The Yagi-Uda Antenna - WordPress

The Yagi-Uda AntennaPart 2Presenter-Tom Kihm, KJ6PST12/15/20201

Part 2 Agenda Empirical design NBS TNComputer-aided design examplesMutual coupling effects on input impedanceMatching approachesConclusions12/15/20202

Yagi Antenna Design Historically Empirical Design– Uda’s Original Research– National Bureau of Standards (NBS) Technical Note Recently, Computer-aided designs– Method of Moments– Induced EMF method– Plus othersSeveral on-line calculators use NBS rules of thumb forreflector, DE and director lengths and spacings12/15/20203

NBS Design CurvesThis photoshows a NBS4l test arrayThe following design curves were derived from experimentaldata taken at 400 MHz that explains data plotted over 10larray lengths: focus is on gain , not F/B ratio12/15/20204

Gain Effect of the Reflector Element-NBS TNTypicallyused spacing3Measured gain in dBdof a dipole and reflectorelement for differentspacings SR.2SR1Dipole gaindBd Spacing SR (l) of reflector behind driven elementOptimum reflector spacing SR (for maximum directivity)is between 0.10 and 0.20 wavelengths12/15/20205

Yagi Gain vs Number of Directors- NBS TNNote: the reflector is includedThese curves cover long arrays. For HF, focus on data for 1larray length. 0.2l element spacing provides slightly moredirective gain than 0.3l spacing12/15/20206

An Interesting ComparisonFrom NBS Tech NoteCommercial Yagi Gain vs # ElementsYagi Gain, Directors spaced 0.2l& 0.3lfrom DEGain, dBd, Hy-gainGain, dBd, Cushcraft12121110987654321010Gain, dBdGain, dBd860.2l spacing, l .382l0.2l spacing, l .411l0.3l spacing, l .382l0.3l spacing, l .411l42Gain, dBd, Long John0012Number of directors3423456012345Number of Elements678Equivalent number of elementsNote the approximate gain agreement for 3-5 elements12/15/20207

3 Element 20,15 &10 meter Design ExamplesFreq.Dir. GainF/BZinSWRZinThese results arefrom computer-aideddesign softwareZinFreq.Dir. GainF/BZinSWRZinFreq.Dir. GainF/BZinSWRNote: Pattern gain, F/B, Zin, change with frequency and Rin 50 Ohms12/15/20208

Yagi Input Impedance The driven element is often a dipole; some designs use afolded dipole to raise the impedance Expect 73 Ohms resistive for free-space, half-wave dipoledriving impedance However, the reflector and director(s) generally reduce thatimpedance due to mutual impedanceThe Yagi input impedance commonly requires matchingto a 50 Ohm transmission line by various techniques.12/15/20209

inductiveDriven Element Free-space Feed ImpedancecapacitiveThese theoretical values are halfthose of the driven dipole element.Note:At resonant length, the reactanceis not 0.Below resonance, the reactance iscapacitiveAbove resonance, the reactance isinductiveNote: the DE self impedance is often tuned for slightlycapacitive reactance when a Beta match is used.12/15/202010

Mutual Impedance Alters Input ImpedanceElement 1Element 2V1I1Isc I2V2 0Port 12 port networkZ11Z12Z21Z22V1V2 0I2 IscPort 2V1 Z11*I1 Z12*I2V2 Z21*I1 Z22*I2Mutual impedance Z12 Z21Z12 Z21 reciprocitySo V1/I1 Zin Z11-(Z12)2/Z22V2 0, I2 -(Z21*I1)/Z22The element 1 E field induces a current I2 in element 2. That elementcurrent radiates an E field inducing a port voltage in element 1,altering port 1 input impedance. Examples shown later.12/15/202011

Mutual Impedance vs Element SpacingE1Port 2Port 1V1Z12 V1/IscI2 IscV1Driven elementparasitic elementAs element spacing increases mutual impedance decreases.Generally 0.2-0.3 l spacing is used.12/15/202012

Simplest Yagi-Uda Array Impedance Examplesd 0.1 ldL1VdL1 0.54 lL2 l/2L3 0.46 lL2VL3Mutual impedanceReflZa DEDE92.47 104.19j , 75.68 11.63j75.68 11.63j , 73.07 41.37jZb Dir73.07 41.37j , 59.77 4.35j59.77 4.35j , 57.65 17.01jNote: the reflector self impedance is inductive while the directorself impedance is capacitive. The mutual impedance values areneeded to calculate the DE driving point impedance.12/15/202013

Matching The Yagi From the 20, 15 & 10 meter design examples, Re(Zin)generally is less than 50 Ohms Matching Choices––––Impedance transformer; N:1 balunGamma matchT match andBeta matchThe choice is generally between the Gamma and Beta match12/15/202014

2019 Nov. QST Dipole Matching Notice balanced vs unbalanced techniques, preferenceis gamma match for a coax feed line12/15/202015

DX Engineering Quote “There are various ways to match the driven element to thefeed-line successfully; Gamma Match, T-Match, and theHairpin (aka Beta Match) are favorites. The Gamma match isan outdated, unbalanced system that typically distorts theantenna radiation pattern. The T-match is basically twoGamma Match systems on either side of the boom, whichmay correct the imbalance, but is a mechanical nightmare andis difficult to tune correctly.”12/15/202016

The Beta or Hairpin MatchCould be attached to boomAt neutral pointDX EngineeringHairpin match;DXE-HMS-1PDXE-HMS-1PChokeUnbalanced transmission lineUsed in MARC Yagis suitable for “balanced” driven element, itraises the Zin to minimize SWR to a 50 Ohm transmission line,the driven element is isolated from the boom12/15/202017

The Hairpin EffectRin Re(Zin)XlXl (Rin x R1/2)/(Rin-R)1/2Hairpin Reactance, Xl, OhmsHairpin Inductance Vs. Driving PointResistance, At 020.00.0TransmissionLine Zo 50 OhmsTransmissionLine Zo 70 Ohms0.0Set Rin Zo20.040.060.0Antenna Driving Point ResistanceRe(Za) R, OhmsShunt inductance, Xl, increasesthe resistive part of Za R, to match Rin.12/15/202018

Conclusions- Part 2 The Yagi Array:– Can be designed using empirical data; “rules of thumb” orcomputer-aided design SW– Exhibits less than 50 Ohms driving point impedance due tomutual impedance– Is compatible with several matching techniques The Yagi performance:– Increases directive gain with more directors (longer array)– Varies with frequency; especially directive gain and F/B ratio– Uses hairpin match; a simple and effective techniqueBottom line : It is a winner12/15/202019

References1. Wikipedia, “Yagi-Uda Antenna”2. Thiele, Gary A., Analysis of Yagi-Uda Type Antennas” IEEE Trans. Onantennas & Propagation, Vol. AP-17, No.1, Jan., 19693. “Yagi Antenna/ Yagi-Uda Aerial”4. Viezbricke, Peter, “Yagi Antenna Design”, Nat. Bur. Standards TN688,December, 19765. Ch25, “Coupled Antennas “ ,http://eceweb1.rutgers.edu/ orfanidi/ewa/ch25.pdf6. Steyer, Martin, DK7ZB, “ 3 Element-Yagi, 20m/15m/10m, 28Ohm Design”,www.qsl.net/dk7zb7. Magliacane, John, KD2BD, “Thoughts on Perfect Impedance Matching of aYagi”8. Wortman, Bill, N6MW, “ The Hairpin Match”9. vu2nsb.com/antenna/yagi-antennas/10. ARRL Antenna Handbook12/15/202020

DX Engineering Quote “There are various ways to match the driven element to the feed-line successfully; Gamma Match, T-Match, and the Hairpin (aka Beta Match) are favorites. The Gamma match is an outdated, unbalanced system that typically distorts the antenna radiation pattern. The T-match is basically two