Lect. 13: Impedance Matching (2)
Smith Chart Solution 2 (not using combined ZY Smith
Chart)
Example 5.1 on Page 225 of Pozar
Design an L section matching network to match a series RC
load with an impedance ZL = 200 - j 100 , to a 100  line, at
a frequency of 500 MHz.
Solution:
Step 1: Convert the load impedance to admittance by
drawing the SWR circle through the load, and a straight line
from the load through the center of the Smith Chart.
Step 2: Move the load impedance to the impedance circle of
1+ jx (done in admittance Smith Chart) -- add j 0.3 in
ELEC4630, Shu Yang, HKUST
susceptance
1
Step 3: Convert back to
impedance.
Step 4: Move to the center
of the Smith Chart by
adding a series inductor
ELEC4630, Shu Yang, HKUST
2
Therefore we have b = 0.3, x = 1.2 (check this result with the
analytic solution). Then for a frequency at f = 500 MHz,
we have
b
C
 0.92 pF
2fZ 0
xZ 0
L
 38.8nH
2f
Is there another solution?
ELEC4630, Shu Yang, HKUST
3
There are two solutions for the matching networks. In this
case, there is no substantial difference in bandwidth
between the two solutions.
ELEC4630, Shu Yang, HKUST
4
• Commonly Used Lumped Elements
– Resistors, Capacitors, Inductors
For small
inductance
(<1 nH)
ELEC4630, Shu Yang, HKUST
For larger inductance
(from 1 to 10 nH),
lower self-resonance
frequency
5
Single-Stub Impedance Tuning
• Using a single opencircuited or shortcircuited length of
transmission line (a
“stub”)
Shunt stub
• Connect either in
parallel or in series
with the
transmission feed
line.
• Tuning parameters:
distance d from the
load and the stub
length l.
Series stub
6
ELEC4630, Shu Yang, HKUST
Design issues:
• Any load impedance can be matched to the line by using single
stub technique. The drawback of this approach is that if the load is
changed, the location of insertion may have to be moved.
• The transmission line realizing the stub is normally terminated by
a short or by an open circuit. In many cases it is also convenient to
select the same characteristic impedance used for the main line,
although this is not necessary.
• The choice of open or shorted stub may depend in practice on a
number of factors. A short circuited stub is less prone to leakage of
electromagnetic radiation and is somewhat easier to realize. On the
other hand, an open circuited stub may be more practical for certain
types of transmission lines, for example microstrips where one
would have to drill the insulating substrate to short circuit the two
conductors of the line.
ELEC4630, Shu Yang, HKUST
7
Impedance Matching Using a Single Shunt Stub
Since the circuit is
based on insertion
of a parallel stub, it
is more convenient
to work with
admittances, rather
than impedances.
Tuning Procedures:
• Find the proper d so that Y = Y0 + jB
• Choose the stub susceptance (decided by l) to be -jB
ELEC4630, Shu Yang, HKUST
8
Example 5.2 on Page 229 of Pozar
For a load impedance ZL = 60- j 80 ,
design two single-stub (short circuit)
shunt tuning networks to
match this load to a 50  line.
Working frequency is 2 GHz.
The load consists of a resistor
and capacitor in series.
Working with the
Smith Chart!
ELEC4630, Shu Yang, HKUST
9
Step 1: Plot the normalized load impedance zL = 1.2-j1.6, construct the
appropriate SWR circle, and convert to the load admittance, yL. For the
remaining steps we consider the Smith chart as an admittance chart.
Step 2: Notice that the SWR circle intersects the 1 + jb circle at two
points, denoted as y1 and y2. Thus the distance d, from the load to the
stub, is given by either of these two intersections. Reading from the
wavelength scale, we obtain
d1  0.176  0.065  0.110
d 2  0.325  0.065  0.260
* Actually, there is an infinite number of distance, d, on the SWR circle
that intersect the 1+jb circle. But it is desirable to keep the matching stub
as close as possible to the load to improve the bandwidth and to reduce
losses.
ELEC4630, Shu Yang, HKUST
10
Step 3: At the two intersection points, the normalized admittances are
(using the susceptance scale)
y1  1  j1.47
y2  1  j1.47
Step 4: The first tuning stub should have a susceptance of -j1.47. If we
use an short-circuited shunt stub, the susceptance can be found on the
Smith chart by starting from y =  (the short circuit) and moving along
the outer edge of the chart (g = 0) toward the generator to the -j1.47. The
length is then
l1  0.095
Similarly, the required short-circuit stub for the second solution is
l2  0.405
ELEC4630, Shu Yang, HKUST
11
Solution 1 has a
significantly better
bandwidth than
solution 2.
Shorter stub produces
wider bandwidth.
ELEC4630, Shu Yang, HKUST
12
Analytic solution:
ELEC4630, Shu Yang, HKUST
13
ELEC4630, Shu Yang, HKUST
14