For the BJT bias circuit shown, what value of Rc in kilohms is needed to allow the maximum possible peak-to-peak signal swing on the collector without clipping? Use Vcc = 8 V, Vee = −7 V, Vb = −2.1 V, and Re = 4.5 kΩ. Assume that to keep the transistor in the forward-active region, the base-collector junction cannot be forward biased. Use β = 133 and ∣Vbe(on)∣ = 0.7 V. Neglect the effects of base-width modulation.
For the BJT bias circuit shown, what value of Rc in kilohms is needed to allow the maximum possible peak-to-peak signal swing on the collector without clipping? Use Vcc = 12 V, Rb1 = 22.1 kΩ, Rb2 = 26.6 kΩ, and Re = 2.5 kΩ. Assume that to keep the transistor in the forward-active region, the base-collector junction cannot be forward biased. Use β = 46 and |Vbe(on)| = 0.7 V. Neglect the effects of base-width modulation. Answer:
Determine the maximum symmetrical swing at the output when VDD = 5 V and VGG = 3,5 V. The parameters of the transistors are λp = 0, VTP = −1 V, and kp = 1000 μA/V2 a. vopp ≃ 4 V b. vopp ≃ 3 V c. vopp ≃ 2 V d. None e. vopp ≃ 1 V
a. Calculate the sensor initial output value (mi) in Volts(V) if the senor indicates 2.5 V after 30 seconds.
What is the off current, loff, in nanoamps for an NMOS FET at 300∘K when it has Vgs = 0 V ? Assume that this MOSFET has a steep retrograde body doping profile with a maximum depletion region thickness of Wdmax = 41 nm, and an effective oxide thickness, Toxe, of 41 angstroms. Use: W = 3.4 μm, L = 0.9 μm, Vt = 309 mV and kT/q = 26 mV at 300∘K. (Please note that you can enter small numbers in Moodle in exponential format. For example, 0.0021 can be entered as 2.1e−3)
What is the minimum value of Vds that will keep a MOSFET in saturation in millivolts, for an NMOS FET with Vgs = 1044 mV, and Vsb = 0 V ? Neglect the effects of velocity saturation, and assume that this MOSFET has a steep retrograde body doping profile with a maximum depletion region thickness of Wdmax = 71 nm. Use: W = 5.6 μm, L = 0.4 μm, Toxe = 29 angstroms, Vt = 421 mV, and μns = 396 cm∧2 /Vs. Answer:
What is the subthreshold swing, S, in millivolts for a MOSFET at 331∘K ? Assume that this MOSFET has a steep retrograde body doping profile with a maximum depletion region thickness of Wdmax = 58 nm, and an effective oxide thickness, Toxe, of 25 angstroms. Use: kT/q = 26 mV at 300∘K. Answer: The correct answer is: 75
What is the off current, loff, in nanoamps for an NMOS FET at 300∘K when it has Vgs = 0 V ? Assume that this MOSFET has a steep retrograde body doping profile with a maximum depletion region thickness of Wdmax = 50 nm, and an effective oxide thickness, Toxe, of 31 angstroms. Use: W = 9.1 μm, L = 0.9 μm, Vt = 301 mV and kT/q = 26 mV at 300∘K. (Please note that you can enter small numbers in Moodle in exponential format. For example, 0.0021 can be entered as 2.1 e−3 ) Answer: The correct answer is: 0.0583
What is the subthreshold leakage current in nanoamps for a PMOS FET at 300∘K when it has Vgs = −116 mV ? Assume that this MOSFET has a steep retrograde body doping profile with a maximum depletion region thickness of Wdmax = 70 nm, and an effective oxide thickness, Toxe, of 28 angstroms. Use: W = 5.0 μm, L = 0.4 μm, Vt = −371 mV and kT/q = 26 mV at 300∘K. Note that since the answer for this question may be very small, be sure to give your answer to at least 3 significant figures! Answer: Check
What is the off current, loff, in nanoamps for an NMOS FET at 300∘K when it has Vgs = 0V ? Assume that this MOSFET has a steep retrograde body doping profile with a maximum depletion region thickness of Wdmax = 42 nm, and an effective oxide thickness, Toxe, of 32 angstroms. Use: W = 2.3 μm, L = 0.2 μm, Vt = 280 mV and kT/q = 26 mV at 300∘K. (Please note that you can enter small numbers in Moodle in exponential format. For example, 0.0021 can be entered as 2.1 e−3 ) Answer: The correct answer is: 0.179
For an ideal n-channel MOSFET, the drain current equation (ID) is given as below. ID = WμnCox 2L[2(VGS − VT)VDS − VDS2] (0 ≤ VDS ≤ VDS(sat)) (a) Derive the saturation drain voltage (VDS(sat)) as a function of (VGS − VT). (b) Derive the saturation drain current (ID(sat)) as a function of (VGS − VT). (c) For very small VDS, describe how to experimentally determine both parameters, i. e. , (i) electron mobility (μn) and (ii) threshold voltage (VT). (d) Derive the transconductance (gm) at the saturation point as a function of VDS. (e) Assume that this n-channel MOSFET has the following parameters: channel length (L) = 1.25×10−4 cm, electron mobility (μn) = 650 cm2 /V−s, gate oxide (SiO2) capacitance (Cox) = 6.9×10−8 F/cm2, and threshold voltage (VT) = 0.65 V. Determine the channel width (W) such that ID (sat) is 4×10−3 A when VGS = 5 V.
What is the drain current in microamps for a PMOS FET with Vgs = −682 mV, Vds = −780 mV, and Vsb = 0 V ? Include the effects of velocity saturation, and assume that this MOSFET has a steep retrograde body doping profile with a maximum depletion region thickness of Wdmax = 60 nm. Use: W = 4.1 μm, L = 0.4 μm, Toxe = 44 angstroms, Vt = −349 mV, μps = 101 cm^2 /Vs, and Vsat = 6×10^6 cm/s.
An NMOS operating with VGS = 1 V, and Vt = 0.5 V exhibits a linear resistance rDS = 1 kΩ when VDS is very small. What is the value of the current iD obtained when VDS is increased to 0.5 V ? and 1 V ? 0.25 mA, 0.25 mA 0.16 mA, 0.25 mA None of them 0.25 mA, 0.16 mA 0.16 mA, 0.16 mA
The MOSFET in the below circuit has k = 1 mA/V2, Vt = 1 V. In what mode is the MOSFET operating? Saturation Region Active Region Triode Region Cut-off Region None of them
Two electric circuits, represented by boxes A and B, are connected as shown in the figure. The reference direction for the current i in the interconnection and the reference polarity for the voltage v across the interconnection are as shown in Part A Determine the power associated with the box for I = 7 , v = 30 V. Part B State whether the power is flowing from A to B or vice versa. Part C Determine the power associated with the box for I = -8 A, v = -20 V, calculate the power in the interconnection. Part D State whether the power is flowing from A to B or vice versa. Part E Determine the power associated with the box for I = 4 A, v = -55 V. Part F State whether the power is flowing from A to B or vice versa. Part G Determine the power associated with the box for I = - 9 A, v = 40 V, calculate the power in the interconnection. Part H State whether the power is flowing from A to B or vice versa.
Part A - Calculating voltage If it takes E = 38.5 mJ of energy to separate Q = 1.21 C of charge, what is the resultant voltage? Express your answer to two significant figures and include the appropriate units. V = Part B - Calculating energy How much energy does it take to separate Q = 1.06 μC of charge if the voltage is V = 4.1 mV ? Express your answer to four significant figures and include the appropriate units. E = VPart C - Calculating current based on movement of charge If Qr = −3.75 C of charge moves to the right in tr = 0.6 s while Ql = 1600 mC of charge moves to the left in tl = 2.7 s, what is the net current to the right? Express your answer to two significant figures and include the appropriate units. I = Part D - Calculating the number of electrons due to the current How many electrons move past a fixed reference point every t = 2.75 ps if the current is i = 0.3 μA ? Express your answer as an integer.
There is no charge at the upper terminal of the element in (Figure 1) for t < 0. At t = 0 a current of 125 e−2500t mA, where t is in seconds, enters the upper terminal. Figure 1 of 1 Part A Derive the expression for the charge that accumulates at the upper terminal for t > 0. q(t) = 50.0(1 − e−2500t) μC q(t) = 125(1 − e−2500t)C q(t) = 50.0 e−2500t μC q(t) = 125 e−2500t C Part B Find the total charge that accumulates at the upper terminal. Express your answer to three significant figures and include the appropriate units. Part C If the current is stopped at t = 0.4 ms, how much charge has accumulated at the upper terminal? Express your answer to three significant figures and include the appropriate units. q = Value Units
In electronic circuits it is not unusual to encounter currents in the microampere range. Assume a 40 μA current, due to the flow of electrons. Part A What is the average number of electrons per second that flow past a fixed reference cross section that is perpendicular to the direction of flow? Express your answer using two significant figures.
When a car has a dead battery, it can often be started by connecting the battery from another car across its terminals. The positive terminals are connected together as are the negative terminals. The connection is illustrated in (Figure 1). Assume the current i in the figure is measured and found to be 40 A. Figure 1 of 1 Part A Which car has the dead battery? carA car B Part B If this connection is maintained for 1 min, how much energy is transferred to the dead battery? Express your answer to three significant figures and include the appropriate units.
The manufacturer of a 1.5 V D flashlight battery says that the battery will deliver 9 mA for 39 continuous hours. During that time the voltage will drop from 1.5 V to 1.0 V. Assume the drop in voltage is linear with time. Part A How much energy does the battery deliver in this 39 h interval? Express your answer to two significant figures and include the appropriate units.
Problem 1.32 The voltage and power values for each of the elements shown in (Figure 1) are given in the table. Figure 1 of 1 Part A Determine the magnitudes of the total power supplied and the total power absorbed in the circuit. Express your answers using three significant figures separated by a comma. Psup , Pahs = 2.50, 2.50 kW Submit My Answers Give Up Correct Part B Does the interconnection satisfy the power check? Express your answer to three significant figures and include the appropriate units. Part C Find the value of the current ia according to the current direction shown in the figure. Express your answer to three significant figures and include the appropriate units. Submit My Answers Give Up Incorrect; One attempt remaining; Try Again Part D Find the value of the current ib according to the current direction shown in the figure. Express your answer to three significant figures and include the appropriate units. ib = Value Units Submit My Answers Give Up Part E Find the value of the current ic according to the current direction shown in the figure. Express your answer to three significant figures and include the appropriate units. ic = Value Units Submit My Answers Give Up Part F Find the value of the current id according to the current direction shown in the figure. Express your answer to three significant figures and include the appropriate units. id = Value Units Submit My Answers Give Up Part G Find the value of the current ie according to the current direction shown in the figure. Express your answer to three significant figures and include the appropriate units. ie = Value Units Submit My Answers Give Up Part H Find the value of the current if according to the current direction shown in the figure. Express your answer to three significant figures and include the appropriate units. if = Value Units Submit My Answers Give Up Part I Find the value of the current ig according to the current direction shown in the figure. Express your answer to three significant figures and include the appropriate units. ig = Value Units Submit My Answers Give Up
A system has the impulse response of: h[n] = δ[n] + δ[n−1] + δ[n−2] If the following signal is input into this system: x[n] = 1 + cos(23πn+15) Enter the output of this system (y[n]) into the blank space provided (use π = p in equations, e. g. 1+2 cos(0.5 pin ) = 1+2 cos(0.5πn)) y[n] =
A first-order system with impulse response function h(t) = e−t/a is excited by a truncated step function x(t) = {1 0 ≤ t ≤ 2 a0 otherwise , where the time constant a = 2 seconds. Determine the following: a. the system output y(t) by applying the convolution integral analytically. (HINT: Break the integral into two intervals: 0 ≤ t ≤ 2a and t > 2a. ) b. the system output y(t) by numerically convoluting the two functions (e. g. in MATLAB). c. produce a graph (e. g. , in MATLAB) that compares the two solutions. d. interpret your response. Does it make physical sense? Why?
The impulse response h(t), of an LTI system is sketched below. a. Is the system BIB0 stable? b. Find the system output for the unit step input u(t). c. Find the system output for the input x1(t) = e−αtu(t). d. Find the system output for the input x2(t) sketched below.
The impulse response and input signal are given by h(t) = e−atu(t) and x(t) = t(u(t−t1) − u(t−t2)). Obtain the output y(t) = x(t)∗h(t) by using the following methods. (a) Time domain convolution integration (b) Fourier transformation (c) By using y(m+n)(t) = x(m)(t)∗h(n)(t).
Fourier Transforms: Warm up Sketch the graph of f(t) = 1 for (1−T) ≤ t ≤ (1+T) and f(t) = 0 otherwise, as a function of t. Without using tables (i. e. , from first principles) find the Fourier transform of f(t). (4 marks)Fourier Transforms: Warm up Use Time-Frequency Duality to find the Fourier Transform F(ω) of f(t) = 14+t2, Give a clear explanation. (4 marks)Fourier Transforms: Warm up Find the inverse Fourier Transform of F(ω) = 1 (3+jω)(1+jω). a) using partial fractions; b) using the convolution theorem.
( 9 marks total) Consider the Fourier series of the function f(t) = t(u(t+1) − u(t−1)) = {t if −1 < t < 10 otherwise defined on the interval [−2, 2]. (a) Sketch the function f(t) and find the Fourier frequencies ωn. (2 marks) (b) Calculate the Fourier coefficients a0, an, and bn. (5 marks) (c) Write down the resulting Fourier series, substituting in the expressions for the Fourier coefficients. (2 marks)
In problems 1 through 6 , determine the Fourier trigonometric series of each function. f(x) = {1−p < x ≤ 01 /20 < x ≤ p f(x) = {x−2 < x < 02−x0 < x < 2 f(x) = x, −π < x < π f(x) = {x+π−π < x < 0 x−π0 < x < π f(x) = |x|, −π ≤ x ≤ π f(x) = x2, −1 < x ≤ 1
First problem in Fourier series A. Compute the Fourier series for the square wave f(x) = {0, −l < x < 0 l, 0 < x < l B. Use your result to show that π4 = 1 − 13 + 15 − 17 +… = ∑n = 0∞(−1)n 2n+1
Answer following questions accordingly. a) Based on your understanding, discuss the use of Fourier series and Fourier transform in linear time invariant analysis and their relation. b) Determine the complex exponential Fourier series of x(t) given as follow Figure 1 c) Determine the Fourier transform of following continuous signals using analysis equation. i. x(t) = t e−2tu(t) ii. x(t) = e−t cost u(t)
Recall how to determine the impulse response of a system by substituting x(t) = δ(t) and y(t) = T[δ(t)] = h(t). Now, for each of the following LTI system T[ ], determine the impulse response. [5×4 = 20] (a) T[x(t)] = −12 x(t−1)+x(t)+12 x(t+1) (b) T[x(t)] = etx(t−1) (c) T[x(t)] = ∫−12 x(t+1−τ)dτ (d) T[x(t)] = ∫−∞tsin(t−τ)x(τ)dτ
A length- M finite impulse response (FIR) can be described by the input-output relation y[n] = ∑m = 0 M−1 bmx[n−m], where bm are the filter coefficients. The coefficients can be optimized for a variety of applications, which makes FIR filters widely popular in digital signal processing. (a) Show that FIR filters are LTI systems. (b) Find the impulse response of an FIR filter using the input-output relationship above. (c) Use the impulse response to find the output of the system for the input x[n] = δ[n]+4 δ[n−1]+δ[n−2]. (d) Plot the impulse response of the system in MATLAB for M = 4 and bm = (1 /4)m. Using these same parameter values, plot the output obtained from (c) in MATLAB.
(b) The Fourier Sine series of g has Fourier coefficient bn which can be expressed by a sum of two integrals, bn = ∫abg1(x)dx + ∫cdg2(x)dx with a < c. Enter the values [a, b, g1(x)] = [c, d, g2(x)] = Evaluate the integral and find bn = , for n ≥ 1.
The impulse response of a linear time-invariant (LTI) system is given by h(t) = 3 t{u(t) − u(t−4)}. (i) Justify whether the system is memoryless, causal, and stable. (ii) Consider the input signal x(t) = 2 rect(t−2 2), where rect(t) = 1, for −0.5 ≤ t ≤ 0.5; and rect(t) = 0 otherwise. It is passed through the system h(t) to produce the output y(t). Sketch h(t), x(t), and the output signal y(t) of the system, respectively.
If the impulse response of a linear time-invariant system is e−tu(t + 1), then which of the following most accurately resembles the output of the system when the input is δ(t+1) − δ(t−1) ? (a) (b)
For the waveform shown in Fig. 2. a. Express g(t) as a Fourier series. b. If f(t) in Problem 1 represents the voltage of a voltage source and g(t) represents the current supplied by this source, find the average power delivered by this source {use 3 harmonics for your calculation}
30 points. Determine the impulse response and frequency response of the system defined by the difference equation y[n] = ay[n−1] + x[n−1] assuming |a| < 1. Your answers will be a function of a. 3.30 points. Suppose you have an LTI system with impulse response h[n] = {1 n = −1, 0, 10 otherwise (a) Determine whether this LTI system is causal and/or stable. (b) Determine the output of this system to the input x[n] = cos(2πn/3 + π/6) for all n.
In this question we will compute the Fourier transforms of specific functions. (a) (25 marks) Compute the Fourier transform for the function f(x) = {e−iax, −2π ≤ x ≤ 2π 0, otherwise (b) (25 marks) Compute the Fourier transform for the function f(x) = {|x|, x∈[−2, 2] 0, otherwise
3.41. In Figure P3.41-1, h[n] is the impulse response of the LTI system within the inner box. The input to system h[n] is v[n], and the output is w[n]. The z-transform of h[n], H(z), exists in the following region of convergence: . 0 < rmin < |z| < rmax < ∞. (a) Can the LTI system with impulse response h[n] be BIBO stable? If so, determine inequality constraints on rmin and rmax such that it is stable. If not, briefly explain why. (b) Is the overall system (in the large box, with input x[n] and output y[n] ) LTI? If so, find its impulse response g[n]. If not, briefly explain why. (c) Can the overall system be BIBO stable? If so, determine inequality constraints relating α, rmin, and rmax such that it is stable. If not, briefly explain why. Figure P3.41-1
The impulse response h[n] for an FIR filter is h[n] = δ[n] + 0.5 δ[n−2] + 0.25 δ[n−3]. (a) Write the difference equation for the FIR filter. (b) Give the implementation as a block diagram in direct form.
Use the definition to calculate the Fourier transformation of the following message signal, m(t). It can be expressed as, 1 j2πf (sinc(f)cos(πf) − 1).
Consider a linear, time-invariant system that has an impulse response of: {h[n]} = 12{δ[n−1]} + 12{δ[n+1]} a. Is the system causal? b. Is the system Bounded-input/Bounded-output stable? c. If the input signal is given by {f[n]} = 2{δ[n]} + {δ[n−1]} − {δ[n−2]} calculate and sketch the resulting output signal. d. What are the numerical values of the frequency response of the system at ω = 0 and ω = π?
The exponential Fourier series coefficients of a signal x(t) are given below This implies that the Fourier series coefficients are defined as |Dn|ej∠Dn (a) Find the exponential series representing x(t). (b) In MATLAB, plot the trigonometric Fourier spectra for x(t), and include the plot here. (c) Find the trigonometric Fourier series representing x(t). (d) Show that the two series are equivalent.
(12 points) LTI Systems and impulse response Consider the following three LTI systems:S1: y(t) = ∫−∞te−3(t−τ)x(τ)dτ S2: y(t) = ∫−∞t−2 x(τ)dτ S3 is characterized by its impulse response: h3(t) = δ(t−3). (a) (4 points) Compute the impulse response h1(t) of S1. (b) (2 points) Define w(t) = S1[x(t)]− S3{S2[x(t)]}. Represent this relationship using a block diagram where x(t) is the input and w(t) is the output. (c) (2 points) Determine the impulse response heq(t) of the above system. (d) (4 points) Determine the response of the overall system to δ(t)+2 δ(t−3).
Problem 4: Fourier Series [24 points] (a) (6 points) Obtain the Fourier series of the signal x(t) given in Figure 3. Using numerical solvers (like Wolfram alpha), sketch the synthesis equation of the Fourier series and see if it gives the same sketch as in Figure 3. Figure 3: Figure for Question 4 part (a) (b) (6 points) Consider a signal g(t) = t2 over the interval (−1, 1) which repeats its self with a period T = 4. Find the trigonometric Fourier Series to represent g(t). Sketch the Fourier Series over frequency. (c)(6 points) Verify Parseval's Theorem for this case given that ∑n = 1∞1 n4 = π490 (d) (6 points) Determine the periodic signal x(t) of period T = 4 whose Fourier series coefficients are given below cn = {jn|n| < 30 otherwise