How to Plot Admittance on a Smith Chart

A unique feature of the Smith chart is that you can make accurate calculations without the need for a calculator. All you need to plot admittance on a Smith chart is a sharp pencil, a compass and a copy of the chart. You can either plot admittance directly on the chart, or you can plot impedance and then get the admittance by simply rotating the chart.

Instructions

Difficulty: Moderate

1. Determine the admittance of the load and the characteristic admittance of the transmission line if you want to plot the admittance directly. If you prefer to use impedances only, then determine the impedance of the load and the characteristic impedance of the transmission line.
2. Divide the load conductance by the characteristic admittance of the transmission line to get the normalized conductance. For the impedance approach, divide the load resistance by the characteristic impedance of the transmission line to get the normalized resistance.
3. Plot the value calculated in Step 2 on the horizontal axis of the Smith chart. This works for both the admittance and impedance approaches.
4. Find the normalized susceptance (reactance) by dividing the load susceptance (reactance) by the characteristic admittance (impedance) of the transmission line. Make careful note of the sign of this result.
5. Trace the circle that intersects the point plotted in Step 3. For a positive sign (as determined in Step 4), go clockwise. For a negative sign, go counterclockwise. Stop at the number calculated in Step 4 and mark this point with a pencil; this is the normalized load admittance (or impedance).
6. Place the point of the compass at the center of the chart and the pencil at the admittance or impedance point found in Step 5. Draw a circle around the center point. If you plotted admittance in Steps 1 through 5, then the chart now shows the normalized input admittance of the load for any given distance along the transmission line. If you plotted impedance in Steps 1 through 5, simply rotate the chart 180 degrees to see the plot of the normalized admittance.
7. Multiply by the characteristic admittance (or impedance) to get the actual value of the admittance (impedance). Remember that the plot shows only the normalized values.

Tips & Warnings

• The more careful and precise you are at each step, the more accurate your results will be.
• This approach to plotting admittance is for the case of lossless transmission lines only. If you include loss in the analysis, then the plot is a spiral rather than a circle. The Smith chart includes information for calculations that take loss into account.

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