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ELEC2133
Analogue Electronics
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 (VPZT) in series with a capacitor (CPZT).
When the actuator is excited (driven) by Vin, it resonates and generates a small VPZT.
(a)
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(b)
Fig. 1: Charge readout circuit (a) with piezoelectric actuator; (b) the piezoelectric actuator
replaced by an equivalent circuit.
PART 1 (Gain Calculation) [20 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].
[5 marks]
(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)?
[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).
[5 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) [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
noninverting amplifier stage (the last stage) and R4 = 1k
and R3 = 280k ,
Large signal limitations
Output voltage saturation
±13V
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] Estimate the bandwidth of the readout circuit.
[5 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?
[5 marks]
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(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?
[5 marks]
PART 3 (DC imperfection) [10 marks]
(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 =
500k , R4 = 1k , R3 = 280k , R1=1k , R2=1k , 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]
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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.
Fig. 2:
A three-stage transistor amplifier
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
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PART I (Amplifiers configuration) [5 marks]
(a) [P] Identify the amplifier configuration used in each stage of the amplifier.[1.5 marks]
(b) [P,C] what are the functions of C1, C2, C3, C4, and C5 capacitors?
[1.5 marks]
(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? [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]
(a) [P] Draw the DC equivalent circuit of the transistor amplifier in Fig, 2. Note that capacitors
act as open circuit in DC conditions.
[2 marks]
(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).
[6 marks]
(c) [P,C] Calculate the transistor model parameters for each transistor, namely gm1, gm2, gm3,
ro1, r02, ro3, rπ2 and rπ3.
[2 marks]
(d) [D] *Comment on the possible range of resistance values that may replace the RC2 =
4.7k
, RD2 = 0.62k
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]
(a) [P,C] Draw a small-signal equivalent circuit of the amplifier in the form suitable for
mid-frequency.
[3 marks]
(b) [DN] Calculate the mid-band voltage gain of the amplifier, input resistance and output
resistance.
[6 marks]
(c) [HD] Calculate the mid-band current and power gain
[4 marks]
PART IV (Calculating bandwidth) [14 marls]
(a) [P,C] Draw small-signal equivalent circuit of the amplifier in the form suitable for
low frequency.
[2.5 marks]
(b) [D] Calculate the lower 3dB frequency, fL, of the amplifier using the appropriate time
constant method.
[4.5 marks]
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(c) [P,C] Draw small-signal equivalent circuit of the amplifier in the form suitable for
high-frequency analysis.
[2.5 marks]
(d) [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]
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