# ELEC 483-Microwave RF Circuits Systems Smith Charts by MHairston

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```									                    ELEC 483-Microwave & RF Circuits & Systems
Smith Charts

BACKGROUND
The Smith Chart, invented in 1941 by Phillip Smith, was an extremely important invention in the
field of electrical and microwave engineering. It helped solve, in a graphical way, many of the
mathematical equations used in transmission line theory.
A Smith Chart or Z Chart is shown on Figure 1 below, the circular lines on the plot correspond to
contour of constant resistance, while the arcing lines correspond to contour of constant reactance.
As you may recall, all the impedance readings on the Smith Chart is normalized to a specific Zo
(normally 50 Ohm).

Figure 1: A Smith-Chart or Z Chart. Circular lines
represent constant resistance. Arcing lines represent
constant reactance.

It is also possible to plot contours of constant conductance and susceptance. Such a chart is called Y
Chart and can be obtained by rotating the Z chart by 180o as shown on Figure 2 below.

Figure 2: Y Chart. Circular lines represent conductance.
Arcing lines represent susceptance.

Figure 3 below shown a ZY Smith Chart, which we will be using most of the time, it is composed

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ELEC 483-Microwave & RF Circuits & Systems
Smith Charts

of Z and Y Charts overlapping each other. With ZY Smith Chart, we can interchange impedance Z
and admittance Y by directly reading off the chart.

Figure 3: ZY Chart.

Review: Admittance is defined as the reciprocal of impedance and denoted Y.
Y = 1 =G jB
z

The real part G is called conductance and the imaginary part, B, is called susceptance. Like
admittance, conductance and susceptance are measured in Siemens (S).
CIRCUIT ELEMENT                    ADMITTANCE (Y)                     SUSCEPTANCE
Resistor                                   G (resistance)                          -
Inductor                                      j(-1/ωL)                           -1/ωL
Capacitor                                        jωC                              ωC

Pre-Lab: Predicting Smith Chart Plots
In this pre-lab, we will try to predict the plot of different impedance values on the Smith Chart.
Note: It may be in your best interest to analyze Figure 1 before beginning. Look at where the
inductive and capacitive impedance values are located. Take note of the direction of the increasing
and decreasing resistance and reactance.
Warning: Remember to normalize the impedance values before plotting!
1. Plot the location of the following resistor values on the Smith Chart bellow: 50 Ohm, 100 Ohm,
200 Ohm, short circuit and open circuit.

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Smith Charts

2. Plot the impedance of a 1 nH inductor as the frequency varies from 0 GHz to 150 GHz. Explain
why the inductor is located at these positions by calculating few impedance values at the given
frequency range.

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ELEC 483-Microwave & RF Circuits & Systems
Smith Charts

Answers:

3. Plot the impedance of a 1 pF capacitor as the frequency varies from 0 GHz to 150 GHz. Explain
why the capacitor is located at these positions by calculating few impedance values at the given
frequency range.

Answers:

4. Now that the basics have been covered, we will combine some elements together. Plot the
location of a 100 Ohm resistor in series with a 1 nH inductor as the frequency varies from 0 GHz
to 150 GHz. Hint: A good starting point would be to find the location of the resistance. Explain
why they are located at these positions by calculating few impedance values at the given

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ELEC 483-Microwave & RF Circuits & Systems
Smith Charts

frequency range.

Answers:

5. Plot the location of a 100 Ohm resistor in series with a 1 pF capacitor as the frequency varies
from 0 GHz to 150 GHz. Explain why they are located at these positions by calculating few
impedance values at the given frequency range.

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ELEC 483-Microwave & RF Circuits & Systems
Smith Charts

Answers:

6. Plot the location of the 100 Ohm resistor in the series with a 1 nH inductor and a 1 pF capacitor
as the frequency varies from 0 GHz to 150 GHz. Hint: Think of which reactance is more
dominant as the frequency increases. Explain why they are located at these positions by
calculating few impedance values at the given frequency range.

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ELEC 483-Microwave & RF Circuits & Systems
Smith Charts

Answers:

SIMULATION
First, we will use ADS to confirm the pre-lab plot predictions that were made for the different
impedance values. Then we will learn how “to move” the load impedance to desired location on the
Smith Chart by inserting passive components in front of the load.

Part I: Smith Chart Overview
1. Login to your computer and start ADS.
2. Open the project by selecting File—Open Project and then select “elec483_2005_prj” if it does
not automatically open.
3. In the schematic window, open the prepared schematic by selecting File—Open Design and then
select “lecture6_SmithChart.dsn”. The circuit should look like Figure 4 below. In this
simulation, we are going to check the predictions that were made in the pre-lab. If you find that
any of the predictions in your pre-lab were incorrect, please fix them. Note: I have deactivated all
the components except for the 100 Ohm resistor.

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Smith Charts

Figure4: lecture6_SmithChart.dsn.
4. Simulate                                                                                 the circuit.
In the Data Display window, plot S11 on a Smith Chart. Add a marker to the Smith chart to
determine the resistors' position on the Smith chart (note that since resistors are not frequency
dependent the “trace” will be a single point and may be hard to see. You will have to click close
to the expected point in order for the marker to connect to the trace)
5. Simulate the circuit for a resistance of 50 Ohm, 200 Ohm, short circuit and open circuit.
Examine the Smith Chart plot.
6. Now deactivate R1 and activate L1 inductor and simulate. Examine the Smith Chart plot.
7. Deactivate L1 and activate C1 and simulate. Examine the Smith Chart plot.
8. Deactivate C1 and activate R2 & L2 and simulate. Examine the Smith Chart plot.
Note: You can output the simulation results into admittance unit. Right click on the Smith Chat
which contains your simulation results and then select Item Options->Plot Options. On the
Coordinate field, select admittance or both. Insert a marker on the data points; right click on the
marker and then select Item Options. Under Smith section, select admittance under Type field.
9. Deactivate R2 & L2 and activate R3 & C2. Examine the Smith Chart plot.
10.Deactivate R3 & C2 and activate R4 & C3 & L3. Examine the Smith Chart plot.
11.Were your predictions from the pre-lab correct? If some were not, go back and determine where
you erred.

Part II: Motion on Smith Chart
Part IIA: Motion on Z-Chart
1. Close current schematic and open “lecture6_SmithChart2.dsn”. In this part, we will use a
DesignGuide called “Smith Chart Utility” to investigate how shunt and series capacitor/inductor
added in front of the load affect the total load impedance ZL and cause ZL “to move” on the Smith
Chart.
2. To open “Smith Chart Utility” program, select DesignGuide->Amplifier->Tools->Smith Chart
Utility.

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Smith Charts

3. Take a few minutes to get similar with the program. Skim through the help section by selecting
Help->Smith Chart Utility Documentation.

4. Click        _from the Smith Chart control window toolbar and return to the
“lecture6_SmithChart2.dsn” schematic window. Then click on the Smith Chart button                  _on
the left side of the schematic window and insert the “SmartComponent” between the
source and load.
5. Back to the Smith Chart Utility window, highlight ZL component on the schematic preview
window (bottom right) and change its impedance value to match R1 impedance on the
lecture6_SmithChart2.dsn schematic window, which is R=50+40*j.
6. Insert a passive component to make the load match the source, which is 50 Ohm. Assume this
circuit is operating at 1 GHz. Record your value on the table below in either Farads (F) or Henry.
To insert a component, click on the component icons on the left side and it will automatically
inserted in front of the load, ZL. To set the operating frequency and normalize impedance in the
Smith Chart Utility, click on the “Set Frequency/Impedance” button on top left.
Shunt/Series               Inductor/Capacitor/Resistor                        Value

Note: The Circuit Data window plots the frequency response of the S-parameters. As expected,
the magnitude of S11 is lowest at 1 GHz because the source and load are perfectly matched at that
particular frequency. Therefore, there is no reflected wave from the load ZL toward the source
ZS.
7. Click the “Build ADS Circuit” button at the bottom left of the Smith Chart Utility window. This
button builds the matching circuit we just created into the Smith Chart SmartComponent. You
can see the matching circuit inside the SmartComponent by highlighting it and           press .
Simulate the circuit, and examine S11 in the Data Display window. Notice how the        total
impedance looking into the load and the matching network is 50 ohms – i.e. it is matched to the
50 ohm source (the TERM element).

8. Now, change R1 on the lecture6_SmithChart2.dsn schematic to 50-40*j. Repeat step 2 and 6
above and record the values on the table below.
Shunt/Series               Inductor/Capacitor/Resistor                        Value

Part IIB: Movement on Y-Chart
1. Now, change R1 to 40-j*20. To view the admittance and susceptance circles in the Smith
Chart Utility program, click Circles ->Option, check G & B boxes.
2. Insert a passive component in front of the load ZL to bring it to the origin of the Smith Chart.
Assume the circuit is operating at 1 GHz. Record the values on the table below.

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ELEC 483-Microwave & RF Circuits & Systems
Smith Charts

Shunt/Series              Inductor/Capacitor/Resistor                    Value

3. Once again, change R1 to 40+j*20. Repeat step 2 above and record the values below.
Shunt/Series              Inductor/Capacitor/Resistor                    Value

Summary of Motion on Smith Chart
With the results above, fill out the table below.
Components                        Motion:           Follows: Resistance Circle/Conductance
Clockwise/Counterclockwise                    Circle.
Series Capacitor
Series Inductor
Parallel Capacitor
Parallel Inductor

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