S-параметры

ECE 5317-6351
Microwave Engineering
Adapted from notes by
Prof. Jeffery T. Williams
Fall 2019
Prof. David R. Jackson
Dept. of ECE
Notes 17
S-Parameter
Measurements
1
S-Parameter Measurements
S-parameters are typically measured, at microwave
frequencies, with a network analyzer (NA).
These instruments have found wide, almost universal, application since
the mid to late 1970’s.
 Vector* network analyzer: Magnitudes and phases of the S parameters are measured.
 Scalar network analyzer: Only the magnitudes of the S-parameters are measured.
Most NA’s measure 2-port parameters. Some measure 4 and 6 ports.
* The S parameters are really complex numbers, not vectors, but this is the
customary name. There is an analogy between complex numbers and 2D vectors.
2
S-Parameter Measurements (cont.)
A Vector Network Analyzer (VNA) is usually used to measure S parameters.
Port 1
Device Under Test (DUT)
Port 2
Note:
If there are more than 2 ports, we measure different pairs
of ports separately with a 2-port VNA.
3
S-Parameter Measurements (cont.)
Vector Network
Analyzer
Port 1 Measurement
plane 1
a1
Measurement Port 2
plane 2
a2
b1
b2
Device
under
test
(DUT)
Test cables
4
S-Parameter Measurements (cont.)
We want to measure
[S] for DUT
m
a
1
Port 1
b1m
Error
Box A
Meas. plane 1
Error
Box B
DUT
Ref. plane
a2m
m
2
Port 2
b
Meas. plane 2
Ref. plane
Error boxes contain effects
of test cables, connectors, couplers,…
A B
C D 


A B
C D 


A
A B
C D 


MEAS
A B
C D 


B
5
S-Parameter Measurements (cont.)
A B
C D 


A B
C D 


MEAS
A
A B
C D 


A B
C D 


MEAS
A
A B
C D 


B
A B A B A B

 


C D  C D  C D 
B
Embedded inside measured ABCD matrix
De-embedded
1
A
MEAS
  A B B 
A B A B  A B


C D    C D   C D 


C D 

 
  



1
6
S-Parameter Measurements (cont.)
Measurement
plane A
 S A 
S 
 S B 
Error box A
DUT
Error box B
Measurement
plane B
Assume error boxes are reciprocal (symmetric matrices)
We need to "calibrate" to find  S A  and  S B  .
If  S A  and  S B  are known  we can extract  S  from measurements.
This is called “de-embedding”.
7
Calibration
“Short, open, match” calibration procedure
Connect
 S  
SC
 L  1
L  1
Short
Error box 
OC
Open
L  0
Z0
Match
Calibration loads
These loads are connected to the end of the cable from the VNA.
S 

S 

m
11SC
S

21
11

1  S22
S 

S 

m
11 OC
S
m
11 match
S
2
2

21
11

1  S22

 S11
Recall from Notes 16:
3 measurements :
( S11m , S11m , S11m
SC
OC
match
)
in  S11 
S21S12  L
1   L S22
3 unknowns:
S , S , S 



11
21
22
8
Calibration (cont.)
“Thru-Reflect-Line (TRL)” calibration procedure
This is an improved calibration method that involves three types
of connections:
1) The “thru” connection, in which port 1 is directly connected to port 2.
2) The “reflect” connection, in which a load with an (ideally) large (but not
necessarily precisely known) reflection coefficient is connected.
3)
The “line” connection, in which a length of matched transmission line
(with an unknown length) is connected between ports 1 and 2.
The advantage of the TRL calibration is that is does not require precise short,
open, and matched loads.
This method is discussed in the Pozar book (pp. 193-196).
9
Discontinuities
 In microwave engineering, discontinuities are often represented
by pi or tee networks.
 Sometimes the pi or tee network reduces to a singe series or
shunt element.
 For waveguide systems, the TEN is used to represent the
waveguide.
10
Discontinuities: Rectangular Waveguide

Inductive iris or strip

Capacitive iris or strip

Resonant iris
11
Discontinuities: RWG (cont.)

Z 01
Z 02
Z 01
Z 02
E plane step

H plane step
12
Discontinuities: Microstrip
Z0

Z0
C
Cs
Z0
Z 01
Z0 
Z 02 
Z0
Z 01
Cp
Cp
L
L
C
Z0
Z 02
Note:
For a good equivalent circuit,
the element values are fairly stable over a wide range of frequencies.
13
Z-Parameter Extraction
Assume a reciprocal and symmetrical waveguide or
transmission-line discontinuity.
T
Examples
g
T
Microstrip gap
Waveguide post
We want to find
Z1 and Z2 to
model the
discontinuity.
Note:
We could also use a
pi network if we wish.
Z1  Z11  Z 21
Discontinuity model
T
T
Z1
Z1
Z0
Z 2  Z 21
Z2
TEN
Z0
14
Z-Parameter Extraction (cont.)
T
T
Z1
Z1
Z0
Z0
Z2
Plane of symmetry (POS)
The Z2 element is split in two:
POS
T
T
Z1
Z0
Z1
2Z 2
2Z 2
Z0
15
Z-Parameter Extraction (cont.)
Assume that we place a short or an open along the plane of symmetry.
T
T
POS
Z1
Short
Z0
Z1
2Z 2
Z0
2Z 2
SC
ZLSC
L  Z1
SC
ZLLSC
Z
POS
Z1
Z1
Open
2Z 2
Z0
2Z 2
Z0
OC
ZZ1122
Z 2Z 2
ZZLOC
L
OC
OC
LL
ZZ
Z1  Z LSC , Z 2 
1 OC
Z L  Z LSC 

2
16
Z-Parameter Extraction (cont.)
The short or open can be realized by using odd-mode or even-mode excitation.
1V
1V
Z0
Z0
Port 2
Port 1
Incident voltage waves
1
1
1
Odd mode excitation
1
Even mode excitation
Even/odd-mode analysis is very useful in analyzing devices (e.g., using HFSS).
17
Z-Parameter Extraction (cont.)
1V
1V
Z0
Z0
Port 1
Port 2
S11SC
Odd mode voltage waves
Z
SC
L
1V
 1  S11SC 
 Z0 
SC 
 1  S11 
1V
Z0
Z0
Port 1
Port 2
S11OC
Even mode voltage waves
Z
OC
L
 1  S11OC 
 Z0 
OC 
 1  S11 
18
Z-Parameter Extraction (cont.)
Discontinuity model
T
T
Z1
Z1
Z0
Z2
Z0
Hence we have:
 1  S11SC 
Z1  Z 0 
SC 
1

S

11 
 1  S11SC  
1   1  S11OC 
Z 2   Z 0 
 Z0 
OC 
SC  

2   1  S11 
1

S

11  
19
De-embeding of a Line Length
We wish the know the reflection coefficient of a 1-port device under test (DUT),
but the DUT is not assessable directly – it has an extra length of transmission line
connected to it (whose length may not be known).
S11DUT
S11m
Recall : Sij  Sij e i li e
L
 j l j
li  l j  L
MEAS
11
S
 i   j    j
DUT  j 2  L
11
S
e
DUT
Meas. plane
Ref. plane

  S
Replace DUT with short circuit S11DUT  1
S11DUT  S11MEAS, DUT e  j 2  L
MEAS, SC
11
  e  j 2  L  1 / e  j 2  L
 1 
S11DUT  S11MEAS,DUT  MEAS,SC 
 S11

20