A New Design of Compact <svg style="vertical-align:-0.45pt;width:46.849998px;" id="M1" height="16.112499" version="1.1" viewBox="0 0 46.849998 16.112499" width="46.849998"  xmlns="http://www.w3.org/2000/svg">
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            <text transform="matrix(1,0,0,-1,-71.95,59.61)">
                <tspan style="font-size: 17.93px; " x="0" y="0">𝟒</tspan>
                <tspan style="font-size: 17.93px; " x="12.947626" y="0">×</tspan>
                <tspan style="font-size: 17.93px; " x="28.405872" y="0">𝟒</tspan>
            </text>

        </g>
    </g>
</svg> Butler Matrix for ISM Applications

<table>(a) Layout of conventional <svg height="10.8625" id="M28" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 33.974998 10.8625" width="33.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.8)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,11.996,10.8)"><path d="M528 54l-36 -38l-198 201l-198 -201l-36 38l197 200l-197 201l36 38l198 -202l198 202l36 -38l-197 -201z" id="xD7"></path></g><g transform="matrix(.017,-0,0,-.017,25.748,10.8)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg> Butler matrices. 
(b) Layout of the proposed <svg height="10.8625" id="M29" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 33.974998 10.8625" width="33.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.8)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,11.996,10.8)"><path d="M528 54l-36 -38l-198 201l-198 -201l-36 38l197 200l-197 201l36 38l198 -202l198 202l36 -38l-197 -201z" id="xD7"></path></g><g transform="matrix(.017,-0,0,-.017,25.748,10.8)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg> Butler matrix.</table>

International Journal of Microwave Science and Technology

fig7

Figure 7

Figure 7: A New Design of Compact <svg style="vertical-align:-0.45pt;width:46.849998px;" id="M1" height="16.112499" version="1.1" viewBox="0 0 46.849998 16.112499" width="46.849998"  xmlns="http://www.w3.org/2000/svg">
    <g transform="matrix(1.25,0,0,-1.25,0,16.1125)">
        <g transform="translate(72,-59.11)">
            <text transform="matrix(1,0,0,-1,-71.95,59.61)">
                <tspan style="font-size: 17.93px; " x="0" y="0">𝟒</tspan>
                <tspan style="font-size: 17.93px; " x="12.947626" y="0">×</tspan>
                <tspan style="font-size: 17.93px; " x="28.405872" y="0">𝟒</tspan>
            </text>

        </g>
    </g>
</svg> Butler Matrix for ISM Applications 

Figure 7 | A New Design of Compact 
    
        
            
                𝟒
                ×
                𝟒
            

        
    
 Butler Matrix for ISM Applications 

International Journal of Microwave Science and Technology

A New Design of Compact 𝟒 × 𝟒 Butler Matrix for ISM Applications

Figure 7

A New Design of Compact Butler Matrix for ISM Applications