Transcription of Impedance Calculations
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Impedance Calculations
11 Revisiting a T-Line With Any Termination 00000000000000000( )2 cos2 sin2 sin2 costantanj zj zLj zj zLj zj zj zj zLLj zj zLLLj zj zLLLLLZZ eeeeZZZ zZZeeZZeeZZZZ eZZ eZz ZjzZZZZ eZZ eZjz ZzZjZzZZjZz In the general case, where a transmission line is terminated inZL,the Impedance along the line is given by:Note:Z(z)=Z0ifZL=Z0 The above equation shows how the input Impedance to anunmatched transmission line changes with electrical length, the electrical length changes with frequency, the inputimpedance to an unmatched line will be frequency CalculationsBecause the formula for Impedance is a bit cumbersome and notintuitive, design Calculations and measurements are often madegraphically using a Smith Chart.
Single-Stub Matching As shown previously, the input impedance (admittance) of a shorted transmission line (a “stub”) is purely reactive. By placing a stub in parallel with another transmission line, the reactive component can be cancelled, leaving a pure-real input impedance. This can be used to achieve a perfect match. Z 0 = 50 Z in = 50 Z L d
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