New answers tagged phase-shift
4
votes
How can I mathematically show that multiplication of j will cause a phase shift?
I think that confusion could be related with the two possible methods for representing sinusoidal time varying signals associated with the complex plane:
1. AS COMPLEX NUMBERS
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1
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Why do inductors and capacitors cause phase shifts between current and voltage?
Why do inductors and capacitors cause this phase shift?
Consider this simple circuit.
simulate this circuit – Schematic created using CircuitLab
Figure 1. Capacitor across mains supply.
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0
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How can I mathematically show that multiplication of j will cause a phase shift?
This is where complex numbers in polar form shine. Let \$r\angle\theta\$ represent the number \$ r e^{j \theta} = r (\sin \theta + j \cos \theta)\$. Then \$\left(a \angle \alpha\right) \cdot \left(b \...
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How can I mathematically show that multiplication of j will cause a phase shift?
e^(jθ) = cos(θ) + j sin(θ)
I get -jAsin(wt) = Acos(wt)-Ae^(jw*t)
You might be better off going to
$$ \sin\theta = \frac{e^{j\theta}-e^{-j\theta}}{2j}$$
However this is not going to get you to \$j\...
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How can I mathematically show that multiplication of j will cause a phase shift?
In the complex plane, the unit vector j is expressed in polar coordinates as 1∠90°.
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