Lessons From

the
Smith Chart
Ward Harriman AE6TY
Pacificon ’13

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Modified from http://xkcd.com/849/
http://creativecommons.org/licenses/by-nc/2.5/

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 The Smith Chart...
A Pragmatic Presentation

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 Simple device
Don’t muddy the waters with equations of ‘Standing Wave
Ratio’ and ‘reflection coefficients’ or ‘complex math’...
Smith chart is just an unusual form of graph paper.
Used to plot complex impedances.
Complex impedances are just impedances with both a
resistive and reactive component.

All graphics here-in are produced using “SimSmith”, a Computer Aided Smith chart program.

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 The Center
j50

This Smith Chart

is quite simple:
The center of the
chart represents
a impedance of
50 ohms. Other
0
infinite
50
important points
are 0, infinite, +j50
and -j50
-j

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 Adding Reactance
Adding a series
reactance causes Decreasing
Parallel
Increasing
Series

movement along Inductance Inductance

the red circles...

Adding a parallel
reactance causes Increasing
Parallel
Decreasing
Series
movement along Capacitance Capacitance

the blue circles.

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 Adding Resistance
Adding series
resistance causes Series
movement along Resistor
the red arcs.
Parallel
Adding a parallel Resistor

resistance causes
movement along
the blue circles.

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 Lesson 1
Transmission lines
translate impedances
through rotations
around their Zo.

Here are 25,37,50,

75,150,300,600
transmission lines.

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 Lesson 1
(cont)
Transmission lines Series
can act much like Inductance

capacitors and Series

Transmission
inductors over small Line
ranges in frequency.

Here we show an
inductor and a series
transmission line...

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 Lesson II
Series Stubs as Reactances
Series
Transmission line Inductor

stubs (shorted and

Series, Shorted
open) can... yep... Transmission line
act like inductors
and capacitors.
Shorted Tlines Series Series, Open
increase inductance Capacitor Transmission Line
as they get longer...
Open lines increase
capacitance as they grow

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 Lesson II
Parallel Stubs as Reactances
Parallel
Inductor
Shorted Tlines Parallel, Shorted
increase inductance Transmission line
as they get longer...
Open lines increase
capacitance as they grow
(but only up to a point)

Series, Open
Transmission Line

Series
Capacitor

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 Lesson III
1/4 WaveLengths
Transmission lines
which are 1/4 wave
25 to 100
lengths long are
‘special’.

They ‘invert’ the

impedance,
(but only at a
single frequency) 200 to 10

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 Lesson III (cont)
1/4 WaveLengths
Impedance isn’t
really ‘inverted’.
25 to 50
Zo = 35
The real formula
is:

Zin Zout = Zo Zo 200 to 50

Zo = 100

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 Lesson IV
half WaveLengths
Half wave lines act
just like two 1/4
wave lines in 25 to 25
Zo = 35
series....
Often described
as having ‘no effect’
but only if the 200 to 200
Zo = 100
frequency is constant.

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 Observation
Change in Frequency = Change in length
For transmission lines: Sweep
Increasing the frequency 5 to 10
of analysis is (much) the
Sweep
same as increasing the 5 to 20
length of a transmission
line.

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 Observation
Sweeps
Smith chart can show
how impedance changes
as frequency changes. Series L Shunt C

For example, here is

a the familiar ‘path’ Frequency
Sweep
of a matching L network
and a frequency ‘sweep’
of the impedance.

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 Observations
Sweeps (cont)
Smith charts are often
used in describing
antenna impedances.
4.5 MHz

Here is the impedance

of a dipole for 80m. 3 MHz

Sweep from 3.0 to 4.5

MHz.

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 Observations
(half wave dipole)

“Resonance” is when Antenna too long...

Decrease length
‘reactance’ is zero.. OR add series C

we can change 4.5 MHz

resonance with
3 MHz
capacitors and
inductors. Antenna too short...
Increase length
OR add series L

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 Observations
Smith chart can show
SWR circles as well.
Here’s an SWR=2
circle.

Unrolling the circle

results in the well
known SWR chart...

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 Observations
Here is the resulting
SWR chart.

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 Application 1
Impedance Transforms
Many methods. All
have the goal of moving
the impedance to the
center of the chart.

Classic LC
1/4 wave
1/12 wave
coax + reactance
1/4 resonant

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 Application 1
Classic LC
Use L to move to R=50
circle. Use C to move Series
center. Capacitance
Shunt
Inductance

SWR = 2
Circle

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 Observations
Impedances lower than 50
Most antennas have an Frequency Sweep
of Antenna
impedance > 50 ohms
but many do not. Here
is a sweep of a 10m
vertical with 4
horizontal radials. Series
Parallel
Capacitance
Inductance
We can match it with
an LC....

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 Lesson V
Parasitic Capacitor

However, if we remember
that an antenna is Frequency Sweep

capacitive below of Antenna

resonance, we can
implement the capacitor
by shortening the Shunt Inductance
antenna! (or piece of line:
‘Hairpin’!)

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 Application 1
1/4 wave section
Here we use a 1/4
wave section to
match our dipole Frequency Sweep
of Antenna
to 50 ohms at
a given frequency.

Here, a 67 ohm line. Frequency Sweep

at Transmitter

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 Application 1
1/12th wave
Add 1/12th wave
of 50, 1/12th wave
of 92... Frequency Sweep
of Antenna
Frequency Sweep
of Antenna

Twelfth Wave
sections

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 Application 1
coax and reactance
Use coax to rotate
impedance to blue Resulting
conductance circle Sweep Folded
Dipole
and then add Sweep
reactance.
Shunt
Here, an inductor Inductor

is used. Series 50
ohm Line

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 Application 1
quarter wave resonant
Use coax to rotate
impedance AND a
piece of coax for Resulting
Sweep
Folded
Dipole
the reactance. Sweep

The total length of Shunt 50

coax is often close ohm Line

to “1/4 wave”. Series 50

ohm Line

(BTW this is how most

jpoles work)

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 Application II
“Q eye”
Sweep of Frequency

“Q” contours are curves of

constant Q. Keeping the Q
low increases the Bandwidth Impedance of
Single Line Match
of a match. Curve of
Q = .55
450 ohm
load

Here 450 is match to 50

ohms. One using 1/4 wave Impedance of

of 146 ohm line. The other Two Line Match

Single line match goes
significantly outside
using 257 & 87. chosen Q Line

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 Application II
“Q eye”
Here is the resulting
Sweep of Frequency
SWR chart. Notice
two line match is
significantly better.

BLUE
Impedance of
BLACK Single Line Match
Impedance of
Two Line Match

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 Lesson VI
Broadbanding
Optimizing the match at
a single frequency can be
suboptimal across a band.
Impedance of Single
Frequency Match
For example, usually, folks
will match the antenna to Sweep
50 ohms and then attach
the feedline:
Quarter wave
Zo = 67

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 Lesson VI
Broadbanding
Here is the resulting SWR

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 Lesson VI
Broadbanding
BUT: if you move the
‘matching’ to other end
of the half wave feed Final
Final Sweep
line you can get: Sweep

After
Half Wave

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 Application III
Broadbanding for 80m band
Here are the two
curves compared
across the 80m
band
BLACK
Impedance of
‘Perfect’ Match

BLUE
Impedance of
‘broadband’
Match

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 Application IV
Broadbanding the 20m folded dipole
For folded dipoles the
‘classic’ solution is to
use a 4:1 transformer
(balun) at the feed
point.
Impedance
before Balun
Here is the Smith Impedance with
4:1 balun
chart for the result:

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 Application IV
Broadbanding the 20m folded dipole
And here is the circuit
and SWR chart:

Impedance with
4:1 balun

Note balun modeled

as perfect transformer

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 Application IV
Broadbanding the 20m folded dipole
But 1/1 baluns are much
easier to build AND we Resulting Impedance
can match the impedance
more easily if we use the Use
Cap to
feed line to our advantage. Match

Use feedline
to move
Impedance

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 Application IV
Broadbanding the 20m folded dipole
Here is a comparison of
the resulting SWRs:

4:1 balun
Matched

Feed line
and Cap
Matched

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 Application V
The 40/80m delta/delta (NI6T)
Dual band delta antenna.
Sides are 76 feet long,
top wire 118 feet.

60 foot, 450 ohm, open

stub in middle of top wire.

(shown as ‘load’ box in

this EZNEC plot)

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 Application V
The 40/80m delta/delta (NI6T)
On 80m, the 60 foot
stub 1/4 wave which
means it is effectively
a ‘short’.

Thus, on 40m the loop

is a one wavelength loop.

(Here is the EZNEC current plot)

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 Application V
The 40/80m delta/delta (NI6T)
On 40m, the 60 foot stub
is 1/2 a wave which means
it is an ‘open’.

Thus, the antenna is a two

wavelength partially folded
dipole. It is relatively high
impedance.

Here is the EZNEC current plot.

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 Application V
The 40/80m delta/delta (NI6T)

Sweep of impedance
from 3.4 to 7.4
(from EZNEC)

3.75 MHz: 300 + 21j

7.20 MHz: 1.5K + 925j

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 Application V
The 40/80m delta/delta (NI6T)

Tune 40m first.

1/4 wave,
300 ohm line.

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 Application V
The 40/80m delta/delta (NI6T)

Then tune 80m

1/4 wave,
100 ohm line

NOTICE: 300 ohm

line has no impact
because impedance
starts close to 300
ohms.

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 Application V
The 40/80m delta/delta (NI6T)
Lots of tradeoffs to
be made but here are
two sweeps. 7.0 to 7.23

3.5 to 3.86

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 Application V
The 40/80m delta/delta (NI6T)

Resulting
SWR chart

400 KHz 3.7

200 KHz 7.2

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 Application V
The 40/80m delta/delta (NI6T)
This antenna uses several techniques. In each case
a piece of transmission line acts one way on 40 and
a completely different way on 80m.
a) the 60 foot stub acts like a switch;
it is a short on 80m and an open on 40
b) the 1/4 wave matching section for 40m
has a Zo which ‘circles’ the impedance
on 80m; essentially, no effect on 80.
c) the 80m 1/4 wave matching section is
1/2 wavelength on 40m; essentially
no effect on 40!

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 Wrap Up
Smith chart provides a ‘two dimensional’ view of
impedances; a picture is worth 1000 words!

Smith chart lends insight to how impedances

transform with a change in circuits or parameters.

Modern Smith chart software removes the drudgery

of performing the complex arithmetic and frees the
designer to see the forest and not just trees.

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