Impedance Matching (1)
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![Page 1: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/1.jpg)
Impedance Matching (1)
![Page 2: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/2.jpg)
Maximum Power Transfer
Choose an RL in order to maximize power delivered to RL.
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Power Delivered to the Load
![Page 4: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/4.jpg)
Numerical Example
• VTH=1 V
• RTH=50 Ω
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Conclusion!
• Maximum power is delivered to the load resistor when RL is equal to RTH.
![Page 6: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/6.jpg)
Max Power Transfer for Complex Source Impedance
At resonant frequency, the series impedance of the inductor and capacitor is zero.
![Page 7: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/7.jpg)
Summary
RL>RS RS>RL
![Page 8: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/8.jpg)
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)
RP must be larger than RS
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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/(ωRLC)QS=RS/(ωL)
![Page 13: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/13.jpg)
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
![Page 17: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/17.jpg)
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 largerthan L match components. E.g. if 2pF is replaced by 6 pF, then this technique will not work.
![Page 20: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/20.jpg)
Resonant Approach
• Resonate any stray reactance with an equal and opposite reactance at the frequency of interest!
![Page 21: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/21.jpg)
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, LS≈LP and CS ≈CP.
• RP is Q2 times RS.
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Summary
RL>RS RS>RL
![Page 29: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/29.jpg)
Smith Chart Derivation
![Page 30: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/30.jpg)
Smith Chart Derivation (2)
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Smith Chart Construction
(The center line represents an axis where X=0.)
(+)
(-)
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zL=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 Utility1. Select Smith Chart Match2. Click on Tools, then select Smith chart utility3. 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
ADS Matlab
Shunt Cap 1.511 pF 1.5 pF
Series L 5.72 nH 5.627 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
![Page 46: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/46.jpg)
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
![Page 49: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/49.jpg)
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.)
(+)
(-)Conductancecircle
Inductive susceptance
Rotate the impedance chart by 180 degrees
Capacitive susceptance
![Page 53: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/53.jpg)
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
![Page 55: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/55.jpg)
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
![Page 56: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/56.jpg)
Adding a Shunt Inductance
Insertion of a shunt inductor causes a rotation counter clockwise along a constant circle of admittance
![Page 57: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/57.jpg)
Shunt Inductance
Neg Ind
High LLow L
fixed frequency
Insertion of a shunt inductor causes a rotation counter clockwise along a constant circle of admittance
![Page 58: Impedance Matching (1)](https://reader034.fdocuments.us/reader034/viewer/2022051401/568133f5550346895d9ae865/html5/thumbnails/58.jpg)
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.