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.