Recent content by wu_weidong

Q is the Quality factor, as described here.

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...

Can I please have a bit more hint? The voltage through ZV1, ZV2 and CV is the same (VV), right?

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 +...

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.

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...

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...

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...

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...

Yes, in the Gronwall's inequality.

|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...

Homework Statement Suppose f(t,x) is a continuous vector valued function on \mathbb{R} \times \mathbb{R}^n. If f is locally Lipschitz with respect to x with the property that \|f(t,x)\| \le C \|x\| for some positive constant C > 0, then prove that the maximum interval of the existence of the...

Do I need to find a Lyapunov function?

I rewrote the question in tex. Suppose the function f(t,x) is locally Lipschitz on the domain G \subset \mathbb{R}^2, that is, |f(t,x_1)-f(t,x_2)| \leq k(t) |x_1 - x_2| for all (t, x_1),(t,x_2) \in G. Define I = (a,b) and \phi_1(t) and \phi_2(t) are 2 continuous functions on I. Assume that...

Homework Statement Let a(t), b(t) and c(t) be continuous functions of t over the interval [0,\infty). Assume (x,y) = (\phi(t), \psi(t)) is a solution of the system \dot{x} = -a^2(t)y + b(t), \dot{y} = a^2(t)x + c(t) Show that this solution is stable. The Attempt at a Solution I...