1. ELEC 412Lecture 51 ELEC 412 RF & Microwave Engineering Fall 2004 Lecture 5

2. ELEC 412Lecture 52

3. ELEC 412Lecture 53

4. ELEC 412Lecture 54

5. ELEC 412Lecture 55

6. ELEC 412Lecture 56

7. ELEC 412Lecture 57 Smith Chart Use

8. ELEC 412Lecture 58 Smith Chart: Reflection If we plot  on the polar plot, and overlay the circles of constant r and x, this yields the Smith Chart, on which we can convert from  to Z (or the reverse) by inspection. To see how the Smith Chart works, first consider a matched load, Z = Z o and  = 0. This point is at the origin of the plot, since  = 0 +j0. This is plotted below left. Next, consider a transmission line terminated with an open circuit at d=0.

9. ELEC 412Lecture 59 Smith Chart - Reflection At d=0, the plane of the open, the current is constrained to be zero, so the reflected wave current must equal the incident wave current and be out of phase (i.e., I- = - I+, so that V- = V+). The impedance Z(0) at this point is ∞, and the reflection coefficient  is  = = 1/0.

10. ELEC 412Lecture 510 Smith Chart – Matched & Open Circuit Loads Matched load (  =0)Open circuit load (  =+1)

11. ELEC 412Lecture 511 Smith Chart – Short Circuit Load Short circuit load (  =-1)

12. ELEC 412Lecture 512 Short through arbitrary line length Smith Chart – Short Circuit Load Through Arbitrary Line Length

13. ELEC 412Lecture 513 Open through arbitrary line length Only the angle of  changes Smith Chart –Arbitrary Line Length Any arbitrary impedance z or reflection coefficient  will have the same behavior if we move along the transmission from the point it is measured toward the generator. And if the impedance is measured at a point on the transmission line other than at the termination, we can move toward the load as well. It is this variation only of the phase angle, and not the magnitude, of .

14. ELEC 412Lecture 514 Smith Chart –Resistance, Reactance, & SWR

15. ELEC 412Lecture 515 Smith Chart Benefits The Smith Chart has at least four benefits: 1.All possible values of , hence all possible values of Z, lie within the unit circle. 2.For a given termination, the variation of  with transmission line position is simply a rotation on the chart with no change in magnitude |  |, and hence, no change in SWR. 3.Lines of constant R and X are uniquely defined circles on the chart, so we can input data in  format and read the result in Z format by inspection. 4.Data from a slotted line can be entered directly in terms of SWR and distance between minima.

16. ELEC 412Lecture 516 The Smith Chart is a mapping onto the complex  plane from the complex z plane. We let  = u + jv and z = r + jx  = u + jv = Smith Chart Z Plane Mapping