(2) A variable dielectric capacitive displacement sensor consists of two square metal plates of side l =5 cm, separated by a gap of d = 1 mm. A sheet of dielectric material 1 mm thick and of the same area as the plates can be slid between them as shown in below. Given that the dielectric constant (ɛ)of air is 1 and that of the dielectric material is 4: (a) Calculate the capacitance, C, of the sensor when the input displacement x = 0.0, 2.5 and 5.0 cm. (b) The sensor is placed into a bridge as shown below. Given V; = cos(400 n t) V , R3/R2 = 1, and the bridge is balanced when C = C min, find the output voltage, Eth , when the input displacement x = 2.5 and 5.0 cm.

(5) A platinum resistance sensor is to be used to measure temperatures between 0 and 200 °C. Given that the resistance R, in Q as a function of the input temperature T °C is given by: R_T=R_0\mleft(1+\alpha T+\beta T^2\mright)^^20^^20where^^20R_0=100\Omega,a=3.91\times10^{-3}and^^20\beta=-5.77\times10^{-7}; (a) Find the maximum non-linearity as percentage of FS. (b) A temperature sensor was inserted into a resistive bridge with DC excitation of V, = 2.5 V as shown in the figure below. i. Assuming the maximum allowed current is through the sensor 1 mA, what would be the value of R4 such that the bridge is balanced when the input temperature is zero? Approximate the result to the next higher standard resistance value. ii. Find the resistance ratio R3/R2 and express the output voltage ETh as a function of RT. iii. Plot the bridge output voltage ETh versus the input temperature T over the specified input temperature range. Estimate the maximum non-linearity in the bridge output as percentage of output voltage FS and compare it to the value you found in (a).

4. Convert the analog voltage E(t) - 2 sin 4nt mV into a discrete time signal. Specifically, use sample time increments of (a) 1/8 second, (b) 1/5 second, (c) 1/3 second, and (d) 1/21 second, and use a data set of 128 points. 4-1) Plot 4 seconds of each series as a function of time using either Excel or Matlab.Discuss apparent differences between the discrete representations of the analog signal. 4-2) Compute and plot the DFT for each (a), (b), (e), and (d) using a data set of 128 points. Use either Excel or Matlab for the DFT. Discuss apparent differences between the DFTs of the analog signal.

For the circuit shown below, assuming zero charge on the capacitor at t= 0, the current flowing may be quantified as... i=\frac{E}{R} e^{\frac{-1}{R C}} Integrate this equation with respect to t and hence find the charge stored in the capacitor one second after the switch is closed. The current (i) through a 10 mH inductor (L) has a relationship with time (t)as follows; i_{L}=\frac{1}{L} \int \cos (100 t) d t Determine the inductor current when the time is 0.9 seconds.

(a) Sketch the energy band diagram of a p-n junction in the steady-state, indicating the barrier Vo and theFermi level: i) With no bias applied ii) With a voltage of +V appiied iii) With a voltage of –V applied (b) In equilibrium, explain how the barrier forms in terms of the carrier currents. (c) Under forward bias, describe the change in minority carrier concentration on either side of the junction and the change in the depletion layer width. (d) A Si p-n junction has an accept or dopant concentration Na= 10'º cm in the p region and a donordopant concentration of Na= 106 cm in the n region. Assuming the semiconductor is non-degenerate,so that np= n² and that at room temperature (300 K) n; = 10'º cm* and all the dopants are fully ionised,calculate the junction barrier voltage at 300 K (give the answer in volts to two decimal places). (e) Will the barrier increase or decrease with temperature? Give a reason for your answer.

2. The vertical line on the left of a ladder diagram is connected to ________of an AC source, and _______of a DC source.The vertical line on the right is connected to _________ an AC source, and________of a DC source. a. L1 b. L2 c. +DC d. -DC or common

5. An experimental analysis of the natural oscillations in a particular structure shows thedominant frequencies of interest appear at below 200 Hz. However, firequency informationalso exists at 350, 450, and 750 Hz. If the signal is sampled at 400 Hz, how will theinformation in the aliased frequencies appear in the sampled data? (Hint: Use the foldingdiagram in the lecture note).

Given the 8-bit signed binary number in sign-magnitude form 10110010. Answer the questions by showing your step by step workout. 1. Find the equivalent signed decimal number. 2. Find the equivalent signed binary number in 2's complement form.

(a) For a pnp bipolar junction transistor: i) Sketch the energy band diagram for the transistor. Indicate in your diagram the doping levels(high, low or intermediate), the majority and minority carrier types in each layer and the approximate relative widths of the layers. (8 marks)ii) With a common emitter bias applied, indicate the directions of all charge carrier flows across the junctions. (b) In the following circuit, the transistor has a current gain Bdc=350:R2 R1 has a resistance of X times 100 k2 and R2 has a resistance of Y kQ. Assuming a voltage drop of 0.7 V across the p-n junctions, calculate i) The base current Ip ii) The collector current Ic iii) The collector-emitter voltage VCE iv) The power dissipated. v) How would you increase the power rating of a transistor?

Locate the co-ordinates of the turning point for the following function and determine whether it isa maxima or minima; y=3 x^{2}-5 x Find the maxima and minima values for the function; y=x^{3}-4 x+6