How Do You Find the Phase Equation of a Lossy Low Pass Filter?

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SUMMARY

The phase equation of a lossy low pass filter can be derived using the formula arctan(wRC), where w represents the angular frequency and RC is the product of resistance and capacitance. In practical applications, discrepancies may arise when comparing theoretical calculations with SPICE simulations due to errors in the calculation process, such as incorrectly multiplying by the negative of the conjugate. Correcting these errors leads to accurate phase equations that align with Bode plots from actual circuits.

PREREQUISITES
  • Understanding of low pass filter design principles
  • Familiarity with Bode plots and their significance in circuit analysis
  • Knowledge of complex numbers and conjugates in electrical engineering
  • Experience with SPICE simulation software for circuit analysis
NEXT STEPS
  • Study the derivation of phase equations for different types of filters
  • Learn how to accurately use SPICE for simulating filter circuits
  • Explore the impact of component tolerances on filter performance
  • Investigate advanced topics in signal processing related to filter design
USEFUL FOR

Electrical engineers, students studying circuit design, and anyone involved in the analysis and simulation of filter circuits will benefit from this discussion.

jonni
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Homework Statement


I'm a bit confused about how to find the phase equation of a lossy low pass filter
eg.
r6yf51.jpg


Homework Equations


For a normal low pass filter it's just arctan(wRC)



The Attempt at a Solution



jja1is.jpg


So I am comparing this by subbing in values and comparing to a bode plot of an actual circuit on a breadboard and a spice version of the circuit. But this is nothing like what i get in spice, I've checked for errors but I think its something wrong with the way I am actually calaculating it... but can't figure out why?
 
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You multplied by the negative of the conjugate. This will screw up your phase equation.
 
Oh thanks so much! Worked out fine now. I feel so stupid haha, i soooo wasn't thinking when i did that! I get the exact same thing except in the last line it's +1 not -1. Makes a big difference though.
 

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