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Mismatch Uncertainty Calculator: A Microwave Freeware Software Tool
1
M
ARCH
A
PRIL
1998
THE INTERNATIONAL JOURNAL OF METROLOGY
Microwave measurement parameters required to verify
the operational performance of modern microwave test
and measurement equipment spans from simple to
complex. Typically these parameters deal with signal
integrity and signal spectral purity. Signal integrity
measurements can range from amplitude accuracy to
modulation index. Spectral purity measurements may be
evaluated in terms of waveform harmonic content, phase
noise, etc. Uncertainties abound when evaluating
microwave measurement parameters and one must be
reasonably certain that measurement results incorporate
all applicable uncertainties in order to establish a units
true performance.
One such measurement scenario is in the verification
of RF power and attenuation. Mismatches and reflections
are uncertainty components that must be considered in
order to determine uncertainties on the actual RF power
and attenuation measurements. It was during a National
Voluntary Laboratory Accreditation Program (NVLAP)
proficiency test for initial accreditation in the
electromagnetic RF/ microwave discipline that the author
developed the Mismatch Uncertainty Calculator. This
program, written for Windows95, proved very
beneficial in performing mismatch uncertainty
calculations used in determining test artifacts values.
The authors laboratory NVLAP proficiency test was
based on the measurement of microwave scattering
parameters (s-parameters) for three coaxial, N-type RF
attenuators of 10 dB, 20 dB and 50 dB. The s-parameters
of interest were S11 (input reflection coefficient), S22
(output reflection coefficient) and S21 (forward
transmission coefficient).
The attenuators were evaluated at discrete frequencies
from 100 MHz through 18 GHz. The S21 parameters were
established using a synthesized microwave generator and
RF measurement receiver equipped with an N-Type RF
power sensor. The S11 and S22 parameters were
established using a scalar network analyzer. The S11
parameters were also obtained using the scalar network
analyzer for the RF power sensor and the microwave
source for the frequencies of interest. This information
was entered into the Mismatch Uncertainty Calculator to
derive mismatch uncertainties.
Measurement Options
The Mismatch Uncertainty Calculator allows four
measurement scenarios:
1. Single Port
2. Load Power/Available Power
3. Load Power/Z0 Power
where: Z0 = characteristic impedance
4. Source to DUT to Load
where: DUT = device under test
Each measurement scenario requires port information
in terms of either return loss, reflection coefficient (p) or
standing wave ratio (SWR). Selecting a known port
parameter is done using the MUCs top right Option
button (Fig. 1). Selecting a measurement scenario is done
using the Measurement Option dropdown listing.
Selecting a measurement option will display the
appropriate data entry boxes as well as associated results
boxes.
All data entries must be in terms of the selected known
port parameter (use of the Single Port measurement
option allows conversion of data to the same parameter).
The resolution used for computing and displaying results
is selected using the Resolution dropdown listing. The
MUC uses scientific notation for all displayed results, even
though entries may be in general numeric format. Entries
Mismatch Uncertainty Calculator:
A Microwave Freeware Software Tool
Christopher L. Grachanen
Compaq Computer
Uncertainties abound when evaluating microwave measurement parameters and one must be reasonably
certain that measurement results incorporate all applicable uncertainties in order to establish a units true
performance. A software tool developed at Compaq Computer may provide some assistance in calculations
for mismatch uncertainty.
Download Mismatch Uncertainty Calculator by visiting our web page at
http://www.callabmag.com
2
M
ARCH
A
PRIL
1998
THE INTERNATIONAL JOURNAL OF METROLOGY
and calculated results may be printed using the Print
command or transferred to the Windows Write program
for printing and archiving using the Write command
(see Fig. 2 for DUT example). The Clear command
erases all entries and sets the MUC to default conditions.
Clicking any calculated result will copy that result to
the Windows Clipboard where it may be pasted in another
program or document. The ? command provides a
quick summary of the calculations used as well as
provides information for registering a copy of the
Mismatch Uncertainty Calculator and contacting the
author with questions and suggestions.
The single port measurement option provides a
convenient means for converting between return loss,
reflection coefficient, and SWR. The core calculations used
for the single port and other measurement scenarios are
as follows:
Return Loss (RL)
-20 Log (p)
SWR
(1+p)/(1-p)
Reflection Coefficient (p) (SWR-1)(SWR+1) or
10^(return loss/-20)
Mismatch Loss
-10 Log (1-p^2)
Load Power/Available Power
Measurement
The load power/available power measurement option
is for a two port, source-to-load configuration. This option
is used to calculate power at the load relative to the
available power at the source. This measurement scenario
is commonly employed in amplifier design work. Load
power/available power calculations take into con-
sideration double reflections, which are computed as
follows:
Double Reflections
20 Log (1
±
ps * pd)
where:
ps = source port reflection coefficient
pd = Load port reflection coefficient
The upper and lower limits for load power/available
power is as follows:
Upper Limit
10 log [(1-ps^2)*(1-pd^2)/((1-ps * pd)^2)]
Lower Limit
10 log [(1-ps^2)*(1-pd^2)/((1+ ps * pd)^2)
The load power/available power worst case upper and
lower limits are calculated and given in dB units as are
their equivalent percentages.
Load Power/Z0 Power Measurement
The Load Power/Z0 Power Measurement option is also
for a two-port, source-to-load configuration. This
measurement scenario describes the following typical
situation: If the load is a calibrated power meter which
reads in W dBm, then the source will deliver W
±
dBm to a
Z0 load. The upper and lower limits in the W dbm reading
being attributable to mismatch errors. Load power/Z0
power limit calculations are as follows:
Upper Limit
10 log [(1-pd^2)/((1-pd*ps)^2)]
Lower Limit
10 log [(1-pd^2)/((1+ pd*ps)^2)]
The load power/Z0 power measurement option is a
convenient means for calculating power for either a
perfect load or perfect source. Entering either the source
Figure 1. Mismatch Uncertainty Calculator allows port parameter selection using the Option Button.
M
ISMATCH
U
NCERTAINTY
C
ALCULATOR
: A M
ICROWAVE
F
REEWARE
S
OFTWARE
T
OOL
C
HRISTOPHER
L. G
RACHANEN
3
M
ARCH
A
PRIL
1998
THE INTERNATIONAL JOURNAL OF METROLOGY
data as zero or the load data as zero (but not both) will
provide this calculation.
Source-to-DUT-to-Load Measurement
The source to DUT to load measurement option is for a
two-port, source to load configuration with a DUT
inserted between the ports. It is assumed that the DUT is
a bilateral two-port device identical forward transmission
coefficient (S21) and reverse transmission coefficient (S12).
Examples of such devices are transmission lines, tuners,
directional couplers, attenuators, connectors and filters.
(Amplifiers, ferrite isolators and mixers are example of
devices that are unilateral.) Source to DUT to load
calculations requires the DUTs insertion loss be entered
in dBs. Source to DUT to load calculations are as follows:
Source to DUT to Load
20 log [a/(bc
±
d)]
For:
a = 1
±
ps *pd
b = 1 -/+ ps * p1
c = 1 -/+ pd * p2
d = ps * Tf * Tr * pd
Where: p1 is DUT reflection coefficient port at source
p2 is DUT reflection coefficient port at load
Note: For a bilateral 2 port device, Tf=Tr= 10^(-Insertion
Loss/20)
The Source to DUT to Load measurement option was
the option used in determining test artifact values for the
authors NVLAP proficiency tests (MUC Source to DUT
to Load printouts were submitted as part of the summary
test results).
Generic Calculations
The Mismatch Uncertainty Calculator also performs the
following generic calculations:
· dB to a percentage (power)
· a (power) percentage to a dB
· dbm to mW (1mW Ref.)
· mW to dbm (1mW Ref.)
Note: the dB to a percentage (power) option is used for
computing percentage limits from dB limits as follows:
Percentage (power) = 100 * [ (10^(dB/10) )-1]
Mismatch Calculator Download Sites
The Mismatch Uncertainty Calculator is a FREEWARE
software program and as such may be freely copied and
distributed (without modification) with no cost. This
program, and similar FREEWARE programs Tolerance
Calculator 3.0 and Uncertainty Calculator 2.1 (new for
1998), may be downloaded (or soon to be added for
downloading) from the following websites:
Cal Lab Magazine
www.callabmag.com
Fluke Corporation
www.fluke.com
H