Smith Chart for Class

SMITH CHART DR. D. GHOSH, SCHOOL OF ELECTRICAL SCIENCES, IIT BHUBANESWAR

SMITH CHART • Impedances, voltages, currents, etc. all repeat every half wavelength • The magnitude of the reflection coefficient, the standing wave ratio (SWR) do not •

change, so they characterize the voltage & current patterns on the line If the load impedance is normalized by the characteristic impedance of the line, the voltages, currents, impedances, etc. all still have the same properties, but the results can be generalized to any line with the same normalized impedances

DR. D. GHOSH, IIT BHUBANESWAR

SMITH CHART Real Impedance Axis


Smith Chart

Imaginary Impedance Axis

Toward Generator

Away From Generator

Constant Reflection Coefficient Circle

Scale in Wavelengths Full Circle is One Half Wavelength Since Everything Repeats


SMITH CHART • Impedance divided by line impedance • Z1 = 100 + j50 • Z2 = 75 -j100 • Z3 = j200 • Z4 = 150 • Z5 = infinity (an open circuit) • Z6 = 0 (a short circuit) • Z7 = 50 • Z8 = 184 -j900

(50 Ohms)

• Then, normalize and plot. The points are plotted as follows: • z1 = 2 + j • z2 = 1.5 -j2 • z3 = j4 • z4 = 3 • z5 = infinity • z6 = 0 • z7 = 1 • z8 = 3.68 -j18S Dr. D. Ghosh, IIT Bhubaneswar

STEPS FOR USING SMITH CHART •

Locate the normalized load impedance on the chart

•

Draw a circle that represents the reflection coefficient or VSWR. The center of the circle is the center of the chart. The circle passes through the normalized load impedance.

•

Any point on the line is located on this circle. Rotate clockwise to move toward the generator (away from the load).

•

The distance moved on the line is indicated on the outside of the chart in wavelengths

•

Exactly opposite to the normalized load is its admittance.

Dr. D. Ghosh, IIT Bhubaneswar

zL = 0.5 + j0.5 Find impedance at l = /4


Locate the normalized load impedance on the chart

zL = 0.5 + j0.5 Find impedance at l = /4

Draw a circle that represents the reflection coefficient or VSWR. The center of the circle is the center of the chart. The circle passes through the normalized load impedance.


direction of increasing l towards generator zL = 0.5 + j0.5 Find impedance at l = /4 Any point on the line is located on this circle. Z( l = /4) = 1 – j 0.9

Rotate clockwise to move toward the generator (away from the load).

The distance moved on the line is indicated on the outside of the chart in wavelengths. Dr. D. Ghosh, IIT Bhubaneswar

ZL = 35 + j65 Z0 = 50 l = for Zx purely resistive

l = 0.091 z( l = 0.091) = 4.4 Z( l = 0.091) =220


Quarter wave matching ZL = 200 – j100 Z0 = 100 Find l of line and Z of stub for matching

l for line = 0.213 Z for stub = 61.6


STEPS FOR SINGLE STUB MATCHING • Locate the normalized load admittance

on the chart and draw the reflection

coefficient circle

• Mark the intersection of the reflection coefficient with the r = 1 circle and read the admittance at the point as

• Note the distance from • Mark the point 0 the length of the stub


to

1

to get the position of the stub from the load and note the distance from short circuit to

to get

Single stub matching ZL = 500 Z0 = 100 Find l of stub and l of line For matching


Locate the normalized load admittance on the chart and draw the reflection coefficient circle


l for line = 0.18


Mark the intersection of the reflection coefficient with the r = 1 circle and read the admittance at the point 1 as

Note the distance from to to get the position of the stub from the load


l for stub = 0.083


Mark the point 0 and note the distance from short circuit to to get the length of the stub


l for line = 0.18 l for stub = 0.083


DOUBLE STUB TUNING

Z0

ZL l

l lB


lA

STEPS FOR DOUBLE STUB TUNING

Z0

ZL /8

From Load to Stub A

/8

lB

lA

• Locate the normalized load admittance on the chart and draw the reflection coefficient circle. • Move from load point to the first stub and mark . Draw the = constant circle. From Stub A to Stub B

• Draw the auxiliary circle for g = 1 by rotating it by the length between the stubs. At Stub A

• Mark the intersection of the coefficient circle with

• Mark the point

= constant circle and the auxiliary circle as

. Draw the reflection

. 0

and note the distance from short circuit to

to get the length of the stub

A

At Stub B

• Draw the g = 1 circle and mark the intersection of the g = 1 circle and the reflection coefficient circle with 1

.

• Mark the point Dr. D. Ghosh, IIT Bhubaneswar

0

and note the distance from short circuit to

to get the length of the stub B

as

Single stub matching ZL = 100 + j 50 Z0 = 50 Find l of stub A and B for matching Z0

ZL /8

lB

/8

lA


From Load to Stub A Locate the normalized load on the chart and admittance draw the reflection coefficient circle. Move from load point to the first . stub and mark = constant circle. Draw the


ZL /8

lB

/8

lA


From Stub A to Stub B Draw the auxiliary circle for g = 1 by rotating it by the length between the stubs.


ZL /8

lB

/8

lA

l for stub A = 0.195


At Stub A Mark the intersection of the = constant circle and the auxiliary circle as . Draw the reflection . coefficient circle with 0 Mark the point and note the distance from short circuit to to get the length of the stub A


ZL /8

lB

/8

At Stub B Draw the g = 1 circle and mark the intersection of the g = 1 circle and the reflection coefficient circle with as 1 .

lA

Mark the point 0 and note the distance from short to get the circuit to length of the stub B

l for stub B = 0.15



ZL /8

lB

/8

lA

l for stub A = 0.195 l for stub B = 0.15



ZL /8

lB

/8

lA

Alternate Solution l for stub A = 0.402 l for stub B = 0.449


Smith Chart for Class

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