Advanced Impedance Matching

AdvancedImpedance Matching

Microwave Engineering

EE 172Dr. Ray Kwok

Advanced Impedance Matching - Dr. Ray Kwok

Advanced Impedance MatchingSo far….

• 2-elements tuning• Lumped Elements (L,C)

• Transmission Lines

• Stubs (single & double)• 1-port network

• single frequency

Now:

• are all tuning the same?

• wideband matching – multiple sections• multi-ports (simultaneously tuned)


Let’s compare our 2-element tuning examples over frequency…

• Lumped Elements (L,C)

• Transmission Lines

• Stubs (Single and Double)• Quarter-Wave transformer


LumpedElements

R=1G=1

If ZL is inside the G=1 circle,

first element cannot be shunt

ZL (0.4, 1)YL (0.34, -0.87)

Z (0.4, 0.48)Y (1, -1.24)

=0.4+j1ZL

jB = +j1.24 = jZoωC

jX = -j0.52 = -j/ωCZo

Z (0.4, -0.48)Y (1, 1.24)

=0.4+j1ZL

jB = -j1.24 = -jZo/ωL

jX = -j1.48 = -j/ωCZo

Z (1, 1.4)Y (0.34, -0.48)


=0.4+j1ZL

jX = -j1.4 = -j/ωCZo

Z (1, -1.4)Y (0.34, 0.48)


=0.4+j1ZL

jX = j1.4 = jωL/Zo

If ZL is inside the R=1 circle,

first element cannot be in series


Return Loss

0.01 0.11 0.21 0.31 0.41 0.5

Frequency (GHz)

Lump

-50

-40

-30

-20

-10

0

DB(|S[1,1]|)

Lump1

DB(|S[1,1]|)

Lump2

DB(|S[1,1]|)

Lump3

DB(|S[1,1]|)

Lump4


Using Stubs

ZL (0.4, 1)YL (0.34, -0.87)

Z (0.4, -0.48)Y (1, 1.24)

=0.4+j1ZL

short shunt stub

jB = -j1.24 = -jcotβl

open series stub

jX = -j1.48 = -jcotβl

Z (1, 1.4)Y (0.34, -0.48)

open shunt stub

jB = +j0.39 = jtanβl

=0.4+j1ZL

open series stub

jX = -j1.4 = -jcotβl

l

l

l

l

β=

β−=

β−=

β=

tanjYY

cotjYY

cotjZZ

tanjZZ

oop

osh

oop

osh

One way, simply replace lumped elements with stubs

Zo can be

anything here

previous example


Open – Short Stubs

0.01 0.11 0.21 0.31 0.41 0.5

Frequency (GHz)

Stubs

-50

-40

-30

-20

-10

0

DB(|S[1,1]|)

Stub1

DB(|S[1,1]|)

Stub2


ZL (0.4, 1)YL (0.34, -0.87)

=0.4+j1ZL

Transmission Line Matching

usually requires 1 more element

previous example

0.130λλλλ

0.185λλλλ

0.055λ

50 Ω

jX = -j1.85 = -j/ωCZo

=0.4+j1ZL

0.435λλλλ

0.305λ

50 Ω

Y (1, 1.9)

short shunt stub


Z (1, 1.85)


Single Stub Tuningrefers to sliding a stub (any kind)

along a transmission line.

previous example

0.130λλλλ

0.064λλλλ

=0.4+j1ZL

0.435λλλλ

0.305λ

50 Ω

Y (1, 1.9)

short shunt stub


In practice, usually shunt stubs,

short stub for waveguides,

open stub for microstrip.

=0.4+j1ZL

0.434λ

50 Ω

open shunt stub

jB = j1.9 = jtanβl

ZL (0.4, 1)YL (0.34, -0.87)

Y (1, -1.9)


Any Stubtanβl can be “+” or “-”

previous example

0.130λλλλ

0.064λλλλ

=0.4+j1ZL

0.435λλλλ

0.305λ

50 Ω

Y (1, 1.9)

open shunt stub

jB = - j1.9 = jtanβlβl = -1.086 + π = 2.055length = 0.327λ > λ/4

can use any type depends on realization.

e.g. use shunt open stub only…

=0.4+j1ZL

0.434λ

50 Ω

open shunt stub

jB = j1.9 = jtanβlβl = 1.086length = 0.173λ

ZL (0.4, 1)YL (0.34, -0.87)

Y (1, -1.9)


Transmission Line + Stub

0.01 0.11 0.21 0.31 0.41 0.5

Frequency (GHz)

xline_stub

-50

-40

-30

-20

-10

0

DB(|S[1,1]|)

single_stub1

DB(|S[1,1]|)single_stub2

DB(|S[1,1]|)

single_stub3

DB(|S[1,1]|)single_stub4

DB(|S[1,1]|)

single_stub5


Double Stub Tuninge.g. 2 shunt short stubs (50Ω)

separated by a 50Ω line of 0.2λ

0.3λλλλ

0.5λλλλ

– 0.2λλλλ

• rotate the 1-circle by line length

• adjust d1 along constant-G circle

• stop at the rotated blue-circle

• xline will bring it to the green circle

• adjust d2 along the green circle to Zo

• not for all ZL !! Forbidden zone.

d1d2

ZL

0.2λ

50 Ω =0.4+j1

ZL(0.4,1)

YL(0.34,-0.87)

Y (0.34,-0.2)

Y (1,1.22)

-cotβd1 = +0.67βd1 = -0.98 +π = 2.16

d1 = 0.344λ

-cotβd2 = −1.22βd2 = 0.687

d2 = 0.109λ

50 Ω50 Ω


e.g. Quarter-Wavee.g. shunt stub (100Ω) then λ/4

ZL = 20 + j 50 Ω

• move Z to the real axis

• normalized Zc = √Z = √3.1; Zc = 1.76

• Zc = 50(1.76) = 88 Ω

ZL(0.4,1)

YL(0.34, -0.87)

Z (3.1,0)

Y(0.34,0)

(1/100) tanβd= (0.87)(1/50)βd = 1.05

d = 0.167λ

d

ZL

λ/4

Zc =0.4+j150 Ω

100Ω


Double Stub / Quarter-wave

0.01 0.11 0.21 0.31 0.41 0.5

Frequency (GHz)

double_n_quarter

-30

-20

-10

0

DB(|S[1,1]|)

double_stub

DB(|S[1,1]|)

quarter_wave


Mixed matching samples

0.01 0.11 0.21 0.31 0.41 0.5

Frequency (G Hz)

Mixed

-40

-30

-20

-10

0

DB(|S[1,1]|)

double_s tub

DB(|S[1,1]|)

Lump1

DB(|S[1,1]|)

quarter_wave

DB(|S[1,1]|)

single_stub2

DB(|S[1,1]|)

Stub 1


2-port tuning

2 – port

network

MatchingNetwork ?

Especially useful for active component design : amplifier (transistor)or inserting devices into a system (such as SAW filter…)

for matched load

11in S=Γ


Unmatched load (from previous lecture)

2 – port

networkb1

b2

a1a2 = ΓLb2

ZL

This is what we measure.

How does that affect our matching process?L22

21L1211in

1

1

L22

121L121111

L22

1212

2L221212221212

2L121112121111

2

1

2221

1211

2

1

S1

SSS

a

b

S1

aSSaSb

S1

aSb

bSaSaSaSb

bSaSaSaSb

a

a

SS

SS

b

b

Γ−

Γ+=Γ≡

Γ−Γ+=

Γ−=⇒

Γ+=+=

Γ+=+=

=


To what we match? (from previous lecture)

( ) ( ) ( )22

g

2

g

2

g

2

g

g

2

g

ininlossLoad

gg

2

XR4

RV

2

1

X2R2

RV

2

1RI

2

1PP

+=

+=== −

( ) 2

g

2

go

o

2

g

o

2

total

g

oLineLoadXRZ

ZV

2

1Z

Z

V

2

1ZI

2

1PP

2

++====

Case 1: match ZL = Zo = real → ΓL = 0, VSWR = 1 on the line

Zin lZo ZL

Zg=Rg + jXgVg

Zin

Zg

Vg

Case 2: match Zin = Zg → Γin = 0, VSWR > 1

g

2

g

2

g

g

2

g

LoadR

V

8

1

R4

RV

2

1P ===

Case 3: match Zin = Z*g → Xin = -Xg

= max power available

conjugate matching

Ideally, match all Zo = Zg = ZL = real, then all 3 PLoad are the same = Pmax.


Conjugate Match

Zo

Output

matching

Input

matching

Device

to be

matched

Zo

Γin

Γout

ΓL

ΓS

L22

21L1211in

S1

SSS

Γ−

Γ+=Γ

S11

21S1222out

S1

SSS

Γ−

Γ+=Γ

*

inS Γ=Γwant *

outL Γ=Γand


Simultaneous Conjugate Match G. Gonzales: Microwave Transistor Amplifiers

21122211

*

11222

*

22111

22

11

2

222

22

22

2

111

2

2

2

2

22

L

1

2

1

2

11

S

SSSSS

SSC

SSC

SS1B

SS1B

C2

C4BB

C2

C4BB

−==∆

∆−=

∆−=

∆−−+=

∆−−+=

−±=Γ

−±=Γ


Example

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

S_ParametersSwp Max

6GHz

Swp Min

6GHz

S[1,1]

ex1_raw_spara

S[2,2]

ex1_raw_spara

Match this FET at 6 GHz

o

2

2

2

2

22

L

o

1

2

1

2

11

S

o*

11222

o*

22111

22

11

2

222

22

22

2

111

o

21122211

9.103718.0C2

C4BB

3.177762.0C2

C4BB

9.1033911.0SSC

3.1774786.0SSC

8255.0SS1B

9928.0SS1B

1103015.0SSSSS

∠=−−

=Γ

∠=−−

=Γ

−∠=∆−=

−∠=∆−=

=∆−−+=

=∆−−+=

∠=−==∆

( )

−∠∠

∠−∠=

oo

oo

7.95572.05.28058.2

3.16057.03.171641.0S

Non-reciprocal, non-symmetrical

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

simulate_conjugateSwp Max

6GHz

Swp Min

6GHz

S[1,1]

ex1_conjugate_s11

S[1,1]

ex1_conjugate_s22

ΓS & ΓL

S11 & S22


What does that mean?Zo

Output

matching

Input

matching

Device

to be

matched

Zo

Γin

Γout

ΓL

ΓS

NEED ΓΓΓΓin & ΓΓΓΓout for matching, which are just ΓΓΓΓ*S & ΓΓΓΓ*L

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

S_ParametersSwp Max

6GHz

Swp Min

6GHz

S[1,1]

ex1_raw_spara

S[2,2]

ex1_raw_spara

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

simulate_conjugateSwp Max

6GHz

Swp Min

6GHz

S[1,1]

ex1_conjugate_s11

S[1,1]

ex1_conjugate_s22

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

para_4matchSwp Max

6GHz

Swp Min

6GHz

S[1,1]

ex1_s11_4match

S[1,1]

ex1_s22_4match

S11 & S22ΓΓΓΓin & ΓΓΓΓout

ΓΓΓΓS & ΓΓΓΓL


Match 1-port at a timeIND

L=ID=

0.4827 nHL1

CAP

C=ID=

1.345 pFC1

1

SUBCKT

NET=ID=

"ex1_s11_4match" S2 PORT

Z=P=

50 Ohm1

CAP

C=ID=

0.899 pFC2

IND

L=ID=

1.572 nHL1

1

SUBCKT

NET=ID=

"ex1_s22_4match" S1

PORT

Z=P=

50 Ohm1

CAP

C=ID=

0.899 pFC2 CAP

C=ID=

1.345 pFC3

IND

L=ID=

0.4827 nHL1

IND

L=ID=

1.572 nHL2

1 2

SUBCKT

NET=ID=

"ex1_raw_spara" S1

PORT

Z=P=

50 Ohm1 PORT

Z=P=

50 Ohm2


Wide-Band Matching

Without using Resistor...

Use Multiple-sectionsGetting into Microwave Filter Design…….


0 0.1 0.2 0.3 0.4 0.5

Frequency (Hz)

2_poles

-50

-40

-30

-20

-10

0

DB(|S[1,1]|)

2_sections

LOAD

Z=ID=

1.355 OhmZ1

CAP

C=ID=

0.622 FC1

IND

L=ID=

0.843 HL1

PORT

Z=P=

1 Ohm1

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

SmithSwp Max

0.5Hz

Swp Min0.01Hz

S[1,1]

2_sections

Example: 1.355ΩΩΩΩ at 0.159Hz


6-sections: 1.355ΩΩΩΩ at 0.159Hz

CAP

C=ID=

0.8618 FC1

IND

L=ID=

1.903 HL1

LOAD

Z=ID=

1.355 OhmZ1

CAP

C=ID=

1.517 FC2

IND

L=ID=

2.056 HL2

CAP

C=ID=

1.404 FC3

IND

L=ID=

1.168 HL3

PORT

Z=P=

1 Ohm1

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Smith_6Swp Max

0.5Hz

Swp Min0.01Hz

S[1,1]

6_sections

0.01 0.11 0.21 0.31 0.41 0.5

Frequency (Hz)

6_poles

-50

-40

-30

-20

-10

0

DB(|S[1,1]|)

6_sections

Loops around the center…

More frequency points can be matched

Many choices (combinations)

Choice of filter topologies.


Example: 1:2 quarter-wave

LOAD

Z=ID=

2 OhmZ1

TLIN

F0=EL=Z0=ID=

1 GHz90 Deg1.414 OhmTL1

PORT

Z=P=

1 Ohm1

1.0

1.0

-1.0

2.0

0.2

-0.2

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

1.2

1.2

1.4

1.6

1.8

0.1

-0.1

0.3

-0.3

0.5

0.5

-0.5

0.7

0.7

-0.7

0.9

0.9

-0.9

N1

Swp Max

2GHz

Swp Min

0.1GHz

S[1,1]

1_section

0.1 0.6 1.1 1.6 2

Frequency (GHz)

N1_RL

-60

-40

-20

0

DB(|S[1,1]|)

1_section


2-sections 1:2 quarter-waveTLIN

F0=EL=Z0=ID=


LOAD

Z=ID=

2 OhmZ1

TLIN

F0=EL=Z0=ID=


PORT

Z=P=

1 Ohm1

1.0

1.0

2.0

0.2

-0.2

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

1.2

1.2

1.4

1.6

1.8

0.1

-0.1

0.3

-0.3

0.5

0.5

-0.5

0.7

0.7

-0.7

0.9

0.9

-0.9

N2

Swp Max

2GHz

Swp Min

0.1GHz

S[1,1]

2_sections

0.1 0.6 1.1 1.6 2

Frequency (GHz)

N2_RL

-50

-40

-30

-20

-10

0

DB(|S[1,1]|)

2_sections

Again, many choices of

the intermediate Z’s


4-sections: 1:2 quarter-waveTLIN

F0=EL=Z0=ID=


TLIN

F0=EL=Z0=ID=


LOAD

Z=ID=

2 OhmZ1

TLIN

F0=EL=Z0=ID=


TLIN

F0=EL=Z0=ID=


PORT

Z=P=

1 Ohm1

1.0

1.0

2.0

0.2

-0.2

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

1.2

1.2

1.4

1.6

1.8

0.1

-0.1

0.3

-0.3

0.5

0.5

-0.5

0.7

0.7

-0.7

0.9

0.9

-0.9

N4

Swp Max

2GHz

Swp Min

0.1GHz

S[1,1]

4_sections

0.1 0.6 1.1 1.6 2

Frequency (GHz)

N4_RL

-60

-50

-40

-30

-20

-10

0

DB(|S[1,1]|)

4_sections


Compare bandwidth

0.1 0.6 1.1 1.6 2

Frequency (GHz)

Return Loss

-60

-40

-20

0

DB(|S[1,1]|)

1_section

DB(|S[1,1]|)

2_sections

DB(|S[1,1]|)

4_sections


To be continued….

Choice of impedance of the intermediate

elements depends on the characteristic of the

performance desires (such as flat passband,

minimum phase variation, limited group delay

variation…etc)

It is a topic of future lectures.

Documents

Advanced Impedance Matching