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# Logarithmic functions and polar form of complex numbers

(See attached file for full problem description with proper symbols)

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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.

#### Solution Preview

Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.
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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 ...

#### 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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