Transcript Design equations of a Single Section Backward

Design equations of a Single
Section Backward-Wave Coupler
4
3
V3
Zc
Zc
l=λo/4
Zc
1
V1
Ze, Zo
Zc
V4
V2
2
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-Cv2sin2 θ) ; θ= (Π/2).( λo/ λ)
IV2/V1I2 = Cv2sin2θ/(1-Cv2sin2 θ)
Coupling in dB = -20 log10IV3/V1I
PARALLEL COUPLED DIRECTIONAL
COUPLER
Single section Backward wave coupler
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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
P3=P1-P2
Isolated Port
P4
Plane of symmetry
3
4
εo εr
w
1
Input Power
P1
Θ
(L=λo/4)
2
Output Power
P2
s
w
BROADSIDE COUPLED STRIPLINE
Isolated Port
P4
Coupled Power
P3=P1-P2
4
3
Plane of symmetry
w1
w
Θ
(L=λo/4)
1
Input Power
P1
2
Output Power
P2
εo εr