Apparent Power and Complex Conjugate Confusion
Apparent Power and Complex Conjugate Confusion
(OP)
Hey all,
I'm trying to make sense of why apparent power is calculated using the complex conjugate of I, and not just regular I. The equations in my textbook go something like this...
P = VI*cos(theta)
Q = VI*sin(theta)
... where theta is the angle of the impedance element, and thus the lead/lag difference between the voltage and current of this system. The text goes on to say...
S = P + jQ
= VI(cos(theta) + jsin(theta))
... then, using Euler's identity...
S = VI*e^(j*theta)
= VI@ angle theta
= VI* {here the * indicates complex conjugate}
It's that last step that is confusing me. How can the angle's polarity just be reversed at the last minute like that?
Thanks for all your help!
I'm trying to make sense of why apparent power is calculated using the complex conjugate of I, and not just regular I. The equations in my textbook go something like this...
P = VI*cos(theta)
Q = VI*sin(theta)
... where theta is the angle of the impedance element, and thus the lead/lag difference between the voltage and current of this system. The text goes on to say...
S = P + jQ
= VI(cos(theta) + jsin(theta))
... then, using Euler's identity...
S = VI*e^(j*theta)
= VI@ angle theta
= VI* {here the * indicates complex conjugate}
It's that last step that is confusing me. How can the angle's polarity just be reversed at the last minute like that?
Thanks for all your help!






RE: Apparent Power and Complex Conjugate Confusion
P = VI*cos(theta)
Q = VI*sin(theta)
(although it should be pointed out P and Q are used in many networks where there is not a single impedance that can be easily associated with P and q).
Since Z = V / I, we know the angle of V minus angle of I is the angle of Z.
i.e. that's what we called theta.
The quantity S = (V I*) has an angle which is the sum of the angle of V and the angle I*.
The angle of I* is the negative of the angle of I.
So the angle of S is the angle of V minus the angle of I. i.e. it is what we called theta.
=====================================
(2B)+(2B)' ?
RE: Apparent Power and Complex Conjugate Confusion
Awesome. This makes sense. Ultimately, apparent power has the same theta at the impedance (even if, as you mentioned, there's no ONE specific impedance element).
Thanks a ton!
Pat
RE: Apparent Power and Complex Conjugate Confusion
RE: Apparent Power and Complex Conjugate Confusion
V= V1 + jV2 and I = I1 +jI2; then average power is algebric sum of the product of the real parts and the product of imaginary parts.
Thus, P = V1I1 + V2I2 in watt
This P may be obtained from the conjugate method of calculating
power. That is,
S = P + jQ = VI* = (V1+jV2)(I1-jI2)
= V1I1 + V2I2 + j (VI2-V1I1) ; real part is P.
RE: Apparent Power and Complex Conjugate Confusion