Please answer this, need this in the next couple of hours, thanks. The design ch
ID: 1799156 • Letter: P
Question
Please answer this, need this in the next couple of hours, thanks.
The design challenge is to modified the RLC characteristic of the transmission line to achieve good sending end to receiving end performance for "0" to "1" transition. A 'good performance' for this problem means t when the sending end goes high (switch up(l)) the receiving end voltage crosses 90% of its final value as quickly as possible (minimum rise time), and does not go back under 90% of its final value after crossing the transmission line. A critically damped circuit will neither overshoot nor ringing, and will approach the final signal value at the receiver faster than an overdamped circuit. A more aggressive design might allow a small amount of ringing in exchange for faster rise time, but for this design problem, critically damped is desired. Determine resistance value to be added to the transmission line.Explanation / Answer
d^2 (i)/dt^2 + (R/L)di/dt + (1/LC)i = 0
response is over damped,,, so the roots are real and unequal
D1,D2 = (-R/2L)(+/-)(SQRT((R/2L)^2 - (1/LC)))
K1= -R/2L ; K2 = SQRT((R/2L)^2 - (1/LC))
D1=K1+K2;D2=K1-K2
i =c1 e^(K1+K2)t + c2 e^(K1-K2)t
for a critically damped circuit, roots are equal,
i = e^(K1t) (c1+c2t)
K1 = -350/(2x9x10^(3)) = -0.0194
roots are equal
so -0.0194 = SQRT((R/2L)^2 - (1/LCR1)
solve for R1 = 195028.08ohms is the required answer