and
students who answer the question correctly are at the level of “pass”. C means
the question could be attempted by students who are at the level of “credit” in
the course. D and HD indicate the question could be attempted by students who
are at the level of “Distinction” and “High Distinction”, respectively.
What does this mean?
If you are targeting to pass or get credit in the course, you may only attempt
those P or C types of questions.
If you are happy or targeting to get distinction, you can attempt those P, C, and
D types of questions.
If you are targeting to get high distinction, you should attempt all the questions
including HD type of questions
2
QUESTION 1 [100 marks]
The circuit in Fig. 1(a) is a sensor readout circuit developed by MEMS/NEMS research group
(simple but effective) at EE&T UNSW for amplifying a small charge (voltage) generated by
a PZT thin film in a micro-lens actuator when the actuator resonates. A PZT stands for lead
zirconium titanate. It is a piezoelectric material that transduces strain into an electrical charge
(voltage) and conversely applied voltage (charge) into strain. Hence, the material is used to
build actuators, which are devices that produce mechanical energy (force, moment and etc)
from electrical energy (applied voltage) – the most precise nanoscale movements in advanced
equipment, robotics, automobile, energy harvesters, and others are enabled by piezoelectric
actuators. The same material is also used to build sensors to detect tiny movements, pressure,
and forces such as touch screens, pressure sensors, accelerometers, gyroscopes and etc.
Fig. 1(b) shows the sensor readout circuit with the PZT actuator replaced by its electrical
equivalent circuit that consists of a voltage source (VPZT) in series with a capacitor (CPZT).
When the actuator is excited (driven) by Vin, it resonates and generates small VPZT. Hence,
VPZT is in phase with Vin.
(a)
(b)
C2
VPZT CPZT
Vin
R1
R2
C1
R5
R3
R4
+V
-V
+V
-V
-V
+V
Vo
PZT Actuator
R1
R2
C1
C2
R5
R3
R4
PZT Actuator
+V
-V
+V
-V
-V
+V
Vo
V
in
3
PART 1 (Gain calculation and op-amp applications) [30 marks]
(a) [P,C] Obtain the expression for the output voltage (Vo) of the amplifier when the
actuator is driven (excited) by an AC source Vin operating at a frequency ω. [Hint:
apply superposition principle and express the sources and the capacitor in complex
frequency]. [10 marks]
(b) [D] The purpose the readout circuit is to amplify the VPZT and reject any output due
to Vin (Vo due to Vin is to be zero). How can the purpose of the amplifier circuit be
achieved based on your expression in (a)?
[5 marks]
(c) [P,C] Assuming R1 = R2 , C1 = C2 = CPZT and R5 ≫
1
2
, obtain the expression for
the gain of the amplifier (Vo/VPZT). [10 marks]
(d) [HD] Could you suggest a modification to the readout circuit (or new altogether) that
improves the gain of the amplifier and better achieve the purpose of the circuit. [5
marks]
PART 2 (Frequency response) [25 marks]
In reference to Fig. 1(a), the op-amps have large signal limitations and other characteristics as
provided in table 1.
Large signal limitations
Output voltage saturation ±10V
Output current limits ±20mA
Slew rate 0.5V/µs
Other characteristics
Internal compensation capacitor 30pF
Open loop voltage gain 100dB
Open loop bandwidth 6Hz
Table 1: The non-ideal op-amp characteristics
(a) [P,C] Assuming the bandwidth of the readout circuit is limited by the non-inverting
amplifier stage (the last stage) and R4 = 1K and R3 = 280K, estimate the
bandwidth of the readout circuit assuming that the internal compensation capacitor
creates the dominant pole in the frequency response of the op-amps? [8 marks]
(b) [P, C] With Vin = VAcos(ωt) and VA=1V and assuming VPZT = 0.005Vin, will there be
a frequency at which the output (Vo) will be distorted? If so, what is that frequency?
[8 marks]
4
(c) [D] With Vin = VAcos(2π*900t) and assuming R5 = 0.5M, R4 = 1K, R3 = 280K,
R1=1K, R2=1K, C1 = C2 = CPZT = 10nf, what is the constrain on the VA if the
output is to be undistorted? [7 marks]
PART 3 (DC imperfection) [30 marks]
(a) [HD] In the non-ideal case, all op-amps in Fig. 1 have the following DC imperfections
Input bias current: IB = 40nA at room temperature
Input offset current: Iio = ±2nA at room temperature
Input offset voltage: Vio = ±2mV at room temperature
Calculate the worst-case output offset voltage at room temperature assuming R5 =
0.5M, R4 = 1K, R3 = 280K, R1=1K, R2=1K, C1 = C2 = CPZT = 10nf.
[Hint: Consider the DC imperfections in all of the op-maps. In DC, capacitor can be
regarded as open] [20 marks]
(b) [D] Propose a method by modifying the readout circuit to reduce the output offset
voltage and explain why the modification may be able to reduce the output offset
voltage. [10 marks]
PART 4 (Simulation) [15 marks]
[P,C] Using LTspice or Pspice simulation, confirm your answer for part 1(c), part 2(a), part 3
(a) and (b). You may use LM301 op-amp and its model for the simulation. The op-amp will
be used in the first lab and there is Pspice manual included in the lab manual you may want to
refer. [15 marks]
