By Gray,Hurst

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**Additional resources for Analysis and Design of Analog Integrated Circuits. Solutions**

**Example text**

IT . w= [ tsm3u+4cosSsm2u+8cosS =2[ t sin3kdcos + 8cos (3kdcosOo) 'IT( l+cos 'IT) sinu+ ( 6+4cos 2'lT) u ] ab S S +4cos ~ sin2kdcos i(1+ cos i)sin kd cos (kd cos ° 0 ) (2kdcosOo) + ( 6 + 4cos 2 'lT ) kd] . 88), we can calculate D when d and 00 are specified. 2 the radiation characteristics for the array with n = 6, d = A/2, and the excitation function shown in Fig. 20. 90) will be more complicated. Note also that there are actually only four excited elements in the array discussed in the above example, because 32.

Characteristics of a five-element improved endfire array: (a) First-null beamwidth, (b) First sidelobe or backlobe level. to 27T/5 radians. Therefore, the process of maximizing the directivity for endfire arrays works in the following manner: As ~ is increased slowly, both the maximum radiation at ()= 0 and the total power radiated decrease, but at different rates to yield an increasing directivity. The directivity eventually reaches its maximum at a value ~m' In what follows, we will try to determine ~m when nand d are specified.

14). This simpler ratio form will be called the array function. The distinct facts concerning such an array function are that the denominator has a finite number of terms and is free of n, and that the numerator also has a fixed finite number of terms with n appearing in the exponents or the coefficients. Thus, an increase in n does not change the number of terms involved nor increase the complexity of the expression for S. Suppose that the envelope of the amplitude excitations in a linear array can be described by a continuous function, f(n, within the interval O