Hi,
I am reading this thread: http://forum.allaboutcircuits.com/showthread.php?t=68238 and I am confused how can we use the WBahn's method in the RC circuit.
v(t) = V*cos(wt+phi) = Re{[V*e^(j*phi)]*e^(jwt)}
Then what step I have to do next?
Here is the method that WBahn mentioned:http://forum.allaboutcircuits.com/showpost.php?p=471718&postcount=8
Let's assume that I have a linear circuit (resistors, inductors, and capacitors along with some simple voltage and current sources) and all of my sources are putting out steady sinusoidal voltages/currents and have been on for a long time (long enough for all of the elements to settle into their steady-state response). Let's focus on one such voltage signal, v(t), which has the form:
v(t) = V*cos(wt+phi)
While it may not be obvious why we would do this, we could express this signal as:
v(t) = V*cos(wt+phi) = Re{[V*e^(j*phi)]*e^(jwt)}
The factor V*e^(j*phi) is what you are used to working with as the "phasor" for this voltage when working with complex impedances. While very hand-wavy, this expression represents the transformation between the time domain and the complex frequency domain and back. In the complex frequency domain, everything has the frequency exponential factor, e^(jwt), multiplying it, so we simply divide it out and work with the phasors to get an answer and then multiply by the frequency exponential factor again and take the real part to get our final time-domain answer. Again, the steps involved in going from the time domain equation to the phasor representation is so simple that we usually do it by inspection.
I am reading this thread: http://forum.allaboutcircuits.com/showthread.php?t=68238 and I am confused how can we use the WBahn's method in the RC circuit.
v(t) = V*cos(wt+phi) = Re{[V*e^(j*phi)]*e^(jwt)}
Then what step I have to do next?
Here is the method that WBahn mentioned:http://forum.allaboutcircuits.com/showpost.php?p=471718&postcount=8
Let's assume that I have a linear circuit (resistors, inductors, and capacitors along with some simple voltage and current sources) and all of my sources are putting out steady sinusoidal voltages/currents and have been on for a long time (long enough for all of the elements to settle into their steady-state response). Let's focus on one such voltage signal, v(t), which has the form:
v(t) = V*cos(wt+phi)
While it may not be obvious why we would do this, we could express this signal as:
v(t) = V*cos(wt+phi) = Re{[V*e^(j*phi)]*e^(jwt)}
The factor V*e^(j*phi) is what you are used to working with as the "phasor" for this voltage when working with complex impedances. While very hand-wavy, this expression represents the transformation between the time domain and the complex frequency domain and back. In the complex frequency domain, everything has the frequency exponential factor, e^(jwt), multiplying it, so we simply divide it out and work with the phasors to get an answer and then multiply by the frequency exponential factor again and take the real part to get our final time-domain answer. Again, the steps involved in going from the time domain equation to the phasor representation is so simple that we usually do it by inspection.
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