ELEC2133 - School of Electrical Engineering and Telecommunication Assignment I

Assignment Overview

The assignment consists of two problems , each containing four parts . Each part includes one or more questions related to topics on operational amplifiers (op-amps) and transistor amplifiers .Each question is labelled with one of the following difficulty levels:

• P (Pass): Correctly answering these questions demonstrates a pass-level
• C (Credit): Correctly answering these questions demonstrates a credit-level performance.
• D (Distinction): Designed for students targeting a
• HD (High Distinction): For students aiming for the highest level of

QUESTION 1 [50 marks]

The circuit shown in Fig. 1(a) is a sensor readout circuit developed by the MEMS/NEMS research group at EE&T, UNSW. Though simple in design, it is highly effective for amplifying the small electrical signal (voltage) generated by a PZT thin film in a micro-lens actuator during resonance.

PZT, or lead zirconate titanate, is a piezoelectric material that converts mechanical strain into electrical charge (voltage), and vice versa—applied voltage into mechanical strain. This dual functionality makes PZT ideal for constructing actuators, which are devices that convert electrical energy into mechanical motion. Piezoelectric actuators enable extremely precise nanoscale movements and are widely used in advanced instrumentation, robotics, automotive systems, energy harvesting devices, and more.

In addition to actuators, PZT is also used in sensors to detect minute movements, pressure, and forces. Applications include touch screens, pressure sensors, accelerometers, gyroscopes, and other precision sensing technologies.

Fig. 1(b) shows the sensor readout circuit with the PZT actuator replaced by its electrical equivalent circuit that consists of a voltage source ( V PZT ) in series with a capacitor ( C PZT ). When the actuator is excited (driven) by Vin , it resonates and generates a small V PZT .

PART 1 (Gain Calculation) [20 marks]

• [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 ].

[5 marks]

• [D] The purpose the readout circuit is to selectively amplify the V PZT and reject any output due to V in (V o due to V in is to be zero). How can the purpose of the amplifier circuit be achieved based on your expression in (a)? [5 marks]

• [P,C] Assuming R1 = R2, C1 = C2 = CPZT and R5 ≫ 1/????????2, obtain the expression for the gain of the amplifier (Vo/VPZT). [5 marks]

• [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 [5 marks]

PART 2 (Frequency response) [15 marks]

In reference to Fig. 1(a), the op-amps have large signal limitations and other characteristics as provided in Table 1. Assuming the bandwidth of the readout circuit is limited by the non- inverting amplifier stage (the last stage) and R4 = 1kW and R3 = 280kW,

• [P, C] Estimate the bandwidth of the readout [5 marks]

• [P, C] With V in = VAcos(ωt) and V A =1V and assuming V PZT = 0.005Vin, will there be a frequency at which the output (V o ) will be distorted? If so, what is that frequency?

[5 marks]

• [D] With Vin = VAcos(2π*900t) and assuming R5 = 0.5MW, R4 = 1kW, R3 = 280kW, R1=1kW, R2=1kW, C1 = C2 = C PZT = 10nf, what is the constrain on the VA if the output is to be undistorted? [5 marks]

PART 3 (DC imperfection) [10 marks]

• [HD] In the non-ideal case, the non-inverting op-amp (last stage) in 1 has the following DC imperfections. Assume all the other op-amps are ideal.

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 = 500kW, R4 = 1kW, R3 = 280kW, R1=1kW, R2=1kW, C1 = C2 = CPZT = 10nf. [ Hint:

Consider the DC imperfections in all the op-amps. In DC, capacitor can be regarded as open ] ` [10 marks]

PART 4 (Simulation) [5 marks]

[P,C] Using LTspice or Pspice simulation, confirm your answer for part 1(c), part 2(a), part 3 (a). You may use LM301 op-amp and its model for the simulation. The op-amp is used in the first lab. [5 marks]

QUESTION 2 [50 marks]

In Question 1, you analysed and designed the charge readout circuit for the PZT actuator shown in Fig. 1(a). A common issue with this circuit is that the final stage—the non-inverting amplifier—tends to amplify low-frequency noise originating from the power supply or environmental vibrations affecting the actuator. Additionally, it can amplify any DC offsets introduced by earlier stages in the circuit. Minimizing output noise while maintaining adequate signal amplification is crucial. Although there are various ways to improve the signal-to-noise ratio of the non-inverting amplifier, in this assignment it will be replaced with a three-stage transistor amplifier, as shown in Fig. 2(a). Your task is to analyse this new amplifier by calculating its gain, input and output impedance, and bandwidth.

The three-stage amplifier consists of one n-channel MOSFET transistor Q1 in depletion mode with W/L = 1 and two BJT transistors Q1 and Q2. The transistors have the model parameters as provided in the table below

PART I (Amplifiers configuration) [5 marks]

• [P] Identify the amplifier configuration used in each stage of the amplifier.[1.5 marks]
• [P,C] what are the functions of C1, C2, C3, C4, and C5 capacitors? [1.5 marks]
• [P,C] Explain what are the purposes of each amplifier, and can a single-stage transistor amplifier (say stage 1 or 2 or 3) be used instead? [ Hint: what are the

requirements of voltage amplifiers in terms of input and output resistance? Remember the non-inverting amplifier (the last stage) in Fig. 2 is a voltage amplifier ] [2 marks]

PART II (Q-point and transistor model parameter calculations) [13 marks]

• [P] Draw the DC equivalent circuit of the transistor amplifier in Fig, 2. Note that capacitors act as open circuit in DC [2 marks]
• [P,C]Show that the Q-Point values are: M1(ID=5mA, VDS=10.9V), Q1 (IC=1.51mA, VCE

= 5.49V), and Q2 (1.99mA, 8.44V). [6 marks]

• [P,C] Calculate the transistor model parameters for each transistor, namely gm1, gm2, gm3, ro1, r02, ro3, rπ2 and rπ3. [2 marks]
• [D] *Comment on the possible range of resistance values that may replace the RC2 =

4.7kW , RD2 = 0.62kW of the BJT Q1 transistor in the amplifier. [Hint: BJT must operate in a forward-active region and MOSFET must operate in a saturation region] [3 marks]

PART III (Calculating mid-band gain, input, and output resistance) [13 marks]

• [P,C] Draw a small-signal equivalent circuit of the amplifier in the form suitable for mid-frequency. [3 marks]
• [DN] Calculate the mid-band voltage gain of the amplifier, input resistance and output [6 marks]

• [HD] Calculate the mid-band current and power gain [4 marks]

PART IV (Calculating bandwidth) [14 marls]

• [P,C] Draw small-signal equivalent circuit of the amplifier in the form suitable for low [2.5 marks]
• [D] Calculate the lower 3dB frequency, fL, of the amplifier using the appropriate time constant [4.5 marks]
• [P,C] Draw small-signal equivalent circuit of the amplifier in the form suitable for high-frequency [2.5 marks]
• [DN, HD] Calculate the higher 3dB frequency, fH, of the amplifier using the appropriate time constant method. [4.5 marks]

PART V (LTSpice or PSpice Simulation) [5 marks]

(a) [DN] Simulate Fig. 2 and compare the results with your calculation of midband gain and bandwidth. The Spice transistor models will be uploaded on Moodle. [5 marks]

Summary of Assessment Requirements

This assignment focuses on advanced topics in electronic circuit design and analysis, particularly operational amplifiers (op-amps) and transistor amplifiers. It is divided into two major problems, each carrying 50 marks and further broken into parts that align with performance levels (Pass, Credit, Distinction, and High Distinction).

Key Requirements:

1. Question 1 – Op-amp Based Sensor Readout Circuit (50 marks):

   • Gain Calculation (application of superposition principle and selective amplification).

   • Frequency Response Analysis (bandwidth estimation, distortion frequency, and constraints).

   • DC Imperfections (impact of bias current, offset current, and voltage on output).

   • Simulation (verification using LTSpice/PSpice).

2. Question 2 – Three-Stage Transistor Amplifier (50 marks):

   • Amplifier Configuration (identification and function of capacitors).

   • Q-point and Model Parameters (bias analysis and transistor parameter calculations).

   • Mid-Band Gain, Input & Output Resistance (circuit analysis using small-signal models).

   • Bandwidth Calculations (lower and higher cut-off frequencies).

   • Simulation (verification of mid-band gain and bandwidth).

Deliverables:

• Analytical derivations with clear expressions.

• Verification using simulation tools.

• Demonstration of understanding across difficulty levels (P, C, D, HD).

Step-by-Step Academic Mentor Guidance

The academic mentor structured the student’s approach by breaking down each section into manageable tasks while ensuring theoretical clarity before moving into calculations and simulations.

1. Introduction to the Task

The mentor first contextualized the role of PZT actuators, explaining their dual function in sensors and actuators, ensuring the student understood the real-world relevance of the circuits being analyzed. This helped the student link theory to application.

2. Approach to Question 1 – Op-amp Circuit

• Part 1: Gain Calculation

  • The mentor guided the student to apply the superposition principle, considering input from both Vin and VPZT.

  • Step by step, the student derived expressions using complex frequency representation.

  • For distinction/HD, the mentor encouraged critical thinking on how the circuit could be modified for improved selectivity.

• Part 2: Frequency Response

  • The mentor directed the student to use given resistor values to calculate bandwidth, reinforcing the importance of non-ideal op-amp limitations.

  • Possible distortion conditions were analyzed using ratios of VPZT and Vin.

  • At higher levels, constraints on amplitude (VA) were derived to maintain undistorted output.

• Part 3: DC Imperfections

  • The student was shown how to account for input bias current, offset current, and offset voltage.

  • The mentor emphasized treating capacitors as open circuits in DC analysis.

• Part 4: Simulation

  • After completing theoretical derivations, the mentor instructed the student to verify results using LTSpice/PSpice.

  • This reinforced the link between theoretical analysis and practical validation.

3. Approach to Question 2 – Transistor Amplifier

• Part 1: Amplifier Configuration

  • Mentor guided the student in identifying common-source MOSFET and BJT amplifier stages, discussing input/output resistance roles.

  • Capacitor functions were clarified in terms of coupling, bypassing, and frequency response shaping.

• Part 2: Q-Point and Parameters

  • Mentor demonstrated how to simplify circuits for DC equivalent analysis.

  • Q-point calculations were guided step by step, with checks for forward-active and saturation regions.

  • Transistor small-signal parameters (gm, ro, rπ) were computed systematically.

• Part 3: Mid-Band Gain & Resistances

  • Using the small-signal equivalent circuit, the mentor explained how to calculate mid-band voltage gain, input, and output resistance.

  • For advanced levels, current and power gain were also derived.

• Part 4: Bandwidth Analysis

  • Mentor instructed on applying the time constant method to determine fL and fH.

  • Separate treatment for low-frequency and high-frequency models was emphasized.

• Part 5: Simulation

  • Student was guided to compare calculated mid-band gain and bandwidth with simulation results.

  • Any discrepancies were discussed as practical learning opportunities.

Outcome and Learning Objectives Achieved

Final Outcome:
By following the step-by-step mentoring process, the student successfully completed both problems with analytical rigor and simulation validation. The structured approach ensured clear derivations, accurate calculations, and meaningful comparisons with simulated data.

Learning Objectives Covered:

1. Circuit Analysis Skills – Application of superposition, frequency response, and small-signal models.

2. Problem-Solving Across Difficulty Levels – From pass-level calculations to high distinction design modifications.

3. Theoretical to Practical Connection – Verification of results using simulation tools.

4. Critical Thinking – Evaluating limitations, imperfections, and circuit modifications.

5. Technical Communication – Organizing responses in structured report format with clarity.

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