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Lecture 17 Antenna Fundamentals

# Lecture 17 Antenna Fundamentals - Lecture Lecture17...

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Lecture 17 Antenna Fundamentals Hayt CH 14 1 McGill ECSE 352, Fall 2011, D. Davis

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Radiation The basic component of all wireless systems is the antenna. The transmit antenna converts current and voltage to electric and magnetic fields. These fields propagation until they strike the receiving antenna. The receiving antenna will convert the incident fields into voltage and current. The signal information is then processed by the system in the usual manner. The antenna works by radiating electromagnetic waves the The antenna works by radiating electromagnetic waves, the principles of radiation are the focus of this section of the lecture. McGill ECSE 352, Fall 2011, D. Davis 2
Radiation The first step will be to relate circuit behaviour (voltage and current) to electromagnetic waves waves. This will be done through the use of potential functions functions. There are two general classes of potential f i l ( V l ) d functions: scalar (e.g. Voltage) and vector potential functions. McGill ECSE 352, Fall 2011, D. Davis 3

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Radiation For our purposes we will define the vector magnetic potential (A) as: We can link this function to electric fields i F d ’ L using Faraday’s Law: ׏ ൈ ܧ ൌ െ ߲ ߲ݐ ׏ ൈܣ ҧ ՜ ׏ ൈቆܧ ߲ܣ ҧ ߲ݐ ቇ ൌ 0 In addition we can write scalar potential: McGill ECSE 352, Fall 2011, D. Davis 4
Radiation This can be written as: h h fi i h b k ܧ ൌ െ ቆ׏ܸ ൅ ߲ܣ ҧ ߲ݐ Note that the first term in the brackets represents the traditional static electric i l d h d h potential and the second represents the contribution due to time varying l i fi ld electromagnetic fields. McGill ECSE 352, Fall 2011, D. Davis 5

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Radiation We will need to define the characteristics of the potential function, starting with Ampere’s Law: F hi ׏ ൈ ׏ ൈ ܣ ҧ ൌ ߤܬ ҧ െ ߤ߳ ߲ ߲ݐ ቆ׏ܸ ൅ ߲ܣ ҧ ߲ݐ From this ׏ 2 ܣ ҧ െ ߤ߳ ߲ 2 ܣ ҧ ߲ݐ 2 ൌ െߤܬ ҧ ൅ ׏ ߤ߳ ߲ܸ ߲ݐ ׏ · ܣ ҧ This will require a definition for the divergence of thepotential function. McGill ECSE 352, Fall 2011, D. Davis 6
Radiation One choice for the divergence of the potential is developed by Lorentz (called the Lorentzian Gauge): Wh i hi d fi i i f h di When using this definition for the divergence of the potential we can write: ׏ 2 ܣ ҧ െ ߤ߳ ߲ 2 ܣ ҧ ߲ݐ 2 ൌ െߤܬ ҧ McGill ECSE 352, Fall 2011, D. Davis 7

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Radiation This relationship for the potential is called the non homogeneous wave equation for vector potential A . There is also an associated wave equation for the scalar potential function V but it will not the scalar potential function V, but it will not be used in this lecture set.
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Lecture 17 Antenna Fundamentals - Lecture Lecture17...

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