phase shifter design tutorialdl.edatop.com/mte/ads/edatop.com_phase_shifter.pdf · like the...

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Phase Shifter Design Tutorial Introduction Phase shifters are devices used to adjust transmission phase in a system, they can be fixed phase digital phase shifters or analogue variable types. Switched-Line Phase shifter These phase shifters are similar to their attenuator equivalent where two SPDT switches are used to switch two line lengths, one of which is X degrees longer in electrical length than the other. The circuit is shown in Figure 1. Vcontrol

Line length 1

Line length 2

Figure 1 Switched-line phase shifter. Line length 2 has a longer electrical length than line length 1 so when switched in line will cause an in-line phase shift ∆φ=β(l2-l1).

( )

eff

12

1 Vpand Vp

Where

β shift phase Required

εωβ

φ

==

−=∆ ll

Example Design a switched-line phase shifter with a 22.5 degree phase shift at 4GHz, on a substrate with a dielectric constant of 9.9.

mm485.1m1.485x102π

0.392*0.0238 2.

2 m0238.0 9.9

075.0

m075.04x103x10 , 4GHz @

0.392rad .2 36022.5 s22.5degree

3

9

8

air

===∆

=∆

=∆∴

====

===

==∆

=∆

−

πφλ

βφ

λπβ

ελ

λ

λ

ωβφ

g

geff

airg

fc

l

l

So we design the micro-strip lines such that line length 2 is 1.485mm longer than line length 1.

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However, we have to be careful in our choice of line lengths so that we don’t get lines lengths of 180 degrees (or multiples of 180 degrees) which, would then form a resonator when switched out of circuit. Loaded-Line Phase shifter For phase shifts of <45 degrees we can make use of loaded-line phase shifters as shown in . These phase shifters work by adding a shunt reactance to the micro-strip line (in the form of an inductor or capacitor) causing the incident signal to undergo a phase shift. (Note in micro-strip the reactive component can be formed by a micro-strip stub).

OR

-jb +jb

Figure 2 Switched-line phase shifter. A shunt susceptance inductive (-jB) or capacitive (+jB) is switched in across the line causing a phase shift on the incident signal.

(dB) 4

b110log be willshifter phase of loss insertion and 2b-tan

jB.Zojb ie elemant) shunt (from esusceptanc normalised the be jb Let

2

101-

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛=∆

=

φ

Sheet

3 of 12

Example Like the previous phase shifter we shall design for a phase shift of 22.5 degrees @4GHz.

( ) 0.68dB 4

8285.0110log of loss insertion resulting a With

nH65.1.4x10241.4

.f2X

L

41.4ohms 50*0.8285 50ohms to back Normalise

esusceptanc inductive ie 0.8285- b -2.tanb above Rearrange

2

10

9L

=⎟⎟⎠

⎞⎜⎜⎝

⎛ −+

===

==

=∆=

ππ

φ

The disadvantage of these phase shifters, are that in order to large values of phase shift, high values of b are required thus increasing the insertion loss. 45-degree phase shift (b = 2) will incur an insertion loss of 3dB. Also as these phase shifters rely on reflecting signals their return losses are very poor. Modified loaded-line Phase shifter The return losses of loaded-line phase shifters can be greatly improved by having two shunt susceptances separated by 90 degrees. If these susceptances are switched in or out by Pin diodes then a switchable phase shifter can be made as below. The equivalent circuit is a transmission line with phase θe.

-jb +jb

-jb

+jb

90 degree line

Figure 3 Improved switched-line phase shifter using two shunt susceptances and a quarter-wave length of transmission line. This circuit has very good input/output return losses.

Sheet

4 of 12

( )

f.N2BC

B.

N L

Zo Ze and 1b So,

b-1Zo Ze circuit of Impedance Also,

bcos length phase Equivalent

2

1e

π

ω

ϑ

=

=

>⇒<

=

−= −

This time we have a 4GHz phase shifter where two switched states give susceptances of +10Ω and -10Ω, and we wish to know the resulting phase shift and equivalent line impedance.

0.159pF .50x1042

0.2 f.N2BC

9.9nH 2.0..4x102

50 B.

N L

51 0.2-1

50 b-1

Zo impedance line Equivalent

degrees 23 78.46-101.5 shift phase alDifferenti

degrees 78.46 0.2 b- cos

degrees 101.5 0.2- b- cos

0.2- )(inductive 10/50- b& 2.0e)(capacitiv 50/10b

9

9

22

offnoffeoff

eononeon

off

on

===

===

Ω===

==∴

⇒==∴

⇒==∴

==

==

ππ

πω

θθ

θθ

The ADS simulation shown in Figure 4 shows the switched line attenuator using a 90-degree micro-strip line designed for 4GHz. For one simulation the inductors are connected resulting in the plots shown in Figure 6 and the other simulation the capacitors are connected resulting in the plots shown in Figure 5.

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5 of 12

S_ParamSP1

Step=4 MHzStop=5.0 GHzStart=3.0 GHz

S-PARAMETERS

LL1

R=L=9.9 nH

LL2

R=L=9.9 nH

CC2C=0.159 pF

CC1C=0.159 pF

MSUBMSub1

Rough=0 mmTanD=0T=0 mmHu=1.0e+033 mmCond=1.0E+50Mur=1Er=9.6H=0.625 mm

MSub

MLINTL1

L=7.4 mmW=0.65 mmSubst="MSub1"

TermTerm1

Z=50 OhmNum=1

TermTerm2

Z=50 OhmNum=2

Figure 4 ADS simulation of the improved switched-line phase shifter given in the example. In this case the inductors have been de-activated to leave the capacitors in circuit resulting in a phase shift of 101.5 degrees.

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m1freq=3.996GHzphase(S(2,1))=-102.295

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

-130

-120

-110

-100

-90

-80

-70

freq, GHz

ph

ase

(S(2

,1))

m1

m2freq=3.996GHzdB(S(2,1))=-0.006

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

-0.5

-0.3

-0.1

0.0

freq, GHz

dB

(S(2

,1))

m2

m3freq=4.000GHzdB(S(1,1))=-57.989

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

-70

-60

-50

-40

-30

-20

-10

freq, GHz

dB

(S(1

,1))

m3

Figure 5 Improved switched-line phase shifter with capacitors switched in circuit.

m1freq=3.996GHzphase(S(2,1))=-79.747

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

-110

-100

-90

-80

-70

-60

-50

freq, GHz

ph

ase

(S(2

,1))

m1

m2freq=3.996GHzdB(S(2,1))=-0.008

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

-0.5

-0.3

-0.1

0.0

freq, GHz

dB

(S(2

,1))

m2

m3freq=4.000GHzdB(S(1,1))=-40.955

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

-70

-60

-50

-40

-30

-20

-10

freq, GHz

dB

(S(1

,1))

m3

Figure 6 Improved switched-line phase shifter with inductors switched in circuit.

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Reflection Phase shifter

Reflection phase shifters work by having switchable terminations which, create switchable reflection coefficients. The main type of reflection phase shifter uses switched line lengths either by using a PIN switch or by a variable reactance (eg varactor) to alter electrical length. In both cases the signal incurs twice the extra electrical length as the signal is reflected back.

Switched Line reflection phase shifter The simplest example is to use a 90-degree hybrid (eg Lange or Rat-race) and two PIN diodes to either short to ground bypassing line length 2 or switched out thus adding line length 2 and adding a longer path for the signal to travel. The schematic of the circuit is shown in Figure 7.

Line length 2 ∆φ/2

Line length 2∆φ/2

Line length 1 Line length 1

90 degree hybrid coupler

Figure 7 Reflection phase shifter using two PIN diodes to switch in or out the additional line lengths 2.

( )

( )

( )

2

0,1,2,3... k where,22φ- : Giving

e ie operation best For

e

e

φj-*

φj

jφ

φπφ

φππφφ

φ

φ

∆−=⇒

=∆−⇒+∆+=

=ΓΓ=Γ

=Γ

=Γ

∆+

∆+

k

kk

ONOFFON

OFF

ON

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Example Switched line reflection phase shifter to give 45 degrees phase shift at 8GHz. Lange coupler length will be ~4mm long.

degrees 5.2222.545 45

degrees 22.5- 245

2 then 0 k If

2

eperformanc loss return best For

45

212

11

*

12

2

1

=−==+∆∴=−=∆

=−=∆

−==∆

−=

Γ=Γ

=−=∆

∠Γ=Γ

∠Γ=Γ

φφφφφφ

φφφπφ

φφφ

φ

φ

k

OFFON

oOFF

oON

The ADS simulation for this circuit is shown in

MLINTL4


MLINTL2


MLINTL1


MLINTL3


MLANGLang1

L=3.9 mmS=0.05 mmW=0.05 mmSubst="MSub1"

S_ParamSP1


S-PARAMETERS MSUBMSub1

Rough=0 mmTanD=0.001T=0 mmHu=1.0e+033 mmCond=1.0E+50Mur=1Er=9.6H=0.625 mm

MSub

TermTerm1

Z=50 OhmNum=1

TermTerm2

Z=50 OhmNum=2

Figure 8 ADS simulation of the switched line reflection phase shifter given in the example. In this case we are simulating the PIN diodes on and shorted to ground by the two ground points at the end of 22.5 degree micro-strip lines TL1 and TL2. The resulting simulation of this circuit is shown in Figure 9. The other case is with the grounds disabled simulating the PINs switched off and the signal having to travel additionally along TL3 & TL4 (and of course back again). The resulting simulation of this is shown in

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m1freq=8.000GHzphase(S(2,1))=47.133

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

20

30

40

50

60

70

freq, GHz

ph

ase

(S(2

,1))

m1

m2freq=7.992GHzdB(S(2,1))=-0.023

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

-0.06

-0.05

-0.04

-0.03

-0.02

freq, GHz

dB

(S(2

,1))

m2

m3freq=8.004GHzdB(S(1,1))=-26.405

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

-28

-26

-24

-22

-20

freq, GHz

dB

(S(1

,1))

m3

Figure 9 Resulting simulation from the circuit shown in Figure 8 with the diodes switched on – shorting to ground and effectively switching out TL3 & TL4.

m1freq=8.000GHzphase(S(2,1))=-1.628

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

-40

-20

0

20

40

freq, GHz

ph

ase

(S(2

,1))

m1

m2freq=7.992GHzdB(S(2,1))=-0.049

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

freq, GHz

dB

(S(2

,1))

m2

m3freq=8.004GHzdB(S(1,1))=-21.355

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

-22

-21

-20

-19

-18

freq, GHz

dB

(S(1

,1))

m3

Figure 10 Resulting simulation from the circuit shown in Figure 8 with the diodes switched off (by disabling the grounds at the end of TL1 & TL2) – adding TL3 & TL4 transmission lines.

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As can be seen there is approximately a 45 degree phase shift (the accuracy of this depends on the Lange coupler dimensions). Variable reactance reflection phase shifter This circuit again uses a 90-degree hybrid but instead of switched line lengths variable reactances are used. A variable reactance is in effect a variable electrical length therefore, using a variable reactance such as a varactor we can form a variable phase shifter. The schematic of the variable reactance reflection phase shifter is shown in Figure 11.

Varctor 1 Varctor 2

90 degree hybrid coupler

Vbias Vbias

If you require a negative bias on the varactor then use another bias circuit here, and replace DC short circuit with a RF short circuit eg stub

Figure 11 Variable reactance reflection phase shifter, using varactors as the variable reactance.

Each varactor is bias via a choke with the same bias. There may be a requirement to use a varactor reference instead of 0V (caused by the DC ground). In this situation the DC ground is replaced by a RF short eg a quarter-wave capacitive stub and another bias circuit added. For example calculate the phase shift of a 4GHz variable reactance reflection phase shifter using Macom varactors type MA46422.

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The MA46422 has a capacitance range of 0.6pF to 6pF (20V to 0.1V). The electrical length needs to be calculated for each capacitor value remembering that the phase is doubled due to the signal reflecting back from the short circuit on the other end of the varactor. From the Micro-strip tutorial we found the following relationship for a shunt capacitor:-

=

Micro-strip Zo

θ

Capacitor C

⎟⎟⎠

⎞⎜⎜⎝

⎛<

=

4λ

9090θ Where

tanω

op00

ZoC θ

(1) Capacitor set to 6pF (ie Control voltage of 0V)

( ) ( ) o164 .50.6x10.4x102tan*2 ω.C.Zotan*2φ

Zo

tanφωC Rearrange

12-91-1-6pF ===

=

π

(2) Capacitor set to 0.6pF (ie Control voltage of 20V)

( ) ( )

degrees 90 74-164 φφ Therefore,

74 .50.0.6x10.4x102tan*2 ω.C.Zotan*2φ

0.6pF6pF

-129-1-10.6pF

==−=∆

===

φ

π o

The ADS simulation in Figure 12 was initially run with the varactors set to 6pF and the PhaseShift element was then set to give 0 degree phase shift at 4GHz to set a reference. The simulation was then run again this time with the varactors set to 0.6pF resulting in the plots shown in Figure 13.

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CC2C=.6 pF

CC1C=.6 pF

PhaseShiftSMLPS1

ZRef=50. OhmPhase=-109.78

MLANGLang1

L=7.8 mmS=0.05 mmW=0.05 mmSubst="MSub1"

S_ParamSP1


S-PARAMETERS MSUBMSub1

Rough=0 mmTanD=0.001T=0 mmHu=1.0e+033 mmCond=1.0E+50Mur=1Er=9.6H=0.625 mm

MSub

TermTerm1

Z=50 OhmNum=1

TermTerm2

Z=50 OhmNum=2

Figure 12 Variable reactance reflection phase shifter. The phase shift was set to give zero phase shift with the varactors set to 6pF (0V) as a reference, then the simulation was run again this time setting the varactors to 0.6pF (20V). The result of the second simulation is shown in Figure 13.

m1freq=4.000GHzphase(S(2,1))=86.568

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

40

60

80

100

120

140

freq, GHz

ph

ase

(S(2

,1))

m1

Figure 13 Simulation from ADS schematic shown in Figure 12, with capacitors now set to 0.6pF (from 6pF) to show that maximum phase shift available if using the MaCOM MA46473 diodes.

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phase shifter design tutorialdl.edatop.com/mte/ads/edatop.com_phase_shifter.pdf · like the...

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