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254 ANTENNA BASICS

⁄
⁄
⁄
90° to 30°. If so, = 30° and < 1 �√3 2 + 1� = 0.536. Note that moderate rise
in the equivalent or real phase velocity above the light speed, i.e. / < 1, allows us to slightly

push elements apart.
Note that the array system comprised of separate receive and transmit array could improve
situation with grating lobes if a beam of receive array has nulls in the direction of transmit array
grating lobes. Consequently, the “two way” pattern of such system would be free of grating
lobes.
5.5.4 True Time Delay (TTD) Steering

Simple inspection of equation (5.91) reveals a distressing phenomenon of the beam squint. It
means that the main beam points in exactly the right direction = only if = and
0
diverges from this angle as frequency deviates. The plots in Figure 5.5.4a clearly illustrate this
effect causing system signal distortion as a consequence of undesired amplitude and phase
modulation (see (5.91)). To explain the nature of this effect recall that the phase difference =
−cos = −(2/)cos between fields emitted by the adjacent radiators is proportional
to frequency while the inter-element phase shift provided by the phase shifters is fixed and
practically independent on frequency. As a result, the difference − = −cos ∓
cos and thus the main beam maxima at = are frequency dependent.
0
Theoretically, the solution is straightforward and follows from the latter expression. We must
develop a phase shifter providing the frequency progressive inter-element phasing, i.e. =

Figure 5.5.4 a) Frequency beam squint in the broadband linear array, b) The same array
with TTD

) and the linear array becomes squint-free
±cos . Then − = −(cos − cos
⁄
(see Figure 5.5.4b). Note that the time delay = = ±(2/)cos of signal
passing such phase shifters is constant, i.e. frequency independent. From here, the term “true-
time-delay” is derived.
The question boils down how to do it practically. Let us consider the schematic block diagram
presented in Figure 5.5.5a that is equivalent to Figure 5.4.9c where the fixed phased shifters are
replaced with TTD units maintaining the progressive time delay and are integer multiples of .
Each TTD unit is a section of transmission line defined as any structure that is capable of
carrying electromagnetic wave energy with little loss. It can be the parallel line, i.e. two
conductor line, coaxial cable, stripline, waveguide, optical fiber, and many others. We refer the
reader to Chapter 6 for details.