How to go from step 4 to step 5 in reflection coefficient derivation

[merlyn]

Hi all, Great forum.
I really don't know if this is the proper place for this,
so if it is not please forgive me.

I have been researching reflective coefficients in transmission lines. I understand everything except steps 4 -> 5.
Perhaps it is a lacking in my math skills but could someone show me the steps in getting from 4 to equation 5.

thank you.

Drforbin.

 

[jtbell]

Are you acquainted with the technique of clearing fractions from an equation by using the least common denominator of all the terms?

(This is really an algebra question, so I've moved this thread to General Math.)

 

[merlyn]

You mean rationalizing the fraction ?

 

[Funestis]

Hi all, Great forum.
I really don't know if this is the proper place for this,
so if it is not please forgive me.

I have been researching reflective coefficients in transmission lines. I understand everything except steps 4 -> 5.
Perhaps it is a lacking in my math skills but could someone show me the steps in getting from 4 to equation 5.

thank you.

Drforbin.

Collect all the V+ terms on one side and all the V- terms on the other side of the equation. Then pull the V+ and V- terms out by clearing the fractions like jtbell said, and at that point all that is left to do is cross multiply and cancel your like terms. You'll need to pull out a negative so you end up with the Zl - Zo on top and the Zl + Zo on the bottom.

 

[merlyn]

Hi guys...I actually did this last night.
I think I have it. Here are my notes. I hope this helps anyone else.
Great Thanks to you all again.
This is a great resource for people trying to learn.
Something in short supply these days. At least in the U.S.

Drforbin.

 

[merlyn]

I forgot last step.