Problem 2. Show that if a Fabry-Perot etalon has an intensity gain per pass of G, its peak (1-R)2G transmission is given as (1-RG)2 Problem 3. Starting with the definition F=m+1 for the finesse of a Fabry-Perot etalon Av1/2 and using semi-quantitative arguments, show why in the case where the root-mean square surface deviation from the perfect flatness is approximately A/N, the finesse cannot exceed FN/(2n), where N is some constant, n is the refractive index of the etalon's medium and the medium outside the etalon is air. [Hint: Consider the spreading of the transmission peak due to a small num- ber of etalons of nearly equal length transmitting in parallel.] Note that A1/2 is the frequency width of the transmission resonance around each resonance frequency Vm such that I/I, 0.5 at v = Vm ± Aas will be discussed in class, also known as full-width half-maximum or FWHM linewidth.

V. a) Sketch a 3 input NOR gate with transistor widths chosen to achieve effective rise and fall resistance equal to that of a unit inverter ( R). Assume all the diffusion nodes are contacted. Draw the equivalent circuit for the falling output transition and the rising output transition.

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.

4. Design a combinational circuit with inputs a, b, c, d and outputs w, x, Y, z. Assume that the inputs a, b, c, d represent a 4-bit signed number (2s complement). The output is also a signed number in which is the 2s complement of the input.

Question 5 (Programmable Logic): Tabulate the PLA programming table for the four Boolean functions listed below.Minimize the number of product terms and draw the PLA circuit. A(x, y, z)=\sum(0,1,5,7) B(x, y, z)=\sum(2,4,5,6) C(x, y, z)=\sum(0,1,2,3,4) D(x, y, z)=\sum(3,6,7)

1. Suppose we have the signal x(n) = (0.9)^n u(n-50) as input to the LTI system with impulse response h(n)= (0.8)^n u(n). a) Compute (using a for-loop) and plot the output y(n) for 0 <= n <= 100. You might want to use the MATLAB function "stem" to plot. b) Compare this to theory. c) Repeat (a-b) for h(n) = (-0.8)^n u(n).

An array of 10 isotropic elements are placed along the z-axis a distance d apart. Assum-ing uniform distribution, find the progressive phase (in degrees), half-power beam width (in degrees), first-null beam width (in degrees), first side lobe level maximum beam width (indegrees), relative side lobe level maximum (in dB), and directivity (in dB) (using equations and the computer program Directivity of Chapter 2, and compare) for (a) broadside (b) ordinary end-fire (c) Hansen-Woodyard end-fire

Figure 1 is a dimensioned plot of the steady state carrier concentrations inside a pn step junction diode maintained at room temperature. Is the diode in forward or reverse bias? Explain your answer. Does low level injec tion prevail? Explain your answer. What are the p- and n-side doping concentrations? Determine the applied voltage, VA. Determine the built-in potential, Vi- If we know this diode is made of silicon, determine the width of the depletionregion, W.

9. If a GSM timeslot consists of 6 trailing bits, 8.25 guard bits, 26 training bits, and 2 traffic bursts of 58 bits of data. Find the total number of bits in each time slot. If a frame has 8 slots, find the total number of bits in each frame, also calculate overhead bits in each frame and frame efficiency.

2. (Streetman 6th 5.24 modified) In a p+-n junction reverse biased at 10 V,the capacitance is 10 pF. If the doping of the n side is doubled and there verse bias changed to 80 V, what is the capacitance? What is the maximum doping on the n side (after doubling) that makes it possible to apply a reverse bias of 80 V in silicon? In GaAs? (see Figure 5-22)

You are required to design a sequence detector circuit which detects all non-overlapped instances of the input pattern "10110" in a string of bits coming through an input line X and generates an active high output Y when detected. ) Produce a suitably labeled Moore machine state diagram for this problem. In the design, make sure that there are no missed patterns and explain the choice of number of states, number of bits in the state representation and the choice of the next state transitions in detail. Write a truth table that tabulates the states / transitions of the sequence detector and the output signal. Derive and simplify the Boolean expressions for the next state logic and the output. Sketch and label a schematic diagram that implements your solution using D-type flip flops and your choice of logic gates. Clearly identify the key blocks of the state machine on the diagram. Sketch the timing diagram for the clock, input, current state and output signals for the following input sequence (assume the state machine is reset at the start of the sequence): 10101110110. Assume the input signal is asynchronous and make sure that you correctly align the transitions for the synchronous signals. Discuss the graphs in terms of transitions on the state diagram presented in Part (a). Demonstrate that your state machine correctly identifies the correct input pattern in the input string given.