ELEC2133: Analogue Electronics Assignment 1

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

Questios

1. 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 (VPZT) in series with a capacitor (CPZT).
When the actuator is excited (driven) by Vin, it resonates and generates a small VPZT.

Part 1 (Gain Calculation)

(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].

(b) [D] The purpose the readout circuit is to selectively 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)? 

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

(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.

Part 2 (Frequency response)

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 noninverting amplifier stage (the last stage) and R4 = 1kΩ and R3 = 280kΩ,

(a) [P, C] Estimate the bandwidth of the readout circuit.

(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?

(c) [D] With Vin = VAcos(2π*900t) and assuming R5 = 0.5MΩ , R4 = 1kΩ , R3 = 280kΩ , R1=1kΩ , R2=1kΩ , C1 = C2 = CPZT = 10nf, what is the constrain on the VA if the output is to be undistorted?

Part 3 (DC imperfection)

(a) [HD] In the non-ideal case, the non-inverting op-amp (last stage) in Fig. 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 = 500kΩ, R4 = 1kΩ, R3 = 280kΩ, R1=1kΩ, R2=1kΩ, C1 = C2 = CPZT = 10nf. [Hint: Consider the DC imperfections in all the op-amps. In DC, capacitor can be regarded as open] 

2. 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) 

(a) [P] Identify the amplifier configuration used in each stage of the amplifier.

(b) [P,C] what are the functions of C1, C2, C3, C4, and C5 capacitors?

(c) [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?

Part II (Q-point and transistor model parameter calculations)

(a) [P] Draw the DC equivalent circuit of the transistor amplifier in Fig, 2. Note that
capacitors act as open circuit in DC conditions. 

(b) [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). 

(c) [P,C] Calculate the transistor model parameters for each transistor, namely gm1, gm2, gm3, ro1, r02, ro3, rπ2 and rπ3. 

(d) [D] *Comment on the possible range of resistance values that may replace the RC2 =
4.7kΩ , RD2 = 0.62kΩ 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]

Part III (Calculating mid-band gain, input, and output resistance)

(a) [P,C] Draw a small-signal equivalent circuit of the amplifier in the form suitable for
mid-frequency.

(b) [DN] Calculate the mid-band voltage gain of the amplifier, input resistance and output
resistance.

(c) [HD] Calculate the mid-band current and power gain.

Part IV (Calculating bandwidth)

(a) [P,C] Draw small-signal equivalent circuit of the amplifier in the form suitable for
low frequency.

(b) [D] Calculate the lower 3dB frequency, fL, of the amplifier using the appropriate time
constant method. [nt circuit of the amplifier in the form suitable for
high-frequency analysis.

(d) [DN, HD] Calculate the higher 3dB frequency, fH, of the amplifier using the
appropriate time constant method.

Assessment Summary

Objective:
The assignment focuses on the analysis and design of operational amplifier (op-amp) circuits and transistor amplifiers. Students are expected to demonstrate both theoretical understanding and practical application of amplifier design, including gain calculation, frequency response, DC imperfections, and transistor modeling.

Key Pointers to Be Covered:

1. Op-Amp Sensor Readout Circuit:

   • Gain calculation and selective amplification.
   • Frequency response and bandwidth estimation.

   • Effects of DC imperfections on output voltage.

2. Transistor Amplifier Design:
   • Stage identification and amplifier configuration.
   • Function and purpose of coupling and bypass capacitors.
   • Q-point calculation and transistor parameter estimation.
   • Mid-band gain, input/output resistance, and power gain.
   • Bandwidth analysis, including low-frequency and high-frequency 3dB points.

Difficulty Levels: The questions were categorized as P (Pass), C (Credit), D (Distinction), and HD (High Distinction), allowing students to target different achievement levels.

Step-by-Step Approach Guided by Academic Mentor

Step 1: Understanding Circuit Functionality

• The mentor began by explaining the purpose of the PZT sensor readout circuit and its role in detecting small voltages generated by mechanical strain.

• Students were guided to identify the key nodes, resistors, and capacitors that influence gain and signal selectivity.

Step 2: Gain Calculation and Selectivity

• Using the superposition principle and complex frequency notation, the mentor helped the student derive the output voltage expression.

• Techniques to maximize VPZT amplification and reject Vin contributions were discussed, ensuring the circuit meets its design purpose.

Step 3: Frequency Response Analysis

• The mentor demonstrated how to estimate the bandwidth of the readout circuit using non-inverting amplifier constraints.

• Students were taught to calculate output distortion and evaluate constraints for undistorted operation.

Step 4: DC Imperfections

• The mentor explained input bias current, offset voltage, and offset current, guiding the student to calculate the worst-case output offset voltage.
• This step highlighted the practical consideration of non-ideal op-amp behavior in circuit design.

Step 5: Transistor Amplifier Analysis

• Students were guided to identify configurations (MOSFET, BJT stages) and capacitor functions in the three-stage amplifier.

• The mentor instructed on Q-point calculations and deriving transistor parameters (gm, ro, rπ).

Step 6: Small-Signal Analysis

• The student learned to draw small-signal equivalent circuits for mid-band, low-frequency, and high-frequency analyses.

• Calculations included mid-band voltage, current, and power gain, as well as input/output resistances.

Step 7: Bandwidth Estimation

• The mentor guided the student to use the time constant method to determine lower and upper 3dB frequencies, ensuring the amplifier met performance specifications.

Outcome and Learning Objectives Covered

Outcome Achieved:

• Complete derivation of gain expressions, frequency responses, and output constraints for op-amp circuits.
• Accurate Q-point and transistor parameter calculations for multi-stage transistor amplifiers.
• Small-signal analysis for mid-band gain, input/output impedance, and bandwidth determination.
• Understanding of practical limitations, such as DC offsets, bias currents, and component selection.

Learning Objectives Addressed:

1. Apply fundamental principles of op-amp and transistor amplifier design.
2. Perform frequency response and bandwidth analysis for practical circuits.
3. Understand and calculate effects of DC imperfections on op-amp circuits.
4. Conduct small-signal modeling and parameter extraction for transistor stages.
5. Integrate theoretical knowledge with practical circuit design considerations.

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