

Network Analyser Calibration
Network analysers effectively compare the power of signals transmitted through, or reflected back from a network port to the power of the incident signal present at the input of that port. A combination of directional couplers, isolators, transmission lines and computer calculation is used to achieve this. A perfect measurement system would have infinite dynamic range, isolation, and
directivity characteristics, no impedance mismatches in any part of the test setup, and a
flat frequency response. Although modern microwave devices for inclusion in an analyser
system can be made to posses excellent response characteristics, there will inevitably be
mismatches and errors in the system. We model the network analyser system response to a 12
term error model in which all possible error coefficients, their direction and position in
the system are allocated. By employing a standard calibration procedure, the individual error terms can be
calculated, so reducing the uncertainty in a given measurement system. In practice, this
'perfect' network analyser is achieved by measuring the magnitude and phase response of
known standard devices, using this data in conjunction with the model of the measurement
system to determine error contributions, then measuring a test device and using vector
mathematics to compute the actual test device response by removing the error terms. Such a calibration routine must be repeated each and every time a part of the test
setup is altered. Changing connector types, frequency ranges, system impedances, length of
transmission line all contribute some alteration in impedance or phase response of the
system, and so must be characterised out to remove uncertainty due to these factors. The dynamic range and accuracy of the measurement is the limited by system noise and
accuracy to which the characteristics of the calibration standards are known. This is the
basic concept of vector accuracy enhancement. 10.2.1 SOURCES OF MEASUREMENT ERRORS Network analysis measurement errors can be separated into two categories: Random Errors. These are nonrepeatable measurement variations that occur due to noise, environmental changes and other physical changes in the test setup between calibration and measurement. These are any errors that the system itself cannot measure or cannot model with an acceptable degree of certainty. Systematic Errors. These are repeatable errors. They include mismatch and leakage terms
in the test setup, isolation characteristics between the reference and test signal paths,
and system frequency response. Thus, any measurement result is the vector sum of the actual test device response plus
all error terms. The precise effect of each error term depends upon its magnitude and
phase relationship tot he actual test device response. Random errors cannot be precisely
quantified, so they must be treated as producing a cumulative ambiguity in the measured
data. It is fortunate that in the case of most microwave measurements, systematic errors are
the ones which produce the most significant measurement uncertainty. Since each of these
errors produces a predictable effect upon the measured data, their effects can be removed
to obtain a corrected value for test device response. For the purpose of vector accuracy
enhancement, these uncertainties are quantified as directivity, source match, load match,
isolation and tracking (frequency response). When accuracy enhancement techniques are
used, the resultant values after correction are termed Effective Directivity, Effective
Source and Load Match, Effective Isolation, and Effective Tracking. 10.2.2 DIRECTIVITY 10.2.3 SOURCE MATCH Source match error is particularly a problem when measuring very high or very low
impedances (large mismatch at the measurement plane). The Effective Source Match can be
improved considerably by using vector error correction techniques. 10.2.4 LOAD MATCH 10.2.5 ISOLATION 10.2.6 TRACKING 10.3 CORRECTING MEASUREMENT ERRORS The HP8510B network analyser system offers a choice between FrequencyResponseOnly,
1Port, and 2Port error models. The frequencyresponseonly error model provides signal
path frequency response error correction for the selected parameter. This model may be
adequate for measurement of well matched low loss devices where vector normalisation of
magnitude and phase frequency response errors provides sufficient measurement accuracy. The 1Port error model provides directivity, source match, and reflection signal path
frequency response vector error correction for reflection measurements. This model is best
applied to high accuracy reflection measurements of oneport devices. The 2Port error model provides full directivity, isolation, source match, load match
and frequency response vector error correction for transmission and reflection
measurements of twoport devices. This model provides best magnitude and phase measurement
accuracy for twoport devices but requires measurement of all four Sparameters of the
twoport device. The following text describes these error models in greater detail, and, more
importantly, explains how they can be characterised and used to reduce measurement
uncertainty. In actual system operation, error correction is not always done exactly as
suggested, but the results are mathematically equivalent. Let us consider measurement of reflection coefficients (magnitude and phase) of some unknown oneport device. No matter how careful we are, the measured data will differ from the actual. Directivity, Source Match, and Tracking are the main sources of error.
Reflection coefficient is measured by first separating the incident voltage wave (I)
from the reflected voltage wave (R), then taking the ratio of the two values. Ideally, (R)
consists only of the wave actually reflected by the test device (S11a). Unfortunately, not all of the incident wave reaches the unknown. Some of (I) may appear
at the measurement system input due to leakage through the signal separation device
(coupler/bridge). Also, some of (I) may be reflected by imperfect adapters between signal
separation device and the measurement plane. The vector sum of the leakage and
miscellaneous reflections is directivity, E_{DF}. Understandably, out measurement
is distorted when the directivity signal combines vectorially with the actual reflected
signal from the unknown S11a.
Since the measurement system test port is never exactly the characteristic impedance
(normally 50 ohms), some of the reflected signal bounces off the test port (or other
impedance changes further down the line) and back to the unknown, adding to the original
incident signal (I). This effect causes the magnitude and phase of the incident signal to
vary as a function of S11a. Levelling the source to produce constant (I) reduces this
error, but since the source cannot be levelled exactly at the test device input, levelling
cannot eliminate all power variations. This rereflection effect and the resultant
incident power variation is caused by the source match error, E_{SF}.
Tracking (frequency response) error is caused by variations in magnitude and phase
flatness versus frequency between the test and reference signal paths. These are due
mainly to imperfectly matched samplers and difference between reference and test signal
paths. The vector sum of these variations is the reflection signal path tracking error, E_{RF}.
It can be shown that these three errors are mathematically related to the actual, S11a,
and measured S11m, data by the following equation.
If we knew the value of these three 'E' errors and the measured test device response at
each frequency step, we could simply solve the above equation for S11a to obtain the
actual frequency response. Because each of these errors changes with frequency, it is
necessary that their values by known at each test frequency. They are found by measuring
(calibrating) the system at the measurement plane using three independent standards whose
S11a is known at all frequencies. One of the standards we apply is a 'perfect' load which makes S11a=0 and essentially
measures directivity. By 'perfect' load we mean a reflectionless termination at the
measurement plane. All incident energy is absorbed. With S11a = 0 the equation can be
solved for E_{DF}, the directivity error term. Of course, in practice, the perfect
load can never be achieved.
Since the measured value for directivity is the vector sum of the actual directivity
plus the actual reflection coefficient of the 'perfect' load, any reflection from the
termination represents an error. System Effective Directivity becomes the actual
reflection coefficient of the 'perfect' load. In general, any termination having a return
loss greater than the uncorrected system directivity reduces reflection measurement
uncertainty. Due to the difficulty of producing a high quality fixed coaxial termination at
microwave frequencies, a sliding load can be used at each test frequency to separate the
reflection of a somewhat imperfect termination from the actual directivity. At any single frequency, moving the sliding termination with respect to the measurement
plane produces a complete circle when the sliding element is displaced onhalf wavelength
of the test frequency. Its reflection coefficient magnitude remains constant but the phase
of the coefficient changes. The radius of that circle is the actual reflection coefficient
of the sliding termination, and the centre of the circle is terminated by the actual
directivity of the test setup and the geometry of the air line within the sliding load. Thus the critical specifications for the sliding load assembly are the mechanical
dimensions (impedance) of the connector, of the transmission line between the measurement
plane and the termination, and that the termination maintains a constant reflection
coefficient magnitude at all positions. The sliding load calibration sequence used here measures the sliding load at 6 or more
positions. The centre of the circle is calculated by the HP8510B firmware, which may be a
20dB improvement over a fixed load. A problem arises in the use of the sliding load at low
microwave frequencies. The line has to be very long, otherwise the points are bunched
together and it is very difficult to determine the centre accurately. In these cases it is
often better to use a fixed load. The convention is to use a fixed load below 2GHz and a
sliding load above 2GHz. Next a short circuit termination is used to establish another condition. The open circuit gives us the third independent condition. Now values for E_{DF},
directivity, E_{SF}, source match, and E_{RF}, reflection tracking, are
computed and stored. Now we measure the unknown to obtain a value for the measured response, S11m, at each
frequency.
This is the 1port error model equation solved for S11a. Since we have the three errors
and S11m for each test frequency, we can now compute S11a.
For reflection measurements on twoport devices, the same technique can be applied, but
the test device output port must be terminated in the system characteristic impedance.
This termination should be at least as good (low reflection coefficient) as the load used
to determine directivity. The additional reflection error caused by an improper
termination at the test device output port is not incorporated into the 1port error
model. 10.4 2PORT MODEL Now consider measurement of transmission coefficients (magnitude and phase) of an
unknown twoport device. The major sources of error are Tracking, Source Match, Load
Match, and Isolation. These errors are reduced or eliminated using the 2port error model.
Transmission coefficient is measured by taking the ratio of the incident voltage wave
(I) and the transmitted wave (T). Ideally, (I) consists only of power delivered by the
source and (T) consists only of power emerging at the test device output. As for the reflection model, source match can cause the incident signal to vary as a
function of test device S_{11A}. Also, since the test setup transmission return
port is never exactly the characteristic impedance, some of the transmitted signal is
reflected from the test set port 2, and other mismatches between the test device output
and the detector, to return to the test device. A portion of this wave may be rereflected
at port 2, thus affecting S_{21M}, or part may be transmitted through the device
in the reverse direction to appear at port 1, thus affecting S_{11M}. This error
term, which causes the magnitude and phase of the transmitted signal to vary as a function
of S_{22A}, is called load match, E_{LF.} The measured value S_{21M}, consists of wave components which vary as a
function of the relationship between E_{SF} and S_{11A} as well as E_{LF}
and S_{22A}, so the input and output reflection coefficients of the test device
must be measured and stored for use in the S_{21A} error correction calculation.
Thus, the test setup is calibrated as described above for reflection to establish
directivity, E_{DF}, source match, E_{SF}, and reflection tracking, E_{RF},
terms for the reflection measurements. Since we now have a calibrated port for reflection measurements, we connect the thru'
and determine load match, E_{LF} by measuring the reflection coefficient of the
thru connection. Transmission tracking is the measured with the thru connection. The data is corrected for source and load match effects, and stored as transmission tracking, E_{TF}. Isolation, E_{XF}, represents the part of the incident wave that appears at the
receiver detectors without actually passing through the test device. Isolation is measured
with the test set in the transmission configuration and terminations installed at the
points at which the test device will be connected. The microwave test set as installed in the Bath University Microwave research
laboratory (HP8515A) can measure both the forward and reverse characteristics of the test
device without the need to manually remove and physically reverse it. For these test sets,
the Full 2port transmission and reflection error model shown above includes terms for: Directivity, E_{DF} (forward) and E_{DR} (reverse) Isolation, E_{XF} and E_{XR} Source Match, E_{SF} and E_{SR} Load Match, E_{LF} and E_{LR} Transmission Tracking, E_{TF} and E_{TR} Reflection Tracking, E_{RF} and E_{RR} Thus there are two sets of error terms, one for each of forward and reverse, with each
set consisting of six error terms. If the test set cannot switch between forward and reverse directions, then the reverse
terms can not be measured directly and the forward error terms are used in their place
when the test device is manually reversed. The Onepath 2port error model makes this
assumption. Below are shown the 2port error model equations for all Sparameters of a two port
device. Note that the mathematics for this comprehensive model uses all forward and
reverse error terms and measured values. Thus to perform full error correction, for any
one parameter of a twoport device, all four Sparameters must be measured.

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