School of Electrical Egieerig EI2400 Applied Atea Theory Lecture 9: Broadbad ateas
Questio 1 What is the badwidth of a atea? It is the rage of frequecies withi which the performace of the atea with respect to some characteristic coforms to a specified stadard. KTH School of Electrical Egieerig www.ee.kth.se 2
Questio 2 Could you defie performace? Iput impedace patter beamwidth polarizatio sidelobe level gai beam directio radiatio efficiecy KTH School of Electrical Egieerig www.ee.kth.se 3
Operatio of the atea Normally by the reflectio coefficiet: - S 11 <-10dB. KTH School of Electrical Egieerig www.ee.kth.se 4
Defiitio of badwidth Narrowbad ateas: - The badwidth is expressed as a percetage of the frequecy differece over the ceter frequecy of the badwidth. - Example: 5%. Broadbad ateas: - The badwidth is ormally expressed as the ratio of the upper-to-lower frequecies of acceptable operatio. - Example: 5:1 KTH School of Electrical Egieerig www.ee.kth.se 5
Other termiology Oe decade is a factor of 10 differece betwee two umbers (a order of magitude differece) measured o a logarithmic scale. - Example of icrease oe decade: 20GHz 200GHz 2THz f decade log 10 f A octave is a doublig or halvig of a frequecy. - The term is derived from the Wester musical scale (a octave is a doublig i frequecy). - Example of icrease oe octave: 20GHz 40GHz 80GHz octave log 2 f f max mi max mi KTH School of Electrical Egieerig www.ee.kth.se 6
Bicoical Extesio of a dipole. Coical shape. Impedace depeds o the agle of the coe. 1000 Z i () 800 600 400 Z i 120lcot 4 200 0 0 20 40 60 80 100 /2 (º) KTH School of Electrical Egieerig www.ee.kth.se 7
Bicoical: Limitatios Bicoical ateas have bee used i VHF ad UHF frequecies. However the solid or shell bicoical structure is impractical for some applicatios: - Elevated weight. - Complex geometry. Approximatios: - Triagular sheet. - Bow-tie. - Wire simulatio. Triagular sheet Bow-tie Wire simulatio KTH School of Electrical Egieerig www.ee.kth.se 8
Discoe It is a implemetatio of the half of a bicoical atea. It is formed by the combiatio of a disk ad a coe. It is a moopolar cofiguratio of the bicoical atea. KTH School of Electrical Egieerig www.ee.kth.se 9
Optios: Wire ateas 1.To icrease the size of the dipole. A. Bow-tie. B. Bicoical. 2.To itroduce more dipoles. A. Log-periodic atea KTH School of Electrical Egieerig www.ee.kth.se 10
Yagi-uda: Yagi-Uda versus log-periodic - Typically all the elemets have the same size with the exceptio of two (reflector ad drive elemets). - Desiged to produce ad ed-fire radiatio. - Purpose: to icrease the directivity of the atea. - Badwidth: Limited. KTH School of Electrical Egieerig www.ee.kth.se 11
Frequecy idepedet ateas It is a termiology which is comig from the 1950s. It refers to ateas i which there is a depedet with a agle which is producig a chage of the frequecy. Examples: - Bow-tie. - Bicoical. KTH School of Electrical Egieerig www.ee.kth.se 12
Frequecy limitatios Lower frequecy: - Our atea ca t be ifiitely large. Higher frequecy: - Our atea has to be feed i a poit ad it ca t be ifiitely small. KTH School of Electrical Egieerig www.ee.kth.se 13
Let s assume that we have two differet ateas which are scaled: Now we ca derive these equatios: Derivatio (I) KTH School of Electrical Egieerig www.ee.kth.se 14 ) ( r F ) ( F K r ) F( C r ) ( ) ( F C K F K C ) ( ) ( C F C C F C ) ( ) ( F K F K ) ( ) ( C F C C F
Derivatio (II) We have that: K F( F( ) K ) C Ad we kow that: r F ( ) So: 1 K K C 1 r r Therefore the solutio is: r e a f ( ) a 1 K K C KTH School of Electrical Egieerig www.ee.kth.se 15
Which ateas ca satisfy this formula? (I) Equiagular spirals: Spiral plate Spiral slot f ( ) A e 0 a 0 r a Ae KTH School of Electrical Egieerig www.ee.kth.se 16
Log-periodic atea: Which ateas ca satisfy this formula? (II) KTH School of Electrical Egieerig www.ee.kth.se 17 1 R R 1 R r 1 1 1 1 s s d d R R l l
Other UWB ateas Moopoles: - Small dimesios. - Compact ateas. - Radiatio patter which depeds of the frequecy. - Radiatio efficiecy very small. KTH School of Electrical Egieerig www.ee.kth.se 18
Recofigurable ateas To be able to chage the frequecy of operatio: - Mechaically. - Electroically: switches varactor diodes MEMs elastomers Broadbad Recofigurable KTH School of Electrical Egieerig www.ee.kth.se 19