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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 • • • • • 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 • • • • 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