lessons from - ae6ty · 2020. 10. 9. · dual band delta antenna. sides are 76 feet long, top wire...

Lessons Fromthe

Smith ChartWard 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 CenterThis Smith Chartis quite simple:The center of thechart representsa impedance of50 ohms. Otherimportant pointsare 0, infinite, +j50and -j50

50 infinite0

j50

-j

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Adding ReactanceAdding a series reactance causesmovement alongthe red circles...

Adding a parallelreactance causesmovement alongthe blue circles.

IncreasingSeries

Inductance

DecreasingSeries

Capacitance

IncreasingParallel

Capacitance

DecreasingParallel

Inductance

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Adding ResistanceAdding seriesresistance causesmovement alongthe red arcs.

Adding a parallelresistance causesmovement alongthe blue circles.

ParallelResistor

SeriesResistor

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Lesson 1Transmission linestranslate impedancesthrough rotationsaround their Zo.

Here are 25,37,50,75,150,300,600transmission lines.

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Lesson 1(cont)

Transmission linescan act much likecapacitors andinductors over smallranges in frequency.

Here we show aninductor and a seriestransmission line...

SeriesInductance

SeriesTransmission

Line

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Transmission linestubs (shorted andopen) can... yep...act like inductorsand capacitors.

Shorted Tlinesincrease inductanceas they get longer...

Open lines increasecapacitance as they grow

Lesson II Series Stubs as Reactances

Series, ShortedTransmission line

SeriesInductor

Series, OpenTransmission Line

SeriesCapacitor

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Shorted Tlinesincrease inductanceas they get longer...

Open lines increasecapacitance as they grow

(but only up to a point)

Lesson II Parallel Stubs as Reactances

Parallel, ShortedTransmission line

ParallelInductor

Series, OpenTransmission Line

SeriesCapacitor

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Transmission lineswhich are 1/4 wavelengths long are‘special’.

They ‘invert’ theimpedance,(but only at asingle frequency)

Lesson III 1/4 WaveLengths

25 to 100

200 to 10

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Impedance isn’treally ‘inverted’.

The real formulais:

Zin Zout = Zo Zo

Lesson III (cont)1/4 WaveLengths

25 to 50Zo = 35

200 to 50Zo = 100

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Half wave lines actjust like two 1/4wave lines inseries....

Often describedas having ‘no effect’but only if the frequency is constant.

Lesson IVhalf WaveLengths

25 to 25Zo = 35

200 to 200Zo = 100

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For transmission lines:Increasing the frequencyof analysis is (much) thesame as increasing thelength of a transmissionline.

ObservationChange in Frequency = Change in length

Sweep5 to 20

Sweep5 to 10

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Smith chart can showhow impedance changesas frequency changes.

For example, here isa the familiar ‘path’of a matching L networkand a frequency ‘sweep’of the impedance.

ObservationSweeps

Series L Shunt C

FrequencySweep

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Smith charts are oftenused in describingantenna impedances.

Here is the impedanceof a dipole for 80m.

Sweep from 3.0 to 4.5MHz.

ObservationsSweeps (cont)

3 MHz

4.5 MHz

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“Resonance” is when‘reactance’ is zero..

we can changeresonance withcapacitors andinductors.

Observations(half wave dipole)

Antenna too long...Decrease lengthOR add series C

3 MHz

4.5 MHz

Antenna too short...Increase lengthOR add series L

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

Unrolling the circleresults in the wellknown SWR chart...

Observations

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Here is the resultingSWR chart.

Observations

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Many methods. Allhave the goal of movingthe impedance to thecenter of the chart.

Classic LC1/4 wave1/12 wavecoax + reactance1/4 resonant

Application 1Impedance Transforms

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Use L to move to R=50circle. Use C to movecenter.

Application 1Classic LC

ShuntInductance

SeriesCapacitance

SWR = 2Circle

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Most antennas have animpedance > 50 ohmsbut many do not. Hereis a sweep of a 10mvertical with 4horizontal radials.

We can match it withan LC....

ObservationsImpedances lower than 50

ParallelInductance

SeriesCapacitance

Frequency Sweepof Antenna

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However, if we rememberthat an antenna iscapacitive belowresonance, we canimplement the capacitorby shortening theantenna!

Lesson VParasitic Capacitor


Shunt Inductance(or piece of line:

‘Hairpin’!)

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Here we use a 1/4wave section tomatch our dipoleto 50 ohms ata given frequency.

Here, a 67 ohm line.

Application 11/4 wave section


Frequency Sweepat Transmitter

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Add 1/12th waveof 50, 1/12th waveof 92...

Application 11/12th wave



Twelfth Wavesections

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Use coax to rotateimpedance to blueconductance circleand then addreactance.

Here, an inductoris used.

Application 1coax and reactance

FoldedDipoleSweep

Series 50ohm Line

Shunt Inductor

ResultingSweep

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Use coax to rotateimpedance AND apiece of coax forthe reactance.

The total length ofcoax is often closeto “1/4 wave”.

(BTW this is how mostjpoles work)

Application 1quarter wave resonant

FoldedDipoleSweep

Series 50ohm Line

Shunt 50ohm Line

ResultingSweep

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“Q” contours are curves ofconstant Q. Keeping the Qlow increases the Bandwidthof a match.

Here 450 is match to 50ohms. One using 1/4 waveof 146 ohm line. The otherusing 257 & 87.

Application II“Q eye”

Impedance ofSingle Line Match

Impedance ofTwo Line Match

Sweep of Frequency

450 ohmload

Curve ofQ = .55

Single line match goessignificantly outside

chosen Q Line

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Here is the resultingSWR chart. Noticetwo line match issignificantly better.

Application II“Q eye”

BLUEImpedance of

Single Line MatchBLACKImpedance of

Two Line Match

Sweep of Frequency

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Optimizing the match ata single frequency can besuboptimal across a band.

For example, usually, folkswill match the antenna to50 ohms and then attachthe feedline:

Lesson VIBroadbanding

Impedance of SingleFrequency Match

Sweep

Quarter waveZo = 67

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Here is the resulting SWR


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BUT: if you move the‘matching’ to other endof the half wave feedline you can get:


Final SweepFinal

Sweep

AfterHalf Wave

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Here are the two curves comparedacross the 80mband

Application IIIBroadbanding for 80m band

BLACKImpedance of

‘Perfect’ Match

BLUEImpedance of‘broadband’

Match

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For folded dipoles the‘classic’ solution is touse a 4:1 transformer(balun) at the feedpoint.

Here is the Smithchart for the result:

Application IVBroadbanding the 20m folded dipole

Impedancebefore Balun

Impedance with4:1 balun

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And here is the circuitand SWR chart:

Note balun modeledas perfect transformer


Impedance with4:1 balun

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But 1/1 baluns are mucheasier to build AND wecan match the impedancemore easily if we use thefeed line to our advantage.


Resulting Impedance

Use feedlineto move

Impedance

UseCap toMatch

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Here is a comparison ofthe resulting SWRs:


4:1 balunMatched

Feed lineand CapMatched

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Dual band delta antenna.Sides are 76 feet long,top wire 118 feet.

60 foot, 450 ohm, openstub in middle of top wire.

(shown as ‘load’ box in this EZNEC plot)

Application VThe 40/80m delta/delta (NI6T)

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On 80m, the 60 footstub 1/4 wave whichmeans it is effectivelya ‘short’.

Thus, on 40m the loopis a one wavelength loop.

(Here is the EZNEC current plot)


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On 40m, the 60 foot stubis 1/2 a wave which meansit is an ‘open’.

Thus, the antenna is a twowavelength partially foldeddipole. It is relatively highimpedance.

Here is the EZNEC current plot.


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Sweep of impedancefrom 3.4 to 7.4(from EZNEC)

3.75 MHz: 300 + 21j

7.20 MHz: 1.5K + 925j


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Tune 40m first.

1/4 wave,300 ohm line.


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Then tune 80m

1/4 wave,100 ohm line

NOTICE: 300 ohmline has no impactbecause impedancestarts close to 300ohms.


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Lots of tradeoffs tobe made but here aretwo sweeps.


7.0 to 7.23

3.5 to 3.86

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ResultingSWR chart

400 KHz 3.7200 KHz 7.2


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This antenna uses several techniques. In each casea piece of transmission line acts one way on 40 anda completely different way on 80m.


a) the 60 foot stub acts like a switch; it is a short on 80m and an open on 40b) 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; essentiallyno effect on 40!

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

Smith chart lends insight to how impedancestransform with a change in circuits or parameters.

Modern Smith chart software removes the drudgeryof performing the complex arithmetic and frees thedesigner to see the forest and not just trees.

Wrap Up

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lessons from - ae6ty · 2020. 10. 9. · dual band delta antenna. sides are 76 feet long, top wire...

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