ELEC 412 RF

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ELEC 412 RF Microwave Engineering
Fall 2004 Lecture 5
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Smith Chart Use
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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 d0.

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Smith Chart - Reflection
At d0, 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 8, and
the reflection coefficient ? is ? 1/0.

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Smith Chart Matched Open Circuit Loads
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Smith Chart Short Circuit Load
Short circuit load (G-1)
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Smith Chart Short Circuit Load Through
Arbitrary Line Length
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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 ?.
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Smith Chart Resistance, Reactance, SWR
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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.

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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