Question

Design a microstrip, single-stub tuner that matches a 50[Ω] microstrip transmission line to load impedance of ZL​=70+j10[Ω]. Assume that the frequency is 10[GHz], the dielectric constant is 2.5 , and the substrate thickness is 1.2[ mm]. Assume that the stub is open circuited and has the same characteris- tic impedance as the transmission line. Show all the critical dimensions of this design (including the 50[Ω] line).

Answer 1

To design a microstrip single-stub tuner for matching a 50Ω line to a 70 + j10Ω load, you need to calculate the normalized load impedance, use a Smith chart or equations to find stub location and length, and then design the transmission and stub dimensions.

Step-by-step explanation:

The design of a microstrip, single-stub tuner to match a 50Ω microstrip transmission line to a load impedance of ZL = 70 + j10Ω involves several steps:

1. Calculate the normalized load impedance (zL) by dividing the load impedance ZL by the characteristic impedance of the line (Z0 = 50Ω), resulting in zL = (70 + j10)/50.
2. Using a Smith chart or equations, find the point of zL on the chart and move towards the generator (counter-clockwise) to reach the real axis. This step determines where the stub should be connected to the line.
3. Calculate the electrical length of the stub required to cancel the imaginary part of the impedance seen at the point where the stub joins the main line.
4. Determine the physical length of the stub using the effective dielectric constant and the frequency of operation.
5. Calculate the dimensions of the microstrip lines required to achieve the characteristic impedance of 50Ω, using substrate properties (dielectric constant and thickness).

Dimensions for the stub and transmission line include the lengths and widths of the microstrip, all based on the equations for microstrip line design, considering factors like the effective dielectric constant, frequency, and substrate thickness.