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S-parameters

MUSEMaterial developed by Prof. L. Dunleavy, USF

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22--Port ParametersPort Parameters

z Recall Z-Parameters:

V Z I Z I

V Z I Z I1 11 1 12 2

2 21 1 22 2

!

VV

Z ZZ Z

II

1

2

11 12

21 22

1

2

2-port V1 V2

I1 I2

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22--Port ParametersPort Parameters

z Recall Z-Parameters:

V Z I Z I

V Z I Z I1 11 1 12 2

2 21 1 22 2

!

VV

Z ZZ Z

II

1

2

11 12

21 22

1

2

2-port network

V1 V2

I1 I2

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22--PORT Parameters (contPORT Parameters (contd)d)z Y-Parameters:

z h-Parameters:

I Y V Y V

I Y V Y V1 11 1 12 2

2 21 1 22 2

!

II

Y YY Y

VV

1

2

11 12

21 22

1

2

V h I h V

I h I h V1 11 1 12 2

2 21 1 22 2

!

VI

h hh h

IV

1

2

11 12

21 22

1

2

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22--Port Parameters (contPort Parameters (contd)d)z 2-port Parameter Determination:

hI

vv11

1

1 20 |

hI

I V212

1 20 |

hV

V I121

2 10 |

(Put a Short Circuit at Port #2)

hI

V I222

2 10 |

(Put an Open Circuit at Port # 1)

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S-ParametersAt high RF and Microwave frequencies direct

measurement of Y- , Z-, or H- parameters is difficult due to:

Unavailability of equipment to measure RF/MW total current and voltage.

Difficulty of obtaining perfect opens/shorts Active devices may be unstable under

open/short conditions.

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SS--ParametersParametersz For a two-port device there are four S-

parameters S11, S21, S12, and S22z S11, and S22 are simply the forward and

reverse reflection coefficients, with the opposite port terminated in Z0 (usually 50 ohms.)

z S21 and S12 are simply the forward and reverse gains assuming a Z0 source and load(again usually 50 ohms).

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SS--Parameters (contParameters (contd)d)

z S-Parameters:

2-port

a1 a2b1 b2

b S a s a

b S a S a1 11 1 12 2

2 21 1 22 2

!

bb

S SS S

aa

1

2

11 12

21 22

1

2

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SS--Parameters (contParameters (contd)d)

a1 a2b1 b2

2-port V1 V2Zs

Vg ZL

z Q. So whats the deal with the as and bs?

z A. a1 and a2 are incident waves; b1 and b2 are reflected waves

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Incident & Reflected Waves:Incident & Reflected Waves:Simplified Case: Z1=Zs=Z2=ZL=Zo (real)Simplified Case: Z1=Zs=Z2=ZL=Zo (real)

aV Z I

Z Z

E

Zi

11 0 1

0 0

1

02 Incident port 1 voltage

aV Z I

Z Z

E

Zi

22 0 2

0 0

2

02 Incident port 2 voltage

bV Z I

Z Z

E

Zr

11 0 1

0 0

1

02 reflected port 1 voltage

bV Z I

Z Z

E

Zr

22 0 2

0 0

2

02 reflected port 2 voltage

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S-Parameter Determination

s a111

1 20

ba

|

s a212

1 20

ba

|

s a121

2 10

ba

|

s a222

2 10

ba

|

= Input reflection coefficient *infor case of ZL=Z0

= Output reflection coefficient *outfor case of Zs=Z0

= Forward transmission (insertion) gainfor case of ZL=Z0

= Reverse transmission (insertion) gainfor case of Zs=Z0

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Desired Measurement Conditionsa1 a2 = 0b1 b2

2-port V2

Zs = Z0

Vg ZL = Z0

a1 b1

1-port Zs = Z0

Vg

* S11=*

Z0

Z0 Z0

Notethe input and output are terminated in Z0

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GRAPHICAL VIEW OF S-PARAMETERS

DeviceUnder Test

S12

S21, Forward GainInsertion Loss,Transmission Phase

S11,InputRefl.Coeff. *in,Return Loss, VSWR

Reverse GainInsertion Loss,Transmission Phase S22,

OutputRefl.Coeff. *out,Return Loss, VSWR

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S-Parameters in DecibelsdB Meaning or interpretation

S11 20 log10 |S11| Corresponds to the algebraic negative of the inputreturn loss of a 2-port with an R0 termination onthe opposite port.

S12 20 log10 |S12| Reverse isolation (active device or amplifier), oralgebraic negative of the insertion loss (I.L.) for apassive device, with R0 at ports 1 and 2.

S21 20 log10 |S21| Power gain (active device or amplifier), or algebraicnegative of the insertion loss (I.L.) for a passivedevice, under matched R0 at ports 1 and 2.

S22 20 log10 |S22| Corresponds to the algebraic negative of theoutput return loss of a 2-port with an R0termination on the opposite port.

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WHAT TO EXPECT

Zo, Hr

T E dS11=S22=0S21=S12=1e-jTS21DB=0

Ideal Lossless T-line

Ideal G dB Gain Amp

PAD

S11=S22=0S21=S12=xe-jTpadS21DB= X=20log(|S21|)x =10-X/20

Ideal X dB Attenuator

S11 = S22 = 0 = S12S21 = gve-jTampS21DB= G=20log(S21)

g v

G

10 20

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WHAT TO EXPECT: Ideal FiltersWHAT TO EXPECT: Ideal Filters

GENERAL IN-BAND

S11=S22=0S21=S12=1e-jTf)S21(dB)=S12(dB)=0dB

Ideal Band Pass

fc1 fc2 fc

Ideal Low Pass

fc

Ideal High Pass

GENERAL OUT-OF-BAND

|S11|=|S22|=1S21=S12=0S11(dB)=S22(dB)=0dB

S21 S21 S21 0dB