Phase relationship at high frequencies

In summary: However, you should assume that frequencies higher than the cutoff frequency are not considered.That is a good question, because it never will actually get to -180 degrees. It approaches that at very high frequencies (much higher than the cutoff). Wolfram Alpha has a nice tool (search for Bode Plot) and you can type in the transfer function and see both the gain plots and phase plots. However, you should assume that frequencies higher than the cutoff frequency are not considered.
  • #1
roinujo1
41
1

Homework Statement


Given the transfer function:
upload_2017-5-7_10-37-25.png


Find the phase relationship between the input and output voltage at high frequencies

Homework Equations


NA

The Attempt at a Solution


My approach was to find the phase of the transfer function, which I got to be:
upload_2017-5-7_10-38-45.png

I assumed that "very high frequencies" meant w = ∞, plugging it in, I get the answer to be 0°.

However, the answer from my teacher was that it was -180, because the transfer function had 2 poles, each at -90. While I can understand this, I wanted to know why my method was wrong.
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  • #2
Try substituting j*w {j is imaginary, and w is omega} for s and then see what the angle becomes. So j is equivalent to +90 degrees. 1/j = -j is equivalent to -90 degrees. So what does j^2 do? (or 1/j^2) What angle would that approach? This is how Bode plots (phase) can be made, if you are familiar with them.
 
  • #3
I rather think, the questioner has already replaced s by jw while deriving the formula as given in 3) .
And - yes - the formula is correct. Hence, there is nothing left than to evaluate the formula for very large frequencies (considering that the arctan function is not unambiguous).
 
  • #4
LvW said:
I rather think, the questioner has already replaced s by jw while deriving the formula as given in 3) .
And - yes - the formula is correct. Hence, there is nothing left than to evaluate the formula for very large frequencies (considering that the arctan function is not unambiguous).
Yes; this is what i was hoping to do. However, plugging w as infinity does not get the -180, so I am confused.
 
  • #5
Keep the x and y components separate rather than forming the ratio y/x for the arctan function. That means retaining any signs associated with them rather than letting them get entangled in the ratio. Then evaluate by inspection how those components will trend as ω gets larger, and where the vector (x,y) formed from them is headed.
 
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  • #6
gneill said:
Keep the x and y components separate rather than forming the ratio y/x for the arctan function. That means retaining any signs associated with them rather than letting them get entangled in the ratio. Then evaluate by inspection how those components will trend as ω gets larger, and where the vector (x,y) formed from them is headed.
I think this works well. I got the awnser I was looking for. Thank You!
 
  • #7
Just another question. Can higher frequencies be assumed that frequencies higher than the cutoff frequency?
 
  • #8
roinujo1 said:
Just another question. Can higher frequencies be assumed that frequencies higher than the cutoff frequency?
Yes.
 
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  • #9
Thank you !
 
  • #10
roinujo1 said:
Just another question. Can higher frequencies be assumed that frequencies higher than the cutoff frequency?
That is a good question, because it never will actually get to -180 degrees. It approaches that at very high frequencies (much higher than the cutoff). Wolfram Alpha has a nice tool (search for Bode Plot) and you can type in the transfer function and see both the gain plots and phase plots.
 

1. What is phase relationship at high frequencies?

Phase relationship at high frequencies refers to the relationship between the phase angles of two or more signals at high frequencies. It describes how these signals are aligned or synchronized with each other in terms of their timing or position within one cycle of a waveform.

2. Why is phase relationship important at high frequencies?

Phase relationship at high frequencies is important because it affects the overall quality and accuracy of a signal. In certain applications, such as in telecommunications and digital signal processing, maintaining a consistent and precise phase relationship between signals is crucial for proper functioning and data transmission.

3. How is phase relationship measured at high frequencies?

Phase relationship at high frequencies is typically measured using instruments such as an oscilloscope or a vector network analyzer. These devices can analyze the phase angles of signals and display them graphically, allowing for a visual representation of the relationship between the signals.

4. What factors can affect phase relationship at high frequencies?

There are several factors that can affect phase relationship at high frequencies, including signal distortion, noise, and interference. Changes in the frequency or amplitude of a signal can also impact the phase relationship between signals, as well as the length and type of transmission medium used.

5. How can we maintain a stable phase relationship at high frequencies?

To maintain a stable phase relationship at high frequencies, it is important to use high-quality components and proper signal conditioning techniques. This can include using filters to reduce noise and interference, as well as implementing proper grounding and shielding to minimize external influences on the signals.

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