In many applications the waveguide feeding networks is used to handle high input power requirement of antenna system. Although feed network made of hollow waveguide is best suited from the point view of power handling but from the weight and compactness point of view, feed networks are not generally made solely of waveguides. In this case, rectangular (or more specifically square) coaxial lines are used as transmission medium for feed in the lower frequency range like L-band, C-band upto X-band. Though, this type of BFN are widely used, the literature elaborating the key design issues is very much limited. Specially the design of different types of transitions from square-X to other transmission medium is very critical for an optimum configuration and no open literature gives any clue to such design. Hence, it is imperative to carry out a systematic study on various aspects of rectangular coaxial line and waveguide beamformer followed by simulation, design, fabrication and RF testing.

The dominant mode of square-x line is TEM mode having zero cut-off frequency. Next higher order mode like TE10, TE11, TE20 and TM 11 can propagate Proper care has been taken to chose dimension so that next higher order mode does not occur. Using FEM tool it has been found that cutoff frequency for next higher order mode.The bandwidth of the rectangular coaxial line for TEM mode propagation starts from DC to the cut-off frequencies of the first higher-order modes.

#### X-Band Square Coaxial Feed Network Design Parameters

- Outer conductor – 9mm x 9 mm
- Inner conductor – 3.5mm x 3.5mm
- b/a= 0.38
- (a-b)/2 =2.75mm
- Impedance – 50 ohms
- Cut off frequency – 11.67 GHz
- Operating frequency 9.6 GHz
- It has to handle – 72 watt average power.
- Separation between inner and outer conductor is – 2.75mm
- Electric field strength is -6.457 volts/mm (from FEM based software for 1 watt)
- For 1 watt average power, voltage is (6.457 x 2.75) – 17.75 volts
- So for 72 watt average power, voltage is (sqrt ( 17.75^2*72) –
**150.6 volts**

- It has to handle 8 kW peak power.
- This power with 0.9 % duty cycle gives – 1588 volts
- So voltage between inner and outer conductor will be – (1588/2.75) -577.5 volts/mm
- Now electric field strength for air breakdown is -3000 volts/mm
- Electric field strength for dielectric breakdown is -2000 volts/mm
- So break down margin for air is (20*log (3000/577.5)) – 14.3 dB
- And for dielectric it is (20*log (2000/577.5)) -10.7 dB

First , I find dimensions of outer and inner conductor for a 50-ohm line that can handle my desired peak power. Also ensured that in this structure no higher mode will be propagate. Main designing task in realization of 3 ports Tee, is impedance matching at junction. Due to sudden discontinuity at junction higher order modes are generated in waveguide. Generation of higher order modes is responsible for storing energy near junction. This increases reactive part of impedance. To cancel this reactive part of impedance I designed a septum that load waveguide with opposite reactive part as it is at junction.

The most challenging task in this work was to realize a 90^{0} transition from square-x line to a 50 ohm line that can be used as feed microstrip antenna. For broadband performance I designed a Multisection transformer, that transformers 25 ohms junction impedance to 50 ohms impedance, by dividing it in three parts. In this way frequency dependency of network minimized and a broadband performance is obtained. I use Chebyshev polynomial to calculate impedances that gives broadband performance. Then realized a circular 90 degree bend. Then 1:2 power divider: then with the combination of 1:2 power dividers realized a 1: 4 and 1:8 power divider.

Square coaxial line to microstrip transition is another important component that provide an interconnect between microstrip feed line and waveguide feed line.

At transition junction due to discontinuity, charges accumulated that increases reactive part of impedance so to cancel that excess reactive part of impedance and balance line to a 50 ohm real part, I kept inner conductor at lamda/4 from short outer conductor. In this way the reflected and direct power at junction are in same phase and power is coupled to circular line. But at higher frequency it is not sufficient to match network. I cut some slots in inner conductor and shape outer conductor to remove mismatches at junction. Then I verified my design performance sing finite element code.