Impedance Matching with Lumped Elements

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# Impedance Matching with Lumped Elements - PowerPoint PPT Presentation

jX 1. jB 2. Y L. Impedance Matching with Lumped Elements. jX 1. Z L. jB 2. Single-Stub Matching. Load impedance . Input admittance=S. Series Stub. Voltage minimum. Input impedance=1/S. Double Stub Matching Network. a. b. Y L. jB 2. jB 1. b. a. x=1. Y L. P open circuit .

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## Impedance Matching with Lumped Elements

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Presentation Transcript

jX1

ZL

jB2

Single-Stub Matching

Series Stub

Voltage minimum

Input impedance=1/S

x=1

YL

Popen circuit

Pshort circuit

r=1

0

r=0.5

Real part of

Refl. Coeff.

Smith Chart

x=-1

x=1

P2

YL

G1=1

Popen circuit

Pshort circuit

r=1

0

r=0.5

Real part of

Refl. Coeff.

P3

Smith Chart

x=-1

Rotate the the G=1 circle through an angle -f

The intersection of G=1 and the GL circle determine

The point P2

x=1

YL

Popen circuit

Pshort circuit

r=1

0

r=0.5

Real part of

Refl. Coeff.

x=-1

Smith Chart

cannot be matched when d=1/8 wavelength

r

Dq

rm

3p/2

p/2

qm

p

q

Bandwidth characteristic for a single

Section quarter wave transformer

1

Z2

G3

G1

ZL

Z1

G2

G

T12

T21

Theory of Small Reflection

q

T21

1

G1

Multiple reflection of waves for a circuit

with two reflection junctions

q

q

q

G3

ZL

Z2

Z1

Z0

ZN

A multi-section quarter-wave transformer

Example

Z3

ZL

Z2

Z1

Z0

Design a three section binomial transformer to match

a 50 Ohms load to a 100 Ohms line. Calculate the bandwidth

For max reflection =.05 over the passband.

Example

Design a two section Chebyshev transformer (two sections) to

Match a line of load impedance =2. The maximum tolerance

Value of r is 0.05.

Design of Complex Impedance Termination

Amplifier

Zc

Zc

Input

Matching

network

ZL

Output

Matching

network

Zs

Microwave amplifier circuit

l

l

jB1

=

ZL

ZL

G=1

Zc

Stub

Transmission Line Matching Network

jX1

jX2

jB2

jB1

ZL

ZL

G=1

G=1

Alternative Matching Networks

l/l = 0.0626

l/l = 0.4375

j1

Generator

1

Y’in

YL

G=2

ZL= 0.4-j0.2

2

Y”in

G=1

-j1

Design Procedure for the Matching Network with Shunt Stub

Z22-Z12

Z11-Z12

ZT

ZS

ZL

ZL

Z12

VS

Voc

ML

Zin

A T matching network

Thevenin equivalent

network

Zg

Z0

Vg

ZL

Impedance Transformation and Matching

Review of Transmission Lines and Smith Chart

Z=L

Z=0

Finite Transmission Line terminated with load impedance

L

Imaginary part of

Refl. Coeff.

x=1

Popen circuit

Pshort circuit

r=1

0

r=0.5

Real part of

Refl. Coeff.

x=-1

Smith Chart

Review of Transmission Lines and Smith Chart

Zg

Z0

Z=L

Vg

Z=0

ZL

L

Finite Transmission Line terminated with load impedance