Let Zin = Rin+jXin and Zg=Rg+jXg then 1 RinP | Vg |2 2( Rin Rg ) ( X in X g ) Consider Zl = Zo, matched load with tx line Max power is delivered under conjugate matching Rin = Rg, Xin = -Xg or Zin=Zg*11 P | Vg |224 Rg It means only half of Pin is delivered to the load12 13. This is called the Smith Chart, after the mathematician, P. Use the mouse or touch to select a point on the Smith chart, representing a pair of complex numbers r (the reflection coefficient) and z (the normalized. Generator and Load Mismatch We discussed terminated tx lines irrespective of generator Investigation of maximum power transfer to load Z L jZo tan( l)1 l e( 2 j l)Zin Zo Zo Zo jZ L tan( l)1 l e( 2 j l) 1 1 1 Vin | Vg | Z inP Re | Vin | Re * 2 Z in Z g 2 2 Zin 11 12. RF engineers have also a tool which assists in the understanding of transmission lines. Quarter wave transformer: multiple reflection view pointZ1 Z o 1 Z1 Z oZ 0 Z1 2 Z 0 Z1 RL Z13 RL Z12 Z1T1 Z1 Z o2Z oT2 Z1 Z o10 11. Example 2.5 Match a load of 100 with a 50 line using quarterwave transformer at frequency 3GHz Solution:Z1 (50)(100) 70.71 Now for 3GHz is 0.1m, /4 = 0.025m Frequency response of (quarter wave transformation) 9 10.
Z L jZ o tan( l ) Z in Z o where l = /2Z o jZ L tan( l )Z12 Zin RL In order for = 0, we put Zin = ZoZ1 Zo RL In this way SWR=1 on tx line The impedance will be matched only for one frequency The method is limited to real loads only Complex loads can be made real by adding properlengths of tx lines 8 9. Quarter Wave Transformer Case when Zo of tx line and ZL are irreplaceable Impedance needs to be matched to avoid reflections(1) /4 transformation (2) Stub matching Initially Zo of tx line and ZL are given Insert a section of lossless tx line between tx line ZL Length of segment is /4 and impedance Z17 8. The Slotted line It is a device to measure arbitrary load attached to line Its a tx line configuration that is used to find E fieldamplitude of standing wave on tx line Device is replaced by VNAs SWR and 1st null from load can be measured 1 | | SWR 1 | |SWR 1 where | | e jSWR 1 2 lmin6 7. ZL connected to /4 Line If an arbitrary ZL is connected to /4 line Z L jZo tan( l ) Zo 2Zin Zo Zo jZ L tan( l ) Z L Under normalized condition 1zin (Admittance)zL Length of /4 corresponds to 180o rotation in Smithchart3 4. Try the original compass for now, no-flair bootlicking statist commie non-degenerate poor anti-consumerism collectivist tax-loving FED-dicksucking fuck. Find at the load, at inputterminals, zin, SWR and return loss.Solution: Normalized input impedance is zL=ZL/Zo=0.4+0.7j Mark the point on the chart Draw a radial line form center to plot edge throughmarked point, and read the angle 104o Open compass from center to that point (radius) Measure SWR and || from the scale below the chart1Ģ. Smooth, flowing lines and elegant finishing details complement the Compass low profile ultra-light inmold construction. Example 2.2 The load impedance of 40+j70 terminates at 100 txline that is 0.1 long. Estimate the magnitude and angle of the complex reflection coefficient, 11, using a compass, and by drawing a line from the center of the Smith chart through.
0 kommentar(er)
