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Lecture 3

# Lecture 3 - RF Circuit Design Lecture 3 Transmission Lines...

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RF Circuit Design Lecture 3 Transmission Lines

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Electromagnetic Waves 0 cos( ) x x E E t z ϖ β = - 0 cos( ) x x E E t z ϖ β = - Electric field propagating in the pos-z direction If the conducting medium is aligned with the z-axis, then the voltage drop along the z-axis can be found: 0 sin( ) ( , ) z z X t z V z t E dl E ϖ β β - = - = The argument of the sinusoidal term couples space and time behavior. There is spatial variation along the z-axis related to wavelength, and time variation along the time axis related to the period.
Using the equation for phase velocity we can then compute the wavelength of a frequency traveling through a material. 1 p r r c v f ϖ λ β εμ ε μ = = = = Now let’s compare the wavelength of two frequencies in a 1.5 cm long wire. Spatial variances in voltage at 10 GHz are significant for a 1.5 cm wire. Transmission Line Circuit Analysis

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Plots show spatial variation at a fixed time (t=0) and time variation at a fixed location (z=0) along the medium. • For low frequency applications we ignore this spatial variation • RF frequencies can have large spatial variations
How can we apply KVL if the voltage at point A varies from point B along a wire? We cannot. Unless… Transmission Line Circuit Analysis

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Unless we partition the electric line into infinitesimal lengths over which voltage and current can be assumed constant.
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Lecture 3 - RF Circuit Design Lecture 3 Transmission Lines...

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