LECTURE 15: LINEAR ARRAYS PART III 1. Advantages of Linear Arrays with ...
LECTURE 15: LINEAR ARRAYS ? PART III (N-element linear arrays with uniform spacing and non-uniform amplitude: Binomial array; Dolph?Tschebyscheff array. Directivity and design.)
1. Advantages of Linear Arrays with Nonuniform Amplitude Distribution
The most often met BSAs, classified according to the type of their excitation amplitudes, are:
a) the uniform BSA ? relatively high directivity, but the side-lobe levels are high;
b) Dolph?Tschebyscheff (or Chebyshev)1 BSA ? for a given directivity with a fixed number of array elements, achieves the lowest side-lobe level;
c) binomial BSA ? does not have good directivity (for a given number of elements) but has low side-lobes (if d = / 2, no side lobes at all).
2. Array Factor of Linear Arrays with Nonuniform Amplitude Distribution
Let us consider a linear array with an even number (2M) of elements, located symmetrically along the z-axis, with excitation, which is also symmetrical with respect to z = 0 . For a broadside array ( = 0),
AF e
=
a1e
j
1 2
kd
cos
+
a2e
j
3 kd 2
cos
+
+
aM
e
j
2
M 2
-1kd
cos
+
+
a1e-
j
1 2
kd
cos
+
a2 e-
j
3 2
kd
cos
+
+
aM
e-
j
2
M 2
-1kd
cos
,
AF e
=
M
2 an
n=1
cos
2n - 2
1
kd
cos
.
(15.1) (15.2)
If the linear array consists of an odd number (2M+1) of elements, located symmetrically along the z-axis, the array factor is
AF o = 2a1 + a2e jkd cos + a3e j2kd cos + ... + aM +1e jMkd cos +
+ a2e- jkd cos + a3e- j2kd cos + ... + aM +1e- jMkd cos ,
M +1
AF o = 2 an cos (n -1) kd cos .
n=1
(15.3) (15.4)
1 Russian spelling is .
Nikolova 2022
1
EVEN- AND ODD-NUMBER ARRAYS
Nikolova 2022
Fig. 6.17, p. 291, Balanis 2
The normalized AF derived from (15.2) and (15.4) can be written in the form
AF e
=
M an
cos[(2n
- 1)u ],
for
N
=
2M
,
n=1
(15.5)
M +1
AF o = an cos[2(n -1)u], for N = 2M +1,
n=1
(15.6)
where u = 1 kd cos = d cos .
2
Examples of AFs of arrays of nonuniform amplitude distribution
a) uniform amplitude distribution (N = 5, d = / 2 , max. at 0 = 90?)
Nikolova 2022
pp. 148-149, Stutzman 3
b) triangular (1:2:3:2:1) amplitude distribution (N = 5, d = / 2 , max. at 0 = 90?)
Nikolova 2022
pp. 148-149, Stutzman 4
c) binomial (1:4:6:4:1) amplitude distribution (N = 5, d = / 2 , max. at 0 = 90?)
Nikolova 2022
pp. 148-149, Stutzman 5
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- arrays 1 github pages
- chapter 8 arrays and files calvin university
- syntax biggest online tutorials library
- chapter 15 javascript 4 objects and arrays
- chapter 6 arrays southeastern louisiana university
- js cheatsheet
- convert array to buffer tutorial kart
- mutual coupling in antenna arrays semantic scholar
- jhtp8 07 santa barbara city college
- lecture 15 linear arrays part iii 1 advantages of linear arrays with
Related searches
- advantages of buying a car with cash
- advantages of paying with cash
- advantages of traveling with friends
- linear equation with 3 variables calculator
- linear equations with inequalities
- linear inequalities with two variables
- solving linear equation with two unknowns
- solving linear equations with 2 variables
- linear equation with no solution
- linear inequalities with two variables examples
- solving linear equations with fractions
- linear algebra with applications pdf