Design equations of a Single Section Backward-Wave Coupler

1
Design equations of a Single Section
Backward-Wave Coupler
4
3
Zc
Zc
V4
V3
l?o/4
Ze,
Zo
V2
Zc
Zc
1
2
V1
2
Specify Midband Operating frequency fo Port
Impedances Zc Mean coupling in dB -20
log10Cv Coupler Parameters Coupling Length
l?o/4 (?o guide wavelength at fo) Ze Zc
((1Cv)/(1-Cv))1/2 , Zo Zc ((1-Cv)/(1Cv)) Freq
uency Response IV3/V2I2 Cv2sin2?/(1-Cv2sin2
?) ? (?/2).( ?o/ ?) IV2/V1I2
Cv2sin2?/(1-Cv2sin2 ?) Coupling in dB -20
log10IV3/V1I
3
PARALLEL COUPLED DIRECTIONAL COUPLERSingle
section Backward wave 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
• 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

4
EDGESIDE COUPLED STRIPLINE
Coupled Power P3P1-P2
Isolated Port P4
Plane of symmetry
3
4
eo er
w
w
s
2
T (L?o/4)
1
Output Power P2
Input Power P1
5
BROADSIDE COUPLED STRIPLINE
Isolated Port P4
Coupled Power P3P1-P2
4
3
eo er
Plane of symmetry
w1
w
T (L?o/4)
1
2
Output Power P2
Input Power P1