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Keysight Technologies
High Attenuation Measurement of
Step Attenuators
White Paper
Abstract
This paper introduces a solution for high attenuation measurement of step
attenuators. Fundamentally, this high attention measurement method is based
on the cascaded 2-port network and S-parameter theory; this method is to
compute S-parameters of high attenuation (> 80 dB) using the measured
S-parameters of lower attenuation ( 80 dB) settings, and the calculations
depend on attenuator card sequence and physical structure of step attenuator.
This method can measure the attenuation high as 120 dB.
This is NOT a straight dB addition, this solution can offer considerable accuracy
only using VNA (Vector Network Analyzer), and it uses T-matrix (as known as
transmission parameter or cascade parameter) method which can make the
calculations easier. Measurement uncertainties are derived from uncertainties
of cascaded S-parameters, for example, measurement uncertainty for 80 dB @
18 GHz is less than 0.8 dB and 110 dB @ 18 GHz is less than 1.0 dB.
Introduction
There was a need to verify the accuracy of an attenuator in a new
synthesizer product. This method provides a simpler procedure for
Calibration Lab using an automatic measurement system to perform
high attenuation measurement of step attenuators. This T-matrix
method was originally suggested by the project manager, and finally
implemented by software engineer. The author of this report, as
metrologist of the project, provided principle verification, experimenta-
tion results review and measurement uncertainty analysis. This method
was also approved by expert from Keysight Technologies Component
Test Division.
This measurement system has been used to calibrate a large number of
step attenuators for many years. This paper describes the T-matrix mea-
surement method for achieving high accuracy, and will introduce details
of using cascade parameters to represent each thru-line and attenuator
section based on attenuator physical structure of step attenuator.
Sulan Zhang, Keysight Technologies
T-matrix Description
The following discussion in general applies to a cascade of N-port networks. For
the sake of simplicity, however, we limited our analysis to two-port networks
only. When cascading a number of two-port network in series, a more useful
network representation is needed to facilitate the calculation of the overall
network parameters.
This representation should relate the output quantities in terms of input quanti-
ties. Using such a representation will enable us to obtain a description of the com-
pleted cascade by simply multiplying together the matrix describing each network.
The following information on 2-port network is available from an Keysight
application note; see reference 2 at the end of this paper. 2-port network (Figure
1) can be used to model many components, and Attenuator is a typical example.
The 2-port network can be characterized by S parameter matrix (Figure 2). For
2-port networks the S -parameters are defined as:
S11 S12
S=
S21 S22
The inputs and outputs of the 2-port network can be denoted as:
b1 S11 S12 a1
=
b2 S21 S22 a2
Where S11 is the input reflection coefficient with the output port terminated by a
a1 a2
matched load (a2 = 0).
b1 2 Port Network b2
Therefore:
b
Figure 1. 2-port network S11 = a1
1 a2=0
a1 a2 Similarly, S21 is the forward transmission coefficient indicating with the output
port terminated by a matched load (a2 =0):
b1 [S] b2
b
S21 = a2
Figure 2. S-parameters for 2-port network 1 a2=0
S22 is the output reflection coefficient with the input terminated by a matched
load (a1 = 0):
b
S22 = a2
2 a2=0
S12 is the reverse transmission coefficient with the input terminated by a
matched load (a1 =0)
b
S12 = a1
2 a1=0
3
T-matrix Description Continued
Transmission matrix [T] is expressed in terms of the waves at the input port and
the waves at the output port. Using this definition the transmission matrix formu-
lation becomes very useful when dealing with multistage circuits or infinitely long
periodic structures such as those used in circuits for traveling wave tubes, etc.
The transmission matrix for a two-port network, as shown in Figure 3, is defined as:
a1 a2
b1 T11 T12 a2
= b1 b1b1 [T]T11 12 12 a2 a2 b
T TT
a1 T21 T22 b2 = = 11 2
a a1 T T21 T22 b b2
1
T
21 22 2
Figure 3. T-parameters for 2-port network
The relationship between S- and T- parameters can be derived using the above
basic definition as follows:
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