HP8510
Lecture 10
Vector Network Analyzers and Signal Flow Graphs
Sections: 6.7 and 6.11
Homework: From Section 6.13 Exercises: 4, 5, 6, 7, 9, 10, 22
Acknowledgement: Some diagrams and photos are from M. Steer’s book “Microwave and RF Design”
Vector Network Analyzers
port 1 port 2
DUT
HP8510
Nikolova 2012 2LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
R&S®ZVA67 VNA2 ports, 67 GHz
Agilent N5247A PNA-X VNA, 4 ports, 67 GHz
Agilent 8719ES
Test
Instruments
MICROPROBERS
UnderDevice
Vector Network Analyzer and IC Probes
HP8510
Nikolova 2012 3LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
measurements of circuits with non-coaxial connectors (HMIC, MMIC)
NETWORKANALYZER
S PARAMETERTEST SET
SYNTHESIZER
CONTROLLER
PROBES
RF
HF
GPIB
GSG Probe
Nikolova 2012
2-Port Vector Network Analyzer: Schematic
1b1a
2a
2b
1a 1b
2b2a
1a
2aLO1
LO2
[Pozar, Microwave Engineering] 4
N-Port Vector Network Analyzer: Schematic
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[Hiebel, Fundamentals of Vector Network Analysis]
1a 1a
1b1b
Vector Network Analyzer: Directional Element
reversed directional coupler
Nikolova 2012 6LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
port 3 terminated with a matched load (power is absorbed, not used)
measure scattered wave bb
a
Signal Flow Graphs used to analyze microwave circuits in terms of incident and
scattered waves used to devise calibration techniques for VNA measurements components of a signal flow graph
nodeseach port has two nodes, ak and bk
branches• a branch shows the
dependency between pairs of nodes
• it has a direction – from input to output
example: 2-port network
1 11 1 12 2
2 21 1 22 2
b S a S ab S a S a
Nikolova 2012
Signal Flow Graphs of Two Basic 1-port Networks
11l S lb a
1bsV
0Z
0
0( )s
ZZ Z
8
a
b
0
0( )s ss
Zb a VZ Z
0
0 0
0
0
, ( )s
s
ss
s
Z VV V bZ Z Z
Z ZZ Z
(a) load
0Z
0
0
ll
l
Z ZZ Z
(b) source
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Decomposition Rules of Signal Flow Graphs
(1) series rule
(2) parallel rule
(3) self-loop rule
(4) splitting rule
9
Nikolova 2012 LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
Signal Flow Graphs: Example
Express the input reflection coefficient Γ of a 2-port network in terms of the reflection at the load ΓL and its S-parameters.
21
221 L
ss
2
rule #4at a
2rule #3 at b
rule #1
10
1 12 2111
1 221L
L
b s ssa s
VNA Calibration for 1-port Measurements (3-term Error Model)
• the 3-term error model is known as the OSM (Open-Short-Matched) cal technique (aka OSL or SOL, Open-Short-Load)
• the cal procedure includes 3 measurements performed before the DUT is measured: 1) open circuit, 2) short circuit, 3) matched load
• used when Γ = S11 of a single-port device is measured
• actual measurements include losses and phase delays in connectors and cables, leakage and parasitics inside the instrument – these are viewed as a 2-port error box
• calibration aims at de-embedding these errors from the total measured S-parameters
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3-term Error Model: Signal-flow Graph
Nikolova 2012 12LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
error box
S-parameters of the error box contain 3 unknowns
00
10 01 11
1E
ee e e
S
10e
01e
00 01
10 11E
e ee e
S
M
[Rytting, Network Analyzer Error Models and Calibration Methods]
Note: SFG branches without a coefficient have a default coefficient of 1.
3-term Error Model: Error-term Equations
Nikolova 2012 13LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
Using the result from the example on sl. 10 and the signal flow graph in sl. 12, prove the formula
00M
111ee
e
error de-embedding formula(see sl. 10)
3-term Error Model
• for accurate results, one has to know the exact values of Γo, Γs and Γm – use manufacturer’s cal kits!Nikolova 2012 14LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
• ideally, in the OSM calibration,
1 o
2 s
3 m
11
0
• the 3 calibration measurements with the 3 standard known loads (Γ1, Γ2, Γ3) produce 3 equations for the 3 unknown error terms
00 11( , , )ee e M 00
M 11 e
ee
error de-embedding
linear system for 00 11[ , , ]Tee e x
2-port Calibration: Classical 12-term Error Model
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consists of two models:• forward (excitation at port 1): models errors in S11M and S21M• reverse (excitation at port 2): models errors in S22M and S12M
port 1
port 2
[Rytting, Network Analyzer Error Models and Calibration Methods]
12-term Error Model: Reverse Model
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port 1
port 2
12-term Error Model: Forward-model SFG
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( )
12-term Error Model: Forward-model SFG
Nikolova 2012 18LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
Using signal-flow graph transformations derive the formulas for S11Mand S21M in the previous slide.
( )
12-term Error Model: Reverse-model SFG
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( )
12-term Calibration Method
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Step 1: Port 1 Calibration using the OSM 1-port procedure.Obtain e11, e00, and Δe, from which (e10e01) is obtained.
Step 2: Connect matched loads (Z0) to both ports (isolation). (S21 = 0)The measured S21M yields e30 directly.
Step 3: Connect ports 1 and 2 directly (thru). (S21=S12=1, S11=S22=0)
Obtain e22 and e10 e32 fromeqns. (*) usingS21 = S12 = 1, S11 = S22 = 0.
• All 6 error terms of the forward model are now known.
• Same procedure is repeated for port 2.
12-term Calibration Method: Error De-embedding
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2-port Thru-Reflect-Line Calibration
• TRL (Thru-Reflect-Line) calibration is used when classical standards such as open, short and matched load cannot be realized
• TRL is the calibration used when measuring devices with non-coaxial terminations (HMIC and MMIC)
• TRL calibration is based on an 8-term error model
• TRL calibration requires three (2-port) calibration structures
thru: the 2 ports must be connected directly, sets the reference planesreflect: load on each port identical; must have large reflectionline (or delay): 2 ports connected with a matched (Z0) transmission line (TL must represent the IC interconnect for the measured DUT)
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Thru, Reflect, and Line Calibration Connections
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(a) thru
(b) reflect
(c) line
Thru-Reflect-Line Calibration Fixtures
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DC needle probes
GSG probes
2-port Calibration: 8-term Error Model
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[Rytting, Network Analyzer Error Models and Calibration Methods]
port 1
port 2
Signal-flow Graph of 8-term Error Model
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port 1
port 2
XT
YT
T
Signal-flow Graphs of the 3 TRL Calibration Measurements
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Signal-flow Graphs of the 3 TRL Calibration Measurements (2)
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Scattering Transfer (or Cascade) Parameters
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• when a network is a cascade of 2-port networks, often the scattering transfer (T-parameters) are used
1 11 12 221 22 21
V VT TT TV V
• relation to S-parameters
11 12 11111 22 12 2121
21 22 22, 1
SS
T T SS S S S ST T S
A BT T TAT BT
1 11 12 2
1 21 22 2
b T T aa T T b
or
8-term Error Model in Terms of T-parameters for TRL Calibration
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error de-embedding
Nikolova 2012 31LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
8-term Error Model for TRL Calibration• the number of unknown error terms is actually 7 in the simple
cascaded TRL network (see sl. 26)
1 110 32 M( )e e T A T B
• TRL measurement procedure
M X Y
M1 X C1 Y
M2 X C2 Y
M3 X C3 Y
(1) measured with DUT(2) measured with 2-port cal standard #1(3) measured with 2-port cal standard #2(4) measured with 2-port cal standard #3
T T TTT T T TT T T TT T T T
Nikolova 2012 32LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
8-term Error Model for TRL Calibration
• measuring the 3 two-port cal standards yields 12 independent equations while we have only 7 error terms
• thus 5 parameters of the 3 cal standards need not be known and can be determined from the calibration measurements
• which 5 parameters are chosen for which cal standards is important in order to reduce errors and avoid singular matrices
cal standard #1 TC1 must be completely known – thru cal standard #2 TC2 can have 2 unknown transmission terms – line cal standard #3 TC3 can have 3 unknowns; if its reflection
coefficients satisfy S11 = S22 (it is best if S11 = S22 are large!) then its 3 coefficients can be unknown – reflect
Nikolova 2012 33LECTURE 10: VECTOR NETWORK ANALYZERS AND SIGNAL FLOW GRAPHS
• errors are introduced when measuring a device due to parasitic coupling, leakage and imperfect connections
• these errors must be de-embedded from the overall measured S-parameters
• the de-embedding relies on the measurement of known or partially known cal standards – calibration measurements, which precede the measurement of the DUT
• 1-port calibration uses the 3-term error model and the OSM method• 2-port calibration may use 12-term or 8-term error models• the 12-term error model requires OSM at each port, isolation, and
thru measurements• the 8-term error model with the TRL technique is widely used for
non-coaxial devices• there exists also a 16-term error model, many other cal techniques
VNA Calibration – Summary