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J. Eur. Opt. Society-Rapid Publ. 21, 2( 2025)
Therefore, it can be concluded that
f max f 0
h 1 = 2 = ð4 sin h M Þ ð16Þ
Among them, Df max is the maximum bandwidth of phased array antenna. Assuming the above equation is satisfied, the maximum beam offset is Dh 1 / 2( h)/ 4, and when h M = 60 °, the antenna beam widths are 1 ° and 2 °, respectively. Therefore, the limitation on the signal bandwidth is
f max f 0
¼ 0:01 or 0:02 ð17Þ
Assuming the radar signal is an L-band signal with a center wavelength of 1300 MHz, the instantaneous bandwidth of the radar signal is 13 – 26 MHz, which is far from sufficient for high-resolution measurement and radar imaging radars.
3 The influence of true time delay on the performance of phased array radar
Figure
2. Traditional phased array without optical delay line generates beam squint.
By taking the derivative of both sides and substituting the u expression in equation( 6), we can obtain
h f ¼� f f 0 tan h m ð13Þ
According to equation( 12), a change in signal frequency will cause a shift in the direction of the antenna beam, and as the signal bandwidth increases, the directional shift Dh f also increases. This phenomenon is called the“ aperture effect” of phased array antennas, which reflects the spatial oscillation of the antenna beam direction with the change in signal frequency, that is, the beam squint phenomenon, as shown in Figure 2.
The directional diagrams of the antenna are shown in the Figure 2 for operating frequencies of 27 GHz, 28 GHz, and 29 GHz. It can be observed that the beam direction varies with different operating frequencies, with a maximum difference of about 8 °, and the antenna sidelobes also vary with different operating frequencies. An important parameter of an antenna is its bandwidth. Here, the limitation for Df can be referred to as the bandwidth criterion for phased array antennas.
Assuming the maximum allowable beam offset angle is one-quarter of the half power point width of the beam, then
h f max ¼ h 1 = 2 ðh M Þ = 4 ð14Þ
Dh 1 / 2( h M) is the half power point width of the beam when scanned to h M, andDh 1 / 2 is the half power point width of the lobe in the normal direction of the array.
h f max ¼ h 1 = 2 = cos h ð15Þ
Based on the above analysis, the traditional method of providing phase shift through phase shifters on each elements cannot obtain a large instantaneous signal bandwidth for scanning. To solve this problem, true time delay( TTD) lines can be used for phase shifting at the level of each unit or sub antenna array.
Taking the linear array shown in Figure 1 as an example, the delay line is used to control the phase of the elements in the linear array. The length difference of the delay lines at both ends of the linear array in the Figure 1 is DL. Assuming that the delay can fully compensate for the spatial distance difference, and the radar signal pointing angle is h m, the relationship between them can be expressed as
The pointing angle h m is
L ¼ L sin h m
h m ¼ arcsin L L ð18Þ
ð19Þ
According to formula( 19), the pointing angle h m is independent of the signal frequency, so the beam pointing remains unchanged.
In fact, for ease of control, the time delay line is usually implemented using a transmission line with a length that is an integer multiple of the wavelength k, that is, it can only be implemented with mk. Therefore, the remaining Dl = L�mk delayed over time and the remaining phase residual are compensated by the phase shifter.
If delay line control is applied to each radiating element and a delay line of length l is inserted into the channel of the Nth element, resulting in a delay T = l / c, then the delay required to be generated in the i-th element is is /( N�1), and the corresponding delay line length is il /( N�1). Under the action of the delay line, the aperture transition time T 0 of the antenna decreases to