Low pass filter (arctan domain)

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SUMMARY

The discussion focuses on the phase characteristic of a single-pole low pass filter (LPF) and the confusion surrounding the arctan function's domain and range. The phase shift for a single-pole LPF ranges from 0 to -90 degrees, with 0 at low frequencies and -90 degrees past the cutoff frequency. The arctan function's domain is indeed between [-π/2, π/2], but the relevant output for the phase response is only the negative half, leading to the observed range of [0, -90] degrees. Clarification was provided through a helpful external link.

PREREQUISITES
  • Understanding of single-pole low pass filters (LPF)
  • Knowledge of the arctan function and its properties
  • Familiarity with phase shift concepts in signal processing
  • Basic graphing skills to interpret phase response diagrams
NEXT STEPS
  • Study the mathematical properties of the arctan function in detail
  • Learn about phase response and its significance in filter design
  • Explore graphical representations of filter characteristics
  • Investigate the behavior of other filter types, such as high pass and band pass filters
USEFUL FOR

Electrical engineers, signal processing students, and anyone involved in filter design and analysis will benefit from this discussion.

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Homework Statement


when I'm trying to calculate and show the graphic of the phase characteristic i don't understand why the domain range of the arctan function is [0,90] :


Homework Equations


aa4a.gif





image392.gif



The Attempt at a Solution


shouldn't be the domain of arctan function between [-Pi/2,Pi/2]?
z_tri59.png
 
Last edited:
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The value of the phase shift is the range of the function, not the domain. The domain is the input range to the function and the range is the output values of the function.

The phase shift for a single-pole LPF varies from 0 to -90 degrees, as shown in the diagram. It is 0 at low frequencies in the passband of the filter, and drops to -90 degrees past the cutoff of the LPF.
 
I see that you've edited your post to add the red arctan curve. I think it may be the shape of the phase response in the first plot that is confusing you. I don't think it is plotted very well -- it make is look like the full arctan() curve, when it is really only half of it.

When ω = 0, you get the arctan(0) which is zero. As the frequency increases, you get half of the arctan() function, going negative because of the sign being negative.

Does that make more sense now?

http://www.electronics-tutorials.ws/filter/filter_2.html

.
 
thank you, the link was helpful too!
 

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