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Unformatted text preview: and: X = A 2 + B 2 tan φ = sin φ cos φ = B/ A 2 + B 2 A/ A 2 + B 2 = B A (6) That is, the equations in (6) provide the equations to convert from A and B to the amplitude X and phase angle φ . Remarks There are alternate ways to write a sum of harmonics in terms of an amplitude and phase: x(t) = Asin ϖ t + Bcos ϖ t = Xsin ϖ t-ψ ( 29 = Xcos ϖ t +η ( 29 = Xcos ϖ t-γ ( 29 In each case, the amplitude X is the same as given in (6) above. However, the phase angles ψ,η and γ are different from the phase angle φ in (6). As an exercise with this approach, derive the phase angles ψ,η and γ in terms of A and B....
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- Fall '09
- Sin, B-2 Spirit, Bcos ωt