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Near and Far Field Attenuation Inverse Laws

  • Thread starter teknodude
  • Start date
  • #1
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Homework Statement



near-field distance attenuation follows an inverse cube law (1/d^3), while in the far-field it follows inverse law (1/d). Prove mathematically how we arrive at 60dB/decade from the inverse distance cube relation and 20dB/decade from the inverse distance
relation.

Homework Equations


20 log (D) where D is the distance


The Attempt at a Solution



I'm pretty sure this problem is similar to control theory in converting magnitude to DB scale with 20 log (D). I can actually see the answer just by doing that; however, I'm thinking I'm missing the big picture somewhere by doing that. Mostly I can't seem to justify using the above equation.
 

Answers and Replies

  • #2
berkeman
Mentor
57,269
7,258

Homework Statement



near-field distance attenuation follows an inverse cube law (1/d^3), while in the far-field it follows inverse law (1/d). Prove mathematically how we arrive at 60dB/decade from the inverse distance cube relation and 20dB/decade from the inverse distance
relation.

Homework Equations


20 log (D) where D is the distance


The Attempt at a Solution



I'm pretty sure this problem is similar to control theory in converting magnitude to DB scale with 20 log (D). I can actually see the answer just by doing that; however, I'm thinking I'm missing the big picture somewhere by doing that. Mostly I can't seem to justify using the above equation.
What is log(1/d^3) ?
 
  • #3
157
0
Maybe I was thinking too much and thought there was more to the proof than just doing 20log(1/d^3) and 20 log (1/d). Thanks.
 
  • #4
berkeman
Mentor
57,269
7,258
Glad to help. :biggrin:
 

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