Compact Butler Matrix Using Asymmetrical T-Couplers

The design of Butler matrices (BM) in classical form is based on microstrip transmission lines which are responsible for the bulky layout of the device. This is mostly due to the constrained imposed by the quarter wavelength transmission lines (TL) employed in the design. This paper alleviates this problem by presenting a compact design of BM from a miniaturized 3dB couplers and crossovers. The miniaturized couplers used in this design are asymmetrical in nature in form of T-sections of TL which gives the proposed BM size reduction of about 64.81% compared to conventional design. This makes the BM highly compact. The results obtained show that all the return losses are better than 21 dB at 6.0GHz. When port 1 is exited, the transmission coefficients S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">51</inf> = −7.29 dB , S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">61</inf> = −6.66 dB, S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">71</inf> = −5.98 dB, and S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">81</inf> = −6.17 dB respectively at the operating frequency. Similarly, when port 2 is exited, the reflection coefficients and transmission coefficients are S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</inf> = −36.81 dB , S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">52</inf> = −6.34 dB , S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">62</inf> = − 6.91dB , S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">72</inf> = −7.01 dB, and S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">82</inf> = −6.95 dB at the center frequency. For both port 1 and 2, the reflection coefficients are better that 21 dB and the transmission coefficients are close to their theoretical value of −6.0 dB with discrepancy less than ±2dB. The proposed design has a good performance in terms of amplitude and progressive phase difference at the output ports.