{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Notes 21 Spring 2005

# Notes 21 Spring 2005 - Notes 21 Spring 2005 Antenna...

This preview shows pages 1–3. Sign up to view the full content.

Notes 21 Spring 2005 Antenna Principles Consider a differential current filament (antenna) of length d carrying a current . Note that this current is uniform along the length, i.e., it is position independent- a temporary simplification. ( ) ( ) ω t cos I t i o = φ d θ l d p v E ° = φ 90 θ d P φ l d θ Wire filament H i x o r θ ( ) θ sin r o ° = φ 0 d z y Earlier in the semester we determined that a magnetic field exists near a wire carrying a steady current. It follows then that a time-varying -field exists if a time-varying current is present in the wire. And through Faraday’s law of induction we know that the time-varying -field in turn produces a time-varying -field and the time-varying E - field produces a time-varying -field via Amperes law, etc., etc., and an EM wave will propagate away from the wire at velocity . H H E H p v It can be shown that in spherical coordinates these fields in phasor form are represented by λ π + λ π θ π φ = φ r 2 j exp r 1 r 2 j sin 4 d I ˆ H 2 o r λ π π λ θ π η = r 2 j exp r 2 j r 1 cos 2 d I E 3 2 o r r λ π π λ + λ π θ π η θ = θ r 2 j exp r 2 j r 1 r 2 j sin 4 d I ˆ E 3 2 o r Together, these are known as the near fields. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Notes 21 Spring 2005 It can be seen in these equations that as the distance (r) from the filament increases the terms involving become negligible and the resulting equations are called the far field equations or the radiation fields . Traditionally there is a rule of thumb where this transition occurs at : 3 2 r and r λ > 10 r λ π θ λ φ = φ r 2 j exp sin r 2 d I j ˆ H o r 0 E r = r Together, these are known as the far fields or radiation fields. λ π θ λ η θ = θ r 2 j exp sin r 2 d I j ˆ E o r These far field equations show that φ θ η = H E , which is precisely the relationship between the fields that we established for the uniform plane wave! The time domain expressions are ( ) and r t sin sin r 2 d I ˆ H 2 o λ π φ ω θ λ φ = r ( ) r t sin sin r 2 d I ˆ E 2 o λ π θ ω θ λ η θ = r We note that represents the equatorial or x-y plane.
This is the end of the preview. Sign up to access the rest of the document.