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Stability of the discretized wave equation. Analyze the stability of the algorithm presented in Problem 3.4 using the von Neumann method. (This will require some steps similar to the leapfrog algorithm.) Does the stability criterion derived here agree with the results of Problem 3.4? 5.6. Stability in the FDTD method. Write a 1D FDTD simulation 400 grid cells long for a wavelength of 1 m, with ?x = λ0/20. Launch a Gaussian pulse from the left end of the space with the same parameters as Problem 5.4 above. Now, increase ?t very slightly to excite an instability, similar to Figure 5.4. Can you measure the growth rate of this instability? Does this growth rate agree with q from Equation (5.14)? 5.7. Stability in the 2D FDTD method. Write a 2D TM mode FDTD simulation that is 100 grid cells in the y-dimension and 500 cells in the x-dimension. Use PEC at the far right boundary; at the top and bottom boundaries, set .,
replace the unknown fields with their counterparts on the opposite boundary. This is called a periodic boundary condition, which we will study in Chapter 12. Launch a plane wave from the leftmost boundary at a frequency suitable to the grid cell size. Now, investigate the stability of this problem by varying ?t; how large can you make ?t before the simulation goes unstable? Can you surpass the CFL condition? Why or why not?
Show the Examples of element characteristics: - Strain gauge, Copper-constantan thermocouple, Accelerometer.
Two charged, parallel, flat conducting surfaces are spaced d = 2.10 cm apart and produce a potential difference ΔV = 500 V between them. An electron is projected from one surface directly toward the second.
Calculate the converter voltage VC1, reactive power, the converter phase current and modulation index.
A person has a problem with hum in a home stereo system and discovers that by disconnecting the ac power, green wire, ground to the amplifier the hum goes away. Why is this not an acceptable solution to the problem?
If an RC circuit is supplied with 24 VDC and the circuit is in its third time constant, how much voltage wouldbe present across the capacitor
The 300-kg block is acted upon by a force P, pulling it as shown. P makes an angle of 36o with the horizontal. If the coefficient of sliding friction between the block and the floor is 0.35, determine the force required to start moving the block.
While in principle it is feasible for business schools to write explicit pay-for performance contracts with professors, this is rarely done
A microwave transmitter has an output of 0.1W at 2GHz. Assume that this transmitter is used in a microwave communication system where the transmitting and recieving antennas are parabolas, each 1.2m in diameter.
Calculate the potential of the outer shell when charge Q is put on it and the inner shell is grounded.
Consider the circuit below containing two ideal (i.e., zero forward voltage drop) Zener diodes whose breakdown voltage is specified. Sketch the transfer characteristic (Vout vs. Vin) between -10V
A measurement of the closed-loop gain of an amplifier shows it to be -25 VN at 120 kHz and -100 VN at S kHz. Estimate the closed-loop gain at low frequencies and the corresponding 3 dB frequency. What is f, for the op amp used? (Bc careful!)
Design the counter using D-flip-flops such that the state codes are the output values of the circuit. For example, when the circuit is in state 011, the output LED's display "off" "on" "on". Thus, no output equations need to be designed.
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