examples

Bern University of Applied Sciences Engineering and Information Technology Division of Electrical and Communication Technology

Smith V3.10

Prof. Fritz Dellsperger 5.2010

Content

Impedance Matching 1 Impedance, Admittance, Reflection Coefficient, VSWR and Return Loss 1 Matching arbitrary impedances to 50 Ohm 2

Example 1: Use 2 reactance elements, Highpass 2 Example 2: Use 2 reactance elements, Highpass 3 Example 3: Use 2 reactance elements, Lowpass 4 Example 4: Use 2 reactance elements, Lowpass 5 Example 5: Antenna Match with 3 or more reactance elements, Low Q, Highpass 6 Example 6: Antenna Match with 3 or more reactance elements, Low Q, Lowpass 7 Example 7: Match Ceramic Filter to 50 Ohm 8 Example 8: Antenna match using reactance and serie line element 10 Example 9: Antenna match using serie line and open stub 11 Example 10: Antenna match using serie line and shorted stub 12 Example 11: Antenna match using double stub tuner 13 Example 12: Nonsynchronous Transformer 15

Low Noise Amplifier Design 18 Example 13: Low Noise Amplifier, 2.0 GHz 18

Conjugate Matching 26 Example 14: Conjugate Match 26

Serial Transmission Line with Attenuation 29 Example 15: Match using transmission line with loss 29

Sweeps 30 Example 16: Input impedance of a Chebyshev lowpass filter 30 Example 17: Broadband load match 31

1

Impedance Matching

Impedance, Admittance, Reflection Coefficient, VSWR and Return Loss

Impedance: Z R jX R: Resistance X: Reactance

0

1Z Z

1

Admittance: Y G jB G: Conductance B: Susceptance

1

ZY

1

YZ

Reflection Coefficient: 0 0

0 0

Z Z Y Y

Z Z Y Y

0Z : Reference Impedance

RL

020

0

Z ZVSWR 110

VSWR 1 Z Z

Voltage Standing Wave Ratio:

0 0

RL20

0RL

020 Z Z Z Z

1 Z Z1 10VSWR

1 Z Z1 10

Return Loss: 0

0

Z ZVSWR 1RL 20 log 20 log 20 log

VSWR 1 Z Z

All values for cursor position in Smith-Chart are displayed in window “Cursor”.

2

Matching arbitrary impedances to 50 Ohm

Example 1: Use 2 reactance elements, Highpass Problem: Match an impedance of 10 j7 to 50 . Use 2 reactance (L,C) in a circuit topology

with highpass characteristic. Frequency: 150 MHz. Smith project file: Example1.xmlsc

3

Example 2: Use 2 reactance elements, Highpass Problem: Match an impedance of 100 j50 to 50 . Use 2 reactance (L,C) in a circuit

topology with highpass characteristic. Frequency: 500 MHz. Smith project file: Example2.xmlsc

4

Example 3: Use 2 reactance elements, Lowpass Problem: Match an impedance of 10 j7 to 50 . Use 2 reactance (L,C) in a circuit topology

with lowpass characteristic. Frequency: 150 MHz. Smith project file: Example3.xmlsc

5

Example 4: Use 2 reactance elements, Lowpass Problem: Match an impedance of 100 j50 to 50 . Use 2 reactance (L,C) in a circuit

topology with lowpass characteristic. Frequency: 500 MHz. Smith project file: Example4.xmlsc

6

Example 5: Antenna Match with 3 or more reactance elements, Low Q, Highpass Problem: Match an antenna impedance of 20 j12 to 50 . Use L and C in a circuit topology

with highpass characteristic and do not exceed a max

X 12Q 0.6

R 20 (for maximum bandwidth).

Frequency: 450 MHz. Smith project file: Example5.xmlsc

7

Example 6: Antenna Match with 3 or more reactance elements, Low Q, Lowpass Problem: Match an antenna impedance of 20 j12 to 50 . Use L and C in a circuit topology

with lowpass characteristic and do not exceed a max

X 12Q 0.6

R 20 (for maximum bandwidth).

Frequency: 450 MHz. Smith project file: Example6.xmlsc

8

Example 7: Match Ceramic Filter to 50 Ohm Problem: For measurement purposes match a 10.7 MHz 300 Ohm Ceramic filter to 50 Ohm using a parallel resonance circuit with capacitive voltage divider and L = 330 nH. Frequency: 10.7 MHz. Smith project file: Example7.xmlsc

f0 10.7 MHz R1 300 L 390 nH

B2 L f0

2

R1791.298 kHz

9

C2

C1

RL

Rres

For Q ≥ 10 following approximations can be used:

ofQ

B

res

1C

2 BR

2o

1L

C

res

L

RN

R

p

QQ

N 2

1

CC

N 1

2C NC

10

Example 8: Antenna match using reactance and serie line element Problem: Match an antenna impedance of 30 j40 to 50 . Use one reactance and one

serie line. Frequency: 430 MHz. Smith project file: Example8.xmlsc

11

Example 9: Antenna match using serie line and open stub Problem: Match an antenna impedance of 30 j40 to 50 . Use one serie line and an open

stub. Frequency: 430 MHz. Smith project file: Example9.xmlsc

12

Example 10: Antenna match using serie line and shorted stub Problem: Match an antenna impedance of 30 j40 to 50 . Use one serie line and a shorted

stub. Frequency: 430 MHz. Smith project file: Example10.xmlsc

13

Example 11: Antenna match using double stub tuner Problem: Match an antenna impedance of 30 j40 to 50 . Use a double stub tuner with

serie line length of 80 mm and r 1 . Frequency: 430 MHz.

Smith project file: Example11.xmlsc

14

Use Edit Element (doubleclick on element in schematic) to adjust for desired line length.

Change value

Push Draw and see on Smith-chart and schematic how this affect transformation

OK when done

15

Example 12: Nonsynchronous Transformer Problem: Match an impedance of 10 j12 to 50 . Use an open stub and a nonsynchronous

transformer. Frequency: 2.4 GHz. Smith project file: Example12.xmlsc

16

Use Edit Element (doubleclick on element in schematic) to adjust for desired line length.

Change value

Push Draw and see on Smith-chart and schematic how this affect transformation

OK when done

17

Properties of Nonsynchronous Trafo: It uses two pieces of line with the same length. One line must have the line impedance of the source and the other line the impedance of the load. The total length depends on impedance ratio and is much shorter than / 4 .

L = Length of one line section

1 2k Z / Z 1

2 11r

L a tan

kk

Nonsynchronous-Transformer

Ltot

0.1 1 100

0.05

0.1

0.15

0.2

k

Lin

elen

gth

in L

ambd

a

L

0.1 1 1015

20

25

30

35

k

Lin

elen

gth

in D

egre

e

L

Line length as function of impedance ratio k

18

Low Noise Amplifier Design

Example 13: Low Noise Amplifier, 2.0 GHz

Problem: Design input and output matching network for a LNA using BFG33G. Frequency: 2 GHz Smith project file: Example13-input.xmlsc

Z0

Z0

Output matching network

Input matching network

11 12

21 22

S S

S S

Transistor

2

Z2

S

ZS

1

Z1

L = 2*

ZL = Z2*

If we choose a source impedance of ZS = (50+j30)Ohm we get a gain of approx. 12 dB and a NF of approx. 3.85 dB with only a serie inductor as input matching network.

19

With a few calculations we get:

S-parameters at 2000 MHz: Source impedance at 2000 MHz:

ZS 50 j 30( )

S0.121 e

j 149 deg

3.756 ej 78.9 deg

0.108 ej 59.4 deg

0.41 ej 54.5 deg

Z0 50

S

ZS Z0

ZS Z00.083 0.275j S 0.287

arg S 73.301deg

2 S2 2

S1 2 S

2 1 S

1 S1 1 S

0.136 0.392j

Z2 Z0

1 2

1 2 45.987 43.54j( )

For the output network we conjugately match Z2 (or 2 ) to 50 Ohm.

There are several possibilities to realize the output matching network.

20

Problem: Output matching network 1 Smith project file: Example13-output1.xmlsc

21

Simulation of LNA with Output matching network 1 versus Frequency in Agilent ADS:

CC1C=1.9 pF

LL2

R=L=3.8 nH

LL1

R=L=2.4 nH

S2PSNP1File="BFG33G.S2P"

21

Ref

TermTerm2

Z=50 OhmNum=2

TermTerm1

Z=50 OhmNum=1

m1freq=S(2,2)=0.015 / 119.981impedance = 49.220 + j1.312

2.000GHz


2.000GHzm5freq=dB(S(1,1))=-8.564

2.000GHz

m6freq=dB(S(2,2))=-36.259

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

-35

-30

-25

-20

-15

-10

-5

-40

0

freq, GHz

dB(S

(1,1

))

m5

dB(S

(2,2

))

m6

Returnloss vs Freq

m5freq=dB(S(1,1))=-8.564

2.000GHz

m6freq=dB(S(2,2))=-36.259

2.000GHz

m4freq=nf(2)=3.852

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

3.7

3.8

3.9

3.6

4.0

freq, GHz

nf(2

)

m4

NF vs Freq

m4freq=nf(2)=3.852

2.000GHzm3freq=dB(S(2,1))=12.005

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

10

11

12

13

14

9

15

freq, GHz

dB(S

(2,1

))

m3

Gain vs Freq

m3freq=dB(S(2,1))=12.005

2.000GHz

freq (1.500GHz to 2.500GHz)

S(2

,2) m1

S(1

,1)

m2

Output 1 Match


2.000GHz


2.000GHz

22


23


m1freq=S(2,2)=9.355E-4 / 17.504impedance = 50.089 + j0.028

2.000GHz


2.000GHz


S(2

,2) m1

S(1

,1)

m2

Output 2 Match

m1freq=S(2,2)=9.355E-4 / 17.504impedance = 50.089 + j0.028

2.000GHz


2.000GHzm5freq=dB(S(1,1))=-8.408

2.000GHz

m6freq=dB(S(2,2))=-60.579

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

-35

-30

-25

-20

-15

-10

-5

-40

0

freq, GHz

dB

(S(1

,1))

m5

dB

(S(2

,2))

m6

Returnloss vs Freq

m5freq=dB(S(1,1))=-8.408

2.000GHz

m6freq=dB(S(2,2))=-60.579

2.000GHz

m4freq=nf(2)=3.852

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

3.7

3.8

3.9

3.6

4.0

freq, GHz

nf(

2)

m4

NF vs Freq

m4freq=nf(2)=3.852

2.000GHzm3freq=dB(S(2,1))=12.006

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

10

11

12

13

14

9

15

freq, GHz

dB

(S(2

,1))

m3

Gain vs Freq

m3freq=dB(S(2,1))=12.006

2.000GHz

24


25


m1freq=S(2,2)=0.013 / -67.850impedance = 50.471 - j1.197

2.000GHz


2.000GHz


S(2

,2) m1

S(1

,1)

m2

Output 3 Match

m1freq=S(2,2)=0.013 / -67.850impedance = 50.471 - j1.197

2.000GHz


2.000GHzm5freq=dB(S(1,1))=-8.289

2.000GHz

m6freq=dB(S(2,2))=-37.854

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

-35

-30

-25

-20

-15

-10

-5

-40

0

freq, GHz

dB(S

(1,1

))

m5

dB(S

(2,2

))

m6

Returnloss vs Freq

m5freq=dB(S(1,1))=-8.289

2.000GHz

m6freq=dB(S(2,2))=-37.854

2.000GHz

m4freq=nf(2)=3.852

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

3.7

3.8

3.9

3.6

4.0

freq, GHz

nf(2

)

m4

NF vs Freq

m4freq=nf(2)=3.852

2.000GHzm3freq=dB(S(2,1))=12.005

2.000GHz

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.41.5 2.5

10

11

12

13

14

9

15

freq, GHz

dB(S

(2,1

))

m3

Gain vs Freq

m3freq=dB(S(2,1))=12.005

2.000GHz

26

Conjugate Matching

Example 14: Conjugate Match

Problem: Conjugately match impedance Z1 (or Gamma 1 ) to 50 Ohm.

Method 1: Start at Z1 and transform with network to 50 Ohm. In this case Z1 is used as load impedance for the network and after transformation we would like to see 50 Ohm at the input of the network. Method 2: Start at 50 Ohm and transform with network to Z1* = conjugate Z1

In this case 50 Ohm is used as load impedance for the network and after transformation we would like to see Z1* into the input of the network. Both method result in the same network.

T1

L1

C1

50

Method 1 Method 2

1

1Z

*1

*1

Z

27

Example: 1Z 10 j10

Method 1: Smith project file: Example14-1.xmlsc

Z1

50

Start here

28

Method 2: Smith project file: Example14-2.xmlsc

Z1*

50

Start here

29

Serial Transmission Line with Attenuation

Example 15: Match using transmission line with loss

Problem: Match an impedance of (23.7 + j 101) Ohm to 50 Ohm using a lossy transmission line with an electrical length of about 2 wavelength, attenuation of 2 dB/m and a serial reactance. Frequency: 500 MHz Smith project file: Example15.xmlsc

30

Sweeps

Example 16: Input impedance of a Chebyshev lowpass filter

Problem: Plot input impedance of a 50 Ohm Chebyshev lowpass filter with n = 3, Ripple = 0.1 dB and cut-off frequency = 100 MHz Frequency: 10 MHz to 450 MHz Smith project file: Example16.xmlsc

31

Example 17: Broadband load match

Problem: Given: Load impedance = (100.8+j24.2) Ohm @ 140 MHz, (106.9+j41.7) Ohm @ 145 MHz, (121.2+j60) Ohm @ 150 MHz Find LC-lowpass network to match within VSWR of 1.2. Use standard component values as possible. Frequency: 140 MHz to 150 MHz Smith project file: Example17.xmlsc

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