EMG3036 Microwave Circuits and Components
Impedance Transformation
Lab 1 - Interactive Impedance Transformation:
Lumped L impedance Matching
Objectives



To illustrate the basic of lumped-elements impedance matching.
To demonstrate the use equations for calculation in schematic and data display windows.
To perform interactive tuning features in Agilent Advanced Design System (ADS) software
for simple impedance matching.
Background
Impedance transformation serves many purposes in high frequency circuits, among them are to: (1)
Enable maximum power transfer between a source and load network. (2) To tune the performance
of the circuit by controlling the impedance of the source or load, for instance in low noise
amplifier design the source impedance determines the noise contribution of the amplifier. In
oscillator design the load impedance will affect the oscillation frequency.
In this lab, impedance transformation principle will be demonstrated using the ADS via the
interactive approach. The convention for terms used in impedance transformation is shown in
Figure 1.1. The impedance network used is the L impedance transformation network. The L
lumped impedance matching approach has two configurations, depending upon the values of
source resistance RS and load resistance RL. The schematics and analytical expressions for the
reactance and susceptance of the L network for the two cases are shown in Figure 1.2.
For greater flexibility, we can use graphical method employing the Smith chart, which can cater to
matching network with more than two elements. The complexity of the analytical expression
grows exponentially with additional component, whereas the complexity of the graphical method
is only linearly dependent on the amount of elements within the matching network.
Zs
Impedance
Transformation
Network
Vs
ZL
Image
impedance ZI
Load
impedance
Figure 1.1 – Nomenclature of impedance transformation.
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EMG3036 Microwave Circuits and Components
Impedance Transformation
jX
jB
ZI = Rs + jXs
RL
+
jXL
a) For RL>Rs
RL
+
jXL
b) For RL< Rs
jX
jB
ZI = Rs + jXs
Figure 1.2 – The two configurations for L impedance matching network.
For RL<RS:
RS  RL
RL
 X S  RS
B
2
RS  X S
X
2
 R SR
L S
2
X
BRS RL  X S
 XL
1  BX S
For RL>RS:
B
XL 
RL
RS
R L  X L  RS R L
2
RL  X L
2
2
2
X
R
1 X L RS

 S  XS
B
RL
RL B
In this lab we want to transform a load impedance ZL = 100−j25 to ZI = 25+j15 at 500 MHz with
configuration (a) from Fig. 1.2 for RL> Rs.
Performing Impedance Matching Using Agilent Advanced
Design System (ADS) Software
1. Create a new schematic design named LC_matching.dsn
a. Run the ADS version 2008 software from the desktop of the Windows NT workstation.
b. From the main window of ADS, create a new project folder named LC Matching under
the directory “D:\ads_user\default\”.
c. The new schematic window will automatically appears once the project is properly created.
Otherwise you can manually create a new schematic window by double clicking the Create
New schematic button on the menu bar
.
2. Create the impedance matching circuit as shown in Figure 1.3:
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EMG3036 Microwave Circuits and Components
Impedance Transformation
a. From the Lump-Components palette, insert a series C capacitor and a shunt L inductor.
Set their values to 0 pF and 0 nH respectively. Also insert an ideal DC block.
b. Insert a Var Eqn (variable equation) from the Data Items palette. Edit and assign the
variables XL = −25, RL = 100 and Z0 = 50.
c. In the Eqn Based-Linear palette, insert a Zip_Eqn 1-port Z-parameter and set the Z[1,1]
value to RL+j*XL, our required load impedance.
d. Insert the S-parameters controller and sweep a single frequency point at 0.5GHz by
setting Start and Stop frequencies to 0.5GHz. You may ignore the step frequency.
e. Insert a single termination port, Term1 from the S-Parameters palette.
f. Insert a MeasEqn (measurement equation ) from the S-Parameters palette and assign ZS
= 25+j*15.
g. Arrange the circuit as the following:
We wish to find
S11 as seen from
Term1
Figure 1.3 – Circuit used in impedance transformation before tuning
3. Perform s-parameters simulation and create the display results
a. Click the Simulate button
to run the simulation.
b. The ADS software will automatically invoke a data display window. The data display
window is used to show the result of the simulation. You can also invoke the data
display window manually by clicking the button
.
c. Insert a Smith chart in the data display window as shown in Figure 1.4.
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EMG3036 Microwave Circuits and Components
Impedance Transformation
Click this button to
insert a Smith chart
Select S(1,1) to show the S11
as measured from Term1 in
the Smith chart
Click this button to insert an
equation in the display area
Figure 1.4 – Inserting a Smith chart in the display area. Also shown equation button.
d. Right-click on the smith chart and click Item Options. You may change the color and
the thickness of the line of the Smith chart by using the Trace Options tab as shown
below.
Figure 1.5 – Changing the color and thickness of the plot
e. Also, change the smith chart format to display both the Z (impedance) and Y
(admittance) coordinates in the Plot Options tab.
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EMG3036 Microwave Circuits and Components
Impedance Transformation
Figure 1.6 – Displaying both the Z and Y lines on the smith chart
f. Your Smith chart should look similar to the one shown in Figure 1.7. Use a Marker to
display the complex value of the S11. Note that both impedance and admittance
coordinates are shown in the Smith chart.
The value of S11
and impedance
as indicated by
the Marker
Position of S11 in
the Smith chart
Figure 1.7 – The Smith chart for S11 at 500 MHz as seen from component Term1.
g. Now we also want to show the S11 of the required image impedance ZI on the Smith
chart. This can be done by first calculating the S11 of ZI = 25+j15 using equation
inserted into the data display area. The equation is shown below. Note that S11 = I ,
the reflection coefficient of the impedance.
Figure 1.8 – Equation for finding S11 of the image impedance ZI (Note that we use ZS = ZI)
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EMG3036 Microwave Circuits and Components
Impedance Transformation
h. Now insert S11 for ZI as shown in Fig. 1.10. The resultant Smith chart should be as
shown in Figure 1.9. At this stage, save the data display as LC_matching.dds.
Due to L1
Due to C1
Impedance
transformation
Figure 1.9 – The final Smith chart, with the effect of adding C1 and L illustrated.
Note:
The function of the L impedance transformation is to transform ZL = 100 − j25 into ZI = 25 +
j15 at 500 MHz. This is accomplished through the effect of adding a susceptance (as created
by C1) and a reactance (as created by L1). Using a graphical method such as Smith chart allow
us to visualize the effect of C1 and L1. These elements modify the position of Marker m5, until
it gradually reaches the position of Marker m6, as illustrated in Figure 1.10. The position of
m6 corresponds to ZI = 25 + j15 (at 500 MHz). When we achieved this, the impedance
transformation network design will be done.
4. Perform impedance transformation using interactive tuning
The ADS software has a powerful tuning feature, which allow us to change the values of the
components in the circuit while it updates the results real-time. A typical simulation process in
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EMG3036 Microwave Circuits and Components
Impedance Transformation
ADS needed a large amount of pre-processing before the actual simulation is carried. The preprocessing involves setting up the appropriate variables and the RAM of the computer based
on the schematic and simulation control. During the “tuning” process, the ADS assumes the
setup of the schematic to be unchanged, therefore the pre-processing is carried out once and
simulation is run whenever the parameter under tuned is changed. This capability is useful for
interactive design such as impedance transformation using graphical method.
a. Return to the schematic window and double-click on the C1 capacitor. Click the
Tune/Opt/Stat/DOE Setup button to enable tuning. Enter the tuning range from 0pF to
10pF in a 0.01pF step, as shown below.
Figure 1.10 – Enabling and setting the tuning range for capacitor
b. Repeat the above for L1 inductor and enter the tuning range from 0nH to 20nH in 0.01nH
step.
c. Now, start the turner by clicking Simulate > Tuning or click the tuning icon,
.
Immediately, the status (simulation) window will appear along with the Tune Control dialog
box as shown in Fig. 1.11. Go ahead and tune by moving the slider or click on the buttons
using the default settings and watch the updated traces appear in the data display window.
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EMG3036 Microwave Circuits and Components
Impedance Transformation
Move the slider or click on the
buttons to tune values. Notice how
the new traces appear on the data plot
after each change
Each tuning creates another
trace. The marker moves to
the most recent simulated
(tuned) trace. This trace is the
dataset, which is changed
each time you tune (simulate).
Figure 1.11 – Tuning feature in ADS
d. Continue tuning until you are satisfied with the matching results at m6 corresponds to ZI =
25 + j15 ohm. You should adjust slider for C1 and then follow by L1. The values of C1 and
L1 should be approximately 19.13 pF and 4.65 nH respectively.
e. Click the Update Schematic button to have the C1 and L1 unit values updated on the
schematic and click the close button to close the tuning window.
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EMG3036 Microwave Circuits and Components
Impedance Transformation
Figure 1.12 – Detail tuning control
Figure 1.13 – After tuning the values of C1 and L1, markers m5 is at m6
f. The final schematic is as shown in Fig. 1.14. Modify the S-parameters simulation control
as shown, with the start frequency at 0.2 GHz and the stop frequency at 1 GHz. Also
enable the calculation of Z-parameters from the S-parameters as by double clicking the Sparameters simulation control and setting the check box as depicted in Fig 1.15.
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EMG3036 Microwave Circuits and Components
Impedance Transformation
Figure 1.14 – Final schematic after tuning
Figure 1.15 – Enabling Z-parameters calculation
g. Save the schematic and run the simulation again.
h. Plot the Z11 as seen by Term1 as two X-Y plots, one showing the real part and the other
showing the imaginary part versus frequency. The result is as shown in Figure 1.17. Using
markers, it is indeed verified that we obtained the required impedance at 500 MHz. Note
that Z11 = ZI in this one-port network.
i. Save the data display window.
j. A final note, by now you would notice that the impedance transforming network only
works at one frequency, i.e. 500MHz for this example. This is true for all impedance
transformation networks. However you would notice that within a small range from
500MHz, known as the bandwidth, the impedance transformation network still works
reasonably well, i.e. the parallel RC load network still tranformed to 25+j15 approximately.
For the L networks, we cannot control the operating range, but for higher order networks
such as T, pi or ladder networks, one can control the bandwidth for a constant load
impedance. Refer to the lecture notes for more details on the bandwidth.
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EMG3036 Microwave Circuits and Components
Impedance Transformation
Figure 1.16 – X-Y plots of real and imaginary parts of ZI.
Lab Procedure
Using the steps discussed and shown previously, design and implement a matching network to
match a load ZL = 100 − j100 ohm to 50 ohm at frequency of 525 MHz.
The followings are required:
a. Choose ONE of these for the matching network design; such as one L-network, two Lnetworks or three L-networks or any combinations or that you have encountered before.
Justify your reasons for selecting this matching network.
b. Compute the exact values for each L and C used in the proposed matching network, using
the analytical formulae for B and X, shown in Figure 1.2.
c. Apply the interactive-tuning features discussed previously to determine the values for L
and C, to match ZL = 100 − j100 ohm to 50 ohm. Compare these values with the calculated
values obtained in part (b).
d. Examine the tuned values for L and C by performing S-parameter simulations (with Zparameters enabled). Evaluate the value of Z11 of the circuit at 525 MHz.
e. Evaluate the value of S11 of the circuit at the frequency range from 500 MHz to 550 MHz.
f. Deduce briefly a wideband matching techniques in order to match the same load, ZL = 100
− j100 ohm to 50 ohm at frequency of 500 MHz to 550 MHz.
NOTE
No report is needed for this experiment. You would be evaluated on-the-spot during the
experiment.
Evaluation Schemes (20%)
Understanding of fundamental concepts – 5%
Ability to explain the procedures involved – 5%
Ability to identify or determine expected results – 5%
Ability to explain or elaborate the results – 5%
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