ELEC 412 RF & Microwave Engineering

ELEC 412 RF & Microwave Engineering Fall 2004 Lecture 5 Lecture 5

Lecture 5

Smith Chart Use Lecture 5

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 = Zo 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. Lecture 5

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. Lecture 5

Matched load (G=0) Open circuit load (G=+1) Smith Chart – Matched & Open Circuit Loads Lecture 5

Smith Chart – Short Circuit Load Short circuit load (G=-1) Lecture 5

Short through arbitrary line length Smith Chart – Short Circuit Load Through Arbitrary Line Length Lecture 5

Open through arbitrary line length Only the angle of G 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 . Lecture 5

Smith Chart –Resistance, Reactance, & SWR Lecture 5

Smith Chart Benefits The Smith Chart has at least four benefits: • All possible values of G, hence all possible values of Z, lie within the unit circle. • For a given termination, the variation of G with transmission line position is simply a rotation on the chart with no change in magnitude |G|, and hence, no change in SWR. • Lines of constant R and X are uniquely defined circles on the chart, so we can input data in G format and read the result in Z format by inspection. • Data from a slotted line can be entered directly in terms of SWR and distance between minima. Lecture 5

Smith Chart Z Plane Mapping The Smith Chart is a mapping onto the complex G plane from the complex z plane. We let G = u + jv and z = r + jx G = u + jv = Lecture 5

ELEC 412 RF & Microwave Engineering