This example shows the results of calculations and simulations of a matching network using distributed elements.

The aim is to match a complex load Z_L=200+j160 W to a 100 W line

. Frequency 10 GHz.

• First calculate the value of the inductance L from X_L=160=(2p10¹⁰)L. L=2.55x10^-9 H
• Either calculate or use the Smith Chart to find the necessery lengths of the transmission lines. Note: there are two solutions. Refer to Matching a Complex Load to a Real Impedance for the procedure and identification of the symbols.
  • lengths of the transmission lines: d₁=0.213l, (second solution d₁=0.370l)
  • lengths of shunt stubs: d₂=0.352l, (Second solution d₂,0.148l)
• Use the Line_Calc to find the physical widths and lengths of the transmission lines (Z_c=100W). For only the first choice:
  • w=0.136 mm
  • d₁=2.540 mm
  • d₂=4.202 mm
• Use HP_Libra to simulate the circuit.

• Be sure that you have the default data items changed in the default directory. Just including them without the extension _DEFAULT does not provide the necessary changes.
• You can plot the results on a linear or log scale or on a Smith Chart.
• Even though match was made at 10 GHz, the simulations show a match at a slightly lower frequency. This is due to slight errors in the values that were entered into the simulations. By an optimication process, the match can be moved to 10 GHz.