1EZ30_2E
AutoKal
Automatic Calibration
of
Vector Network Analyzer
ZVR
by
Hans-Gerd Krekels
Ruhr-University Bochum
Application Note 1EZ30_2E
30 August 1996, Hans-Gerd Krekels, Ruhr-University Bochum
Products:
ZVR incl. Option ZVR-B1
ZVRE incl. Option ZVR-B1
Contents
1.
1.1
1.2
2.
2.1
2.1.1
2.1.2
2.2
3.
3.1
3.2
4.
5.
6.
1.
Introduction ....................................................................................................................... 2
Error Model of Network Analyzers ....................................................................................... 2
Manual Calibration Procedures ........................................................................................... 4
The AutoKal Procedure .................................................................................................... 5
Theoretical Description ........................................................................................................ 6
Fundamental Calibration ..................................................................................................... 8
Automatic Calibration .......................................................................................................... 9
AutoKal for Analyzers with three Receiver Channels .......................................................... 9
Practical Realization and Application of the AutoKal Procedure ............................... 11
Realization of the Switching Unit ....................................................................................... 11
Implementation of the AutoKal Procedure......................................................................... 12
References ...................................................................................................................... 12
Further Application Notes................................................................................................13
Ordering Information........................................................................................................13
Introduction
Vector network analyzers are used in high frequency applications to measure the complex scattering
parameters of an unknown device-under-test (DUT). In general, the DUT characteristics can be
evaluated by using electromagnetic waves. The correlation between the incident, reflected and
transmitted wave quantities at the DUT is defined by its scattering matrix S.
a1
a2
b1
b2
DUT
b1
=
S 11 S 12
S 21 S 22
a1
a2
b2
Figure 1: Scattering parameter description of a two-port device.
For a two-port DUT (Fig. 1), the scattering parameters have the following meaning:
S11: Reflection at port 1 with port 2 matched
S21: Forward transmission with port 2 matched
S12: Reverse transmission with port 1 matched
S22: Reflection at port 2 with port 1 matched
Since network analyzers which measure the wave quantities ai, bi (i = 1, 2) are no ideal measuring
instruments, the determination of the required scattering parameters is subject to errors. A significant
enhancement of measurement accuracy, however, is possible by utilizing appropriate mathematical
system error correction procedures. Therefore the non-ideal characteristics of the network analyzer
must be known. The determination of these non-ideal characteristics can be performed by using a
calibration procedure.
1.1
Error Model of Network Analyzers
A block diagram of a vector network analyzer equipped with four receiver channels, e.g. ZVR, is shown
in Fig. 2.
1EZ30_2E.DOC
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29 May 1998
I
m
test set switch
m
4
1
a
a
1
2
DUT
G
b
m
II
H
b
1
2
m
2
3
Figure 2: Block diagram of a vector network analyzer, e.g. ZVR
The analyzer consists of a test set switch (SPDT switch) and two reflectometers G and H as well as
four receiver channels mi (i = 1...4). The block DUT represents a device-under-test located between
the two test ports.
The correlation between the wave quantities ai, bi at the test ports and the measurement values mi is
given by two error two-ports as described by the matrices G and H (Eq. 1) according to a four-port /
two-port reduction [1]. The calculation of these two matrices is the task of the calibration procedure.
 b1  G11 G 12  m 1
  =
 
 a1  G 21 G 22  m 2
 a 2  H 11 H 12  m 3
  =
 
 b 2  H 21 H 22  m 4
;
.
(1)
Besides the description of a DUT by scattering parameters, characterization with transmission matrices
is also possible. The transmission matrix N is defined by a linear combination of the transmitted and
reflected waves, however, in a different relationship. For a two-port, Eq. 2 is valid.
 b1  N11 N12  a 2
  =
 
 a1  N 21 N 22  b 2
N=
;
1  − det( S ) S11


1
S 21  −S 22
.
(2)
A combination of Eq. 1 and Eq. 2 leads to the expression:
 m1
−1
  = G NH
2
m
 
 m 3
 
 m 4
(3)
The block diagram of Fig. 2 reduces to a cascaded network consisting of two error two-ports and the
DUT.
1EZ30_2E.DOC
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29 May 1998
m
m
1
3
G
-1
N
H
m
m
2
4
Figure 3: Cascaded network of two error two-ports and the device-under-test.
The elimination of the waves ai, bi (i = 1, 2) in Eq. 1 by application of the scattering parameters yields
the vector equation:
 G 11 m 1 + G12 m 2   S11 S12  G 21 m1 + G 22 m 2

 =


 H 21 m 3 + H 22 m 4  S 21 S 22  H 11 m 3 + H 12 m 4
( 4)
A second vector expression is derived for the second position of the test set switch. If the measurement values of the second switch position are defined by m’ i (i = 1...4), a combination of the two vector equations yields the matrix expression:
 G11 m1 + G12 m2 G11 m’1 + G12 m’2   G 21 m1 + G 22 m2 G 21 m’1 + G 22 m’2
S=


 H 21 m3 + H 22 m4 H 21 m’3 + H 22 m’4  H11 m3 + H12 m4 H11 m’3 + H12 m’4
−1
(5)
This expression can be used during calibration of the network analyzer. Moreover, the transformation
of Eq. 5 for a known scattering matrix S results in four linear, independent equations which are useful
during the calculation of the error parameters contained in the matrices G and H.
A determination of the scattering matrix for an unknown DUT can also be performed with Eq. 5 if the
system errors of the network analyzer are known.
1.2
Manual Calibration Procedures
Commonly used procedures for the calibration of vector network analyzers, e. g. TOM or TRM [2] (T =
Through, M = Match, O = Open, R = Reflect) are based upon the measurement of various known or
partially unknown calibration standards. Depending upon the type of procedure, the individual calibration standards must be manually connected to the test ports of the network analyzer in order to perform
a measurement of the calibration standards.
TOM procedure
TRM procedure
T
T
O
R
M
M
Figure 4: Manual calibration techniques.
1EZ30_2E.DOC
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29 May 1998
The parameters found by manual calibration procedures have the hidden risk of being in error because
of possible contact problems which may occur when the standards are frequently connected to the test
ports. The consequence is an erroneous system error correction.
At the conclusion of a correctly completed calibration procedure, the non-ideal characteristics of the
measuring instrument are known. Unavoidable changes in electrical characteristics due to temperature
instability or to other drifts in the network analyzer, which occur after the calibration, lead to errors in
the measurement results. On the other hand, the characteristics of mechanical components (lines,
connectors, etc.) are highly reproducible and change only slightly over long periods of time.
The specified measurement accuracy requirements dictate the interval between two calibrations. This
interval may be from one to several days, but may also be just a matter of hours. Hence, the calibration
effort (connection of standards) can be considerable. In an industrial measurement environment, the
repetition of a calibration is often very difficult and expensive since on-going production may have to be
interrupted or even the analyzer system may have to be dismantled.
2.
The AutoKal Procedure
The AutoKal (Automatic Calibration) procedure is based upon the application of an automated, passive switching unit controlled by the network analyzer. For purposes of calibration, the switching unit
must be able to take on three independent, reproducible switching states.
As shown in Fig. 5, the network analyzer is modified at a test port (e.g. port 2) by the extension of the
switching unit E. The switching unit is a permanent part of the analyzer and will not be removed after
completion of the calibration procedure. An additional transmission network TN represents the interconnection between the switching unit E and port 2’.
I
m
m
3
1
G
m
II
1
2’
TN
E
2
H
m
2
4
Figure 5: Configuration of the network analyzer.
The AutoKal calibration is divided into two procedural steps, fundamental calibration and automatic
(transfer) calibration.
1EZ30_2E.DOC
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29 May 1998
Fundamental Calibration:
In order to characterize the switching unit, it is necessary to perform a manual calibration. Since the
switching unit is a passive, very stable component, it is only necessary to carry out a fundamental calibration at intervals of several months. Another possible reason for repeating the fundamental calibration is a change in the transmission network, e.g. a change of the connector type at a test port 2’.
Automatic (transfer) Calibration:
The automatic (transfer) calibration is the actual calibration procedure which leads to the determination
of the error parameters of the network analyzer.
The transfer calibration is performed automatically by the network analyzer. The user is only required
to provide the interconnection between the two test ports and simply press the AutoKal softkey in the
CAL menu. In comparison to manual calibration procedures, the AutoKal calibration leads to a considerable simplification in the handling of calibration standards.
2.1
Theoretical Description
The starting point of the description of the procedure is the equivalent circuit of a network analyzer as
derived in Section 1.1 by the application of the four-port/two-port reduction method. Fig. 6 illustrates the
configuration of the cascaded two-ports with the analyzer being extended by the switching unit E and
the transmission network TN. The block N represents a two-port located between the test ports.
reference plane
m
m
1
3
-1
G
TN
E
H
m
m
2
4
N
Figure 6: Realization of virtual calibration standards.
A mathematical description of the two-port configuration yields:
 m1
 m 3
−1
  = G N TN E H  
 m 2
 m 4
.
(6)
The switching unit must take on three different switching states. Table 1 indicates the transmission
matrix for these three states.
Switching State
0
1
2
Transmission Matrix E
E = E0
E = E1 • E0
E = E2 • E0
Table 1: Transmission matrix E for three switching states.
E0 represents the transmission matrix of the initial state. E1 and E2 include the changes of the switching network for the second and third positions.
1EZ30_2E.DOC
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29 May 1998
The basis of the AutoKal procedure is a virtual transformation of the switching network standards
into the reference plane. The network standards are realized via three states of the switching unit.
Since both test ports of the analyzer must present an exact through-connection during the automatic
(transfer) calibration, the initial state of the switching unit is converted to a through-connection.
E0
1 0
N=

 0 1
→
(7)
The transformation of the two switching states which deviate from the initial position is shown in Eq. 8.
E1 E0
→
~
E1
E2 E0
→
~
E2
(8)
If the switching unit is in its second state, the deviation from the initial position E1 is transformed to a
~
modified E 1 which is virtually located between the reference planes.
reference plane
m
m
1
3
-1
G
TN
E
1
E
0
H
m
m
2
4
reference planes
m
m
1
3
-1
G
~
E
1
TN
E
0
m
H
m
2
4
Figure 7: Transformation of network standards.
In view of the transformation (Eq. 8), the effect of the two two-port configurations of Fig. 7 must be
identical. Mathematically, this yields:
G −1 TN E1 E0 H
=
~
G −1 E1 TN E0 H
( 9)
~
Rearranging this equation, E 1 is the result of a similarity transformation, that is, a virtual transformation
of the deviation E1 into the reference plane.
~
E1
=
TN E1 TN
−1
(10)
As can be seen from Eq. 10, it is not necessary to know the initial state E0 of the switching unit. For
calibration purposes, only the virtual changes must be known. In addition, Eq. 10 also clarifies the
technical requirements imposed upon the switching unit. The transmission network and any changes of
the switching unit need not be known, only a high degree of reproducibility is required.
1EZ30_2E.DOC
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29 May 1998
2.1.1
Fundamental Calibration
~
~
The purpose of the fundamental calibration is the calculation of the scattering matrices S 1 and S 2 of
the virtual calibration standards
~
~
E1and E 2 .
First, it is necessary to calibrate the network analyzer using a manual calibration procedure, e.g. TOM.
Here, the switching unit E is in the initial state (Fig. 8).
m
G
m
m
1
3
^
H
TN
E0
H
m
2
4
Figure 8: Initial state of the network analyzer
The calibration, e.g. TOM, yields the system error matrices G and H which describe the reflectome-
ters G and H$ .
In the next step, the test ports are combined to form an exact through-connection and the switching
~
unit is switched to its second state so that the virtual standard E 1 is realized. An analyzer measurement under these conditions generates the desired virtual scattering parameters when Eq. 5 is applied.
 G11 m1 + G12 m2 G11 m’1 + G12 m’2 
~
S1 =  $
$ 22 m4 H
$ 21 m’3 + H
$ 22 m’4 *
 H 21 m3 + H
 G 21 m1 + G 22 m2 G 21 m’1 + G 22 m’2
$
$ 12 m4 H
$ 11 m’3 + H
$ 12 m’4
 H11 m3 + H
−1
(11)
~
In a similar way, S 2 can be determined after setting the switching device to the third state. Once the
~
~
matrices S 1 and S 2 have been found, the task of the fundamental calibration is completed.
A fundamental calibration requires a total of five analyzer measurements. The individual measurements with the corresponding calibration standard and the required state of the switching unit are
summarized in Table 2.
Measurement
1
2
3
4
5
DUT
T
T
T
O
M
Switching state
0
1
2
0
0
Table 2: Measurements for fundamental calibration using TOM
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29 May 1998
Since the AutoKal switching unit E is a mechanical, passive device and has very stable electrical characteristics, it is usually only necessary to perform a fundamental calibration at intervals of several
months.
2.1.2
Automatic Calibration
The frequently performed transfer calibration AutoKal for the determination of the currently valid error
matrices G and H takes place automatically. Here, it is only necessary to provide a through-connection of the two test ports.
During this automatically controlled calibration, the network analyzer performs three measurements at
the three states of the switching unit. The results of the measurements yield the following equations:
$,
G-1 H
~ $
= G -1 E1 H
,
~ $
= G −1 E2 H
,
M1 =
M2
M3
(12)
where
 m 1 m’ 1  m 3 m’ 3
Mi = 


 m 2 m’ 2  m 4 m’ 4
−1
, (i = 1...3)
.
(13)
With a knowledge of the measurement matrices Mi (i = 1...3) as well as the transmission matrices of
the virtual network standards determined during the fundamental calibration, the desired system matrices G and H can be found.
For the measurement and the calculation of an unknown DUT, the switching unit must be in its initial
state.
2.2
AutoKal for Analyzers with three Receiver Channels
The application of AutoKal procedure is not limited to network analyzers with four receiver channels, as
ZVR. It can be shown in the following that the configuration for an automatic calibration can also be
implemented on uni- or bi-directional network analyzers with only three receiver channels, e.g. ZVRE.
A bi-directional network analyzer with three receiver channels is shown in Fig. 9 on the next page.
1EZ30_2E.DOC
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29 May 1998
m
I
a
a
1
G
2
DUT
b
m
II
H
b
1
2
m
1
4
Figure 9: Block diagram of a vector network analyzer with three receiver channels, e.g. ZVRE
The two reflectometers G and H are each connected to one receiver channel. The third receiver channel is fed between the RF source and the test set switch. The information provided by the third receiver
channel m is a measure of the incident wave transmitted to the DUT. With reference to the algebra of
Section 1.1, m represents the coefficient m2 for the first position and the coefficient m’3 for the second
position of the test set switch.
Due to configuration of the third receiver channel m the test set switch must be included in the error
model of the network analyzer. Consequently, there are different system errors for each test set switch
position:
Position I:
G
H
H’
Position II:
G’
For the first test set switch position, Eq. 14 describes the relationship between the measurement coefficients m, mi (i = 1, 4) and the waves aj, bj (j = 1, 2) at the two test ports.
 b1  G11 G 12  m1
  =
 
 a1  G 21 G 22  m 
 a 2  H 11 H 12  0 
  =
 
 b 2  H 21 H 22  m 4
;
.
(14)
Eq. 15 is valid for the second position of the switch.
 b1   G ’11 G ’12  m ’1 
 =
 
 a1   G ’21 G ’22  0 
 a 2   H ’11 H ’12  m ′ 
 =

 .
 b 2   H ’21 H ’22  m ’4 
;
(15)
The combination of expressions Eq. 14 and Eq. 15 and the application of the scattering parameters
yields Eq. 16.
G’ 11 m’ 1
G’ 21 m’ 1
 G 11 m 1 + G 12 m
  G 21 m 1 + G 22 m

S=


H 22 m 4
H’ 21 m’ + H’ 22 m’ 4 
H 12 m 4
H’ 11 m’ + H’ 12 m’ 4

−1
(16)
In view of this correlation, the application of the AutoKal procedure to analyzers with three receiver
channels is similar to that of analyzers with four receiver channels.
A well-known calibration technique for determining the virtual calibration standards during the AutoKal
fundamental calibration for analyzers with three receiver channels is the 12-term procedure TOSM.
1EZ30_2E.DOC
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29 May 1998
3.
3.1
Practical Realization and Application of the AutoKal Procedure
Realization of the Switching Unit
The switching unit, necessary for the performance of automatic transfer calibration, must exhibit three
independent switching states. For defining the switching states, simple resistor configurations with nonprecision specifications can be used. The resistive networks used must possess stable, long-term
characteristics.
A matched pi-attenuator is a simple, well-known circuit for the realization of a switching unit which
guarantees a well-matched test port. The pi -network shown in Fig. 10 contains two additional switches
which allow the three different switching states (Fig. 11) to be realized. The switches may be electromechanical and, therefore, automatically controlled.
S
1
Z
2
Z
3
Z
1
S
2
Figure 10: Switching unit realization.
State 0
State 1
State 2
Z
2
Z
1
Z
2
Z
3
Z || Z
1
3
Z
1
Figure 11: Switching states of the pi-network
Another version of a switching unit is shown in Fig. 12. Here, the networks NW1 and NW2 are switched
into the signal path during the second and third states as a function of position of the synchronously
operating switches S1 and S2.
1EZ30_2E.DOC
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29 May 1998
S
1
0
1
2
0
NW
NW
1
1
2
2
S
2
Figure 12: Realization of the switching network.
3.2
Implementation of the AutoKal Procedure
The implementation of the AutoKal procedure is accomplished by modifying a network analyzer to include a control unit and a switching device. The control unit may be contained either within the analyzer
chassis itself or located remotely with a connection to the network analyzer interface. The switching
device, realized here as module ZVR-B1, is connected to the test ports of the analyzer. The test ports
of the AutoKal unit are the actual test ports at which the fundamental calibration and all measurements
of unknown DUTs are carried out. A control cable connects the AutoKal module to the control unit,
which is a part of the ZVR vector network analyzer.
The internal switching device is inserted between one test port pair, i.e. PORT1 (male) and PORT1
(female), within the AutoKal unit ZVR-B1. The connection between the other test port pair, i.e. PORT2
(male) and PORT2 (female), is realized by a direct through line.
4.
References
[1]
SCHIEK, B., Meßsysteme der Hochfrequenztechnik, Hüthig-Verlag, Heidelberg 1984
[2]
EUL, H.-J., SCHIEK, B., A Generalized Theory and New Calibration Procedures for Network
Analyzer Self-Calibration, IEEE-MTT, Vol. 39, April 1991, pp 724-731.
[3]
KREKELS, H.-G., SCHIEK, B., Ein Netzwerkanalysator Kalibrierverfahren für eine redundante
Anzahl an Kalibrierstandards, Proceedings of the national URSI conference 1993, Kleinheubach
(Germany), vol. 37 , pp 117-126.
[4]
KREKELS, H.-G., SCHIEK, B., An Automatic Procedure for a Calibration of a Network Analyzer,
Proceedings of the Conference on Precision Electromagnetic Measurements 1994 (CPEM),
Boulder, USA, pp 123-124.
[5]
KREKELS, H.-G., Verfahren zur Kalibrierung und Etablierung von vektoriellen Netzwerkanalysatoren mit Anwendung auf Doppelsechstor-Anordnungen, Shaker-Verlag, Aachen 1996
Hans-Gerd Krekels
Ruhr-University Bochum
30 August 1996
1EZ30_2E.DOC
12
29 May 1998
5
[1]
[2]
Further Application Notes
Order designation
H.-G. Krekels: Automatic Calibration of Vector
Network Analyzer ZVR, Appl. Note 1EZ30_1E.
Vector Network Analyzers (test sets included) *
O. Ostwald: 4-Port Measurements with Vector
Network Analyzer ZVR, Appl. Note 1EZ25_1E.
[4]
T. Bednorz: Measurement Uncertainties for
Vector Network Analysis, Appl. Note
1EZ29_1E.
[6]
[7]
[8]
[9]
Ordering Information
O. Ostwald: 3-Port Measurements with Vector
Network Analyzer ZVR, Appl. Note 1EZ26_1E.
[3]
[5]
6
3-channel, unidirectional,
50 Ω, passive
3-channel, bidirectional,
50 Ω, passive
3-channel, bidirectional,
50 Ω, active
4-channel, bidirectional,
50 Ω, passive
4-channel, bidirectional,
50 Ω, active
3-channel, bidirectional,
50 Ω, active
4-channel, bidirectional,
50 Ω, active
P. Kraus: Measurements on FrequencyConverting DUTs using Vector Network Analyzer ZVR, Appl. Note 1EZ32_1E.
J. Ganzert: Accessing Measurement Data and
Controlling the Vector Network Analyzer via
DDE, Appl. Note 1EZ33_1E.
Type
Frequency
range
Order No.
ZVRL
9 kHz to 4 GHz
1043.0009.41
ZVRE
9 kHz to 4 GHz
1043.0009.51
ZVRE
300 kHz to 4 GHz
1043.0009.52
ZVR
9 kHz to 4 GHz
1043.0009.61
ZVR
300 kHz to 4 GHz
1043.0009.62
ZVCE
20 kHz to 8 GHz
1106.9020.50
ZVC
20 kHz to 8 GHz
1106.9020.60
Alternative Test Sets *
75 Ω SWR Bridge for ZVRL (instead of 50 Ω) 1)
75 Ω, passive
J. Ganzert: File Transfer between Analyzers
FSE or ZVR and PC using MS-DOS Interlink,
Appl. Note 1EZ34_1E.
ZVR-A71
9 kHz to 4 GHz
1043.7690.18
75 Ω SWR Bridge Pairs for ZVRE and ZVR (instead of 50 Ω) 1)
75 Ω, passive
75 Ω, active
O. Ostwald: Group and Phase Delay Measurements with Vector Network Analyzer ZVR,
Appl. Note 1EZ35_1E.
ZVR-A75
ZVR-A76
9 kHz to 4 GHz
300 kHz to 4 GHz
1043.7755.28
1043.7755.29
AutoKal
Time Domain
Mixer Measurements 2)
Reference Channel Ports
Power Calibration 3)
3-Port Adapter
Virtual Embedding Networks 4)
4-Port Adapter (2xSPDT)
4-Port Adapter (SP3T)
ZVR-B1
ZVR-B2
ZVR-B4
ZVR-B6
ZVR-B7
ZVR-B8
ZVR-K9
0 to 8 GHz
same as analyzer
same as analyzer
same as analyzer
same as analyzer
0 to 4 GHz
same as analyzer
1044.0625.02
1044.1009.02
1044.1215.02
1044.1415.02
1044.1544.02
1086.0000.02
1106.8830.02
ZVR-B14
ZVR-B14
0 to 4 GHz
0 to 4 GHz
1106.7510.02
1106.7510.03
Controller (German) 5)
Controller (English) 5)
Ethernet BNC for ZVR-B15
Ethernet AUI for ZVR-B15
IEC/IEEE-Bus Interface for
ZVR-B15
ZVR-B15
ZVR-B15
FSE-B16
FSE-B16
FSE-B17
-
1044.0290.02
1044.0290.03
1073.5973.02
1073.5973.03
1066.4017.02
Generator Step Attenuator
PORT 1
Generator Step Attenuator
PORT 2 6)
Receiver Step Attenuator
PORT 1
Receiver Step Attenuator
PORT 2
External Measurements,
7)
50 Ω
ZVR-B21
same as analyzer
1044.0025.11
ZVR-B22
same as analyzer
1044.0025.21
ZVR-B23
same as analyzer
1044.0025.12
ZVR-B24
same as analyzer
1044.0025.22
ZVR-B25
10 Hz to 4 GHz
(ZVR/E/L)
20 kHz to 8 GHz
(ZVC/E)
1044.0460.02
Options
O. Ostwald: Multiport Measurements using
Vector Network Analyzer, Appl. Note
1EZ37_1E.
[10] O. Ostwald: Frequently Asked Questions
about Vector Network Analyzer ZVR, Appl.
Note 1EZ38_3E.
[11] A. Gleißner: Internal Data Transfer between
Windows 3.1 / Excel and Vector Network
Analyzer ZVR, Appl. Note 1EZ39_1E.
[12] A. Gleißner: Power Calibration of Vector Network Analyzer ZVR, Appl. Note 1EZ41_2E
[13] O. Ostwald: Pulsed Measurements on GSM
Amplifier SMD ICs with Vector Analyzer ZVR,
Appl. Note 1EZ42_1E.
[14] O. Ostwald: Zeitbereichsmessungen mit dem
Netzwerkanalysator ZVR, Appl. Note
1EZ44_1D.
1)
To be ordered together with the analyzer.
Harmonics measurements included.
Power meter and sensor required.
4)
Only for ZVR or ZVC with ZVR-B15.
5)
DOS, Windows 3.11, keyboard and mouse included.
6)
For ZVR or ZVC only.
7)
Step attenuators required.
2)
3)
* Note:
Active test sets, in contrast to passive test sets, comprise internal bias
networks, eg to supply DUTs.
1EZ30_2E.DOC
13
29 May 1998
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