Under the constraint that the filter has only one coefficient co, no that in output simplifies to:= c‘,X,„ find the coefficient co that minimizes the mean-squared error MSE =E((S5— Se).

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Infinite sequence

Let {5,} be an infinite sequence of i.i.d.Al(1, 1) random variables.

Define a new random uquence X, by subtracting 1 from the product of three conucutive Sk values, according to:

X, = S„,S,S,_, —1.

Let  =   be an estimate of &arrived at by passing X, through en LTI filter:

  S,         Al(1, 1)                     X, = Se ,S,S,_,— 1

Under the constraint that the filter has only one coefficient co, no that in output simplifies to:= c‘,X,„ find the coefficient co that minimizes the mean-squared error MSE =E((S5— Se).

Under the constraint that the filter has only two coefficients co and q, so that its output is:

Sk= c„.X, + c,X,_ „

find the coefficients ca, c, that minimize the mean-squared error MSE = Eqk — Se).

In the unconstrained case when there are an infinite number of filter coefficients without any causality comb-ail., no that the filter output is:

the frequency response C(e0) = E,-,o of the filter that minimize MSE =               — V)

can be written as:

A+ Been(e) + Ccos (20)

D + E cos (I)) + Fens (28)

Find numeric values for the constants A, B, C, D, E, and F.

 

Choose a suitable sampling rate (T). Explain why? Compare between the performance of the above controllers in terms of time and frequency characteristics.

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Electrical Engineering

Consider a system described by the transfer function:  where b equals the last two digits of your student number (for example: if your number is 438123456 then b=56).

A) Provide a FULL and comprehensive system analysis of the continues system in both time and frequency domain (unit step time response for k=1: delay time, rise time, settling time, steady state error, maximum overshoot, gain margin, phase margin, etc).

B) Choose a suitable sampling rate (T). Explain why?

C) Obtain the discrete transfer function when the system is preceded by a sampler and zero order hold.

D) Repeat part A) above for the discrete system using bilinear transformation then compare the results of the discrete vs continuous (time and frequency characteristics).

E) Try to improve the speed of the system and the overshoot using the following controllers:

  • ‐phase lag
  • ‐phase lead
  • ‐phase lead‐lag
  • ‐PI
  • ‐PD
  • ‐PID
  • ‐State feedback
  • ‐Output feedback

F) Compare between the performance of the above controllers in terms of time and frequency characteristics.

G) Comment on your results.

 

Find the Freundlich isotherm constants (K and 1/n) for your waste and the carbon you used. Include the isotherm plot you used to determine these values.

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Exercise #4: Activated carbon treatment

  1. Your factory produces a waste containing 1,4 dioxane that you must treat before discharge.

You have decided to use activated carbon for this purpose. You perform laboratory-scale tests to see how well the 1,4 dioxane in your waste will adsorb to the activated carbon you will use. You put 0.5 liters of wastewater containing 2500 mg/L of 1,4 dioxane into 6 separate containers. Each container holds a different amount of carbon (GAC). After equilibrium is established, you measure the 1,4 dioxane concentration that remains in the liquid in each of the containers (Cf). The data you collect are in the table below.

  1. Find the Freundlich isotherm constants (K and 1/n) for your waste and the carbon you used. Include the isotherm plot you used to determine these values. Hint:Use Excel to make a table of your data and follow the methods described in class (and in the text) to make a graph of log(Xeq/M) versus log Ceq.
  1. You produce 8000 L of waste containing 2500 mg/L of 1,4 dioxane each day. You are required to reduce the 1,4 dioxane concentration to 1 mg/L before discharging your waste. How much carbon would need to be used each day to treat your waste?
  1. There are two types of waste: 1) Wastewater with dissolved polychlorinated biphenyls (PCBs), and 2) Wastewater with dissolved heavy metals and particulate matter. For which of these two wastes would activated carbon adsorption be more appropriate? Fully explain why it is more appropriate and why the other waste is less appropriate.
  1. You must deal with wastewater containing two dissolved chemicals. For each case (a and b), determine which chemical will i) adsorb more strongly and ii) which chemical you might expect to see later in the effluent at high concentrations. Fully explain your reasoning. Use the Freundlich parameters provided in the table below.
  1. 2,4 Dichlorophenol and 1,1,2-Trichloroethane
  2. Phenol and Hexachlorocyclopentadiene

Compound 1/n K (mg/g)(C-units)1/n

2,4 dichlorophenol 0.15 157

1,1,2 TCA 0.60 6

hexachlorocyclopentadiene 0.17 370

phenol 0.54 21GAC (mg) Cf (mg/L)

25 2340

100 1940

200 1550

300 1260

400 1060

500 900

 

 

 

Provide a FULL and comprehensive system analysis of the continues system in both time and frequency domain. Choose a suitable sampling rate (T). Explain why?

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Electrical Engineering

Consider a system described by the transfer function: G(s)={k(s+1.5)}/{s^2+(1+b/99)s+4} where b equals the last two digits of your student number (for example: if your number is 438123456 then b=56).

A) Provide a FULL and comprehensive system analysis of the continues system in both time and frequency domain (unit step time response for k=1: delay time, rise time, settling time, steady state error, maximum overshoot, gain margin, phase margin, etc).

B) Choose a suitable sampling rate (T). Explain why?

C) Obtain the discrete transfer function when the system is preceded by a sampler and zero order hold.

D) Repeat part A) above for the discrete system using bilinear transformation then compare the results of the discrete vs continuous (time and frequency characteristics).

E) Try to improve the speed of the system and the overshoot using the following controllers:

  • phase lag
  • phase lead
  • phase lead‐lag
  • PI
  • PD
  • PID
  • State feedback
  • Output feedback

F) Compare between the performance of the above controllers in terms of time and frequency characteristics.

G) Comment on your results.

Using the fully differential amplifier designed above , design a MOSFET-c second order low pass filter with a pole frequency of 2MHz and a dsc gain of 4. Use an integrating capacitor of 5pF and Vc= 3V.

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Electrical Engineering

Assignment1: Advanced Analog Mixed Signal Design MEL ZG 625

  1. For the CMOS operational amplifier shown in calculate the open-loop voltage gain, unity gain bandwidth, and slew rate. Assume that the gate of M9 is connected to the positive power supply and that the W/L of M9 has been chosen to cancel the right half-plane zero. [6]

Show your results with a SPICE simulation.

Assume that Kn= 60.4μA/V2 Kp= 30.2μA/V2 . Leff= L-2Ld- Xd where Ld= 0.3μm & Xd= 1μm 𝜆𝑛 × 𝐿 = 0.2μm/V, 𝜆𝑝 × 𝐿 = 0.1μm/V

Now using this develop a fully differential amplifier and .

There is a LT spice folder uploaded. One can use those circuits to understand the design steps. The design of single stage is already available in book.

 

Assignment1: Advanced Analog Mixed Signal Design MEL ZG 625

  1. Using the fully differential amplifier designed above , design a MOSFET-c second order low pass filter with a pole frequency of 2MHz and a dsc gain of 4. Use an integrating capacitor of 5pF and Vc= 3V.

 

Use the report included with the package to highlight the main issues and executive summary.

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Civil Engineering

Geotechnical Elements: Use the report included with the package to highlight the main issues and executive summary. Maxmume is 2 pages with heighlighting major topices.

 

According to the client, the maximum allowable settlement is 1.00 inch. Determine the predicted settlement for your footing and loading based on both the CPTu and PMT data.

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Civil Engineering

Determine the difference in the predicted settlements based on two approaches. One approach is based on Cone Penetration Testing (CPT) data (Section 9.5 in Text) which was developed by John Schmertmann and the other is based on Pressuremeter (PMT) testing (Section 9.8 in Text) that was developed by Jean-Louis Briaud.

Testing was conducted at the location shown in the Google Earth Image given below.

The CPTu or Piezocone (i.e., cone tests with pore water pressures measured) data from a 2018 sounding 25 feet deep in the former Olin Engineering Overflow parking lot is included at the end of this file. This sounding was performed by Jim Handley of the In-situ Group in Sebastian Florida. Note the corrected cone resistance (Qt) and corrected friction resistance (Lf) are used to calculate the friction ratio in % using Lf /Qt*100.

The PMT data from two separate PMT tests (one at 5 feet and the second at 17 feet) are included in this Canvas Folder. These tests include an unload-reload loop, which is performed by unloading from the existing pressure within the linear portion of the curve to ½ that pressure.

They also include unloading data once the maximum volume of water is injected. These two sets of data are highlighted in the spreadsheets. They should be EXCLUDED from your settlement prediction since they were not used in the development of Briaud’s 2007 procedure.

Each student in the class has been assigned the load and footing dimensions shown in the table below. All footings are to be located 3 feet below the ground surface. Assume that the ground water table is at a depth of 5 feet. According to the client, the maximum allowable settlement is 1.00 inch. Determine the predicted settlement for your footing and loading based on both the CPTu and PMT data.

Type up one paragraph (300 words or less) summarizing your findings.

 

How would you consider each one and choose the worst case for analysis and design? You need to consider the LCC for each structural elements.

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Load Calculations and Structural Analysis

For this project, you need :

  1. Rain Loads
  2. Assume the total head of 2”.
  3. Load case combinations (LCC): You must discuss all 6 load cases in the written report to include

How would you consider each one and choose the worst case for analysis and design. You need to consider the LCC for each structural elements.

include steps and references.

 

In LTSpice do a DC operating point simulation (.op) with both inputs connected to ground (i.e., 𝑉𝐶𝑀 = 0 𝑉). Find the simulated DC values for 𝐼𝑅1, 𝐼𝐶3, 𝐼𝐶4, 𝐼𝐶1, 𝐼𝐶2, 𝑉𝐵3, 𝑉𝐸1,2, 𝑉𝑂1, 𝑉𝑂2. Compare them with your hand calculations. Additionally, comment on the matching between 𝐼𝑅1 𝑎𝑛𝑑 𝐼𝐶3 and comment on the theoretical vs. simulated match between 𝐼𝑅1 𝑎𝑛𝑑 𝐼𝐶3.

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Differential Amplifier Design

In this assignment, you will design the microphone pre-amplifier highlighted with red in the block diagram, which is a differential amplifier as shown in the schematics below.

Your design should satisfy the required differential gain, input impedance, single-ended common-mode gain, and the power dissipation specifications provided in Section A below. Then in Sections B and C, you will simulate your circuit on LTSpice to compare the simulation results with hand calculations.

  1. Hand design: Design the bipolar differential amplifier and the current source and bias network

(𝑅1, 𝑄3, 𝑎𝑛𝑑 𝑄4) above such that:

(i) Differential gain: 𝐴𝑑 ≥ 200 𝑉 𝑉,

(ii) Input differential resistance: 𝑅𝑖𝑑 ≥ 50 𝑘Ω,

(iii) 𝐴𝑐𝑚 < 0.1 where 𝐴𝑐𝑚 is the single-ended common-mode gain (the gain to a common-mode input signal when the output is measured not differentially but from one of the outputs with respect to ground).

(iv) To keep the battery discharge lifetime long, the power consumption of the differential amplifier, 𝑃𝑇𝑂𝑇𝐴𝐿, must be less than 2 milliwatts.

Design the circuit with BJTs having 𝛽 = 200, 𝑉𝐴 = 100 𝑉, 𝑎𝑛𝑑 𝑉𝐵𝐸 = ~0.7 𝑉 𝑖𝑛 𝐹𝑜𝑟𝑤𝑎𝑟𝑑 𝐴𝑐𝑡𝑖𝑣𝑒. Use +𝑉𝐷𝐷 = 9 𝑉 and −𝑉𝑆𝑆 = −9 𝑉. Clearly show your steps.

Design Suggestion for Part A.

  1. Derive the expression for 𝑅𝑖𝑑 (ignore 𝑟𝑜 of Q1 and Q2.). Replace the small signal parameter(s) with “dc currents”, “resistors”, “𝑉𝑡ℎ”, “𝛽”, “𝑉𝐴”, etc. and simplify the expressions to the extent possible (e.g., manipulate the expressions and then replace 𝑉𝐴 = 100 𝑉, 𝛽 = 200, etc.). The 𝑅𝑖𝑑 design specification will let you find an upper limit for Q1 (and Q2) dc collector current, 𝐼𝐶1(= 𝐼𝐶2).
  1. The total power dissipation is 𝑃𝑇𝑂𝑇𝐴𝐿 = 𝑃𝑉𝐷𝐷 + 𝑃𝑉𝑆𝑆 = 9𝑉 ∗ (𝐼𝑉𝐷𝐷 + 𝐼𝑉𝑆𝑆). Here, 𝐼𝑉𝐷𝐷 is the sum of all dc currents leaving the +𝑉𝐷𝐷 and 𝐼𝑉𝑆𝑆 is the sum of all dc currents entering the −𝑉𝑆𝑆. In 𝑃𝑇𝑂𝑇𝐴𝐿 write 𝐼𝑉𝐷𝐷 and 𝐼𝑉𝑆𝑆 in terms of Q1 (or Q2) collector currents (ignore the current on the reference current generation branch formed by 𝑅1 and 𝑄4). The 𝑃𝑇𝑂𝑇𝐴𝐿 design specification will let you find another upper limit for 𝐼𝐶1(= 𝐼𝐶2).
  1. Derive the expressions for 𝐴𝑑 and 𝐴𝑐𝑚. (When deriving 𝐴𝑑, include 𝑟𝑜 of Q1 or Q2. When deriving 𝐴𝑐𝑚 ignore 𝑟𝑜 of Q1 and Q2 but include 𝑟𝑜 of Q3.). Replace the small signal parameter(s) with “dc currents”, “resistors”, “𝑉𝑡ℎ”, “𝛽”, “𝑉𝐴”, etc. and simplify the expressions to the extent possible (e.g., manipulate the expressions and then replace 𝑉𝐴 = 100 𝑉, 𝛽 = 200, etc.). The 𝐴𝑑 and 𝐴𝑐𝑚 design specifications will let you respectively find lower and upper limits for the product 𝑅𝐶 ∗ 𝐼𝐶1.
  1. Consider the forward-active region requirement of Q1 (or Q2). For 𝑉𝐶𝑀 = 0 𝑉, find another upper limit for the product 𝑅𝐶 ∗ 𝐼𝐶1.
  1. Consider the upper limits for 𝐼𝐶1 to pick an 𝐼𝐶1. Find 𝑅1 based on the value you pick for 𝐼𝐶1. Then use the upper and lower limits for 𝑅𝐶 ∗ 𝐼𝐶1 to pick 𝑅𝐶. In your simulations, use the BJT model 2N2222 of NXP, which has a SPICE model as below with 𝑉𝐴 and 𝛽 highlighted:

 

  1. DC Analysis: In LTSpice do a DC operating point simulation (.op) with both inputs connected to ground (i.e., 𝑉𝐶𝑀 = 0 𝑉). Find the simulated DC values for 𝐼𝑅1, 𝐼𝐶3, 𝐼𝐶4, 𝐼𝐶1, 𝐼𝐶2, 𝑉𝐵3, 𝑉𝐸1,2, 𝑉𝑂1, 𝑉𝑂2. Compare them with your hand calculations. Additionally, comment on the matching between 𝐼𝑅1 𝑎𝑛𝑑 𝐼𝐶3 and comment on the theoretical vs. simulated match between 𝐼𝑅1 𝑎𝑛𝑑 𝐼𝐶3.
  1. Transient Analysis: In LTSpice do a transient simulation (.tran) for 100 ms.

For differential small-signal input simulations:

Apply 𝑣𝑖𝑑 = 1 𝑚𝑉𝑝 𝑠𝑖𝑛𝑢𝑠𝑜𝑖𝑑𝑎𝑙 𝑠𝑖𝑔𝑛𝑎𝑙 𝑎𝑡 100 𝐻𝑧. [i.e., 𝑣𝑖𝑑1 = + 𝑣𝑖𝑑 2 = 0.5 𝑚𝑉 sin (2 ∗ 𝜋 ∗ 100𝐻𝑧 ∗ 𝑡) and 𝑣𝑖𝑑2 = − 𝑣𝑖𝑑 2 = 0.5 𝑚𝑉 sin ((2 ∗ 𝜋 ∗ 100𝐻𝑧 ∗ 𝑡) + 𝜋) with DC offset = 0V. ]

For common-mode small-signal input simulations:

Apply 𝑣𝑐𝑚 = 1 𝑚𝑉𝑝 𝑠𝑖𝑛𝑢𝑠𝑜𝑖𝑑𝑎𝑙 𝑠𝑖𝑔𝑛𝑎𝑙 𝑎𝑡 100 𝐻𝑧. [i.e., 𝑣𝑖𝑐𝑚1 = 𝑣𝑖𝑐𝑚2 = 𝑣𝑐𝑚 = 1 𝑚𝑉 sin (2 ∗ 𝜋 ∗ 100𝐻𝑧 ∗ 𝑡) with DC offset = 0V.]

  1. For the differential small-signal input, what is the expected emitter voltage of Q1 and Q2, 𝑣𝑒1(= 𝑣𝑒2)? Plot the simulated waveform. What is the simulated value of 𝑣𝑒1(= 𝑣𝑒2)?
  1. Plot 𝑣𝑖𝑑, 𝑣𝑜𝑑(𝑣𝑜𝑑 = 𝑣𝑜2 − 𝑣𝑜1), 𝑎𝑛𝑑 𝑖𝑖𝑑. Note that 𝑖𝑖𝑑 is the base current of Q1 (𝑖𝑖𝑑 = 𝑖𝑏1). Calculate the simulated 𝐴𝑑 = 𝑣𝑜𝑑/𝑣𝑖𝑑 and 𝑅𝑖𝑑 = 𝑣𝑖𝑑/𝑖𝑖𝑑. Compare the values with your design targets.
  1. If the simulation results do not match the design constraints, tune your circuit to achieve the goals.
  1. For the common-mode small-signal input, plot 𝑣𝑐𝑚 and 𝑣𝑜𝑐𝑚. (𝑣𝑜𝑐𝑚 = 𝑣𝑜𝑐𝑚2 = 𝑣𝑜𝑐𝑚1 𝑤ℎ𝑒𝑛 𝑡ℎ𝑒 𝑖𝑛𝑝𝑢𝑡 𝑖𝑠 𝑎 𝑐𝑜𝑚𝑚𝑜𝑛 − 𝑚𝑜𝑑𝑒 𝑠𝑖𝑔𝑛𝑎𝑙)

 

A 2 m wide continuous foundation is placed at I m depth within a 1.5 m thick sand layer (4)’ = 30°, y = 18 kN/m’) that is underlain by a weaker clay layer (undrained shear strength = 27 MVOs’ y = 19.5 kNinf). What would be the maximum wall load allowed with es = 4?

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Civil Engineering

Problem 1. A 2m x 3m foundation shown below is subjected to the loads indicated. Determine the factor of safety using Merrhors effective area method.

Problem 2; A 2.0 m wide continuous foundation is placed at 1.5 m depth in a saturated clay where c, = 40 kbUm’ and y = 17 kN/m’. At 2.0 m below the ground level, this clay layer is underlain by a stiffer clay where s = 60 kN/m• and y = 18 kN/m’. What would be the maximum wall load allowed with ES — 4? Use Eq. 7.11.

Problem 3; A 2 m wide continuous foundation is placed at I m depth within a 1.5 m thick sand layer (4)’ = 30°, y = 18 kN/m’) that is underlain by a weaker clay layer (undrained shear strength = 27 MVOs’ y = 19.5 kNinf). What would be the maximum wall load allowed with es = 4?

Problem 4; A square foundation of B =4 m applies a uniform pressure of 17.5 kblins’ to the underlaying ground. Determine the vertical stress increase using at a depth of lin below the center using: a) 2:1 method b) m and n method (Table 8.5) c) Stress isobars (Figure 8.10) d) Newmark Method (See powcrpoint for chart)

Problem 5; B 6fi CUE 211 E D 0 411 A 411 Using the m and n method and Table 8.5 find the change in stress I Oft below point 0 below with a load of 2I6kips applied

Problem 6

Problem 6 Design a square foundation to be embedded 3ft in the sand layer at a site with a soil profile as shown in Figure below, to support load of 50 kips. The design criteria are FS=3and maximum tolerable settlement is 1 in.

2m(610

Sand 3 m (10 It) Tnaxial tests- o„. 37′, y = 16 5 ktilm3 (105 pd). 17 kNim3 (108 Pd). = 45 MPa (940 ks1). V=0.3

Stitt clay 2,6ftt Triax(al test 4„ = 60 kPa (1250psf). or = E„ = 40 MPa (835 ks15. v’= 0.35. Consoldation tests: OCR = 5. C, = 0.3, C, = 0.05 Phys.’ tests = = 35ao, G, = 2.7

13 m (40 ft) Dense gravel N. 52 (average)