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A horizontal beam of laser light of wavelength 585 nm passes through a narrow slit that has width 0.0620 mm. The intensity of the light is measured on a vertical screen that is 2.00 m from the slit.... The siliconsilicon single bond that forms the basis of the mythical silicon-based creature the Horta has a bond strength of 3.80 eV. What wavelength of photon would you need in a (mythical) phasor... Eyeglass lenses can be coated on the inner surfaces to reduce the reflection of stray light to the eye. If the lenses are medium flint glass of refractive index 1.62 and the coating is fluorite of... After an eye examination, you put some eye drops on your sensitive eyes. The cornea (the front part of the eye) has an index of refraction of 1.38, while the eye drops have a refractive index of... Monochromatic x rays are incident on a crystal for which the spacing of the atomic planes is 0.440 nm. The first-order maximum in the Bragg reflection occurs when the incident and reflected x rays... The VLBA (Very Long Baseline Array) uses a number of individual radio telescopes to make one unit having an equivalent diameter of about 8000 km. When this radio telescope is focusing radio waves of... In a laboratory, light from a particular spectrum line of helium passes through a diffraction grating and the second-order maximum is at 18.9 from the center of the central bright fringe. The same... The maximum resolution of the eye depends on the diameter of the opening of the pupil (a diffraction effect) and the size of the retinal cells. The size of the retinal cells (about 5.0 m in diameter)... The thin glass shell shown in Fig. E34.12 has a spherical shape with a radius of curvature of 12.0 cm, and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 cm from the... A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. The person looks at a penny that is on the bottom of the pool directly below her. The penny appears to... Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see... An inductor with L = 9.50 mH is connected across an ac source that has voltage amplitude 45.0 V. (a) What is the phase angle for the source voltage relative to the current? Does the source voltage... A flat, round iron ring 5.00 cm in diameter has a cur-rent running through it that produces a magnetic field of 75.4 T at its center. This ring is placed in a uniform external magnetic field of 0.375... A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is... In Figs. 18.6 and 18.7, look at the different pairings of controllers. Which one has the larger stability region? How does this compare with the preferred pairing indicated by the RGA (is it the same... A batch reactor converts component A into B, which in turn decomposes into C: where k 1 = k 10 e -E 1 RT and k 2 = k 20 e -E 2 RT . The concentrations of A and B are denoted by x 1 and x 2 ,... A brewery has the capability of producing a range of beers by blending existing stocks. Two beers (suds and premium) are currently available, with alcohol concentrations (by volume) of 3.0% for suds... Given the vector field E = 4zy 2 cos 2xa x + 2zy sin 2xa y + y 2 sin 2xa z for the region |x|, |y|, and |z| less than 2, find (a) The surfaces on which E y = 0; (b) The region in which E y = E z ;... A field is given as G = [25/(x 2 + y 2 )](xa x + ya y ). Find (a) A unit vector in the direction of G at P(3, 4,2); (b) The angle between G and ax at P; (c) The value of the following double integral... The surfaces r = 2 and 4, = 30 and 50, and = 20 and 60 identify a closed surface. Find (a) The enclosed volume; (b) The total area of the enclosing surface; (c) The total length of the twelve edges... Consider the block diagram in Fig. E24.2 of the multiple feedback loops involved in the Central Dogma schematic from Fig. 24.3, namely, genetic regulation C 1 , transnational regulation C 2 , and... As a specific biological example for Exercise 24.2 and Fig. E24.2(b), the synthesis of tryptophan can be described by the following set of material balances: where k 1 , k 2 , k 3 , and k 4 represent... In free space, a volume charge of constant density = 0 exists within the region < x < , < y < , and d/2 < z < d/2. Find D and E everywhere. In spherical coordinates, E = 2r/(r 2 + a 2 ) 2 a r V/m. Find the potential at any point, using the reference (a) V = 0 at infinity; (b) V = 0 at r = 0; (c) V = 100 V at r = a. Two equal but opposite-sign point charges of 3 C are held x meters apart by a spring that provides a repulsive force given by F sp = 12(0.5 x) N. Without any force of attraction, the spring would be... Redraw Figure 3.10 to illustrate the generation of upper-side band SSB. Give the equation defining the upper side band filter. Complete the analysis by deriving the expression for the output of an... An AM modulator has output x c (t) = A cos[2(200)t] + B cos[2(180)t] +B cos[2(220)t] The carrier power is P 0 and the efficiency is E ff . Derive an expression for E ff in terms of P 0 , A, and B.... Two conducting plates, each 3 6 cm, and three slabs of dielectric, each 1 3 6 cm, and having dielectric constants of 1, 2, and 3, are assembled into a capacitor with d = 3 cm. Determine the two... It is desired to transmit data at 9 kbps over a channel of bandwidth 7 kHz using raised-cosine pulses. What is the maximum value of the roll-off factor, , that can be used? (a) For what value of > 0 is the function f(x) = x -2 u(x - ) a probability-density function? Use a sketch to illustrate your reasoning and recall that a pdf has to integrate to one. [u(x) is the... Write a MATLAB program that will produce plots like those shown in Figure 5.2 assuming a random binary data sequence. Include as an option a Butter worth channel filter whose number of poles and... A random variable X is defined by f X (x) = 4e -8|x| The random variable Y is related to X by Y = 4 + 5X. (a) Determine E[X], E[X 2 ], and 2 x . (b) Determine f Y (y). (c) Determine E[Y], E[Y 2 ],... Assume that two random variables X and Y are jointly Gaussian with m x = m y = 1, 2 x = 2 y = 4. (a) Making use of (6.194), write down an expression for the marginal pdfs of X and of Y. (b) Write... Noise n (t) has the power spectral density shown in Figure 7.16. We write n(t) = n c (t) cos (2Ïf 0 t + θ) - n s (t) sin(2Ïf 0 t + θ) Make plots of the power... The electric field intensity in the region 0 < x < 5, 0 < y < /12, 0 < z < 0.06 m in free space is given by E = C sin 12y sin a z cos 2 10 10 ta x V/m. Beginning with the E relationship, use... Which of the following functions are suitable auto correlation functions? Tell why or why not. ( 0 , 0 , 1 , A, B, C, and f 0 are positive constants.) (a) A cos 0 (b) A (/ 0 ), where (x) is the... In an old-fashioned amusement park ride, passengers stand inside a 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then... A conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. FIGURE P8.47 shows that the string traces out... A rocket-powered hockey puck has a thrust of 2.0 N and a total mass of 1.0 kg. It is released from rest on a frictionless table, 4.0 m from the edge of a 2.0 m drop. The front of the rocket is... A new car is tested on a 200-m-diameter track. If the car speeds up at a steady 1.5 m/s 2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential... The weight of passengers on a roller coaster increases by 50% as the car goes through a dip with a 30 m radius of curvature. What is the cars speed at the bottom of the dip? Mass m 1 on the frictionless table of FIGURE EX8.13 is connected by a string through a hole in the table to a hanging mass m 2 . With what speed must m 1 rotate in a circle of radius r if m 2 is to... A highway curve of radius 500 m is designed for traffic moving at a speed of 90 km/h. What is the correct banking angle of the road? Find the zeros in for the E-plane pattern of a dipole antenna for which (a) = ; (b) 2 = 1.3. Use Figure 14.8 as a guide. A filamentary conductor on the z axis carries a current of 16 A in the a z direction, a conducting shell at = 6 carries a total current of 12 A in the a z direction, and another shell at = 10... Consider a composite material made up of two species, having number densities N 1 and N 2 molecules/m 3 , respectively. The two materials are uniformly mixed, yielding a total number density of N = N... Consider the system shown in Figure 8.24. The noise is white with two-sided power spectral density 1/2 N 0 . The power spectral density of the signal is The parameter f 3 is the 3-dB bandwidth of the... On October 15, 2001, a planet was discovered orbiting around the star HD 68988. Its orbital distance was measured to be 10.5 million kilometers from the center of the star, and its orbital period was... Plot P E from Equation (9.183) versus z 0 for = 0.5 and m / T = 0.2, 0.6, and 1.0. Develop a MATLAB program to plot the curves. Design an emitter-coupled pair of the type shown in Fig. 3.53a. Assume I TAIL = 0 and select values of R C and R TAIL to give a differential input resistance of 2 MΩ, a differential... A diffused resistor has a length of 200 m and a width of 5 m. The sheet resistance of the base diffusion is 100/D and the emitter diffusion is 5/D. The base pinched layer has a sheet resistance of 5... List and explain at least three reasons to select a two-stage op amp with an n-channel input pair instead of with a p-channel input pair for a given application. Find the small-signal voltage gain of the NE5234 op amp under the same conditions given in this chapter except use F(npn) = 0(npn) = 80 and F(pnp) = 0(pnp) = 20. Ignore F(npn) and F(pnp) from dc... Use half-circuit concepts to determine the differential-mode and common-mode gain of the circuit shown in Fig. 3.80. Neglect r o , r μ , and r b . Calculate the differential-mode and... An integrated npn transistor has the following characteristics: F = 0.25 ns, small-signal, short-circuit current gain is 9 with I C =1 mA at f = 50 MHz, V A = 40 V, 0 = 100, r b = 150, r c = 150, C... An amplifier has a low-frequency forward gain of 200 and its transfer function has three negative real poles with magnitudes 1 MHz, 2 MHz, and 4 MHz. Calculate and sketch the Nyquist diagram for this... An amplifier has a low-frequency forward gain of 40,000 and its transfer function has three negative real poles with magnitudes 2 kHz, 200 kHz, and 4 MHz. (a) If this amplifier is connected in a... Examine the effect of velocity saturation on MOSFET characteristics by plotting I D V DS curves for V GS = 1 V, 2 V, and 3 V, and V DS = 0 to 3 V in the following cases, and by comparing the results... Calculate the total parasitic junction capacitance associated with a 10-kΩ base-diffused resistor if the base sheet resistance is 100 Ω/D and the resistor width is 6... Calculate the small-signal model parameters of the device shown in Fig. 2.74, including g m , g mb , r o , C gs , C gd , C sb , and C db . Fig. 2.74 Assume the transistor is biased at a drain-source... An integrated electronic subsystem is to be fabricated, which requires 40,000 square mils of silicon area. Determine whether the system should be put on one or two chips, assuming that the... Determine the direct fabrication cost of an integrated circuit that is 150 mils on a side in size. Assume a wafer-fab cost of $130.00, a package and testing cost of $0.40, a die-fab yield of 0.8, and... A source output consists of five messages [m 1 , m 2 , m 3 , m 4 , m 5 ] with respective probabilities [0.35, 0.25, 0.2, 0.15, 0.05]. Determine the binary code words for the second-order source... An NMOS transistor has parameters W = 10 m, L=1 m, k =194 A/V 2 , = 0.024 V 1 , t ox = 80 A, f = 0.3 V, V t0 = 0.6 V, and N A = 510 15 atoms/cm 3 . Ignore velocity saturation effects. (a) Sketch... Estimate the series base resistance, series collector resistance r c , base-emitter capacitance, base-collector capacitance, and collector-substrate capacitance of the high-current npn transistor... Determine the required bias current and device sizes to design a source-coupled pair to have the following two characteristics. First, the small-signal transconductance with zero differential input... Determine the input offset voltage of the source-coupled pair in Fig. 3.50 for which I TAIL = 50 µA. The drawn device dimensions are W = 10 µm and L = 1 µm. Use the process... Design a simple MOS current mirror of the type show in Fig. 4.4 to meet the following constraints: Figure 4.4: Hypothetical band-gap reference circuit (a) Transistor M 2 must operate in the active... Calculate the output resistance of the circuit of Fig. 4.9, assuming that I IN =100 A and the devices have drawn dimensions of 100 m/1 m. Use the process parameters given in Table 2.4, and assume for... For the circuit of Fig. 4.56, assume that (W/L) 8 = (W/L). Ignoring the body effect, find (W/L) 6 and (W/L) 7 so that V DS6 = VDS 7 = V ov8 . Draw the schematic of a double-cascode current mirror... A binary three-hop communication system has transition probabilities i , i , and i (i = 1,2,3,4). Determine the transition probabilities for the overall three-hop system. Solve this problem two... A source has five outputs denoted [m 1 , m 2 , m 3 , m 4 , m 5 ] with respective probabilities [0.30, 0.25, 0.20, 0.15, 0.10]. Determine the entropy of the source. What is the maximum entropy of a... A source consists of six outputs denoted [A, B, C, D, E, F] with respective probabilities [0.30, 0.25, 0.20, 0.1, 0.1, 0.05]. Determine the entropy of the source. A binary symmetric channel has an error probability of 0.007. How many of these channels can be cascaded before the overall error probability exceeds 0.02? A channel has two inputs, (0, 1), and three outputs, (0, e,1), where e indicates an erasure; that is, there is no output for the corresponding input. The channel matrix is Compute the channel... Repeat Problem 4.12, but now assuming that 2-k¦ resistors are inserted in series with the emitters of Q 3 and Q 4 . Repeat Problem 4.12: Determine the unloaded voltage gain ν o... A binary symmetric channel with error probability p 1 is followed by an erasure channel with erasure probability p 2 . Describe the channel matrix that results from this cascade combination of... Determine the capacity of the channel described by the channel matrix shown below. Sketch your result as a function of p and give an intuitive argument that supports your sketch. (Note: q = 1 - p.).... From the entropy definitions given in (12.25) through (12.29), derive (12.30) and (12.31). Determine the quantizing levels, in terms of , so that the entropy at the output of a quantizer is maximized. Assume that there are six quantizing levels and that the input to the quantizer is a... Repeat Problem 4.14, but now assuming that 2 k¦ resistors are inserted in series with the sources of M 3 and M 4 . Ignore the body effect? Repeat Problem 4.14: Determine the unloaded voltage... Repeat Problem 4.16 except replace the npn and pnp transistors with n-channel and p-channel MOS transistors, respectively. Assume W n = 50[1]µm and W p = 100[1]µm. For all transistors,... Determine the value of sensitivity S of output current to supply voltage for the circuit of Fig. 4.62, where S = (V CC /I OUT )(I OUT /V CC ). Fig. 4.62: Vcc= 15 V |IOUT 10 k2 R1 Q2 1 k2 R2 QPSK is used to transmit data through a channel that adds Gaussian noise with power spectral density N 0 = 10 -11 V 2 / Hz. What are the values of the quadrature modulated carrier amplitudes required... Redo the derivation of Section 9.1 for the case where the possible transmitted signals are either 0 or A for T seconds. Let the threshold be set at AT / 2. Express your result in terms of signal... (a) Prove that any load line tangent to a power hyperbola makes contact with the hyperbola at the midpoint of the load line. (b) Calculate the maximum possible instantaneous power dissipation in Q 1... A receiver for base band digital data has a threshold set at instead of zero. Rederive (9.8), (9.9), and (9.11) taking this into account. If P(+A) = P(-A) = 1/2, find E b / N 0 in decibels as a... Calculate the incremental slope of the transfer characteristic of the circuit of Problem 5.1 at the quiescent point and at the extremes of the signal swing with a peak sinusoidal output of 1 V and R... The circuit of Fig. 5.10 has V CC = 15 V, R L = 2 kΩ, V BE(on) = 0.6 V, and V CE(sat) = 0.2 V. (a) Sketch the transfer characteristic from V i to V o assuming that the transistors turn on... In the circuit of Fig. 5.13, V CC = 12 V, I Q = 0.1 mA, R L = 1 kΩ, and for all devices I S = 10 15 A, β F = 150. Calculate the value of V i and the current in each device for... For the output stage of Fig. 5.18, assume that V CC = 15 V and for all devices V CE(sat) = 0.2 V, V BE(on) = 0.7 V, and β F = 50. Fig. 5.18: (a) Calculate the maximum positive and... The analysis of a propeller that operates in water at 70F shows that the pressure at the tips of the propeller drops to 0.1 psia at high speeds. Determine if there is a danger of cavitation for this... Using the schematics from Fig. 5.35 and Problem 5.24, design the output stage shown in Fig. 5.32 to satisfy the following requirements. (a) V DD = V SS = 2.5 V. (b) The standby power dissipation... A 0.03-in-diameter glass tube is inserted into kerosene at 68°F. The contact angle of kerosene with a glass surface is 26°. Determine the capillary rise of kerosene in the tube. -0.03 in... An object has density . a. Suppose each of the objects three dimensions is increased by a factor of 2 without changing the material of which the object is made. Will the density change? If so, by... Rank in order, from largest to smallest, the pressures at a, b, and c in FIGURE Q14.2. Explain. f b Once the offset voltage of the differential amplifier in Problem 6.4 is adjusted to zero, the input-referred offset voltage must remain less than 1 mV in magnitude for common-mode input voltages... Consider the differential amplifier shown in Fig. 6.4. Choose values of R 1 and R 2 for which the gain is equal to10 and the magnitude of the dc output voltage is less than or equal to10 mV with V 1... Cylinders A and B have equal heights. Cylinder A is filled with helium gas at 1.0 atm pressure and 0C. The diameter of cylinder B is half that of cylinder A, and cylinder B is filled with glycerin.... a. 50 g of gasoline are mixed with 50 g of water. What is the average density of the mixture? b. 50 cm 3 of gasoline are mixed with 50 cm 3 of water. What is the average density of the mixture
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