Design Specifications for the GMRT Antennas

The ${f/D}$ ratio for the GMRT antennas was fixed at the value $0.412$ based both on structural design issues as well as preliminary studies of various feeds radiation patterns. Since the antennas are to work at meter wavelengths prime focus feeds were preferred. Cassegrain feeds at meter wavelengths would result in impractically large secondary mirrors (the mirror has to be several $\lambda$ across) and concomitant large aperture blockage.

Six bands of frequencies had been identified [1] for the GMRT observations. It was deemed essential to be able to change the observing frequency rapidly, and consequently the feeds had to mounted on a rotating turret placed at the prime focus. If one were to mount all the six feeds on a rotating hexagon at the focus, the adjacent feeds will be separated by $60^{\circ}$. If one wants to illuminate the entire aperture, then one has to have a feed pattern that extends at least up to the subtended angle of the parabola edge, which is $\theta_0 = 62.5^{\circ}$ (Note that ${\cot({{\theta}_0}/2)} = 4f/D$, Figure 19.1). Hence this arrangement of feeds would cause the one feed to ``see'' the feeds on the adjacent faces. It was decided therefore to mount the feeds in orthogonal faces of a rotating cube. Since one needs six frequency bands, this leads to the constraint that at least two faces of the turret should support dual frequency capability. For astronomical reasons also dual frequency capability was highly desirable.

One specific aspect of GMRT design is the use of mesh panels to make the reflector surface[1]. Since the mesh is not perfectly reflective, transmission losses thorough the mesh have to be taken into account. Further, the expected surface errors of the mesh panels was $\sim 5$ mm. This implies that the maximum usable frequency is (see Section 19.2) $\sim 3000$ MHz, independent of the transmission losses of the mesh. (Incidentally, since the mean-spacing of feed-support legs, ${\bar{L}} = 23.6$ m, the lowest usable frequency is around 6 MHz).

Several analytical methods exist in literature to compute the transmission loss through a mesh as a function of the cell size, the wire diameter and the wavelength of the incident radiation. The one chosen for our application is has good experimental support [2,3]. At the GMRT, the mesh size is $10\times 10$ mm for the central 1/3 of the dish, $15\times 15$ mm of the middle 1/3 of the dish and $20\times 20$ mm for the outer 1/3 of the dish. The wire diameter is $0.55$ mm. The transmission loss for at two fiducial wavelengths for these various mesh sizes is given in Table 19.2.

Table 19.2: Transmission losses through the GMRT wire mesh

Mesh	${\lambda} = 21$ cm.	${\lambda} = 50$ cm.
size
10 mm.	-15.8 dB	-23.3 dB
15 mm.	-11.4 dB	-18.4 dB
20 mm.	-8.1 dB	-14.6 dB

Each section of the dish not only has a separate mesh size but also a separate surface rms error. If we call these rms surface errors ${{\sigma}_1}, {{\sigma}_2}, {{\sigma}_3}$ and the respective transmission losses (at some given wavelength) ${{\tau}_1}, {{\tau}_2}, {{\tau}_3}$, then the surface rms efficiency given by Eqn 19.4.15 has to be altered to a weighted rms efficiency:

$${{\eta}_r} = {\frac{{A_{1}}+{A_{2}}+{A_{3}}}{\int_{0}^{{\theta}_0} {\vert E({\theta})\vert^2{\sin({\theta})}d{\theta}}}}$$

where,

$${A_{1}} = {\exp{\left[ -{\left( {\frac{4{\pi}{{\sigma}_1}}{\lambda}} \right... ...]}} {\int_{0}^{{\theta}_2}{\vert E({\theta})\vert^2{\sin({\theta})} d{\theta}}}$$ (19.5.17)

$${A_{2}} = {\exp{\left[ -{\left ({\frac{4{\pi}{{\sigma}_2}}{\lambda}} \right... ..._{{\theta}_2}^{{\theta}_1}{\vert E({\theta})\vert^2{\sin({\theta})} d{\theta}}}$$ (19.5.18)

$${A_{3}} = {\exp{\left[ -{\left( {\frac{4{\pi}{{\sigma}_3}}{\lambda}} \right... ..._{{\theta}_1}^{{\theta}_0}{\vert E({\theta})\vert^2{\sin({\theta})} d{\theta}}}$$ (19.5.19)

and ${{\theta}_2},~{{\theta}_1}$ are the subtended angles of the first and second points of mesh-transition-zones, as illustrated in Figure 19.4

Figure 19.4: Schematic of the sub division of the GMRT antenna surface into 3 zones. The mesh size as well as the rms surface error is different in the different zones.

The transmission loss gives a corresponding mesh-leakage or mesh-transmission efficiency, $\:{{\eta}_{mt}}\:$, which is given by

$${{\eta}_{mt}} = {\frac{{B_{1}}+{B_{2}}+{B_{3}}}{\int_{0}^{{\theta}_0} {\vert E({\theta})\vert^2{\sin({\theta})}d{\theta}}}}$$ (19.5.20)

where,

$${B_{1}} = (1-{{\tau}_1}){\int_{0}^{{\theta}_2}{\vert E({\theta})\vert^2{\sin( {\theta})}d{\theta}}}$$ (19.5.21)

$${B_{2}} = (1-{{\tau}_2}){\int_{{\theta}_2}^{{\theta}_1}{\vert E({\theta})\vert^2 {\sin({\theta})}d{\theta}}}$$ (19.5.22)

$${B_{3}} = (1-{{\tau}_3}){\int_{{\theta}_1}^{{\theta}_0}{\vert E({\theta})\vert^2 {\sin({\theta})}d{\theta}}}$$ (19.5.23)

Efficiencies computed for the different GMRT feeds (using their measured pattern, being the input) are given in Table 19.4.