RF Engineering – Passive Circuit
Impedance Transformation
Interactive Impedance Transformation: Lumped L impedance
Transformation
1.0 Objectives
 To learn the basic of 2-elements lumped impedance matching/transformation method.
 To learn the interactive feature and the “tuning” capability of the Advance Design
System (ADS) software.
2.0 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.
Such network is usually called impedance matching 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 experiment, impedance transformation principle will be demonstrated using
the ADS software. The convention for terms used in impedance transformation is
shown in Figure 2.1. The impedance network used is the L impedance transformation
network. The L impedance transformation approach uses two reactive components,
and 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 are shown in Figure 2.2.
 For greater flexibility, we can use graphical method employing the Smith chart,
which can cater to transformation networks with more than two elements. The
complexity of the analytical expression grows exponentially with additional
component, and is not suitable when the impedance transformation network contains
more than 3 elements.
Zs
Impedance
Transformation
Network
Vs
ZL
Image
imepdance ZI
Load
impedance
Figure 2.1 – Nomenclature of impedance transformation.
F. Kung
1
May 2007
RF Engineering – Passive Circuit
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 2.2 – The two configurations for L impedance transformation network.
For RL<RS:
B
RS  RL
RL
 X S  RS
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 
R L  X L  RS R L
2
RL
RS
RL  X L
2
2
2
X
R
1 X L RS

 S  XS
B
RL
RL B
3.0 Introduction to the Experiment
In this example we want to transform a complex load impedance to ZI = 35+j20 at 450.0
MHz. The load is modeled by a 300 resistor in parallel with a 0.82 pF capacitor. At
450.0 MHz, the load impedance ZL can be calculated as:
Z L  R // j1C 

R
1  jRC
  2 450  10 6

Z L  202 .1852  j140 .6297
Since Re Z L   RL  202 .1852  Re Z s   Rs  35 , configuration (a) of Figure 2.2 is used.
4.0 The Experiment Procedures
1. Log into workstation.
F. Kung
2
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
2. Run the ADS version 2003A software (you might use a newer version of the
software).
3. From the main window of ADS, create a new project folder named
“Impedance_Transform” under the directory “D:\ads_user\default\” (Figure 4.1).
Figure 4.1 – Opening a new project in ADS.
4. The new schematic window will automatically appear 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.
5. Draw the schematic as shown in Figure 4.2. In using configuration (a) of Figure 2.2,
we assume that the susceptance B can be synthesized by capacitor C 1 while the
reactance X can be synthesized by inductance L1. Initially set C1 = 0 and L1 = 0.
Save the schematic as “schematic1.dsn”. The various components used in Figure 4.2
can be obtained from the palette list of the draw schematic window as shown in
Figure 4.3. We see from Figure 4.2 that this is an S-parameter simulation, requesting
the software to calculate the S-parameters as seen from component Term1 at
frequency 450 MHz. In this case the parameter Step in the S-parameter simulation
control is ignored.
F. Kung
3
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
We wish to find
s11 as seen from
Term1
Figure 4.2 – The schematic.
Figure 4.3 – The pallete for lumped components.
6. Now run the simulation by clicking the button
F. Kung
4
.
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
7. 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
.
8. Insert a Smith Chart in the data display window as shown in Figure 4.4.
Click this button to insert
an X-Y plot
Click this button to insert
a Smith chart
Display area
Click this button to insert
an equation in the display
area
Select S(1,1) to show the
s11 as measured from
Term1 in the Smith chart
Figure 4.4 – Inserting a Smith chart in the display area. Also shown are typically used
buttons.
F. Kung
5
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
9. You can change the color, the thickness of the line and the format of the Smith chart
by using the Trace Option and Plot Options tab as shown in Figure 4.5.
Figure 4.5 – Changing the properties of a plot. Enabling both impedance and admittance
coordinates in the Smith chart.
Hints: To show both impedance and admittance lines on the Smith chart, double click on
the chart and modified the plot options, select “both” for the coordinate.
10. Your Smith Chart should look similar to the one shown in Figure 4.6. Use a Marker
to display the complex value of the s11. Note that both impedance and admittance
coordinates are shown in the Smith Chart (See Figure 4.5 again if you do not know
how to set this).
F. Kung
6
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
Marker
The value of S11
and impedance as
indicated by the
Marker
Position of S11 in the
Smith chart
Figure 4.6 – The Smith chart for s11 at 450 MHz as seen from component Term1.
11. 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 = 35+j20 using equations
inserted into the data display area. The equations are shown in Figure 4.7. Note that
s11 = I , the reflection coefficient of the impedance.
Figure 4.7 – The equations for finding s11 of the image impedance ZI (Note that we use
ZS = ZI in this case).
12. Now insert s11 for ZI as shown in Figure 4.8a. The resultant Smith Chart should be as
shown in Figure 4.8b. At this stage you should save the data display, save it as
“schematic1.dds”.
F. Kung
7
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
Figure 4.8a – Selecting the result of equations.
Impedance
transformation
Due to L1
Due to C1
Figure 4.8b – The final Smith Chart, with the effect of adding C1 and L1 illustrated.
13. The function of the L impedance transformation is to transform ZL = 202.1852j140.6297 into ZI = 35 + j20 at 450 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 allows us to visualize the effect of C1 and L1.
These elements modify the position of Marker m1, until it gradually reaches the
position of Marker m2, as illustrated in Figure 4.8b. The position of m2 corresponds
F. Kung
8
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
to ZI = 35 + j20 (at 450 MHz). When we achieved this, the impedance transformation
network design will be done.
14. The ADS software has a powerful tuning feature, which allows us to change the value
of the components in the circuit while it updates the results in real-time. A typical
simulation process in ADS needs a large amount of pre-processing before the actual
calculation is carried out. The pre-processing involves setting up the appropriate
variables and the memory of the computer based on the schematic and simulation
control. During the “tuning” process, the ADS assumes the setup of the schematic
and simulation to be unchanged, therefore the pre-processing is carried out once and
calculation is run whenever the parameter-under-tuned is changed. This capability is
useful for interactive design such as impedance transformation using the graphical
method.
15. Enable the “tuning” mode by pressing the following pushbutton in the standard
toolbar
.
16. Use the mouse cursor to select the parameter of L1 and C1 in the schematic window,
press Details button and set the step size and max step value as shown in Figure 4.9.
The software will automatically rerun the simulation after each change is detected on
value L1. Also set Trace History to 0 or 1. Now adjust the sliders control for L1 and
C1 until the marker m1 moves to m2 in the Smith chart. You should adjust the slider
for C1 and then follow by L1 (can you figure out why?). The final Smith Chart is
shown in Figure 4.10. After you are satisfied with the result, press the Update button
to permanently change the values of L1 and C1 in the schematic window.
Figure 4.9 – The tuning dialog box.
F. Kung
9
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
Figure 4.10 – After tuning the values of L1 and C1, both Markers m1 and m2 overlap on
each other, signifying the impedance transformation is done.
17. The final schematic is as shown in Figure 4.11. Modify the S-parameters simulation
control as shown, with the start frequency at 200 MHz and the stop frequency at 1000
MHz. Also enable the calculation of Z-parameters from the S-parameters by double
clicking the S-parameters simulation control and setting the check box as depicted in
Figure 4.12. Now save this schematic as “schematic2.dsn”.
Figure 4.11 – The final schematic.
F. Kung
10
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
Figure 4.12 - Enabling the Z-parameters calculation.
18. Now run the simulation again, after which the software will invoke a second data
display window for “schematic2.dsn”. This time instead of plotting the s11 as seen by
Term1 in a Smith chart, 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 4.13. Using the markers, it is verified that we obtained
the required impedance at 450 MHz. Note that z11 = ZI in this one-port network.
F. Kung
11
May 2007
RF Engineering – Passive Circuit
Impedance Transformation
Figure 4.13 – X-Y plots of real and imaginary parts of ZI.
19. A final note, by now you would notice that the impedance transforming network only
works at one frequency, i.e. 450 MHz for this example. This is true for all impedance
transformation networks. However you would notice that within a small range of
frequency centered at 450 MHz, known as the bandwidth, the impedance
transformation network still works reasonably well, i.e. the parallel RC load network
still tranformed to 35+j20 approximately. For the L networks, we cannot control the
operating frequency 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.
20. Extra procedure – Use the analytical formulae for B and X of Figure 2.2 to derive the
exact values for L1 and C1. Compare these with the values obtained using interactive
approach in ADS software.
NOTE
No report is needed for this experiment. You would be evaluated on-the-spot during
the experiment.
F. Kung
12
May 2007