Post on 19-Jun-2015
transcript
M i r M u h a m m a d L o d r o
L e c t u r e r D e p a r t m e n t o f E l e c t r i c a l E n g i n e e r i n g
S u k k u r I B A
2-Port Network Parameters
Contents
Introduction
Two Port Networks
Z Parameters
Y Parameters
S Parameters
Return Loss
Insertion Loss
Transmission (ABCD) Matrix
VNA Calibration
SOLT Structure
Microwave and Radar Engineering
Two Port Networks
Linear networks can be completely characterized by parameters measured at the network ports without knowing the content of the networks.
Networks can have any number of ports. Analysis of a 2-port network is sufficient to explain the theory and applies
to isolated signals (no crosstalk).
The ports can be characterized with many parameters (Z, Y, S, ABDC). Each has a specific advantage.
Each parameter set is related to 4 variables: 2 independent variables for excitation 2 dependent variables for response
2 Port
NetworkPo
rt 1
I1
+
-
V1
Po
rt 2
I2
+
-
V2
Microwave and Radar Engineering
Z Parameters
Advantage: Z parameters are intuitive.
Relates all ports to an impedance & is easy to calculate.
Disadvantage: Requires open circuit voltage measurements, which are difficult to make.
Open circuit reflections inject noise into measurements.
Open circuit capacitance is non-trivial at high frequencies.
IZV
Impedance Matrix: Z Parameters for 2-port Network
2221212
2121111
IZIZV
IZIZV
2
1
2221
1211
2
1
I
I
ZZ
ZZ
V
V
Microwave and Radar Engineering
Y Parameters
VYI
Admittance Matrix: Y Parameters for 2-port Networks
2221212
2121111
VYVYI
VYVYI
2
1
2221
1211
2
1
V
V
YY
YY
I
I
Advantage: Y parameters are also somewhat intuitive.
Disadvantage: Requires short circuit voltage measurements, which are difficult to make.
Short circuit reflections inject noise into measurements.
Short circuit inductance is non-trivial at high frequencies.
Microwave and Radar Engineering
Example- Z-parameters
ZC
ZA
ZB
+
-
+
-
V1
V2
I1
I2
Po
rt 1
Po
rt 2
CA
CA
I
ZZ
ZZV
V
I
VZ
1
1
1
111
02
CC
I
ZI
ZI
I
VZ
2
2
2
112
01
CC
I
ZI
ZI
I
VZ
1
1
1
221
02
CB
CB
I
ZZ
ZZV
V
I
VZ
2
2
2
222
01
2221212
2121111
IZIZV
IZIZV
Microwave and Radar Engineering
Frequency Domain: Vector Network Analyzer (VNA)
VNA offers a means to characterize circuit elements as a function of frequency.
VNA is a microwave based instrument that provides the ability to understand frequency dependent effects.
The input signal is a frequency swept sinusoid.
Characterizes the network by observing transmitted and reflected power waves.
Voltage and current are difficult to measure directly.
It is also difficult to implement open & short circuit loads at high frequency.
Matched load is a unique, repeatable termination, and is insensitive to length, making measurement easier.
Incident and reflected waves the key measures.
We characterize the device under test using S parameters.
Microwave and Radar Engineering
S Parameters
We wish to characterize the network by observing transmitted and reflected power waves.
ai represents the square root of the power wave injected into port i.
bi represents the square root of the power wave injected into port j.
2 Port
Network
a1
+
-
V1
Po
rt 2
a2
+
-
V2
Po
rt 1
b1
b2
RVP
2
R
VPai
1
R
Vb
j
j
Microwave and Radar Engineering
S Parameters
We can use a set of linear equations to describe the behavior of the network in terms of the injected and reflected power waves.
For the 2 port case:
2
1
2221
1211
2
1
a
a
SS
SS
b
b
2 Port
Network
a1
+
-
V1
Po
rt 2
a2
+
-
V2
Po
rt 1
b1
b2
2221212
2121111
aSaSb
aSaSb
iport at measuredpower
jport at measuredpower
i
j
ija
bS
Microwave and Radar Engineering
Scattering Matrix – Return Loss
S11, the return loss, is a measure of the power returned to the source.
When there is no reflection from the load, or the line length is zero, S11 is
equal to the reflection coefficient.
50
50
0
00
1
1
0
1
0
1
1
111
02
Z
Z
V
V
V
V
Z
V
Z
V
a
bS
incident
reflected
a
0
0,0
jjai
iii
a
bS
In general:
Microwave and Radar Engineering
Scattering Matrix – Return Loss
When there is a reflection from the load, S11 will be composed of multiple reflections due to standing waves.
Use input impedance to calculate S11 when the line is not perfectly terminated.
)0(1
)0(1)0(
z
zZzZZ oin
If the network is driven with a 50 source, S11 is calculated as follows:
RS = 50
Zin
S11 for a transmission line will exhibit periodic effects due to the standing waves.
In this case S11 will be maximum when Zin is real. An imaginary component implies a phase difference between Vinc and Vref. No phase difference means they are perfectly
aligned and will constructively add.
50
5011
in
inv
Z
ZS
Microwave and Radar Engineering
Scattering Matrix – Insertion Loss
When power is injected into Port 1 and measured at Port 2, the power ratio reduces to a voltage ratio:
incident
dtransmitte
o
o
aV
V
V
V
Z
V
Z
V
a
bS
1
2
1
2
021
221
2 Port
Network
a1
+
-
V1
Po
rt 2
a2
+
-
V2
Po
rt 1
b1
b2
Z0
Z0
S21, the insertion loss, is a measure of the power transmitted from port 1 to port 2.
Microwave and Radar Engineering
S Parameters
aSb
jkkaj
iij
a
bS
,0
jkk
jkk
Vj
j
i
i
aj
iij
Z
V
Z
V
a
bS
,0
,0
0
0
Sij = Gij is the reflection coefficient of the ith port if i=j with all other ports matched
Sij = Tij is the forward transmission coefficient of the ith port if I>j with all other ports matched
Sij = Tij is the reverse transmission coefficient of the ith port if I<j with all other ports matched
Microwave and Radar Engineering
Comments on Losses
True losses come from physical energy losses.
Ohmic (i.e. skin effect)
Field dampening effects (loss tangent)
Radiation (EMI)
Insertion and return losses include other effects, such as impedance discontinuities and resonance, which are not true losses.
Loss free networks can still exhibit significant insertion and return losses due to impedance discontinuities.
Microwave and Radar Engineering
Reflection Coefficients Reflection coefficient at the load:
0
0
ZZ
ZZ
L
LL
0
0
ZZ
ZZ
S
SS
L
L
L
Lin
S
SS
S
SSS
11
2
1211
22
211211
11
S
Sout
S
SSS
11
211222
1
Reflection coefficient at the source:
Input reflection coefficient:
Output reflection coefficient:
Assuming S12 = S21 and S11 = S22.
Microwave and Radar Engineering
Transmission Line Z0 Measurements
Impedance vs. frequency
Recall
Zin vs f will be a function of delay () and ZL.
We can use Zin equations for open and short circuited lossy transmission.
lZZ openin tanh0,
lZZ shortin coth0,
lj
lj
ine
eZZ
2
2
01
1
openinshortin ZZZ ,,0
Using the equation for Zin, rin, and Z0, we can find the impedance.
Microwave and Radar Engineering
Advantages/Disadvantages of S Parameters
Advantages:
Ease of measurement: It is much easier to measure power at high frequencies than open/short current and voltage.
Disadvantages:
They are more difficult to understand and it is more difficult to interpret measurements.
Microwave and Radar Engineering
Transmission (ABCD) Matrix
The transmission matrix describes the network in terms of both voltage and current waves (analagous to a Thévinin Equivalent).
The coefficients can be defined using superposition:
221
221
DICVI
BIAVV
2
2
1
1
I
V
DC
BA
I
V
02
1
2
IV
IC
2 Port
Network
I1
+
-
V1
Po
rt 2
I2
+
-
V2
Po
rt 1
02
1
2
VI
ID
02
1
2
VI
VB
02
1
2
IV
VA
Microwave and Radar Engineering
Transmission (ABCD) Matrix
Since the ABCD matrix represents the ports in terms of currents and voltages, it is well suited for cascading elements.
I1
+
-
V1
I2
V2
I1
I3
+
-
V3
The matrices can be mathematically cascaded by multiplication:
3
3
22
2
2
2
11
1
I
V
DC
BA
I
V
I
V
DC
BA
I
V
3
3
211
1
I
V
DC
BA
DC
BA
I
V
This is the best way to cascade elements in the frequency domain.
It is accurate, intuitive and simple to use.
2DC
BA
1DC
BA
Microwave and Radar Engineering
Converting to and from the S-Matrix
The S-parameters can be measured with a VNA, and converted back and forth into ABCD, the Matrix
Allows conversion into a more intuitive matrix
Allows conversion to ABCD for cascading
ABCD matrix can be directly related to several useful circuit topologies
Microwave and Radar Engineering
Advantages/Disadvantages of ABCD Matrix
Advantages: The ABCD matrix is intuitive: it describes all ports with voltages and
currents.
Allows easy cascading of networks.
Easy conversion to and from S-parameters.
Easy to relate to common circuit topologies.
Disadvantages: Difficult to directly measure: Must convert from measured
scattering matrix.
Microwave and Radar Engineering
VNA Calibration
Proper calibration is critical!!!
There are two basic calibration methods
Short, Open, Load and Thru (SOLT)
Calibrated to known standard( Ex: 50)
Measurement plane at probe tip
Thru, Reflect, Line(TRL)
Calibrated to line Z0
Helps create matched port condition.
Microwave and Radar Engineering
SOLT Calibration Structures
OPEN SHORT
LOAD THRU
Calibration Substrate
G
G
S
S
G
S
Signal
Ground
G
S
G
S
Microwave and Radar Engineering
Microwave and Radar Engineering
Thanks