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Impedance Matching (1) Maximum Power Transfer Choose an RL in order to maximize power delivered to RL. Power Delivered to the Load Numerical Example • VTH=1 V • RTH=50 Ω Conclusion! • Maximum power is delivered to the load resistor when RL is equal to RTH. Max Power Transfer for Complex Source Impedance At resonant frequency, the series impedance of the inductor and capacitor is zero. Summary RL>RS RS>RL L Network • Different L netowrk • Difference bewteen highpass and low pass • Examine butterworth filter from the point of view of matching…. Resistance Transformation RP must be larger than RS (See derivation in the handout) Matlab Calculation Simulation Results High Pass Match Note: There is not a DC path to ZL. RS must be larger than RL! See derivation! QS=sqrt(RS/RL-1) QS=1/(ωRLC) QS=RS/(ωL) Matlab Calculation ADS Simulation Dealing With Complex Load • Absorption Approach • Resonance Technique Match Via Absorption Approach • Ignore stray component • Match the load resistance to the source resistance with an L-match • Subtract the stray component from the L-match value Absorption Example Calculation Neglecting Stray Components Account for Stray Components This technique will not work if the stray components is much larger than L match components. E.g. if 2pF is replaced by 6 pF, then this technique will not work. Resonant Approach • Resonate any stray reactance with an equal and opposite reactance at the frequency of interest! Example Resonate the 40 pF with a parallel L. Parallel Resonant Network Determine the Matching Network Resonant Approach Example Series to Parallel Conversion for RC Circuits Series to Parallel Conversion for RL Circuits Intuition • If the Q is sufficiently large, LS≈LP and CS ≈CP. • RP is Q2 times RS. Summary RL>RS RS>RL Smith Chart Derivation Smith Chart Derivation (2) Smith Chart Construction (+) (-) (The center line represents an axis where X=0.) zL=1±j Adding a Series Capacitance to an Impedance Use Smith Chart Matching SmithChartMatch Smith Chart Utility 1. Select Smith Chart Match 2. Click on Tools, then select Smith chart utility 3. Select first option Change the Load Impedance to 75 Ohms Lock Load/Source Impedance Add a Shunt Capacitance Negative Capacitance! Negative capacitance Add a Series Inductor (1) (2) Double click on the smith chart to drop the component Build ADS Circuit Comparison with Matlab Vs. ADS ADS Matlab Shunt Cap 1.511 pF 1.5 pF Series L 5.72 nH 5.627 nH 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 Series Inductance Low L High L Neg L fixed frequency 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 Series Capacitance Neg C High C Low L fixed frequency Insertion of a series capacitor to an impedance move impedance downward, causes a rotation counter clockwise along a constant circle of resistance Admittance Admittance Example Method 1 Method 2 1. Find the Z. 2. Rotate Smith Chart 180 degrees Smith Chart Construction Inductive susceptance Conductance circle (-) (+) Rotate the impedance chart by 180 degrees (The center line represents an axis where X=0.) Capacitive susceptance Enable Admittance Chart Adding a Shunt Capacitance Insertion of a shunt capacitor causes a rotation clockwise along a constant circle of admittance Adding a Shunt Capacitance Neg C High C Low C fixed frequency 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 Shunt Inductance Low L High L Neg Ind fixed frequency Insertion of a shunt inductor causes a rotation counter clockwise along a constant circle of admittance Next Class • • • • Pi Network T Network Smith Chart Genesis The Pi Network The virtual resistance must be less than RS and RL.