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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. V TH =1 V R TH =50 Ω. Conclusion!. Maximum power is delivered to the load resistor when R L is equal to R TH. - PowerPoint PPT Presentation
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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
(See derivation in the handout)
RP must be larger than RS
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 largerthan 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 Utility1. Select Smith Chart Match2. Click on Tools, then select Smith chart utility3. 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
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
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
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
Admittance
Admittance Example
Method 1
Method 2
1. Find the Z.2. Rotate Smith Chart 180 degrees
Smith Chart Construction
(The center line represents an axis where X=0.)
(+)
(-)Conductancecircle
Inductive susceptance
Rotate the impedance chart by 180 degrees
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
High C Low C
Neg 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
Neg Ind
High LLow L
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.
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