Log Periodic Antennas Notes PDF

# Log Periodic Antenna **Look!!** - It is interesting to note that the structure contains different lengths of centre-fed dipoles, arranged in a conical fashion. - Dipoles (increasing in length) - Balanced transmission line (feed) - Transposed feed lines - 2x - apex angle formed. **Log periodic An...

# Log Periodic Antenna **Look!!** - It is interesting to note that the structure contains different lengths of centre-fed dipoles, arranged in a conical fashion. - Dipoles (increasing in length) - Balanced transmission line (feed) - Transposed feed lines - 2x - apex angle formed. **Log periodic Antenna (or) log periodic dipole Array (LPDA)** - is a broadband antenna. - The antenna structure can be expanded or contracted in proportion to wavelength. - The structure is adjusted in such a way that all the electrical properties of the dipoles arranged are repeated periodically with the logarithm of frequency. - Note: electrical properties like length of dipoles, spacing between them etc... - Principle of log periodic array **Now, as you see, LPDA consists of a number of center-fed dipoles of different lengths and spacings.** - Length of dipoles increases from feed point to other end. - The entire antenna structure is fed using a balanced transmission line and it is further transposed between each adjacent pairs of terminals of dipoles. - We can see an included angle formed at the imaginary apex - 2x - called apex angle. ## Design ratio/Scale factor: - The dipole lengths and the spacing between two adjacent dipoles are related through a parameter called design ratio/scale factor (τ). - Look at the fig: after nth dipole you can take one more, that is (n+1)th dipole loo. So, let, for the case, take last dipole as (n+1)th dipole and second last as your nth dipole. - So τ = (S_n/L_n) = (S_n+1/L_n+1). Also where τ = k where k is a constant - τ is also called periodicity factor which is always less than 1 ## Regions of the LPDA: - Depending on the length of the dipoles, we get three regions on the structure. - **Feed** - **Inactive region** - **Active region** - **Inactive stop region** ### Inactive transmission line region:- (L < 1/2 ) - Here length of dipoles less than 1/2 - Elements in this region provide smaller impedance. - Element spacing is comparatively smaller. - Currents in this region is measured very small. - These currents lead the voltage supplied by the transmission line. ### Active region:- (L~1/2) - Here lengths of dipole are approximately equal to 1/2. - Elements in this region offer resistive impedance. - Currents in this region are therefore measured large. - These currents are in phase with the voltage supplied by the transmission line. - This is the central region of the array where maximum radiation takes place. ### Inactive stop region:- (L > 1/2) - Here lengths of the dipole are greater than 1/2 - Dipoles in this region offer inductive impedance. - Currents are smaller in this region. - These currents lag the supplied voltage. - This region is also called 'reflective region' as any wave incident on this region gets reflected back due to the large inductive impedance. ## Relationship between the apex angle (2x), spacing (s) and length (L):_ - Consider a section of the array as shown. - Note: Only two nearby dipoles are drawn (last one & second last):- - From fig: - tan(d) = (L_n+1 - L_n) / 2S - tan(d) = (L_n - L_{n - 1})/ 2S - tan(d) = (1 - (L_n+1/L_n)) * (L_n/2S) - But L_n+1 = k, i.e L_n = k/L_n+1 - Substituting, tan(d) = (1 - k/L_n+1) * (L_n+1/2S) = (1 - k)/(2S) - For active region, L_n+1 ~ 1/2 - Therefore tan(d) = (1 - k) *(1/2)/(2S) = (1 - k) / (4S) - tan(d) = (1 - k) / (4S) - d = apex angle - k = scale factor - A = wavelength - S = Spacing b/w immediate half dipoles. ## Frequency ratio (F) or Bandwidth of LPDA:- - It is the ratio of the last element (here ( n+ 1)^th element) to the first element. - F = (L_n+1/L₁) and L_n+1 = kⁿ - When the length of first element is L₁, then the length of n + 1^th element is kⁿ time greater than L₁.