Phase shift - circuit

[nForce]

Hello,

why do we calculate phase shift between voltage U1 and U2 as an arg, of the circuit:



That rectangle is a resistor. (It's a European symbol)
Those two voltages (U1,U2) are alternating, right? Because there is no phase shift in DC.

Thanks.

[Benta]

Because phase shift is an angle, and Arg(H(jw))) is an angle.

[nForce]

Yes, but there are also other functions, where the result is an angle. I know for the phase shift that it's an angle.

What about this question?:

Those two voltages (U1,U2) are alternating, right? Because there is no phase shift in DC.

[Benta]

It makes no sense to talk about phase shift for DC. Phase shift is only appropriate for AC signals.

Arg(U2/U1) just says that the phase shift is the difference between output phase and input phase.

That being said, I understand your confusion here.
Using capital letters for AC signals is bad style. Correct would be:
Arg(u₂/u₁)

[Mattjd]

something else that should be noted. OP used arg() but then Benta used Arg(), there is a difference.

[Benta]

something else that should be noted. OP used arg() but then Benta used Arg(), there is a difference.

True. I used Arg(), because that was used in the schematic, though for this use, arg() would be correct.
A wonder where that circuit came from? It seems to ignore all conventions.

[Mattjd]

something else that should be noted. OP used arg() but then Benta used Arg(), there is a difference.

True. I used Arg(), because that was used in the schematic, though for this use, arg() would be correct.
A wonder where that circuit came from? It seems to ignore all conventions.

'

I didn't notice the difference between OP and circuit. My point was more to just not mince the two.

arg() is definitely correct. Whether Arg im this case is bounded to a half or full circle is typically defined the by the author. Without knowing the text, we can't know.

[nForce]

So the function arg(), came from electronics and electrical engineering?

[Benta]

So the function arg(), came from electronics and electrical engineering?

No, arg() and Arg() end come from mathematics, specifically complex analysis.

https://en.wikipedia.org/wiki/Argument_(complex_analysis)

[nForce]

I have another question here:

Why don't the arg function take two arguments? Because now it takes only H(jw). But it should be like this Arg(Re(H(jw)),Im(H(jw))).

We don't need the fraction as a whole, but Real and Imaginary part of the H(jw)

[Mattjd]

Look at the definition, it's just the angle from the real axis to the vector representing the transfer function. I'm not sure why you are getting confused.

You do need the fraction as a hole. You need to find the magnitude and then use arctan to find the angle.

[MrAl]

Hello,

why do we calculate phase shift between voltage U1 and U2 as an arg, of the circuit:



That rectangle is a resistor. (It's a European symbol)
Those two voltages (U1,U2) are alternating, right? Because there is no phase shift in DC.

Thanks.

Hi,

Yes when we talk about phase we are talking about AC voltages.  That does not mean there is no DC response though, and we might want to calculate that too, but it will not have a phase shift associated with it like the AC components will.

For your circuit the input output relationship is:
Vout(jw)/Vin(jw)=(R*(R-w^2*C*L*R))/((R-w^2*C*L*R)^2+w^2*L^2)-(j*w*L*R)/((R-w^2*C*L*R)^2+w^2*L^2)

so the imaginary part is:
ip=-(w*L*R)/((R-w^2*C*L*R)^2+w^2*L^2)

and the real part is:
rp=(R*(R-w^2*C*L*R))/((R-w^2*C*L*R)^2+w^2*L^2)

and the best way to calculate the phase shift for the usual analysis is like so:
Ph=atan2(ip,rp)

where atan2() is the two argument inverse tangent function and is defined over the whole 0 to 2pi range.

The two argument atan function figures out the correct sign of the result as it checks the sign according to the  four quadrant possibilities:
+ip,+rp
-ip,+rp
-pi,-rp
+ip,-rp

as well as some limits.