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

Component Q=4.73RV=4.424 Ohms

Circuit Q Q of Vin/VS=102.2/( )=2.416 Q of Vout/VS=98/( )=2.21Circuit Q is different from component Q!

Four Combinations of L-Match R L >R S R S >R L

Split a Pi Network into Two L Networks

Virtual Resistor R L >R S R S >R L Virtual Resistance must be smaller than source resistance! (Blocks DC)

Design a Pi-Match RS=100 Ohms RL=1000 Ohms Resonant Frequency: 100 MHz Q2=15 R2/R=(Q )/(Q ) (See attached) Q2Q2 Q1Q1

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

R L >R S R S >R L

Calculation in Matlab

Schematic Q2=4.472Q1=10 RV=1050 Ohms

Vin/VS

Review of Smith Chart 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 j Ohms. (We need to have match the source and load to their complex conjugates)

Starting Smith Chart (load) (source)

Four Combinations of L-Match R L >R S R S >R L (Series L causes clockwise Movement on constant R on smith chart… …) (The only one)

C=39.46 pF; L= nH

Constant Q Q of series impedance=ratio of reactance to resistance

Constant Q Circle

Example 4-4 Constant Q of 15 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) pF22.36 pF nH147.9 nH68.55 pF75.49 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