Design equations of a Single Section BackwardWave Coupler

Design equations of a Single Section Backward-Wave Coupler 4 3 V 3 Zc l=λo/4 Zc 1 V 1 Zc Ze, Zo Zc V 4 V 2 2

Specify: Midband Operating frequency : fo Port Impedances : Zc Mean coupling in d. B : -20 log 10 Cv Coupler Parameters: Coupling Length l=λo/4 (λo : guide wavelength at fo) Ze= Zc ((1+Cv)/(1 -Cv))1/2 , Zo = Zc ((1 -Cv)/(1+Cv)) Frequency Response: IV 3/V 2 I 2 = Cv 2 sin 2θ/(1 -Cv 2 sin 2 θ) ; θ= (Π/2). ( λo/ λ) IV 2/V 1 I 2 = Cv 2 sin 2θ/(1 -Cv 2 sin 2 θ) Coupling in d. B = -20 log 10 IV 3/V 1 I

PARALLEL COUPLED DIRECTIONAL COUPLER Single section Backward wave coupler l l l Offer much larger BWs as compared with the Branch Line coupler Mostly backward wave couplers although forward wave couplers are also possible with the case of INHOMOGENOUS medium Most commonly used Parallel coupled DC is the TEM mode single section Backward wave coupler. The term BACKWARD wave coupler implies the ELECTRIC and MAGNETIC FIELD interaction between the parallel coupled conductors causes the coupled signal to travel in the direction opposite to that of the INPUT SIGNAL. Maximum coupling occurs when the length of the coupling region is equal to ONE QUARTER wavelength in propagating medium

EDGESIDE COUPLED STRIPLINE Coupled Power P 3=P 1 -P 2 Isolated Port P 4 Plane of symmetry 3 4 εo εr w 1 Input Power P 1 Θ (L=λo/4) 2 Output Power P 2 s w

BROADSIDE COUPLED STRIPLINE Isolated Port P 4 Coupled Power P 3=P 1 -P 2 4 3 Plane of symmetry w 1 w Θ (L=λo/4) 1 Input Power P 1 2 Output Power P 2 εo εr