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Input and Output Impedance MatchingAuthor: Leonard Krugman Equations 313 and 321 indicate that the input resistance is affected by the load resistance and, conversely, the output resistance depends on the generator internal resistance.
Solving in terms of r_{12}r_{21}
Substituting for R_{g} and r_{o} in equation 321
Again solving in terms of r_{12}r_{21}
Equating equations 327 and 329
Cross multiplying and cancelling equal terms,
or
This latter equation indicates that matching the input and output resistances for maximum power gain requires their values to be in the same ratio as the opencircuit characteristics of the transistor. The absolute value of the generator internal resistance and its matched input resistance in terms of transistor opencircuit parameters can now be determined. Substituting the equality into equation 326,
In terms of the stability factor, , which will be defined later in the chapter, the input image resistance
For the typical pointcontact transistor previously considered, when r_{11} = 250 ohms, r_{12} = 100 ohms, r_{21} = 24,000 ohms, and r_{22} = 12,000 ohms, the numerical value of r_{1} is For the typical junction transistor, when r_{11} = 550 ohms, r_{12} = 500 ohms, r_{21} = 1,900,000 ohms, and r_{22} = 2,000,000 ohms, The output image resistance of a transistor can be determined in a similar fashion from the ratio Substituting this equality into equation 328
In terms of the stability factor ; the output image resistance
For the typical pointcontact transistor, Forthe typical junction transistor These values may be checked on the R_{L} vs r_{i} and R_{g} vs r_{o} characteristics plotted for these typical transistors in Figs. 311, 312, 314, and 315.


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