Sheet

1 of 13

1

(1) BranchLine Coupler - Quadrature Zo

2

Zo

λ/4 90°

NOTE This device is sensitive to load mismatches. (2) Lange Coupler (Quadrature)

λ/4 Input Directive

CoupledOutput

φ90° Broadband coupling

3dB → ≈20dB

Quadrature

To calculate the finger dimensions and spacings, we need to calculate the even and odd mode line impedances:-

0)1/()1(2

89340

0)1/()1(2

89340

10

2

2

20tcoefficien Coupling

ZCCCCCoZ

ZCCCCCeZ

C

−+−−+

=

+−−+−

=

=

Armed with these line impedances the finger widths and spacings can be read from the graph plotting coupled micro-strip line data against even and odd mode line impedances.

Sheet

2 of 13

2

Even and odd-mode characteristic impedance design data for coupled micro-strip lines. Example Lange coupler for use at 7.5GHz, 3dB split into 50 ohms. Coupler made from Alumina 0.508mm thick, Dielectric constant 8.8. Determine S and W of fingers.

( )

( )Ω=

−+

−−+=

Ω=+−

−+−=

==

52.6 50*)707.01/()707.01(707.0*2

707.0*893707.0*40

176.2 50*)707.01/()707.01(707.0*2

707.0*893707.0*40

0.707 10

2

2

20-3(dB)

oZ

eZ

C

Sheet

3 of 13

3

~176ohms

~52ohms

From the graph we read S/d ~ 0.075 and W/d = 0.08 The thickness of substrate = 0.508mm so the dimensions of the fingers are:- Width = 0.04mm and Spacing = 0.038mm. One quarter wavelength on this material is 4.15mm long (50 ohm line is 0.5mm wide). To check our rough design we can enter the parameters into the ADS MLANGE model and analyse.

Sheet

4 of 13

4

ADS simulation setup

MLANGLang1

L=4.35 mmS=0.0381 mmW=0.0406 mmSubst="MSub1"

S_ParamSP1

Span=800 MHzCenter=7.5 GHz

S-PARAMETERS

TermTerm4

Z=50 OhmNum=4

TermTerm3

Z=50 OhmNum=3

TermTerm2

Z=50 OhmNum=2

TermTerm1

Z=50 OhmNum=1MSUB

MSub1

Rough=0 mmTanD=0T=0 mmHu=1.0e+033 mmCond=1.0E+50Mur=1Er=8.8H=0.508 mm

MSub

The Lange length was increased by 0.2mm to centre the response shown below:-

Sheet

5 of 13

5

m1freq=7.501GHzdB(S(4,1))=-2.963

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

-2.980

-2.975

-2.970

-2.965

-2.960

freq, GHz

dB(S

(4,1

))

m1

m3freq=7.502GHzphase(S(4,1))=-0.129

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

-4

-2

0

2

4

freq, GHz

phas

e(S

(4,1

))

m3

m2freq=7.502GHzdB(S(3,1))=-3.081

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

-3.085

-3.080

-3.075

-3.070

-3.065

freq, GHz

dB(S

(3,1

))

m2

m4freq=7.501GHzphase(S(3,1))=-90.053

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

-94

-92

-90

-88

-86

freq, GHz

phas

e(S

(3,1

))m4

Sheet

6 of 13

6

(3) Lumped Quadrature (90 degree) Coupler This lumped element hybrid provides a 3dB split with a 90 degree phase shift. It’s bandwidth is very narrow being approximately 1-2%. The element values are given by:-

C1L

1 Co ; Z.11

R L ; Z1 1 2 −=+

==ωωωω C

C

1 3

L 2C 2C

4 2

L

C

2C 2C

C

(4) Lumped 180 degree Coupler This lumped element hybrid provides a 3dB split with a 180 degree phase shift. It’s bandwidth is approximately 20%. The element values are given by:-

1.414Zo L C1

== ωω

1 3

L 2C 2C

4 2

C 2C 2C

L

L

L

Sheet

7 of 13

7

Wilkinson Power Divider & Passive Dividers (In Phase) Microstrip The wilkinson power splitter provides a 3-dB split with no phase shift. In microstrip form the two arms are usually made from quarter wavelength lines with an impedance of 70.7 ohms in a 50-ohm system.

2.Zo

Zo. 2

λ/4

Zo

Zo

Zo

Lumped The bandwidth of the lumped Wilkinson is approximately ½ of the micro-strip version.

2

L

C

1

3

2C 2C C

L

2R

[C] R22

1 C ; [H] 2R L

Zo*2 R

ff ππ==

=

Sheet

8 of 13

8

Passive (6dB power split) A resistive splitter provides a broad-band power split, but has a greater insertion loss through each port (6dB) and only has 6dB of isolation between output ports.

2

1

3

R/3R/3

R/3

R

R

R

Hybrid Ring

λ/4

λ/4

λ/4

3λ/4

A D

B CInput outputs

at A B C D

A 0 1∠-90° 0 1∠-270°

B 1∠-90° 0 1∠-90° 0

C 0 1∠-90° 0 1∠-90°

D 1∠-270° 0 1∠-90° 0

antiphase in phase

Signal Flow Graphs 2 - Port B1 = S11.a1 + S12.a2 B2 = S21.a1 + S22.a2

Sheet

9 of 13

9

S11 S22

S12

S21

b1 a2

a1 b2

“Value” of outgoing wave at each node ie b1 or b2 is equal to :- ∑ (branch value) x ingoing node ∴ b1 = S11.a1 + S12.a2 b2 = S21.a1 + S12.a2 Couplers (1) Microstrip Backward Coupler

λ/4 Input Output

Coupled Directive (Isolated)

We use a similar design process for designing this coupler as used with the Lange coupler in that we need to calculate the odd and even mode line impedances given a particular coupling coefficient:-

CCZoZ

CCZeZ

C

+−

=

−+

=

=

1100

1100

10 20tcoefficien Coupling

Sheet

10 of 13

10

And once we have found the line impedances we can again read off the values of W and S from the Normalised even and odd mode characteristic impedance design data for edge coupled strip-line graph. Note This type of coupler can only be used for loose couplings, as the track spacing becomes too narrow at low coupling factors to be manufactured. Example:- Design a 15dB Microstrip directional coupler for 7.5GHz, using Alumina substrate 0.508mm thick and a dielectric constant of 8.8.

41.8ohms 1778.011778.01*500

59.8ohms 1778.011778.01*500

0.1778 10 20-15

=+−

=

=−+

=

==

oZ

eZ

C

Using the graph below we can read off the values of S and W

~60ohms

~42ohms

Sheet

11 of 13

11

From the graph we read off S/d = 0.85, therefore S = 0.508*0.85 = 0.43mm And W/d = 0.9, therefore W = 0.508*0.9 = 0.46mm. ¼ Wavelength @ 3GHz in this material = 10.5mm These values were entered into the ADS model for a coupled line namely and analysed. ADS schematic for analysing coupler circuit.

TermTerm4

Z=50 OhmNum=4

MCLINCLin1

L=4.45 mmS=0.4 mmW=0.46 mmSubst="MSub1"

S_ParamSP1

Step=Stop=Start=

S-PARAMETERS

TermTerm3

Z=50 OhmNum=3

TermTerm2

Z=50 OhmNum=2Term

Term1

Z=50 OhmNum=1

Sheet

12 of 13

12

Analysed results

m1freq=7.501GHz dB(S(2,1))=-0.188 m1freq=7.501GHz dB(S(2,1))=-0.188

7.0 7.2 7.4 7.6 7.8 8.0-0.1885 -0.1880 -0.1875 -0.1870 -0.1865

freq, GHz

dB(S(2,1))

m1

m2 freq=7.495GHzdB(S(3,1))=-15.295 m2 freq=7.495GHzdB(S(3,1))=-15.295

7.0 7.2 7.4 7.6 7.8 8.0-20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10

freq, GHz

dB(S(3,1))

m2

Coupled Output

m3freq=7.507GHz dB(S(4,1))=-20.837 m3freq=7.507GHz dB(S(4,1))=-20.837

7.0 7.2 7.4 7.6 7.8 8.0 -21.6

-21.4

-21.2

-21.0

-20.8

-20.6

-20.4

-20.2

freq, GHz

dB(S(4,1))

m3

Directivity

Eqn Isolation=m3+m2 Isolation-36.132

Through path

(2) Lumped Coupler (loosely coupled) This lumped approximation of the microstrip backward wave coupler gives ~ 10% bandwidth for 20dB directivity.

L

C

Input

C

Cc

2C

L Isolated

Cc

L

L

Coupled

Output

Sheet

13 of 13

13

15dB- CF Zo.2

0.18 Cc Note

Zo.210 ~ Cc ;

Zo.21 C ;

2Zo L

(CF/20)

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ExampleMicrostripLumpedHybrid RingCouplers