5.00) Please solve it complete, correctly and clear a), b), c), d), e), f) and g
ID: 2085684 • Letter: 5
Question
5.00) Please solve it complete, correctly and clear a), b), c), d), e), f) and g) to avoid disputes, after the professor grades the homework, you will receive multiple thumbs up, if the solution is correct. Thanks.
5. Consider the following expression for the total phasor voltage along a lossless 50-2 transmission line that has polyethylene insulation (Er = 2.25) 7(z ) = 0.80e-jo 48"e-jo 22:-0. I 3ejo 15mejo 22: mV, where z = 0 is the location of the load a. What is the frequency of operation in Hz? b. What is the wavelength in the dielectric? c. What is the complex coefficient, Vo*, of the forward (+z propagating) voltage Wave? d. What is the complex coefficient, lo-, of the reflected (-z propagating) current Wave? e. What is the phasor representation (in polar form, i.e. Amplitude ZPhase°) of the total voltage at the load's location? What is the phasor representation (in polar form) of the total voltage at z =-20 m? g. What is the phase shift between the total voltages calculated in parts e and f? Final answers: a,f=7MHz b.=29 m g. = 1230 or-2370Explanation / Answer
Answer:-a) The total voltage equation gives us the value of wave number or phase constant "beta" = 0.22. But wavelenth "lambda" = 2x3.14 / "beta" = 2x3.14 / 0.22 = 28.55 m. Now velocity of signal in transmission line of dielectric constant 2.25 is = speed of light /(2.25)0.5 = 2 x 108 m/s. Hence frequency = (2 x 108)/28.55 Hz = 7 Mz.
b) As calculated above wavelength = 28.55 m.
c) The complex coefficient of forward propagating voltage can be seen in given total voltage equation and is equal to e-j0.48xpie = sin(0.48*pie) - jcos(0.48*pie) = 0.998 - j0.0627 .
d) The complex coefficient of reflected current is equal to complex coefficient of reflected voltage = e-j0.75xpie = sin(0.75*pie) - jcos(0.75*pie) = 0.707 + j0.707 .
e) Keeping z = 0(since load is at distance z = 0) in the above equation and do the calculations, we get V(t) = 0.7|_3.370 mV.
f) keeping z = -20 in the given equation we get V(t) = 0.78|_23.630 mV.
g) phase difference = 20.260 .
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