Logarithmic functions and polar form of complex numbers
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1/ If the amplitude ratio, N in decibels, of an electrical system is given by the formula.
N = 10log
And the power is given by
P =
Show that for matched input and output resistances the output voltage Vo is related to the input voltage Vi by:
Vo = Vi10
If N is increased by 6db, show that the output voltage is approximately doubled for the same input. Following to polar form giving the arguments in degrees
2/ convert the Following to polar form giving the arguments in degrees:
a/ 4 - j2.4
b/ -5.1 + j1.7.
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Solution Summary
I have answered two questions. One involves the logarithmic formula for amplitude ratio. The other involves the writing of complex numbers and their polar form.
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Answer:
It is given that P = V^2 / R
Let Po = Vo^2 / R and Pi = Vi^2 / R
Substituting in (1),
N = 10 log[(Vo^2 / R) / Vi^2 / R]
N = 10 log[(Vo^2 / Vi^2 ]
N = 10 log (Vo /Vi)^2 = 20 log (Vo/Vi)
N = 20 log ...
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