Solving this partial fraction - phasors

In summary, partial fraction decomposition is a method used to break down rational functions into simpler fractions. Phasors, which represent complex numbers in magnitude and phase angle, can be used to simplify and solve complex integrals involving trigonometric functions in the context of partial fraction decomposition. They offer advantages such as quicker and easier solution of integrals and visualization of signal and circuit behavior in the frequency domain. However, phasors have limitations in that they can only be used for linear systems and may not accurately capture transient behavior.
  • #1
katta002
5
0
I'm having some difficulty Solving this partial fraction:

(3.84e7)/(s(s^2+6.4e4s+1.6e9))= (3.84e7)/(s(s-3.2e4+j2.4e4)(s-3.2e4-j2.4e4)

how do u find the angle?
I know the equation but I don't know how to find the B with it conjugate.
eq: 2B/_theta

but I don't know how to find theta and the B. Please can u help me
 
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  • #2


You've got to show us how you started and where you got stuck, then we'll help you.
 

1. What is a partial fraction decomposition?

A partial fraction decomposition is a method used to break down a rational function into smaller, simpler fractions. This is often used in calculus and complex analysis to solve integrals and differential equations.

2. How do phasors relate to partial fraction decomposition?

Phasors are a representation of complex numbers in the form of magnitude and phase angle. They are used in electrical engineering and physics to analyze circuits and signals. In the context of partial fraction decomposition, phasors are used to simplify and solve complex integrals involving trigonometric functions.

3. Can you give an example of solving a partial fraction using phasors?

Sure! Let's say we have the rational function F(x) = (x+2)/(x^2+3x+2). Using partial fraction decomposition, we can rewrite this as F(x) = 1/(x+1) + 1/(x+2). Converting this to phasor form, we get F(x) = 1/(√2e^jπ/4) + 1/(√2e^j3π/4). We can then use the properties of phasors to simplify this expression further.

4. What is the advantage of using phasors in partial fraction decomposition?

Phasors can help us solve complex integrals more quickly and easily by converting them into simpler trigonometric expressions. They also allow us to visualize and understand the behavior of signals and circuits in the frequency domain.

5. Are there any limitations to using phasors in partial fraction decomposition?

One limitation is that phasors can only be used for linear systems, so they may not be suitable for all types of partial fraction decompositions. Additionally, phasors only provide a representation of the steady-state behavior of a system, so they may not capture the transient behavior accurately.

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