Design equations of a Single Design equations of a Single Section Backward-Wave CouplerSection Backward-Wave Coupler

3 4

1 2

l=λo/4Zc Zc

Zc Zc

Ze, Zo

V3

V1

V4

V2

Specify:Midband Operating frequency : fo

Port Impedances : Zc

Mean coupling in dB : -20 log10Cv

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:

IV3/V2I2 = Cv2sin2θ/(1-Cv

2sin2 θ) ; θ= (Π/2).( λo/ λ)

IV2/V1I2 = Cv2sin2θ/(1-Cv

2sin2 θ)

Coupling in dB = -20 log10IV3/V1I

PARALLEL COUPLED DIRECTIONAL PARALLEL COUPLED DIRECTIONAL COUPLERCOUPLER

Single section Backward wave couplerSingle section Backward wave coupler

Offer much larger BWs as compared with the Branch Line couplerOffer much larger BWs as compared with the Branch Line coupler Mostly backward wave couplers although forward wave couplers Mostly backward wave couplers although forward wave couplers

are also possible with the case of INHOMOGENOUS mediumare also possible with the case of INHOMOGENOUS medium Most commonly used Parallel coupled DC is the TEM mode single Most commonly used Parallel coupled DC is the TEM mode single

section Backward wave coupler.section Backward wave coupler. The term BACKWARD wave coupler implies the ELECTRIC and The term BACKWARD wave coupler implies the ELECTRIC and

MAGNETIC FIELD interaction between the parallel coupled MAGNETIC FIELD interaction between the parallel coupled conductors causes the coupled signal to travel in the direction conductors causes the coupled signal to travel in the direction opposite to that of the INPUT SIGNAL.opposite to that of the INPUT SIGNAL.

Maximum coupling occurs when the length of the coupling region is Maximum coupling occurs when the length of the coupling region is equal to ONE QUARTER wavelength in propagating mediumequal to ONE QUARTER wavelength in propagating medium

3

1

4

2Θ(L=λo/4)

Coupled Power P3=P1-P2

Isolated Port P4

Output Power P2

Input Power P1

Plane of symmetry

w ws

εo εr

EDGESIDE COUPLED STRIPLINE

Coupled Power P3=P1-P2

Isolated Port P4

Output Power P2

Input Power P1

Θ(L=λo/4)

w1

w

3

1

4

2

εo εrPlane of symmetry

BROADSIDE COUPLED STRIPLINE