The UserFriendlySmith ChartBy RadCom Technical Editor Peter Dodd , G3LDO·

General ec natrucuen oltheSmith chart calculator.

would be plotted on an impedance map orchart as shown in Fig 3. On the impedancechart we use + or -j instead of E or W longi·tude.

IMPEDANCE M EA SUREMENTBEFORE WE CAN MAKE full use an imped­ance chart we need an instrumen t for deter­mining a posi tion on the chart. A simp leinstrument for measuring impeda nce wasdescribed by Ed Chicken G3BIK [1]. A evensimpler and more accura te impedancemeas­uri ng techn ique , known as tne a-Meter

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WHAT ISIMPEDANCE?THE BEST WAY TOTELL what ishappen ,ing at theleedpointolan antenna is tomeasure its imped­ance directly.

I m p e d a n c e(whose symbol is Z)is a general term,which can be applied10 any erecmcar cir­cuit that impedes thef1 ow oI AC current. Anantenna is a tunedcircuit having induct­ance, capacitanceand resistanceandanequivalent ci rcuit isshown in Fig 1.

When transmitterpower is led to theantenna the currentin Ihe resistive part is in phase with Iheapplied Voltage ;while the current in me induc­tive or capacitive part (reactance) is 90 de­grees out 01 phase with the applied voltage.Thus the phase relationship between cur rentand vol tage in a tuned circuit or antennaeleme nt can be anything between zero andplus or minus 90 degrees, depending on theratio 01 resistance and reactance.

Because 01 this, impedance is always ex­pressed in two parts ; resistive and reactive.An impedance hav ing an resis tance of 75Uand a inductive react ance sonis convention­ally written as:

75 +j50The j symbol bothers a rotor people. This is

probably due to the way it is described inliterature as 't he square root of minus one" or"imaginary". Furthermore , impedance is de­scribed as "complex". All these terms arederived from the mathematics used in imped­ance calculations. For our consideration 01impedance, j can simply be regarded as aconvent ion lor reactance, The '+j' indicatesinductive reactance and a 'oj' indicates ca­pacitive reac tance. When the antenna is at itsresonant frequency the -i and -l parts areequa l and opposite so only the resistive partremains.

An impedance value can be plolted as co­con nates on a rectangular chart or map in justthe same way that a OTH longitude andlatitude is plotted on a map .A posit ionol, say ,52°N 3°E would be plotted on a map as shown Fig 2: Map showing co-ordlnates 01 reut uee andin Fig 2. Our impedance value of 75 +j50 longilude.'J 7 roo Rldtngs.. Elist P,estM. West $uo;sex 8Nl6 2 TW

THE SWR METERTHERE ODES NOTSEEM10beany problemwith a general understanding of standingwave ratio (SWR). Even themost non-techni­cal radio amateur is aware thaI the coaxialtransmission line connecting the rig to theantenna has a characteristic impedance,which is arou nd son:and that an SWR metercan be used to measure any 'slanding waves'on the coaxial line caused by the antennaimpedance hav ing a dif ferent value to that ofthe coa xial line . In nea rly every ham shackthere is usually a SWR meter connectedpermanently into the coaxial between thetransmi tter and the ante nna or antenna sys­tem .

The method 01 antenna adjustment usingan SWR meter is well known. You connect upyour anten na sys tem then make a number ofadjustments 10 the antenna and then seewhich one improves the SWR. This approachis fine with simple antenn as such as dipoles.However, things don't a lways go smoothly. Itis not unusual 10hea r: "I've tried everythingbut I can 't get the SWR down", The setting upand adjustm ent of a gamma match on abeam , or matching network on a com pactantenna can be qui te frustrating il Ihe onlyindication that you have is an SWR meter.

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Fig1;Equlvolenl antenna circuit

NEARLY EVERY MAJOR bookonantennashasadescriptionofa complicated circular graphknown as a Smith chart , withinslructions on how lo useil. The

Smith chart is very useful and is used by theprofessionals to design antennas and imped­ance matching networks. In spite of this Ihave never, in 37years 01 amateur radio, metanyone who uses the Smith chart to solve apractical antenna problem . So why shouldthis be? And what's wrong with the good OldSWR meter for solving antenna matchingproblems?

40 RADIO COMMUNICAliON April 1995

SMITH CHART

Gene,al Rad io 1606 Impedanca bridge, showinglhe res islonce and reactance scales.

method, is desc ribed in TheAmenna Experi­menters Guide, available from the R$GB,see page 90.

A professiona l impedance bridge is shownin the above phot o. As you can see there aretwo cal ibrated contro ls . one for R and theother lor j. Information from the calibrateddials on me instrument can be used to estab ·lish the impedance position on the chart .

The chart inFig 3 also illustrates the nmna­nons 01SWR as a means 01determining thecharacteristics of the feedpoint of an an­tenna. The two circles shown in Fig 3 arecircles of constant SWR, one for 2:1 and theother for 1.5:1. Using our map analogy theycan be regarded as SWR con tours . Whenyou measure SWR to try to find out what isgoing on at the antenna you are measuringthe effect 01the antenna not hav ing the samevalue of impedance as the antenna . Hew­ever, an impedance 01100 +jOwould give the

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Fig 3: Impedonce map showing ec-crdinates 01ret;ISlance llnd reactance.

same SWR as an imped ance of 25 +jO. Youwill see that there is a large numberot imped­ance values that can give an SWR or 2:1. Ifyou measure an SWR valueol2:1then all youknow is that you are some where on the 2:1circ le. This expl ains why an SWR meter is notnecessari ly the best instrument lor adjus tingan antenna with a matching network such asa Gam ma match.

If you make several impedance measure­ments 01an antenna over a range ctfrequen­cies they can be used to produce an imped­ance 'signature' of the antenna. Fig 4 showstwo of these signatures, which were obtainedwhen evaluat ing the G2AJ V double toroidantenna {2]. Plot A shows mettne resistanceis around SU at resonance, and explains why

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Fig 4: Impedance 's lgnatures ' 01 a dOllble 10 roIdanl enna .

no amount 01 antenna pruning would bringthe SWR value to usable proportions. With asui table matching circui t, the impedance isvery close to SOU at resonance as shown inprot a.

(Resonance is where the inductive andcapaci tive reactances in a tune d circui t orantenna elementare equal and opposite,andthis condition exists only on the 0 reactancevertical line 01Figs 3 and 4)

To obtain the results shown in Fig 4 it isnecessary to measure the antenna teedpcin timpedance attne point where the coaxial isconnec ted to it. There are many practicaldiff iculties in doing this and it is much more

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A Radio Society of Great BritainV Lambda House, Cranborne Road, Potters Bar, Herts EN6 3JE

RAOIOCOMMUNICATION April 1995 41

SMITH CHART

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42 RADIO COMMUNICATION April 1995

SMITH CHART

Fig 6: Smith chart . with tr ansmi ssion li neeleelrleal lengtll scal e,superimpose don two leng lh& 01coax iel ceble.

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is ittustrated in Fig 6. An additional scale isadde d around the circumference. calibratedin eiecmcat wavelength. Halfway round thecha rtequalsO.25 0rq uarterwavelength ,whilea futl rotation equals 0.5 or hall wavelength.

Two lengths of son coa xial feede r areshow n superimposed around the circumter-

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The Smith chart,by convention, hasthe resistance sca ledecreasing towardsthe top.Wilhthispro-jectioo me SWR cir­cles are concentric,centred on the SOUpoint , whi ch isknown as the primecentre .

II you are familiarwith a normal Smith @, .......chart you witt recoq­nise that the oneshown in Fig 5 is sim­pli fied . The cuter­ences and the rea­sons for simplifica­tion are describedtater.

Oneadvantageofthe Smith project ionis that it can be usedfor calculating im-pedancetransformsover a lengt h of co-axial feeder. Be ­cause the reuecteoimpedance variesalong the feede r it follows thai you need toknow the electrical length of your coaxialfeeder totheantenna. You can tnen cajcuratethe transform of impedance measured at theshack end 01 the feeder using the noisebridge.

The impedance transformation Smith cha rt

Fig 5: a esre s lmplllied Smi th chert .

convenient if impedances could be measuredvia a length of coaxial cable. Now while SWRis the same anyw here along a transmissionline (neglecting any losses ) the measuredimpedance at one end depends on the-trans­mission line electrical leng th, This is wherethe Smith chart comes in.

The Smith chart , shown in Fig 5 is animpedance map similar to the ones shown inFigs 3 and 4. It can be considered as just adifferent projection, just as maps have diller­ent projections, such as the Mercator Projec­tion or the Great Circle projection. The mostobvious difference with the Smith chart is thatall the co-o rdinate lines are sections 01 acircle ins tead 01being straight.

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A Radio Society of Great BritainV Lambda House, Cranborne Road, Potters Bar, Herts ENG 3JE

RADIO COMMUNICATION April 1995 43

SMITH CHART

ence of a Smith chart in Fig 6: one leng thquarter wav e long and the other 3/8 wave­lengt h). Both lengths are connected to a loadhaving an impedance of 25 +jO. The quarterwave length of line (0,25) gives a measuredimpedance of 100 +jO althe other end whil ethe 3/8 section (0.375) gives an impedan ce of40 +j30. It can also be seen from Fig smatahanwevelength of coaxial cable would tra ns­form the impedance back to 25 +jO.

A PRACTICAL SMITH CHARTCALCULATORYO U CA N USE EITHER of the charts onPage 42 to construct a Sm ith chart calculator.

Chart (a) has a restricted im pedance rangebu t is easier 10 use. n is used whe re theim peda nce excu rsions are lim ited and do notcause an SWR much greater Ihan 2.5:1.

Chart (b) is the standard Chart which cov­ers impedances fro m (theoretica lly ) zero toinfinity ,

For this ex ercise we will ma ke an imped­ance calcu lator using the restricted rangechart, whi ch is easier rea d and use , see thephotograph on page 40.

Make a photocopy of the cha rt enla rging itto bring it to a usable size. I suggest anenlargeme nt l rom A410 A3; a single chart w illthen fit on a single piece of A4 paper. Thechart is men glued to a circu lar sheet of sliffca rdboard or thin alum inium . A small hole isdr illed in the chart and back ing material at the50 +jO point.

From a piece of very thin perapex ortrans­pare nt p lastic or ce lluloid cut a ci rcle the samesize as the chart to ma ke an overlay. A holeis then drilled exaclly at the overlay cen tre ,Identifyi ng the ce ntre point should be noproble m if a pai r of compasses is used tomark the overlay before cuttinq.

Make a curs or by drawing a line along theradius of the ove rlay, using a lin e tippedmark er pen. cove-me line with a strip of cenc­tape to prevent the line rub bing out. Trim oilthe excess tap e.

Fix the trans parent overlay to the chart witha nut and bol t wi th the tape covered lineag ainst the chart . Ad just the nut and bolt sothat the overlay can be easil y rotated, asshown in the photograph.

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fig 7: View 018 n orma lized a landa rd Sm ith c ha rt.

USING THE CALCULATORTHE USES TO WHICH this ca lculator can beput are too nu merous to be included in thisarticle. But here are three examples.

MEASURING COAXIAL CABLEELECTRICAL LENGTHYOU CA N FIND THE elec trical length 01coaxial cabl e by physically measuring itslength and mulliplying it by the cable veloc ityfac tor.

A more accurate method is to measure theelect rical length directly us ing an RF imped­ance measur ing inst rument (eg a noisebridg e). It also assumes the re are no cablelosses: in practice this means that the proce­dure wi ll only work with relatively short lengthsof fairly good quality coax ial cab le. You shouldbe using reaso nab le grade coaxia lanyway tomeasure antenna charactensncs -even SWR.

Terminate the load (antenna) end of thecable with a 22U resistor.

2 Measure the impedance at the other end01 the feeder.

3 Move the cursor so lhat it inte rsects themea sured impedance point. The cu rsorwill now point to the electrical wavel engthof the feeder marked on the out er scalemark ed 'wavelengths towards gen erato r'.

Th e cable may be severalhal f wavelengthsand part of a half wave length long. The Sm ithchart w ill only regis ter the 'part of a halfwave leng th', which is all we are interested inrega rding the impedance transform effect.

CALCULATING ANTENNAIMPEDANCETHIS IS A METHOD 01 calculating antennaimpedance from a measured impedancevalue, using coaxia l cable whose electricallength has already been determined,

1 Connect the cable to the an tenna.

2 Measure the impedance at the other end01the coa xial.

3 Move the cursor over the measured im ­pedance point and mark the point on theoverlay with a wax pencil.

5 Follow the cursor radi ally outwards to Ihescale mar ked 'wavelengths towards load ',Write this number down.

6 Add the length of cable in wavelengths totntsnumber,

7 II the number is larger than 0,5, subtract0.5.

8 Rota te the overlay unti l the cu rsor pointsto this number on the 'wavelengths to­wards load' sca le.

9 The an tenna impedance will be lound onthe cursor direct ly under the wax penci lmark.

EXAMPLEThe measu red impedance is 35 +j20 (} andthe cursor points to 0.407 on the 'wave­lengths towards load ' scale.

Th e cable electrical length was measuredas 0.13 wav elengths.

Then 0.407 + 0.13 = 0.537 wavelengths .Off scale - too big! So subtract 0.5 wave­lengths = 0 ,037 wavelengths.

Ro tate in s overlay until the cursor points to0.037on the 'wavelengths towards load ' scale.

The antenna impedance is shown as28 -j8n under the cursor anne same radiusas the measured impedance.

MEASUREMENT OF SWRCALCULATION O F SWR is very simple us­ing the Smith chart. Th e result is usefu l torco rrelating impedance measurements withSWR measurements . To measure SWA:

1 Mov e the cursor over the measured im­pedance po int

2 Mark the point on the overlay w ith a waxpencil.

3 Move the cursor to the 0 point on theoutside scales.

4 The SWR can be read off asSO divi ded bythe mark on the cursor. Th e impedancemeasured abo ve gives a reading of 27 +jO.50 divided by 27 equals 1.85: the SWR inthis cas e is 1.85;1.

You can , of course, ca libra te the cursor inSWR, Just p lace the curso r in the verticalzero position and place marks on the cursorat the 33.3, 25 and 20 resistance points togive SWR marks at 1.5:1, 2:1 and 2.5: 1respective ly.

CONCLUSIONUS ING THE SMITH CHART, as describedabove, doesn't seem so complicated . so whyis it not mo re widely used?

It is probably because the Sm ith chart isdesigned for pro fess ion al use and is requiredto have high resolution to give accu racy to Iheresu lts. Like any graphic aid, the higher theline density the greater is its resolution but theharde r it is to read as you can see in Fig 7,

In addi tion most Smi th cha rts are 'no rma l­ized' so tnat they can be used at any imped­ance and not restricted to son, as are theones described in this artic le.This is achievedby assi gn ing 1 to the prime cen tre: oth ervalu es , tor exa mple, are o.stcr zsnanuz for1DOn in a sonsystem.

NOTEYOU COULD OBV IOUSLY measure the im­pedance of the antenna using a halfwave, ora mul tiple ot a hall wavelen gth, of co axialcab le and dispense w ith the Smith chartaltogether. In fact this is of ten done but thereare a couple or disadvantages, Because thecable is resonant it can result in antennacur rents on the cable, which can give incon­sis tent impedance measurem ent results. Alsoif you make several impedance measure­ments over a range of freque ricies rememberthat the cable is a half wavelength long on onefrequency only .

ACKNOWLEDGEMENTTO PETER SWALLOW , G8EZE . for ch eck­ing the ma nuscript and help on a proc edurefor us ing the Smith chart.

REFERENCES[ l J 'Tone Mo dulated HF Impedance Bridge',

E Chicken, G3B IK, Radio communce­lion, June/July 1994,

[2J 'Evaluation of the G2AJV Toroidal An­ten na', Peter Dodd, G3LDO, Radio Com­munication, August 1994 . •

RADIO COMMUNICATION April 1995