This work presents a novel planar branch-line coupler topology developed for dual-band operation using an E-shaped impedance transformer network to supplant the conventional microstrip line. Explicit closed-form design equations for dual-band operation are derived using the ABCD matrices. The studied coupler features a large dual-band frequency ratio with a compact size. https://herbsdailyes.shop/product-category/specimen-collection-specimen-collection-kits/