S-parameter measurements using real-time oscilloscopes
A method for determining scattering parameters of a device under test using a real-time oscilloscope. The method includes calculating a reflection coefficient of each port of a device under test with N ports, wherein N is greater than one, based on a first voltage measured by the real-time oscilloscope when a signal is generated from a signal generator. The method also includes determining an insertion loss coefficient of each port of the device under test, including calculating the insertion loss coefficient of the port of the device under test to be measured based on a second voltage measured by the real-time oscilloscope when a signal is generated from a signal generator.
1. A method for determining scattering parameters of a device under test using a real-time oscilloscope, comprising:
determining a reflection coefficient for a first port of a device under test including:
terminating a second port of the device under test with a resistor,
sending, via a signal generator, a first signal to a first port of a power divider,
measuring, based on a synchronized trigger that provides an absolute time reference between the signal generator and the real-time oscilloscope, a voltage level of the first signal by the real-time oscilloscope at a second port of the power divider while a device under test is connected, via the first port of the device under test, to a third port of the power divider, and
calculating the reflection coefficient of the first port of the device under test utilizing the measured voltage level of the first signal; and
determining a reflection coefficient for the second port of the device under test including:
terminating the first port of the device under test with a resistor,
sending, via the signal generator, a second signal to the first port of the power divider,
measuring, based on the synchronized trigger, a voltage level of the second signal by the real-time oscilloscope at a second port of the power divider while a device under test is connected, via the second port of the device under test, to the third port of the power divider, and
calculating the reflection coefficient of the second port of the device under test utilizing the measured voltage level of the second signal; and
determining an insertion loss coefficient of the first port of the device under test, including:
sending, via the signal generator, a third signal to the second port of the device under test and to the real-time oscilloscope;
measuring, based on the synchronized trigger, a voltage level of the third signal by the real-time oscilloscope at the first port of the device under test;
calculating, by the real-time oscilloscope, the insertion loss coefficient of the first port utilizing the measured voltage level of the second signal and the determined reflection coefficients of the first port and the second port of the device under test; and
utilizing, by the real-time oscilloscope, the reflection coefficient and the insertion loss coefficient of the first port of the device under test to perform a de-embed operation.
2. The method of claim 1 , wherein the resistor is a 50 Ohm resistor.
3. The method of claim 1 , wherein the reflection coefficient of the first port of the device under test is calculated using the equations:
b
2
v
s
1
=
1
2
·
(
1
-
s
22
ss
)
(
s
21
+
s
23
s
~
11
DUT
s
31
)
1
-
s
22
ss
s
12
s
~
11
DUT
s
31
-
s
23
s
~
11
DUT
s
32
s
11
scope
and
s
~
11
DUT
=
s
11
DUT
[
1
-
s
33
s
11
DUT
]
-
1
where b 2 is the measured voltage level of the first signal,
ν s1 is the first signal,
s 22 ss is an impedance of the signal generator,
s 21 , s 12 , s 31 , s 23 , s 32 , s 33 are the scatter parameter terms of the power divider,
s 11 scope is an input impedance of the real-time oscilloscope, and
s 11 DUT is the reflection coefficient.
4. The method of claim 1 , wherein the reflection coefficients are calculated for the second port of the device under test using the equations:
b
2
v
s
2
=
1
2
·
(
1
-
s
22
ss
)
(
s
21
+
s
23
s
~
11
DUT
s
31
)
1
-
s
22
ss
s
12
s
~
11
DUT
s
31
-
s
23
s
~
11
DUT
s
32
s
11
scope
and
s
~
11
DUT
=
s
11
DUT
[
1
-
s
33
s
11
DUT
]
-
1
where b 2 is the measured voltage level of the second signal,
ν s2 is the second signal,
s 22 ss is an impedance of the signal generator,
s 21 , s 12 , s 31 , s 23 , s 32 , s 33 are the scatter parameter terms of the power divider,
s 11 scope is an input impedance of the real-time oscilloscope, and
s 22 DUT is the reflection coefficient.
5. The method of claim 4 ,
wherein the insertion loss coefficient is calculated for each of the first port and second port of the device under test using the equation:
b
2
v
s
=
1
2
·
(
1
-
s
22
ss
)
s
21
DUT
1
-
s
22
ss
s
11
DUT
-
s
22
DUT
s
11
scope
where s 21 DUT is the insertion loss coefficient.