Matching with lumped elements

Recall the input impedance looking into a T-line varies periodically

As shown in Fig. 9.36, move a distance ? ₁ away from the load such that the real part of Z _in has the desired value. Then place a shunt or series impedance on the T-line to obtain the desired reactive part of the input impedance (e.g. zero reactance for a real match). For instance, for a shunt match, the input admittance looking into the line is

Figure 9.36: A section of transmission line and a shunt reactance can be used to match a load to a desired impedance.

At a distance ? ₁, we desire the normalized admittance to be y ₁ = 1 ? jb. Substitute ? L = ?e ^{j ?} and solve for ? ₁ and let ? = 2 ?z + ?

Solve for ? (and then ? ₁) from ( y) = 1

At ? ₁, the imaginary part of the input admittance is

Placing a reactance of value ? b in shunt provides impedance match at this particular frequency. If the location of ? ₁ is not convenient, we can achieve the same result by moving back a multiple of ?/2.

Matching with T-line stubs

At high frequencies the matching technique discussed above is difficult due to the lack of lumped passive elements (inductors and capacitors). But...