Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.
Welcome to our site! Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.
When you have experience with doing time averages and if you remember a key trig identity, you can go from expression 1 to expression 2 in your head, without any work. If you are unable to do that, then you have to formally write out the time average integral, and you will arrive at that result.
To do it in your head, consider the following. The time average of a sum of terms is the sum of the time averages of each term. The term with sin(2wt) is a sine wave with no DC offset, and hence the time average of that part is zero. The terms with cos^2 and sin^2 in them can be handled with a trig identities that say cos^2 and sin^2 are DC shifted cosine waves at twice the frequency. The harmonic variations of a sine or cosine wave always average to the DC value of that sine wave, so you don't need to evaluate any integrals, and the DC components of each term are all that matter.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.