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Impedance Matching (1)

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Maximum Power Transfer Choose an RL in order to maximize power delivered to RL.

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Power Delivered to the Load

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Numerical Example V TH =1 V R TH =50 Ω

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Conclusion! Maximum power is delivered to the load resistor when R L is equal to R TH.

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Max Power Transfer for Complex Source Impedance At resonant frequency, the series impedance of the inductor and capacitor is zero.

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Summary R L >R S R S >R L

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L Network Different L netowrk Difference bewteen highpass and low pass Examine butterworth filter from the point of view of matching….

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Resistance Transformation (See derivation in the handout) R P must be larger than R S

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Matlab Calculation

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Simulation Results

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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/(ωR L C) QS=RS/(ωL)

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Matlab Calculation

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ADS Simulation

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Dealing With Complex Load Absorption Approach Resonance Technique

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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

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Absorption Example

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Calculation Neglecting Stray Components

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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.

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Resonant Approach Resonate any stray reactance with an equal and opposite reactance at the frequency of interest!

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Example Resonate the 40 pF with a parallel L.

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Parallel Resonant Network

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Determine the Matching Network

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Resonant Approach Example

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Series to Parallel Conversion for RC Circuits

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Series to Parallel Conversion for RL Circuits

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Intuition If the Q is sufficiently large, L S ≈L P and C S ≈C P. R P is Q 2 times R S.

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Summary R L >R S R S >R L

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Smith Chart Derivation

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Smith Chart Derivation (2)

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Smith Chart Construction (The center line represents an axis where X=0.) (+) (-)

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z L =1±j

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Adding a Series Capacitance to an Impedance

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Use Smith Chart Matching

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SmithChartMatch

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Smith Chart Utility 1. Select Smith Chart Match 2.Click on Tools, then select Smith chart utility 3. Select first option

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Change the Load Impedance to 75 Ohms

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Lock Load/Source Impedance

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Add a Shunt Capacitance

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Negative Capacitance! Negative capacitance

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Add a Series Inductor (1) (2) Double click on the smith chart to drop the component

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Build ADS Circuit

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Comparison with Matlab Vs. ADS ADSMatlab Shunt Cap1.511 pF1.5 pF Series L5.72 nH5.627 nH

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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

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Series Inductance Neg L High LLow 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

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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

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Series Capacitance High C Low L Neg C fixed frequency Insertion of a series capacitor to an impedance move impedance downward, causes a rotation counter clockwise along a constant circle of resistance

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Admittance

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Admittance Example

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Method 1

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Method 2 1. Find the Z. 2. Rotate Smith Chart 180 degrees

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Smith Chart Construction (The center line represents an axis where X=0.) (+) (-) Conductance circle Inductive susceptance Rotate the impedance chart by 180 degrees Capacitive susceptance

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Enable Admittance Chart

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Adding a Shunt Capacitance Insertion of a shunt capacitor causes a rotation clockwise along a constant circle of admittance

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Adding a Shunt Capacitance High C Low C Neg C fixed frequency Insertion of a shunt capacitor causes a rotation clockwise along a constant circle of admittance

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Adding a Shunt Inductance Insertion of a shunt inductor causes a rotation counter clockwise along a constant circle of admittance

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Shunt Inductance Neg Ind High L Low L fixed frequency Insertion of a shunt inductor causes a rotation counter clockwise along a constant circle of admittance

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Next Class Pi Network T Network Smith Chart Genesis

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The Pi Network The virtual resistance must be less than RS and RL.

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Chapter 12 © Copyright 2007 Prentice-HallElectric Circuits Fundamentals - Floyd Chapter 12.

Chapter 12 © Copyright 2007 Prentice-HallElectric Circuits Fundamentals - Floyd Chapter 12.

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