1 University of South Florida
S-parameters
MUSEMaterial developed by Prof. L. Dunleavy, USF
2 University of South Florida
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
3 University of South Florida
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
4 University of South Florida
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
5 University of South Florida
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)
6 University of South Florida
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.
7 University of South Florida
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).
8 University of South Florida
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
9 University of South Florida
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
10 University of South Florida
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
11 University of South Florida
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
12 University of South Florida
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
13 University of South Florida
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
14 University of South Florida
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.
15 University of South Florida
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
16 University of South Florida
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