Chapter 7, Problem 15QAP

Light-emitting diodes (LEDs) are diodes made with III-V compound semiconductor materials such as aluminum gallium arsenide (AlGaAs), aluminum indium gallium phosphide (AlInGaP) or indium gallium nitride (InGaN), instead of silicon. The LEDs emit light when the device is operated under forward bias. LEDs of different colors have different turn-on voltages VD(on). For example:  VD(on) : Red: ~ 1.6 V Yellow: ~ 1.7 V Green: ~ 1.8 V Blue: ~ 2.8 V White: ~ 3.8 V   (a) Model these five LEDs with a simplified piecewise linear model (b) A rule of thumb is that it takes about 1 mA of current to “light” an LED while ~ 10 mA is needed for it to appear bright. Use the piecewise linear model for the LEDs, for the over-voltage indicator circuit to the right, find the values of Vin which will cause D1 or D2 to light (i.e. when ID1 or ID2 exceeds 1 mA).

The farming plan of steel structure has 30 ft long simply supported beams spaced at 8 ft apart. The beams carry dead loads (D) and live loads (L). The selected beam size is W 18x50. 1) Based on 0.3Fy allowable stress limit due to dead loads only (D), what will be the maximum D load in psf that can be applied to the beams? Ignore beam weight. 2) Using the D load obtained from Part 1 and based on 0.6Fy allowable stress limit due to combined dead loads and live loads, what will be the maximum live load L in psf  that can be applied to the beams? 3) If the maximum mid span deflection due to live loads (L) is L/360 ( or 1.0 in in this case), what will be the maximum L load in psf  that can be applied to the beams?

Consider a fixed and updated instrumentation amplifier (where two resistors are lumped into one resistor), analyze the circuit if a common voltage source (VICM) is connected to two inputs. A₁ R₂ + R₁ R₂, RA www www R₁ R₁ www A3 X R₁ R₂ www www R₁₂ + Vo RA A2 V2 O- + R₂ 12 R₁

Show that the input impedance of a lossy transmission line of length L connected to a load impedance of Z is given by Z₁Cosh(yL) + ZoSinh(yL) Zin = Zo ZoCosh(YL) + Z₁Sihh(YL) ex Where Cosh(x) = and Sinh(x) = are the hyperbolic cosine and sine, respectively. 2 2

A sinusoidal source of V = 10 and Z = 50 - j40 is connected to a 60 lossless transmission line of length 100 m with ẞ = 0.25. What is the Thevenin's equivalent of this system seen looking into the load end of the transmission line?

2. On a distortionless transmission line, the voltage wave is given by v(L,t) = 110e0.005L Cos(10³t + 2L) +55e-0.005L Cos(108t-2L) where L is the length of the transmission line as measured from the load. If Z = 30002, find a,ẞ, vp, and Zo.

1.[30 pts] Computers generate color pictures on a video screen or liquid crystal display by mixing three different colors of light: red, green, and blue. Imagine a simple scheme, with three different lights, each of which can be turned on or off, projecting onto a glass screen: We can create eight different colors based on the absence (0) or presence (1) of light sources R,G and B: R G B Color 0 0 0 Black 0 0 1 Blue 0 1 0 Green 0 1 1 Cyan 1 0 0 Red 1 0 1 Magenta 1 1 1 0 Yellow 1 White 1 Each of these colors can be represented as a bit vector of length 3, and we can apply Boolean operations to them. a. The complement of a color is formed by turning off the lights that are on and turning on the lights that are off. What would be the complement of each of the eight colors listed above? b. Describe the effect of applying Boolean operations on the following colors: Λ 1. Red(100) ^ Magenta(101)= Blue(001) 2. Bue(001) | Green(010)= 3. Yellow(100) & Cyan(011)= 2.[30 pts] Perform the following…

A 50 transmission line is to be connected to a 72 load through a 1/4 quarter wave matching transformer. (a) What must be the characteristic impedance of the transmission line that is used to form the quarter wave transformer? (b) If the frequency of operation is 7 MHz and the phase velocity through the quarter wave section is 2c/3, what is the length of the quarter wave section? You may assume the transmission line forming the quarter wave section is lossless.

2) Ammonia (NH3) is an important base, particularly in wastewaters. Consider a solution that contains a total of 10-3 M of ammonia in water. NH4+ = NH3 + H+ KA=10-9.3 a) Use the equilibrium expression and concept of mass balance to write an expression for each of the following species: log [NH4*] and log [NH3]. b) Prepare a log C-pH diagram for the solution described above. Label each line on your graph with the name of the chemical species it represents. [Notes: Your diagram should contain 4 lines, one for each of the four species in the system. You may draw your diagram by hand or using Excel or other software.] c) Use your diagram to find the equilibrium pH of the solution. Use a circle or “X” to mark your answer point on the diagram. d) Now consider a new solution made by adding 10-3 M of NH4Cl to water. Write the charge balance or proton condition for this solution. Use your diagram to determine the equilibrium pH of this solution. e) Suppose it is winter and your water…