Design equations of a Single Section Backward-Wave Coupler l=λo/4 ZcZc ZcZc ZcZc ZcZc Z e, ZoZo V3V3 V1V1 V4V4 V2V2

Specify: Midband Operating frequency : f o Port Impedances: Z c Mean coupling in dB : -20 log 10 C v Coupler Parameters: Coupling Length l=λ o /4 (λ o : guide wavelength at f o ) Z e = Z c ((1+C v )/(1-C v )) 1/2, Z o = Z c ((1-C v )/(1+C v )) Frequency Response: IV 3 /V 2 I 2 = C v 2 sin 2 θ/(1-C v 2 sin 2 θ) ; θ= (Π/2).( λ o / λ) IV 2 /V 1 I2 = C v 2 sin2θ/(1-C v 2 sin2 θ) Coupling in dB = -20 log 10 IV 3 /V 1 I

PARALLEL COUPLED DIRECTIONAL COUPLER Single section Backward wave coupler Offer much larger BWs as compared with the Branch Line coupler 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 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. 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. 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 Maximum coupling occurs when the length of the coupling region is equal to ONE QUARTER wavelength in propagating medium

Θ (L=λ o /4) Coupled Power P 3 =P 1 -P 2 Isolated Port P 4 Output Power P 2 Input Power P 1 Plane of symmetry wws ε o ε r EDGESIDE COUPLED STRIPLINE

Coupled Power P 3 =P 1 -P 2 Isolated Port P 4 Output Power P 2 Input Power P 1 Θ (L=λ o /4) w1w1 w ε o ε r Plane of symmetry BROADSIDE COUPLED STRIPLINE