# Recent content by wu_weidong

1. ### Calculate attenuation constant of an aperture

Homework Statement The shielding efficiency of an aperture depends on e−αd, where α is the frequency-dependent attenuation constant of the aperture and d is the thickness of the material (or the cutoff waveguide) at frequencies below cutoff. where ωc=2πfc. Calculate α for an air-vent...
2. ### Estimating loss-limited transmission distance

Q is the Quality factor, as described here.
3. ### Estimating loss-limited transmission distance

Homework Statement A high-speed optical data communication system is composed of a transmitter, an unamplified transmission fiber link, and a receiver. The optical transmitter generates a 10-Gb/s non-return-to-zero (NRZ) signal using a 1550-nm laser diode (linewidth=2 MHz) followed by a...
4. ### Solving voltage divider involving capacitors

Can I please have a bit more hint? The voltage through ZV1, ZV2 and CV is the same (VV), right?
5. ### Solving voltage divider involving capacitors

Homework Statement Given ZV1 = ZV2 = 100Ω, ZCCV = ZCV = 2000/j = -2000j, and VV/VC = 0.04789. I'm trying to get the given VV/VC result. Homework Equations I know that 1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV VV = ZV / (ZV + ZCCV) * VC The Attempt at a Solution 1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV = 1/100 +...
6. ### Cable-to-cable crosstalk (Capacitative Coupling)

ZV is close to 2K ohms? Why is that? I thought the combined resistance ZV is calculated as ZV = [1/100 + 2000 + 1/100]-1 = 0.0005 if CV = CCV. This gives me the voltage divider ZV / (ZV + [jwCCV]-1) = 0.005/(0.005 + 2000) = 2.5 * 10-7, which doesn't give me the CCC value of -26.4dB.
7. ### Cable-to-cable crosstalk (Capacitative Coupling)

Homework Statement Compute the cable-to-cable crosstalk due to capacitive coupling in a harness between two cable pairs having an average separation distance of 3 mm and a 10 m in a cable tray. The cable diameters are 1 mm and both cables are operating at a 100 ohm impedance level. Assume h = 5...
8. ### Deriving relationship between LVDT and mass spring damper

Homework Statement [/B] I have this system below. It is the schematic of a linear accelerometer moving horizontally, where m is the total mass of the slide, b denotes the viscous damping, and k represents the spring constant. The relative position between the moving mass and the case is...
9. ### Derive a third order accurate scheme

Homework Statement Hi all, I need help with deriving a third order accurate scheme for the inhomogeneous equation u_t + a u_x = f based on the approach used to derive the Lax-Wendroff scheme, that is, replacing the time derivatives of u by space derivatives of u. The Attempt at a...
10. ### Accuracy of finding eigenvalues of defective matrix

Homework Statement Hi all, I need help with determining the accuracy of finding eigenvalues of defective matrix. The question asks: When a matrix has a defective eigenvalue, the condition number for computing its eigenvalues is infinity. Does this mean that these eigenvalues cannot be...
11. ### Determining critical points

Homework Statement Consider the plane dynamic system \dot{x} = P(x,y), \dot{y} = Q(x,y) with the condition that O(0,0) is a critical point. Suppose P(-x,y) = -P(x,y) and Q(-x,y) = Q(x,y). Is the critical point (0,0) a center? Why? The Attempt at a Solution I know that for (0,0) to be a...
12. ### MATLAB Matlab: Solving linear system with QR/Householder

Homework Statement Hi all, I'm trying to implement the QR method for solving the linear system Ax = b. The QR factorization is achieved using Householder method. The Attempt at a Solution The main function is function x = lin_solve(A,b) [R,v] = householder(A); y = Qt_times_b(v,b); x...
13. ### Matrix/Vector differentiation

Homework Statement Hi all, I need help proving the result: Let g(x) = x'Mx, where M is a n-by-n real constant matrix and x' denotes the transpose of vector x. Then the derivative of g(x) = (M + M')x. The Attempt at a Solution I was thinking of using product rule on x'(Mx) to get...
14. ### Lipschitz ODE problem

Yes, in the Gronwall's inequality.
15. ### Lipschitz ODE problem

|E_1(t)| + |E_2(t)| = E(t) Taking Gronwall's inequality, that is, \phi(t) \leq a \int^t_{t_0} \psi(s) \phi(s) \, ds + M,\, \, \, t_0 \leq t \leq t_0 + T gives for t_0 \leq t \leq t_0 + T \phi(t) \leq M e^{a \int^t_{t_0} \psi(s) \, ds} Therefore, taking \delta + E(t) as M...