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
ZZ1122
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
