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Slide 1 0 RF & Microwave Fundamentals Jan 2006 Anritsu Korea

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Slide 2 0 Basic Fudamentals Definition of Terms Definition of Terms What Does RF Mean? What Does RF Mean? Basic Concepts Basic Concepts Transmission Lines Transmission Lines Coaxial Cable Coaxial Cable Waveguide Waveguide Transmission Line Theory Transmission Line Theory Transmission measurements and error analysis Transmission measurements and error analysis Return Loss measurements and error analysis Return Loss measurements and error analysis Advanced Measurement Techniques (air lines) Advanced Measurement Techniques (air lines) S Parameters & VNA measurement fundamentals S Parameters & VNA measurement fundamentals Common Microwave Devices and measurements Common Microwave Devices and measurements Synthesizer related RF Concepts Synthesizer related RF Concepts

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Slide 3 0 Electromagnetic Spectrum l RF Radio Frequency. A general term used to describe the frequency range from 3 kHz to 3.0 GHz (Gigahertz ) l Microwave. The frequency range 3GHz to 30.0 GHz. Above 1 GHz, lumped circuit elements are replaced by distributed circuit elements. l Millimeter wave. The frequency range 30 GHz to 300 GHz. The corresponding wavelength is less than a centimeter.

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Slide 4 0 Range of RF Frequencies l Medium Frequency (300 KHz - 3 MHz) l High Frequency (HF) ( MHz) l Very High Frequency (VHF) ( MHz) l Ultra High Frequency (UHF) ( MHz)

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Slide 5 0 Some Terms You Will Hear l dB l dBm l Impedance l Return Loss (RL) l Insertion Loss (Cable Loss) l VSWR l DTF l Watts

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Slide 6 0 Linear vs Log l Some things are very, very large. l Some things are very, very small. It is difficult to express comparison of sizes in common units of measure with a linear scale. It is difficult to express comparison of sizes in common units of measure with a linear scale. One would not usually express a flea’s dimensions in miles, for example. One would not usually express a flea’s dimensions in miles, for example.

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Slide 7 0 Bel l A bel is defined as the logarithm of a power ratio. P o P o bel = log P i P i

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Slide 8 0 Decibel (dB) l Decibel (dB) is a logarithmic unit of relative power measurement that expresses the ratio of two power levels. P o P o dB = 10 log P i P i

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Slide 9 0 dBm l dBm is the decibel value of a signal compared to 1 m w.

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Slide dB rule l +3 dB means double the power (multiply by 2) l - 3 dB means halve the power (divide by 2)

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Slide 11 0 Power Conversion Table Power Conversion Table l Some common decibel values and power- ratio equivalents.

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Slide 12 0 Basic Concept Wavelength ( ) Length

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Slide 13 0 Wavelength ( ) V C ( ) = ε r f ε r f Where: V C = velocity of propagation through air ε r = relative dielectric constant ε r = relative dielectric constant f = frequency of oscillation f = frequency of oscillation

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Slide 14 0 Velocity of Propagation l Electromagnetic energy travels at the speed of light.

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Slide 15 0 Time Domain and Frequency Domain

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Slide 16 0 Transmission Line Theory Must be applied when line lengths are > ( / 4 ) Must be applied when line lengths are > ( / 4 ) Standard lumped-circuit analysis can be applied when the line lengths are << ( / 4 ) Standard lumped-circuit analysis can be applied when the line lengths are << ( / 4 )

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Slide 17 0 Impedance l The impedance of a transmission line can be complex Z = R ± jX If X is positive, it is called the inductive reactance If X is negative, it is called capacitive reactance Impedance plot in a rectangular coordinate

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Slide 18 0 Different Types Transmission Line There are many different types of transmission lines and we will talk about three of them. Coaxial Waveguide Microstrip

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Slide 19 0 Coaxial Cable

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Slide 20 0 Waveguide l Waveguide is a hollow, conducting tube, through which microwave frequency energy can be propagated.

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Slide 21 0 Microstrip Transmission Line

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Slide 22 0 Characteristic Impedance of Coax For a lossless line R=G=0

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Slide 23 0 Characteristic Impedance Z 0 = (138/ ε R ) Log (D/d)

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Slide 24 0 Propagation Modes of Coax l Patterns set up by electric and magnetic fields.

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Slide 25 0 Cutoff Frequency l The lowest frequency at which the next higher order mode can propagate is called the cut-off frequency of the next higher order mode.

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Slide 26 0 Velocity of Propagation In free space C = 3x10 8 m/sec Wavelength = λ = C/f Where f = frequency (Hz) Z

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Slide 27 0 Relative Velocity Constant (k) k = (1/ ε R ) for Teflon: ε R = 2.04 k = (1/ 2.04) = 0.7

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Slide 28 0 Phase of The Signal at One Wavelength The phase of the signal at one wavelength intervals along the line will be in phase. In this instance λ 0 is 21 cm at 1 GHz.

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Slide 29 0 Well Matched Transmission Line If Z 0 = Z L then P 0 = P L No reflection Therefore P L = P I

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Slide 30 0 Poorly Matched Transmission Line If Z L ≠ Z 0 then P L ≠ P I Reflection is present Therefore P L = P I - P R

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Slide 31 0 Example Short at the end of the line

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Slide 32 0 SWR Vs Impedance Z L 0, Z L and Z L Z 0

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Slide 33 0 VSWR l Voltage Standing Wave Ratio (VSWR) E max E R + E I E max E R + E I l VSWR = = E min E R - E I E min E R - E I E R E R (reflection coefficient) = (reflection coefficient) = E I E I

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Slide 34 0 Reflection Terms & Relationships

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Slide 35 0 Reflection

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Slide 36 0 Reflection Coefficient l Reflection coefficient is the ratio of the reflected signal to the incident signal. Z L - Z 0 Z L - Z 0 E R /E i = = | | = Z L + Z 0 Z L + Z 0

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Slide 37 0 Mismatch Mismatch is a measure of the efficiency of power transfer to the load. The percentage of the power reflected from the Load. 0 dB return loss or infinite VSWR indicate perfect reflection by the load. Infinite return loss or unity VSWR indicate perfect transmission to the load. perfect transmission to the load.

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Slide 38 0 Basic Measurements Transmission Loss/Gain = P out /P in Return Loss = P reflected /P in

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Slide 39 0 Transmission Measurement l Combining Signals

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Slide 40 0 Calculating dB Difference

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Slide 41 0 Power Gain Gain is the ratio of the output power level of an amplifier to the input power level to that amplifier. Gain is the ratio of the output power level of an amplifier to the input power level to that amplifier. P o P o Gain = Gain = P i P i

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Slide 42 0 Transmission Measurement (Loss/Gain Measurement) l Transmission Power Gain = 20 log (V o /V i )

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Slide 43 0 Making a Transmission Measurement l Measure incident power going into the device. l Measure the output power coming out of the device. l The difference in power is transmission loss (or gain).

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Slide 44 0 Measure Incident Power Using detector directly on the test port. Using detector directly on the test port.

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Slide 45 0 Measure Output Power

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Slide 46 0 Transmission Measurement Errors Calibration ErrorCalibration Error Test Port MatchTest Port Match Detector MatchDetector Match Using AdaptersUsing Adapters

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Slide 47 0 Calibration Error

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Slide 48 0 Determining Calibration Error

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Slide 49 0 Test Port Match Error

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Slide 50 0 Detector Match Error

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Slide 51 0 Calculating the Errors

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Slide 52 0 Error Calculation

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Slide 53 0 Error Example

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Slide 54 0 Error Calculation

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Slide 55 0 Maximum Effect

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Slide 56 0 RSS

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Slide 57 0 Total Error

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Slide 58 0 What happens when you add an adapter?

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Slide 59 0 Example 1

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Slide 60 0 Example 2

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Slide 61 0 Improving Transmission Loss Measurements l Use detectors with better match. l Use attenuator pads or isolators between test port and DUT and detector and DUT to diminish magnitude of the error signals.

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Slide 62 0 Return Loss b Return Loss Measurements b Uncertainty analysis

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Slide 63 0 Return Loss Measurements Problem: How do you separate reflected signal from incident signal

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Slide 64 0 Solution to R L Measurements l Solution: Directional Devices l Definition:A directional device is able to separate either the incident or the reflected signal from the environment where both exist.

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Slide 65 0 Solution to RL Measurements Directional Devices: Couplers (Coaxial and Waveguide), Bridges, Autotesters

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Slide 66 0 Making a Return Loss Measurement Two requirements when measuring return loss Separation of incident and reflected signal Establish a 100% reflection reference

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Slide % Reflection Reference For COAX two references exist: Open circuit Short circuit They are 180° out of phase They are 180° out of phase For Waveguide two reference can be used short circuit and offset short

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Slide % Reflection Reference The Average of an Open & Short represents a “true” 100% reflection.

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Slide 69 0 Return Loss Block Diagram

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Slide 70 0 Errors to Consider DirectivityDirectivity Test port matchTest port match Termination errorTermination error

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Slide 71 0 Calculating Directivity Directivity = 20 log ( V in / V out ) dB Example: V in = 1 Volt, and V out = 10mV Directivity = 20 log ( 1/.01) = 40 dB

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Slide 72 0 Test Port Match

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Slide 73 0 Termination Error Errors in Return Loss Termination Error: The additional reflection that an imperfect termination causes.

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Slide 74 0 Termination Error

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Slide 75 0 Calculating the Errors Directivity Error + Test Port Match Error + Test Port Match Error + Termination Error + Termination Error? Do it exactly the same way as you did transmission loss.

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Slide 76 0 Calculating the Errors Calculate how far below the desired signal the error signal is (in dB). Convert the dB into linear (reflection coefficient) form. Use reflection chart or calculate. E = log -1 [ -dB error/20] For worst case, add up all linear terms. Sum = E1 + E2 + E3

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Slide 77 0 Calculating the Errors l Effect on the measurement is the linear sum adding in phase or subtracting out of phase from the nominal return loss of the device under test. Measurement = DUT ± SUM In dB, meas. Max = - 20 log [ DUT - SUM ] Min = - 20 log [ DUT + SUM ] Min = - 20 log [ DUT + SUM ]

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Slide 78 0 Error Signal Return Loss (Reflection)

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Slide 79 0 Calculating the Errors AutotesterDUT Directivity = 40 dB (.01 )Input/Output Match = 15 dB(.178 ) Test Port = 20 dB (.1 )Insertion Loss = 1 dB TerminationDetector Return Loss = 40 dB (.01 )Return Loss = 20 dB (.1 )

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Slide 80 0 Return Loss Measurement Errors With Termination Errors: A) 2(I.L.) + Termination 2 dB + 40 dB = 42 dB(.008 ) 2 dB + 40 dB = 42 dB(.008 ) B) 2 (DUT) + Test Port B) 2 (DUT) + Test Port 30 dB + 20 dB = 50 dB(.0032 ) C) Directivity = 40 dB(.01 ) C) Directivity = 40 dB(.01 ) Total Error =

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Slide 81 0 Measured Results For Using Termination DUT =.178 (15 dB) (1.43 SWR) DUT =.178 (15 dB) (1.43 SWR) Plus Total Error .199 = (14.02 dB) ( 1.50 SWR) DUT =.178 (15 dB) (1.43 SWR) DUT =.178 (15 dB) (1.43 SWR) Minus Total Error .157 = (16.08 dB) (1.37 SWR).157 = (16.08 dB) (1.37 SWR)

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Slide 82 0 Measured Results For Using Detector With Detector (as termination) A)2 (I.L.) + Detector 2 dB + 20 dB = 22 dB(.079 ) B)2(DUT) + Test Port = 50 dB(.0032 ) C)Directivity = 40 dB(.01 ).092 Measured Results DUT + Total Error.178 =.270 (11.37 dB) (1.74 SWR) DUT - Total Error.178 =.086 (21.31 dB) (1.19 SWR)

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Slide 83 0 Error Signals Directivity = 40 dB Test Port Match = 20 dB Test Port Match = 20 dB Adapter = 36 dB Adapter = 36 dB DUT = 15 dB DUT = 15 dB A- Effective Directivity Directivity = 40 dB (.01 ) Adapter = 36 dB (.0158 ) Minimum Effective Directivity Autotester = 40 dB =.01 Plus Adapter Error .0258 = dB.0258 = dB B- Effective Test Port Match Autotester = 20dB = (.1 ) Adapter = 36 dB = (.0158) Minimum Effective Test port Match Autotester = 20dB =.1 Plus Adapter error .1158 = dB.1158 = dB

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Slide 84 0 Input Match Errors Due to Sweeper Output and SWR Autotester Input Match Effective Input Match dB dB Sweeper Input Match 16 =.159 Autotester Input Match 20 =.10 Effective Input Match = 11.7 dB dB Effective Input IL = 6.5 dB

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Slide 85 0 Input Match Error Signal Error = DUT + IL + Input + IL + DUTdB 15 dB dB dB + 15 dB dB dB dB + 15 dB Error Analysis dB Directivity =40 =.01 Test Port 2(DUT) + Test Port =50 =.0032 Input =54.7 = Total Error DUT = 15 dB =.178 Plus Error = dB.1931 = dB DUT = 15 dB =.178 Minus Error = dB.1630 = dB

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Slide 86 0 Example 3

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Slide 87 0 Example 4

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Slide 88 0 Have We Forgotten Something? l Instrumental Errors l Connector Repeatability

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Slide 89 0 Instrumental Errors l Signal source harmonics l Network Analyzer/Detector deviation from logarithmic response (.01 dB per dB of measurement) l Readout Error (manual.03 to.1 dB, automated.01 dB) l Signal source power and frequency stability

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Slide 90 0 Connector Repeatability APC-7Typically±0.02 dB NTypically±0.03 dB SMATypically±0.04 dB KTypically±0.035 dB VTypically±0.045 dB

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Slide 91 0 Summary

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Slide 92 0 S Parameters & VNA Measurement Fundamentals

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Slide 93 0 S Parameters Port 1Port 2 a1a1 b2b2 a2a2 b1b1 S 11 FORWARD REFLECTION S 22 REVERSE REFLECTION DUT S 21 FORWARD TRANSMISSION S 12 REVERSE TRANSMISSION

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Slide 94 0 S Parameters

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Slide 95 0 S Parameters Defined S 11 = Forward Reflection (b 1 /a 1 )S 11 = Forward Reflection (b 1 /a 1 ) S 21 = Forward Transmission (b 2 /a 1 )S 21 = Forward Transmission (b 2 /a 1 ) S 22 = Reverse Reflection (b 2 /a 2 )S 22 = Reverse Reflection (b 2 /a 2 ) S 12 = Reverse Transmission (b 1 /a 2 )S 12 = Reverse Transmission (b 1 /a 2 ) All are Ratios of two signals - (Magnitude and Phase)All are Ratios of two signals - (Magnitude and Phase)

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Slide 96 0 Diagram for S-Parameters

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Slide 97 0 Impedance Components The relationship between the reflection coefficient and the impedance on a transmission line

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Slide 98 0 Smith Chart

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Slide 99 0 Impedance Components The impedance components in the Smith chart are: l The resistive components l The reactive components A- Inductive B- Capacitive

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Slide Constant Resistance Circles

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Slide Inductive Reactance Circles

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Slide Capacitive Reactance Circles

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Slide Using Smith Chart

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Slide What’s the difference between a VNA and a Scalar Analyzer? A Vector Network Analyzer not only measures the magnitude of the reflection or transmission, but it also measures its PHASE.A Vector Network Analyzer not only measures the magnitude of the reflection or transmission, but it also measures its PHASE. A Scalar Network Analyzer uses a diode to convert energy to a DC voltage. It can only measure magnitude with limited dynamic range.A Scalar Network Analyzer uses a diode to convert energy to a DC voltage. It can only measure magnitude with limited dynamic range. A Vector Analyzer uses a tuned receiver followed by a quadrature detector, so phase can be measured. Ratio measurements and the benefits of the heterodyne process all contribute to over- all accuracy and dynamic range.A Vector Analyzer uses a tuned receiver followed by a quadrature detector, so phase can be measured. Ratio measurements and the benefits of the heterodyne process all contribute to over- all accuracy and dynamic range.

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Slide What is phase? t These two signals have the same magnitude but are 90 degrees out of phase!

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Slide Phase Using phase information, one can calculate the electrical delay through a device.Using phase information, one can calculate the electrical delay through a device. Analyzing the variation of phase shift through a device with respect to frequency, one can calculate group delay.Analyzing the variation of phase shift through a device with respect to frequency, one can calculate group delay. Group delay is one cause of distortion in voice transmission and bit errors in digital transmission systems.Group delay is one cause of distortion in voice transmission and bit errors in digital transmission systems.

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Slide What happens when two equal signals which differ by 180 degrees are summed? b b The resultant depends on their relative amplitudes b b If the amplitudes are equal - They completely b b cancel - b b This is not hypothetical - When a full reflection b b occurs at the end of a transmission line, all of the b b incident energy is reflected back to the generator b b This causes high standing waves b b Depending where you “look” along the line, b b you could see ZERO or Twice the loaded Voltage !!

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Slide How does a VNA display the S-parameters? Log Magnitude and Phase

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Slide Another VNA Display Mode Smith Chart

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Slide VNAs and Calibration

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Slide VNA Test Set and Source a1 a1 b1 b1 b2 b2 DUT a2 a2 Rear Panel Reference Loops* Port 1Port 2 Transfer Switch 40dB Step Attenuator** 4 Samplers Coupler Source Power divider

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Slide Without calibration a VNA cannot make accurate measurements b Calibration means removing errors b Types of errors to deal with: Random Errors (i.e. Connector Repeatability)Random Errors (i.e. Connector Repeatability) –Cannot be calibrated out, due to randomness. Systematic ErrorsSystematic Errors –CAN be reduced via calibration –Transmission and Reflection Frequency Response Errors –Source and Load Match Errors –Directivity and Isolation (Crosstalk) Errors

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Slide Error Vectors x actual DUT performance raw VNA measurement error coefficient b Once the error vector is known (Mag. & Phase) b It can be vectorially added to the raw VNA measurement b Resultant is the actual DUT performance!

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Slide Error Vectors

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Slide Error Vectors

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Slide How to Calibrate- b To reduce the systematic errors for both ports (Forward and Reverse), a 12 term calibration is required. b Open Short Load Through (OSLT) The most common coax calibration methodThe most common coax calibration method b Other calibration techniques LRL, LRM, TRM, Offset Short...LRL, LRM, TRM, Offset Short... b Exercise Good Techniques for best results Practice/Care/Knowledge/Clean PartsPractice/Care/Knowledge/Clean Parts

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Slide How does calibration work? b The VNA measures KNOWN standards. b It will compare the measured value to the known value, and calculate the difference. b The difference is the error. It will store an error coefficient (Magnitude and Phase) at every frequency/data point, and use it when making measurements.

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Slide START HERE ALL MEASUREMENT ARE REFERENCED TO A STARTING POINT PHASE MEASUREMENTS BEGIN BY UNDERSTANDING WHERE THE REFERENCE PLANE IS POINT IS THE REFERENCE PLANE

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Slide WHY MUST WE MEASURE PHASE??? ERROR CORRECTION REQUIRES THAT WE HAVE PHASE AND MAGNITUDE INFORMATION – EVEN IF WE ARE ONLY CONCERNED WITH MAGNITUDE DURING TESTING! All four S Parameters are interdependent, so we must constantly reverse to compensate for Source Match, Load Match, Directivity, Frequency Response (Reflection), Frequency Response Transmission, and Isolation.

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Slide Systematic Error b Transmission Frequency Response b Reflection Frequency Response b Source Match b Load Match b Directivity b Isolation (Crosstalk) Reduced by Calibration b These Six Terms on both Ports, yield 12 Term Error Corrected Data.

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Slide Corrected S-parameters

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Slide Calibration - (Open, Short Load, Thru) The most common calibration type is the OSL. b Open Infinite ImpedanceInfinite Impedance Voltage MaximumVoltage Maximum O degree Phase ReflectionO degree Phase Reflection Reflection Magnitude = 1Reflection Magnitude = 1 b Load (Broadband) 50 Ohms (match )50 Ohms (match ) Reflection Magnitude = 0Reflection Magnitude = 0 b Short Zero Ohms ImpedanceZero Ohms Impedance Voltage NullVoltage Null 180 degrees Phase Reflection180 degrees Phase Reflection Reflection magnitude = 1Reflection magnitude = 1 b Through Test ports connected together for transmission calibration measurementTest ports connected together for transmission calibration measurement

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Slide Calibration – OSL Sliding Load b Due to the difficulty of producing a high quality coaxial termination (load) 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 b Broadband measurements required high accuracy must use 12 Term sliding load calibration

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Slide VNA Measurement Uncertainties The quality of a VNA measurement can be affected by the following : The quality of a VNA measurement can be affected by the following : b The Quality of the Calibration Standards b Error Correction Type used – 12 Term, 1 Path 2 Port, and etc. b Dynamic Range of the measurement system (VNA) – IFBW, Averaging and etc. b Cable stability and Connector repeatability

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Slide Uncertainty Curve

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Slide Exact Uncertainty b A Windows based program is available to help obtain the uncertainty data that is appropriate for the customer’s specific application. b CDROM part number b Application Note

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Slide Measurement Uncertainty Exercise

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Slide Common Microwave Devices

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Slide What do our Customers manufacture? Amplifiers Mixers Power Dividers Power Splitters Combiners Couplers Circulators Isolators Attenuators Filters

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Slide Amplifier b An Amplifier is an active RF component used to increase the power of an RF signal. b Four fundamental properties of amplifiers are: Input/Output Matches Input/Output Matches Gain Gain Noise figure Noise figure Linearity - 1 dB Compression point Linearity - 1 dB Compression point Small signal in Big signal out

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Slide Match and Gain b Use the Transmission/Reflection Measurement mode of the VNA to measure these parameters: Input match – S11Input match – S11 Output match – S22Output match – S22 Gain – S21Gain – S21

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Slide Noise b We are interested in specific man- made signal b But there are some unwanted signals combined with our desired signal. b Thermal Noise

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Slide Noise Measurement b There are many ways to express noise. b Noise may be expressed in Noise Factor which is defined as the input signal-to-noise ratio to the output signal-to-noise ratio. Si/Ni F = So/No

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Slide Noise Figure b Noise can be expressed in Noise Figure which is the logarithmic equivalent of Noise Factor. Si/Ni Si/Ni NF = 10 log So/No So/No

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Slide Noise Figure Measurement

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Slide Linearity b Linearity is a measure of how the gain variations of an amplifier as a function of input power distorts the fidelity of the signal. Output power VS Input power of an amplifier

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Slide dB Compression Point Input signal (dBm)

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Slide Gain Compression b Traditionally, power meter is used for this measurement – tedious procedure b VNA can now be used – very quick and simple b Two VNA approaches are available: Swept Frequency Gain CompressionSwept Frequency Gain Compression Swept Power Gain CompressionSwept Power Gain Compression

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Slide Swept Frequency Gain Compression

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Slide Swept Power Gain Compression

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Slide Third-order Intercept Point (TOIP)

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Slide TOIP Third-order intercept point (TOIP)

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Slide Intermodulation Products b Understanding the dynamic performance of the receiver requires knowledge of intermodulation products (IP). b How intermodulation is created? b What are the intermodulation products?

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Slide Intermodulation (Continued) l Frequencies causing problem l Overdriven amplifier or receiver

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Slide IMD/TOI Measurement Setup

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Slide IMD Measurements

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Slide TOI Measurement

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Slide Mixer b A Mixer is a three-port component used to change the frequency of one of the input signals. b Fundamental properties of mixers are: Conversion gain/lossConversion gain/loss Port MatchPort Match IsolationIsolation Intermodulation Distortion (IMD)Intermodulation Distortion (IMD)

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Slide Conversion Gain/Loss, Isolation & Port Matches

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Slide Mixer IMD Measurement

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Slide Power Divider b A Power Divider (also called three-resistor power splitter) is a bi-directional device that equally divides an RF signal with a good match on all arms. Input Input Output 1 Output 2

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Slide Power Splitter l A Power Splitter (also called two-resistor power splitter) is a passive RF device that equally divides an RF signal into two RF signals. Output 1 Input Output 2

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Slide Combiner b A Combiner is a passive RF device used to add together, in equal proportion, two or more RF signals.

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Slide Coupler l Directional coupler l Bidirectional coupler AC B

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Slide RF Hybrid Coupler b The RF hybrid coupler is a device that will either (a) split a signal source into two directions or (b) combine two signal sources into a common path.

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Slide Applications of hybrids Combining two signal sources

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Slide Circulator and Isolator b A circulator is a passive junction of three or more ports in which the ports can be accessed in such an order that when power is fed into any port it is transferred to the next port, the first port being counted as following the last in order. b An isolator is a 3-port circulator with the third port terminated with a load so that power can only be transferred in one direction from the first port to the second port.

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Slide Multi-port Devices

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Slide Attenuator b An Attenuator is a RF component used to make RF signals smaller by a predetermined amount, which is measured in decibels.

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Slide Dynamic Range b Dynamic Range is basically the difference between the maximum and minimum signals that the receiver can accommodate. It is usually expressed in decibels (dB). b It is essential that the measurement instrument has sufficient dynamic range to accurately characterize an attenuator.

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Slide Attenuator Measurements

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Slide Attenuator Measurements

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Slide Filter b A Filter transmits only part of the incident energy and may thereby change the spectral distribution of energy: High pass filters transmit energy above a certain frequencyHigh pass filters transmit energy above a certain frequency Low pass filters transmit energy below a certain frequencyLow pass filters transmit energy below a certain frequency Band pass filters transmit energy of a certain bandwidthBand pass filters transmit energy of a certain bandwidth Band stop filters transmit energy outside a specific frequency bandBand stop filters transmit energy outside a specific frequency band

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Slide Filter Measurements

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