How to find steady state response

[love_electronic]

Hi
I want to know how the terms in red block are solved.
I know that e^jwt=cos(wt)+j*sin(wt)
how to solve j term in j*sin(wt)?

 

[Ratchit]

Well, Exp(0.2 i) = cos(0.2)+sin(0.2) i = 0.980067 + 0.198669 i , right? Then subtract 0.1 to get 0.880067 + 0.198669 i . Next subtract 0.5 from 0.980067 + 0.198669 i to get 0.480067 + 0.198669 i. Then multiply (0.880067 + 0.198669 i) by (0.480067 + 0.198669 i) to get 0.383021 + 0.270217 i . The reciprocal is 1.74321 - 1.22981 i and the absolute is 2.13335 . Multiply by 3 gives 6.40006 . The argument of (1.74321 - 1.22981 i) is -0.6144. Easy, right?

Ratch

 

[MrAl]

Hi,

Convert that expression into R+I*j using two applications of your known conversion to sin and cos, then multiply the denominator of the fraction by the complex conjugate of what you find. That gives you a form that looks like N/D where N might be complex and D is always real, then dividing each part of N by D you get a single complex number in the form Real+Imag*j. The complex absolute value is the front multiplier, and the complex part is inside the cos() function, then use the two argument inverse tangent function to get the phase shift from that complex part (dont use the single argument inverse tangent function).

 

[love_electronic]

thanks ratchit and mral, but i have a confusion about reciprocal and absolute values. reciprocal is 1/(any number) right? 1/0.383021 is 2.610822 but how 1.74321 comes?
and how to find out absolute value?

 

[Ratchit]

thanks ratchit and mral, but i have a confusion about reciprocal and absolute values. reciprocal is 1/(any number) right? 1/0.383021 is 2.610822 but how 1.74321 comes?
and how to find out absolute value?

You need to get up to speed on "complex arithmetic". This is one site that explains it. There are many others and textbooks. You won't get far in electronics without becoming proficient in complex numbers.
https://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/

Ratch

 

[love_electronic]

i get the results

 

[love_electronic]

kindly tell me about the argument (1.74321 - 1.22981 i) is -0.6144 "Ratchit"

 

[love_electronic]

i have solve one problem Ratchit.kindly tell me if this is right? also how to solve the angle portion?

 

[Ratchit]

kindly tell me about the argument (1.74321 - 1.22981 i) is -0.6144 "Ratchit"

Why don't you Google for "complex argument" and get https://www.mathcentre.ac.uk/resources/sigma complex number leaflets/sigma-complex9-2009-1.pdf ?

Ratch

 

[Ratchit]

i have solve one problem Ratchit.kindly tell me if this is right? also how to solve the angle portion?View attachment 85955

Now that you read the link describing what the argument is, you should get -0.241806 radians. The modulus or absolute value looks correct. I would advise you to Google more. The gurus here don't like simple basic questions, only hard ones.

Ratch

 

[MrAl]

Hello again,

To get the phase angle you could use the two argument inverse tangent function as i pointed out previously.

The phase angle is (note the two arguments not one):
Theta=atan(ImagPart,RealPart)

If you have difficulty with this let us know, and there are other ways to do this too.