RF/uW Measurement Uncertainty: Calculate, Characterize ... · PDF fileStandard & Relative Measurement Uncertainty ... - Use torque wrench and torque as specified ... Agilent recommends

© 2013 Agilent Technologies

Aerospace & Defense Symposium

RF/uW Measurement Uncertainty: Calculate, Characterize, Minimize

Antonio Castro, Agilent Technologies



2 © 2013 Agilent Technologies


Measurement Uncertainty

Measurement Uncertainty is an important but often ignored or not well characterized parameter when making signal measurements.

Applications when Measurement Uncertainty is important:

1. Measured value is near specification of the instrument.

2. Mismatch between device under test (DUT) and test equipment.

3. Signal amplitude measurement near noise level.

4. Measurements under different test setup.





What is Measurement Uncertainty?

Uncertainty of a measurement is defined as a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measured value.

If the measured value is represented as P, then

the measurement uncertainty interval extends

from P – u to P + u.

u = Measurement Uncertainty

P = Measured Value

The measurement uncertainty interval is defined

as

P ± u




Aerospace & Defense Symposium Page 4

The ISO Process/Method

A standardized method to determine measurement uncertainty • ISO/IEC 17025 – General Requirements for the Competence of

Calibration and Testing Laboratories

• ANSI/NCSL Z540-2-1997 – U.S. Guide to the Expression of

Uncertainty in Measurement

Application of the ISO Method • Production line measurements to meet specifications.

• Device characterization by metrology laboratories.

• Test equipment calibration by metrology laboratories.

• R&D feasibility studies.



Page 5

Measurement Uncertainty in our Measurement Process





Definitions Related to Specifications

Specification - Describe the performance of parameters covered

by product warranty over a temperature range, i.e. 0 to 55°C.

95th Percentile Values - Indicate the breadth of the population

(≈2σ) of performance tolerances expected to be met in 95% of

the cases with a 95% confidence, for a given ambient

temperature, usually 20 to 30°C.

Typical Values – Describe additional product performance

information that is not covered by the product warranty. It is

performance beyond specification that 80% of the units exhibit

with a 95% confidence level over a temperature range, usually

20 to 30°C.

Nominal Values – Indicate expected performance, or describe

product performance that is useful in the application of the

product, but is not covered by the product warranty.



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Standard & Relative Measurement Uncertainty

Relative Uncertainty is defined as the standard uncertainty of measurement divided by the true value of the measurand. In practice, the true measurand value (or quantity of interest) is estimated.

u(y)

y = Measurement Uncertainty

Standard Uncertainty, u(y), is

defined as the uncertainty of

measurement expressed as a

standard deviation.





Categories of Measurement Uncertainty

ISO • Type A – Can be quantified with statistical methods

• Type B – Determined with other methods usually based on prior

information

Engineering (Hardware Perspective) • Mismatch Uncertainty

• Instrumentation Uncertainty

Other Categories (We avoid using) • Systematic

• Random





Mismatch Uncertainty

Mismatch affects the accuracy of measurements made using

RF, uW, and mmW equipment and components such as power

meters, signal analyzers, noise figure meters, network

analyzers, high frequency oscilloscopes, signal generators,

attenuators, couplers, cables and adapters.

The measurement uncertainty due to mismatch is often a major

component of the total uncertainty for RF, uW, and mmW

measurements.



10

Sensor and Source Mismatch

Signal

Source Power Sensor Power Meter

Ideal impedance = Z0

Impedance Z0

VSWR

Z0

Impedance Z0


Transmission Line with

Impedance = Z0





Mismatch from Two Reflection Coefficients

ρ1

ρ2

ρ1 = 0.05

ρ2 = 0.5

Worst Mismatch

Uncertainty

±0.2-dB





Reducing One Reflection Coefficient

Controlling mismatch uncertainty is as simple as reducing the

reflection coefficient on any transmission lines or components

that are part of the test arrangement. Assuming that equipment

with the lowest practical VSWR has been selected, many other

simple measures can be taken to ensure that the performance

of the test system does not become degraded.





Techniques to Reduce Mismatch Uncertainty

Simple Techniques • Select test equipment with lowest VSWR

• Keep cable lengths as short as possible

• Cables, Connectors, and Adapters:

- Select appropriately, keep clean

- Use torque wrench and torque as specified

- Minimize number of adapters

- Do not use dissimilar families of connectors





Techniques to Reduce Mismatch Uncertainty

Advanced Techniques

• Use an attenuator (pad) - Return loss of attenuator is better than original source or load

- Place at end of the line with the worst return loss

- Increase generator level, if needed

• Use a leveling loop to improve the effective source/line matching - Requires a two-resistor power splitter or a directional coupler,

power sensor/meter





Standard Uncertainty of Mismatch Model

Uniform

Fixed

Rayleigh





Rayleigh Distribution

Probability density of the magnitude

of the reflection coefficient is

Rayleigh distributed if the probability

density of both complex parts is

Gaussian distributed

Real

Imaginary





Mismatch Uncertainty Examples

Reflection Coefficient for 26.5-GHz PXA • Bands 1 – 4

• Preamp On

• 0-dB Attenuation

By inspection, the level that exceeded 5% of the frequency

points is: SWR = 1.6. Hence, Γ95 = 0.23.

The probability density of the magnitude of the reflection

coefficient (or VSWR) is Rayleigh distributed for all X-Series

signal analyzers, sources, and power sensors. This is very

useful information. There is no need to characterize and model.





Example: Obtaining Magnitude and Phase

Information for Г

Known magnitude and phase information for Г of a given sample

determines its distribution characteristic. • Measure S11 (magnitude and phase) with network analyzer

• At each frequency point of interest, set the signal analyzer to zero

span and measure S11 with network analyzer using a marker at the

tuned frequency of the signal analyzer.

• Network analyzer should be calibrated over frequency range of

interest. Its settings should not change while data acquisition.





X-Series Analyzer Reflection Coefficient

X-Series analyzers have a reflection coefficient that is well modeled

with a Rayleigh probability distribution.

Agilent recommends using the methods outlined in Application Note

1449-3 and companion Average Power Sensor Measurement

Uncertainty Calculator to compute mismatch uncertainty.

Use the 95th percentile VSWR information and the Rayleigh model

(Case C or E in the application note) with that process.





Mismatch Uncertainty Examples

The observed Γ95 is 0.0219.

Reflection Coefficient for 8481A

Power Sensor

• Frequency Range: 0 to 8 GHz

Estimate Γ95 from Γmax

• Γmax = 0.0826

• Γ95 = 0.712 Γmax

• Γ95 = 0.0588

Estimate Γ95 from Γmean

• Γmean = 0.014

• Γ95 = 1.953Γmean

• Γ95 = 0.0273





Instrumentation Uncertainty

Now, we are going to switch our attention to the

instrumentation uncertainty

• This is the uncertainty inherited to each measurement instrument

• Lets consider the following instruments

- Signal analyzer

- Power Sensor

- Power Meter





Signal Analyzer Block Diagram

0-3.6 GHz low band

3 Hz-50 GHz

Input

Cal input

2 dB-step mech atten μW converters

8.3-17 GHz LO

10.9M

.3M

4.8 GHz LO

RF converter

3.8-8.73 GHz LO

Ext. Mixing

FPGA

300 MHz LO

200 MHz CK

100 MHz CK

ADC

ADC

Switched filters,

F0=22.5 MHz

X1 3.6 - 17.1

GHz

X2 17.0 - 34.5

GHz

X4 34.4 – 50

GHz

140 MHz

3.5-50 GHz high band

FPGA

160 MHz

Front End

Swept IF & 10 MHz BW

& 25 MHz BW (option B25)

25 MHz

966K

303K

79K

9K

Switched filters,

F0=322.5 MHz

160 MHz BW (option B1X)

30 2 2 6 10 20

RF preamp

40 MHz

400 MHz CK

40 MHz BW (option B40)

ADC

F0=250 MHz

F0=300 MHz

F0=322.5 MHz

Linearity

Corrections

Low noise path

(LNP)

μW preamp

YIG filter

1 dB-step electronic atten

F0= 5.1225 GHz

4 GHz

ASIC

2Gbyte

SDRAM

ASIC

2Gbyte

SDRAM

MPB





Switching Uncertainty of Signal Analyzer




Aerospace & Defense Symposium Page 24

Reduce Overall Measurement Uncertainty

from a Signal Analyzer

Minimize changes when making a measurement • Before taking any data, step through a measurement to see if any

controls can be left unchanged.

- Input attenuation (mechanical and electronic)

- Resolution bandwidth

Allow signal analyzer to run Alignments

Characterize signal analyzer • Use a calibration signal closer to the frequency of interest

• Use a leveling loop (power splitter and power sensor/meter)

Improve sensitivity when measuring low level signals

Add a well-matched pad (attenuator) to the analyzer input to

reduce mismatch uncertainty



25

Sources of Power Measurement Uncertainty

• Sensor and Source Mismatch Errors

• Power Sensor Errors

• Power Meter Errors

Mismatch

Sensor

Meter



26

Power Sensor Uncertainties

Various sensor

losses

DC

Power

Sensor

Power Meter

P r

Element

P i P in

Cal Factor : h e

P K

b = in

P i

(he = Effective Efficiency)

• Printed on sensor label (8480 series)

• Stored in EEPROM (E-series and P-series)



27

Power Meter Instrumentation Uncertainties

Power

Reference

Uncertainty

Instrumentation Uncertainty



28

Calculating Measurement Uncertainty Using ISO Model

Identify significant uncertainties sources • Mismatch and Instrumentation

Estimate measurement uncertainty from each source • Type A (statistically) or Type B (known information)

• Use appropriate divisor for each distribution

Combine uncertainties and determine expanded uncertainty • Worst-case (Very Conservative)

- All sources of error at their extreme values

- Errors add constructively

• Root Sum of the Squares (RSS) method



29

Calculation of Uncertainty using ISO Method

Signal Source

Power Sensor Power Meter


Impedance Z0

VSWR

Instrument Uncertainty Mismatch Uncertainty

E4418B E9300A

Measurement Conditions: 2-GHz at -13-dBm



Calculation of Uncertainty using ISO Method

30

Rayleigh

Uniform

0.21%

1.8%

3.6%



31

References

AN 1316: Optimizing Spectrum Analyzer Amplitude Accuracy

AN 1286-1: 8 Hints for Better Spectrum Analysis

AN 1303: Spectrum Analyzer Measurements and Noise

AN 1449: Fundaments of RF and Microwave Power

Measurements

White Paper: Revisiting Mismatch Uncertainty with the

Rayleigh Distribution

AN 1408-20: High-Accuracy Noise Figure Measurements

Using the PNA-X Series Network Analyzer

AN 1408-21: Active Device Characterization in Pulsed

Operation Using the PNA-X

Documents

RF/uW Measurement Uncertainty: Calculate, Characterize ... · PDF fileStandard & Relative Measurement Uncertainty ... - Use torque wrench and torque as specified ... Agilent recommends