Prepared by: Eng. Talal F. Skaik

Transcription

1 Islamic University of Gaza Faculty of Engineering Electrical & Computer Dept. Prepared by: Eng. Talal F. Skaik Microwaves Lab Experiment #3 Single Stub Matching Objectives: Understanding Impedance Matching, Using single shunt stub(open/short) for making impedance matching. Use Smith_Chart2 to design and use TRLINE to verify the answer. Theoretical Background: Given a transmission line of characteristic impedance Z 0 and phase velocity u drives a load Z L. Z L Z 0 The reflection coefficient is Γ L = Z L + Z 0 The generator supplies power Pin ; 2 o part of the input power is delivered to the load: (1 ΓL ) Pin 2 o part of the input power is reflected back to the generator: Γ L Pin The reflected power is wasted: o some generators cannot absorb much reflected power. o often an isolater is used to absorb power reflected back to the generator. Ideally, the load should be matched to the transmission line,, so that the reflection coefficient is zero and all the incident power is absorbed by the load. The objective of impedance matching is to insert a matching network between the transmission line and the load such that the input impedance Z in is a better match than Z L. Then the reflection coefficient is smaller than ΓL and so less power is reflected back to the load. Matching networks are often designed to achieve a perfect match (Γ=0).

2 Jjhjjkhlk Single Stub Matching: Single open or short circuited transmission line (stub) with length(l) connected either in shunt or series at certain distance (d) from load. * For the following transmission line, a short-circuited stub transmission line with length(l) is connected in parallel(shunt) at a distance (d) from the load(z L ). At terminals AA we want to have Yin=Y 0 =1/Z 0 to make matching. Yin is made up of Y1 in parallel with Ys. Since parallel admittances add, we have Y in =Y 1 +Y s. We can decompose Y into conductance and susceptance as Y 1 =G 1 +jb 1 and Y s =jb s So, we can write Y in =Y 1 +Y s =G 1 +jb 1 +jb s =G 1 +j(b 1 +B s ). We can obtain the match by choosing: G 1 =1/Z 0 B s =-B 1 ( Y s = -jb 1 ). Then, Y in =Y 1 +Y s =Y 0 +jb 1 -jb 1 =Y 0 (Y in =Y 0 matching)

3 At matching, if we take normalized values : y in =y 1 +y s y 1 =1+jb 1, y s =jb s, then y in =1+jb 1 +jb s =1+j(b 1 +b s ) with b s = - b 1 and y in =1. Smith Chart Method for Designing Single-Stub Matching Example) For Z L =15+j10 Ω, we want to design two (single-stub shunt-open) tuning networks to match load to 50Ω line. Run Smith_Chart2 software. Select from main menu Y-Chart. Select DATAPOINT from the Toolbox, then fill the load impedance with 15+j10. From the Toolbox, select (series line) with characteristic impedance 50 Ω and εr=1. From the load (point#1), move clockwise toward generator until intersecting the 0.02+jB circle at point#2. then the distance from the load to stub=d=0.044λ.

4 From the Toolbox, choose SHUNT LINE, with characteristic impedance 50Ω and εr=1. then choose stub type OPEN END. Now, move from point#2 clockwise until the input admittance(y) becomes 0.02+j0 (POINT#3, where matching happens). Record the stub length, L=0.147λ.

5 Solution 2:- We note that by moving from load POINT#1 clockwise toward generator, we intersect the 0.02+jB circle in two points. The previous solution was for the first point. Now, we repeat all previous steps but for the other point, and find another solution(d=0.387λ and L=0.353λ).

6 * Now, to verify our solution, we will use TRLINE.EXE software. Choose Singlestub matching circuit.(from the previous procedure, d=0.044λ and L=0.147λ) Now fill in the following parameters: Generator: Voltage source=1vrms, internal resistance=50ω, frequency=300mhz. Choose the propagation velocity for the three lines =300meter per microsecond. Then, the wavelength=u/f=3*10 8 /300*10 6 =1m.

7 Choose Line #1, Characteristic impedance=50 Ω, the length of line #1 is not important here, we are interested in the lengths of lines 2 and 3 for matching. Now, choose Line #2, and fill the following parameters.(d=0.044λ=0.044m) Choose Line #3, and fill the following parameters.(l=0.147λ=0.147m) Choose Load #1, Z L =15+j10. Choose Load #2, (Open Circuit, Z= ).

8 Choose(draw Smith Chart as a function of the line length). Choose Line #2. Note that the input admittance=20-j26.6(ms)=y 0 +jb. So, for matching, the input admittance for the stub must equal to +26.6mS, and the total admittance will equal to 20-j26.6+j26.6=20mS=Y 0 =1/Z 0. Click on Exit, then choose Line #3 Note that Load admittance=0+j0(open circuit). Note that Input admittance=+j26.5ms(approximately as expected).

9 Experimental Procedure: Problem(1) Antenna with impedance 40+j30 Ω is to be matched to a100-ω lossless line with a shunt shorted stub. Determine the stub length and the distance between the stub and the antenna. Note: You have to find two solutions(for d=distance from load to stub and L=stub length). you also have to find the input admittance for the stub when matching occurs. Use Smith_Chart2 to design and TRLINE to verify your solution. Problem(2) At 850 MHz, an antenna with an input impedance Z L =100-j45 of ohms must be matched to a transmission line of characteristic impedance Z 0 =50 ohms. The speed of travel on the transmission line is u=30 cm/ns. Design a short circuited single-stub matching circuit by choosing values for d and L. Note: You have to find two solutions(for d=distance from load to stub and L=stub length). you also have to find the input admittance for the stub when matching occurs. Use Smith_Chart2 to design and TRLINE to verify your solution.