Notes 13 - Transverse resonance method.pdf - ELC05177...

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Notes 13 ELC05177 Microwave Engineering Part Transverse Resonance Method 1
Transverse Resonance Method This is a general method that can be used to help us calculate various important quantities: 2 Wavenumbers for complicated waveguiding structures (dielectric- loaded waveguides, surface waves, etc.) Resonance frequencies of resonant cavities We do this by deriving a “ Transverse Resonance Equation (TRE) .”
Transverse Resonance Equation (TRE) R = reference plane at arbitrary x = x 0 To illustrate the method, consider a lossless resonator formed by a transmission line with reactive loads at the ends. We wish to find the resonance frequency of this transmission line resonator. 3 R 0 Z 0 Z x x = x 0 2 2 L L Z jX 1 1 L L Z jX x = L
Examine the voltages and currents at the reference plane: R + V r - + V l - I r I l x = x 0 4 TRE (cont.) R 0 Z 0 Z x x = x 0 2 2 L L Z jX 1 1 L L Z jX x = L
TRE (cont.) Hence: Define impedances: r in r l in l V Z I V Z I in in Z Z   r l r l V V I I Boundary conditions: R + V r - + V l - I r I l x = x 0 in Z in Z  x 5
in in in in Z Z Y Y     TRE (cont.) R in Z in Z  or TRE Note about the reference plane: Although the location of the reference plane is arbitrary, a “good” choice will keep the algebra to a minimum. 6
Example 0 0 , r Z k k x 2 2 L L Z jX 1 1 L L Z jX L Derive a transcendental equation for the resonance frequency of this transmission line resonator.
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