<Dl> <Dd> P avg = 1 n ∑ k = 1 n V (k) I (k) (\ displaystyle P_ (\ text (avg)) = (\ frac (1) (n)) \ sum _ (k = 1) ^ (n) V (k) I (k)) </Dd> </Dl> <Dd> P avg = 1 n ∑ k = 1 n V (k) I (k) (\ displaystyle P_ (\ text (avg)) = (\ frac (1) (n)) \ sum _ (k = 1) ^ (n) V (k) I (k)) </Dd> <P> Since an RMS value can be calculated for any waveform, apparent power can be calculated from this . For active power it would at first appear that we would have to calculate many product terms and average all of them . However, if we look at one of these product terms in more detail we come to a very interesting result . </P> <Dl> <Dd> A cos ⁡ (ω 1 t + k 1) cos ⁡ (ω 2 t + k 2) = A 2 cos ⁡ ((ω 1 t + k 1) + (ω 2 t + k 2)) + A 2 cos ⁡ ((ω 1 t + k 1) − (ω 2 t + k 2)) = A 2 cos ⁡ ((ω 1 + ω 2) t + k 1 + k 2) + A 2 cos ⁡ ((ω 1 − ω 2) t + k 1 − k 2) (\ displaystyle (\ begin (aligned) &A \ cos (\ omega _ (1) t + k_ (1)) \ cos (\ omega _ (2) t + k_ (2)) \ \ = () & (\ frac (A) (2)) \ cos \ left (\ left (\ omega _ (1) t + k_ (1) \ right) + \ left (\ omega _ (2) t + k_ (2) \ right) \ right) + (\ frac (A) (2)) \ cos \ left (\ left (\ omega _ (1) t + k_ (1) \ right) - \ left (\ omega _ (2) t + k_ (2) \ right) \ right) \ \ = () & (\ frac (A) (2)) \ cos \ left (\ left (\ omega _ (1) + \ omega _ (2) \ right) t + k_ (1) + k_ (2) \ right) + (\ frac (A) (2)) \ cos \ left (\ left (\ omega _ (1) - \ omega _ (2) \ right) t + k_ (1) - k_ (2) \ right) \ end (aligned))) </Dd> </Dl>

Whats the ideal quality factor (q) for ac to dc conversion