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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


the message signal m(t) has the Fourier transform shown in Figure P-3.11(a). This signal is applied to the system shown in Figure P-3.11(b) to generate the signal y(t).The 1. Plot Y(f), the Fourier transform of y(t). 2. Show that if y(t) is transmitted, the receiver can pass it through a replica of the system shown in Figure P-3.11 (b) to obtain m(t) back. This means that this system can be used as a simple scrambler to enhance communication privacy.


\text { Consider the continuous-time signal } x_{c}(t)=4 \cos (2 \pi 1000 t)+6 \cos (2 \pi 9000 t) \text {. } a) Assume that this signal is ideally sampled with a sampling frequency F, and then ideally reconstructed by passing the sampled signal through an ideal low pass filter with cutoff frequency F. = F:/2 and gain G = T. Sketch both the sampled and reconstructed signals in the frequency domain and obtain a time-domain expression for the reconstructed signal. i) Fs = 10,000HZ ii) F, = 1000H z b) Repeat (a) if the cosines are replaced by sines in the equation for xe(t), i.e.,= 4sin(2 pi 1000t) + 6sin(2pi9000t).


4. Consider the following state-transition diagram given in Figure 3, with one input x, and one outputF. (a) Determine the state-transition table (b) Assign bits to to each state and determine the truth table (c) Determine Boolean Algebra expressions for each state bit, and output (d) Design circuitry to perform the operation of the state-transition diagram


Which of the following timing diagrams correctly represents the signal at pin 13 of theCD405382 ОАОвОс


3. Consider the following state-transition diagram of a circuit with 2 inputs (x and y) and 1 output (F). (a) Reduce the number of states in the state transition diagram (b) Assign bits to each state (e) Determine Boolean Algebra expressions for each state bit and output (d) Design circuitry to perform the operation of the updated state-transition diagram


Problem 2: Consider the amplifier shown in Figure 2. Ignore CL. Assume that all transistors are in saturation. (a) Express the small signal transconductance of M3 namely gm3, in terms the small signal transconductance of M2, namely gm2. Hint: You can assume that VSD is the same for M2 and M3. (b) Determine the gain, Ay, of the amplifier. (3+7= 10 points) Bs M₂ W/L WHhM₁ R₂. Figure 2 M₂ 4W/L C₂₁


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