Frequency Independent Antenna • Log Periodic Antennas

𝑅

𝑟0

𝛼𝛽

𝑅1

𝑅2

𝑎1𝑎2

Self-complementary:When metal is replaced by air and vice versa, the resultant antenna is identical to the original one 𝛽=45 °

𝛼=135 °Teeth width and gap equalized:

𝜎=𝑎𝑛

𝑅𝑛

=𝑅𝑛+1

𝑎𝑛

=√𝜏

Frequency Independent Antenna • Log Periodic Antennas

Frequency Independent Antenna • Log Periodic Dipole Array (N elements)

𝛼 𝐿1

𝑅𝑛+1

𝑅𝑛

𝑑𝑛

𝜏=𝑅𝑛+1

𝑅𝑛

=𝐿𝑛+1

𝐿𝑛

<1

𝜎=𝑑𝑛

2𝐿𝑛

𝐿1

𝑅1

=𝐿2

𝑅2

=…=𝐿𝑁

𝑅𝑁

𝑑𝑛=𝑅𝑛−𝑅𝑛+1

¿ (1−𝜏)𝑅𝑛

tan𝛼2

=𝐿𝑛

2𝑅𝑛

𝜎=1−𝜏

4 tan𝛼2

𝐿1≈𝜆𝐿

2𝐿𝑁 ≈

𝜆𝑈

2

Frequency Independent Antenna • Log Periodic Dipole Array (N elements)

𝛼 𝐿1

𝑅𝑛+1

𝑅𝑛

𝑑𝑛

Frequency Independent Antenna • Log Periodic Dipole Array (LPDA)

Gain contour

Frequency Independent Antenna • LPDA Design Example

Gain contour𝑓 =54 216 MHz

Gain

𝜏=0.822𝜎=0.149

𝐿1=λ𝐿2

=5.562

=2.78m

𝐿𝑁=λ𝑈2

=1.3892

=0.694m

Frequency Independent Antenna • LPDA Design Example

𝑓 =54 216 MHzGain

𝜏=0.822𝜎=0.149

𝐿1=2.78 m

2.78 0.828

2.29 0.682

1.88 0.560

1.54 0.459

1.27 0.378

1.04 0.310

0.858 0.256

0.705 0.210

0.579 N/A𝑑𝑛=2𝜎 𝐿𝑛=0.298𝐿𝑛

𝐿𝑁=0.694 m

Frequency Independent Antenna • LPDA Design Example II

𝑓 =200 600 MHzGain

𝜏=0.917𝜎=0.169

𝐿1=λ𝐿2

=1.52

=0.75 m

𝐿𝑁=λ𝑈2

=0.52

=0.25 m

Frequency Independent Antenna • LPDA Example II

Voltages

Frequency Independent Antenna • LPDA Example II

Currents

Frequency Independent Antenna • LPDA Example II: Patterns

Frequency Independent Antenna • LPDA feed schemes

Frequency Independent Antenna • LPDA feed schemes

Yagi-Uda Antenna• Antenna with parasitic elements

~

Driven element

Reflector Directors

Yagi-Uda Antenna

Yagi-Uda Antenna

Yagi-Uda Antenna• Computer program (Prof. Balanis)

• N = 15• Number of directors = 13• Number of reflectors = 1• Length of reflector = 0.5 • Length of driven element = 0.47 • Length of directors = 0.406 • Spacing between reflector and driven element = 0.25 • Spacing between directors = 0.34 • Radius of wires = 0.003

Yagi-Uda Antenna• Computer program (Prof. Balanis)

• E-plane pattern (red)• H-plane pattern (blue)• HPBW: 26.48 (E), 27.37(H)• Directivity: 14.8 dB

Yagi-Uda Antenna• Computer program (Prof. Balanis)

• E-plane pattern (red)• H-plane pattern (blue)• HPBW: 26.48 (E), 27.37(H)• Directivity: 14.8 dB• Front to back ratio:

o 31.1 dB (E)o 31.0 dB (H)