Impedance Matching (2)
Outline
• Three Element Matching
– Motivation
– Pi Network
– T Network
• Low Q or Wideband Matching Network
• Impedance Matching on Smith Chart
– Two-Element
– Three-Element Matching
• Multi-Element Matching
• Genesis
RV=4.424 Ohms
Component Q=4.73
Circuit Q
Q of Vin/VS=102.2/(125.4-83.1)=2.416
Circuit Q is different from component Q! Q of Vout/VS=98/(117.6-73.4)=2.21
Four Combinations of L-Match
RL>RS
RS>RL
Split a Pi Network into Two L
Networks
Virtual Resistor
Virtual Resistance must be
smaller than source resistance!
RL>RS
RS>RL
(Blocks DC)
Design a Pi-Match
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RS=100 Ohms
RL=1000 Ohms
Resonant Frequency: 100 MHz
Q2=15
R2/R=(Q22+1)/(Q12+1) (See attached)
Q1
Q2
Calculation
Design Sequence:
1. Q1, Q2
2. RV
3. L2, C2
4. L1, C1
Pi-Match Schematic
Use Pi-Match to Produce
Matching at 100 MHz
T-Match
T-Match
RL>RS
RS>RL
Calculation in Matlab
Schematic
Q1=10
Q2=4.472
RV=1050 Ohms
Vin/VS
Review of Smith Chart
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Adding an inductor in series
Adding a capacitor in series
Adding a capacitor in parallel
Adding an inductor in parallel
Adding an Inductor in Series
Insertion of a series inductor to an impedance moves the impedance upward,
causing a rotation clockwise along a constant circle of resistance
Adding a Capacitor in Series
Insertion of a series capacitor to an impedance move impedance
downward, causes a rotation counter clockwise along a constant circle of
resistance
Adding a Shunt Capacitance
Insertion of a shunt capacitor causes a rotation clockwise along a
constant circle of admittance
Adding a Shunt Inductance
Insertion of a shunt inductor causes a rotation counter clockwise along a
constant circle of admittance
Example
Design a matching network with a source impedance of
25+15j Ohm and output impedance of 100+25j Ohms.
(We need to have match the source and load to their
complex conjugates)
Starting Smith Chart
(source)
(load)
Four Combinations of L-Match
(Series L causes clockwise
Movement on constant R
on smith chart…
…)
(The only
one)
RL>RS
RS>RL
C=39.46 pF; L=156.35 nH
Constant Q
Q of series impedance=ratio of
reactance to resistance
Constant Q Circle
Constant Q of 15
Example 4-4
Q=15
The end of large terminating resistor will determine the Q.
Example 4-4 (Adding a Series L)
Get the admittance circuit with a
series L
Example 4.4
Get back with the center of chart with a shunt cap.
Example 4-4 (Q=15)
Compare the Smith Chart
Design with Calculation in
Matlab
C2
(matlab)
C2(Smith
Chart)
L1+L2
(matlab)
L1+L2 (Smith
chart)
C1 (matlab)
C1 (Smith
chart)
23.87 pF
22.36 pF
138.63 nH
147.9 nH
68.55 pF
75.49 pF
Example 4.8
• Design a T network to match Z=15+15j
Ohm source to a 225 Ohm load at 30
MHz with a loaded Q of 5.
Example 4.8
Get on Constant Q=5 curve