RF Microwave Fundamentals Jan 2006 Anritsu Korea

RF & Microwave Fundamentals Jan 2006 Anritsu Korea Slide 1 0

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

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

Range of RF Frequencies Medium Frequency (300 KHz - 3 MHz) l High Frequency (HF) (3 - 30 MHz) l Very High Frequency (VHF) (30 - 300 MHz) l Ultra High Frequency (UHF) (300 - 3000 MHz) l Slide 4 0

Some Terms You Will Hear d. B l d. Bm l Impedance l Return Loss (RL) l Insertion Loss (Cable Loss) l VSWR l DTF l Watts l Slide 5 0

Linear vs Log Some things are very, very large. l Some things are very, very small. l 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. Slide 6 0

Bel l A bel is defined as the logarithm of a power ratio. Po bel = log Pi Slide 7 0

Decibel (d. B) l Decibel (d. B) is a logarithmic unit of relative power measurement that expresses the ratio of two power levels. Po d. B = 10 log Pi Slide 8 0

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

3 d. B rule +3 d. B means double the power (multiply by 2) l - 3 d. B means halve the power (divide by 2) l Slide 10 0

Power Conversion Table l Some common decibel values and powerratio equivalents. Slide 11 0

Basic Concept Wavelength ( ) Length Slide 12 0

Wavelength ( ) VC ( ) = εr f Where: VC = velocity of propagation through air εr = relative dielectric constant f = frequency of oscillation Slide 13 0

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

Time Domain and Frequency Domain Slide 15 0

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

Impedance l The impedance of a transmission line can be complex Z = R ± j. X 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 Slide 17 0

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

Coaxial Cable Slide 19 0

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

Microstrip Transmission Line Slide 21 0

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

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

Propagation Modes of Coax l Patterns set up by electric and magnetic fields. Slide 24 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. Slide 25 0

Velocity of Propagation In free space C = 3 x 108 m/sec Wavelength = λ = C/f Where f = frequency (Hz) Slide 26 0

Relative Velocity Constant (k) k = (1/ εR) for Teflon: εR = 2. 04 k = (1/ 2. 04) = 0. 7 Slide 27 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. Slide 28 0

Well Matched Transmission Line If Z 0 = ZL then P 0 = PL No reflection Therefore PL = PI Slide 29 0

Poorly Matched Transmission Line If ZL ≠ Z 0 then PL ≠ PI Reflection is present Therefore PL = PI - PR Slide 30 0

Example Short at the end of the line Slide 31 0

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

VSWR Voltage Standing Wave Ratio (VSWR) Emax ER + E I l VSWR = = Emin ER - EI l ER l (reflection coefficient) = EI Slide 33 0

Reflection Terms & Relationships Slide 34 0

Reflection Slide 35 0

Reflection Coefficient Reflection coefficient is the ratio of the reflected signal to the incident signal. ZL - Z 0 ER/Ei = = | | = ZL + Z 0 l Slide 36 0

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

Basic Measurements Transmission Loss/Gain = Pout/Pin Return Loss = Preflected/Pin Slide 38 0

Transmission Measurement l Combining Signals Slide 39 0

Calculating d. B Difference Slide 40 0

Power Gain l Gain is the ratio of the output power level of an amplifier to the input power level to that amplifier. Po Gain = Pi Slide 41 0

Transmission Measurement (Loss/Gain Measurement) l Transmission Power Gain = 20 log (Vo/Vi) Slide 42 0

Making a Transmission Measurement 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). l Slide 43 0

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

Measure Output Power Slide 45 0

Transmission Measurement Errors • • Calibration Error Test Port Match Detector Match Using Adapters Slide 46 0

Calibration Error Slide 47 0

Determining Calibration Error Slide 48 0

Test Port Match Error Slide 49 0

Detector Match Error Slide 50 0

Calculating the Errors Slide 51 0

Error Calculation Slide 52 0

Error Example Slide 53 0

Error Calculation Slide 54 0

Maximum Effect Slide 55 0

RSS Slide 56 0

Total Error Slide 57 0

What happens when you add an adapter? Slide 58 0

Example 1 Slide 59 0

Example 2 Slide 60 0

Improving Transmission Loss Measurements 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. l Slide 61 0

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

Return Loss Measurements Problem: How do you separate reflected signal from incident signal Slide 63 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. Slide 64 0

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

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

100% Reflection Reference For COAX two references exist: Open circuit Short circuit They are 180° out of phase For Waveguide two reference can be used short circuit and offset short Slide 67 0

100% Reflection Reference The Average of an Open & Short represents a “true” 100% reflection. Slide 68 0

Return Loss Block Diagram Slide 69 0

Errors to Consider • • • Directivity Test port match Termination error Slide 70 0

Calculating Directivity = 20 log ( Vin/ Vout) d. B Example: Vin = 1 Volt, and Vout = 10 m. V Directivity = 20 log ( 1/. 01) = 40 d. B Slide 71 0

Test Port Match Slide 72 0

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

Termination Error Slide 74 0

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

Calculating the Errors § § Calculate how far below the desired signal the error signal is (in d. B). Convert the d. B into linear (reflection coefficient) form. Use reflection chart or calculate. GE = log-1 [ -d. B error/20] For worst case, add up all linear terms. Sum = GE 1 + GE 2 + GE 3 Slide 76 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 = GDUT ± GSUM In d. B, meas. Max = - 20 log [GDUT - GSUM] Min = - 20 log [GDUT + GSUM] Slide 77 0

Error Signal Return Loss (Reflection) Slide 78 0

Calculating the Errors Autotester Directivity = 40 d. B (. 01 G) d. B(. 178 G) Test Port = 20 d. B (. 1 G) Termination Return Loss = 40 d. B (. 01 G) DUT Input/Output Match = 15 Insertion Loss = 1 d. B Detector Return Loss = 20 d. B (. 1 G) Slide 79 0

Return Loss Measurement Errors With Termination Errors: A) 2(I. L. ) + Termination 2 d. B + 40 d. B = 42 d. B B) 2 (DUT) + Test Port (. 008 G) 30 d. B + 20 d. B = 50 d. B (. 0032 G) C) Directivity = 40 d. B (. 01 G) Total Error = 0. 021 G Slide 80 0

Measured Results For Using Termination DUT =. 178 G (15 d. B) (1. 43 SWR) Plus Total Error +. 021 G. 199 G = (14. 02 d. B) ( 1. 50 SWR) DUT =. 178 G (15 d. B) (1. 43 SWR) Minus Total Error -. 021 G. 157 G = (16. 08 d. B) (1. 37 SWR) Slide 81 0

Measured Results For Using Detector With Detector (as termination) A) B) C) 2 (I. L. ) + Detector 2 d. B + 20 d. B = 22 d. B 2(DUT) + Test Port = 50 d. B Directivity = 40 d. B (. 079 G) (. 0032 G) (. 01 G). 092 G Measured Results DUT + Total Error. 178 G +. 092 G =. 270 G DUT - Total Error. 178 G -. 092 G =. 086 G (11. 37 d. B) (1. 74 SWR) (21. 31 d. B) (1. 19 SWR) Slide 82 0

Error Signals Directivity = 40 d. B Test Port Match = 20 d. B Adapter = 36 d. B DUT = 15 d. B A- Effective Directivity = 40 d. B (. 01 G) Adapter = 36 d. B (. 0158 G) Minimum Effective Directivity Autotester = 40 d. B =. 01 G Plus Adapter Error +. 0158 G. 0258 = 31. 77 d. B B- Effective Test Port Match Autotester = 20 d. B = (. 1 G) Adapter = 36 d. B = (. 0158) Minimum Effective Test port Match Autotester = 20 d. B =. 1 G Plus Adapter error +. 0158 G. 1158 G = 18. 73 d. B Slide 83 0

Input Match Errors Due to Sweeper Output and SWR Autotester Input Match Effective Input Match d. B Sweeper Input Match 16 = Autotester Input Match 20 = G. 159. 10 Effective Input Match = 11. 7 d. B. 259 11. 7 d. B Effective Input IL = 6. 5 d. B Slide 84 0

Input Match Error Signal Error = DUT + IL + Input + IL + DUT 15 d. B + 6. 5 d. B + 11. 7 d. B + 15 d. B Error Analysis Directivity Test Port 2(DUT) + Test Port Input d. B 54. 7 d. B = 40 G. 00185 G = = 50 = = 54. 7 = Total Error . 01. 0032. 00185. 01505 DUT = 15 d. B =. 178 Plus Error +. 01505. 1931 = 14. 28 d. B DUT = 15 d. B =. 178 Minus Error -. 01505. 1630 = 15. 78 d. B Slide 85 0

Example 3 Slide 86 0

Example 4 Slide 87 0

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

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

Connector Repeatability APC-7 N SMA K V Typically Typically ± ± ± 0. 02 d. B 0. 03 d. B 0. 04 d. B 0. 035 d. B 0. 045 d. B Slide 90 0

Summary Slide 91 0

S Parameters & VNA Measurement Fundamentals Slide 92 0

S Parameters S 21 FORWARD TRANSMISSION Port 1 Port 2 a 1 S 11 FORWARD REFLECTION b 2 DUT S 22 REVERSE REFLECTION b 1 a 2 S 12 REVERSE TRANSMISSION Slide 93 0

S Parameters Slide 94 0

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

Diagram for S-Parameters Slide 96 0

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

Smith Chart Slide 98 0

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

Constant Resistance Circles Slide 100 0

Inductive Reactance Circles Slide 101 0

Capacitive Reactance Circles Slide 102 0

Using Smith Chart Slide 103 0

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 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 overall accuracy and dynamic range. Slide 104 0

What is phase? t These two signals have the same magnitude but are 90 degrees out of phase! Slide 105 0

Phase • 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. • Group delay is one cause of distortion in voice transmission and bit errors in digital transmission systems. Slide 106 0

What happens when two equal signals which differ by 180 degrees are summed? b b b The resultant depends on their relative amplitudes If the amplitudes are equal - They completely cancel - b This is not hypothetical - When a full reflection occurs at the end of a transmission line, all of the incident energy is reflected back to the generator b This causes high standing waves b Depending where you “look” along the line, you could see ZERO or Twice the loaded Voltage !! b b b Slide 107 0

How does a VNA display the S-parameters? Log Magnitude and Phase Slide 108 0

Another VNA Display Mode Smith Chart Slide 109 0

VNAs and Calibration Slide 110 0

VNA Test Set and Source Transfer Switch Power divider Rear Panel Reference Loops* a 2 a 1 4 Samplers Coupler 40 d. B Step Attenuator** b 2 b 1 Port 2 DUT Slide 111 0

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) – Cannot be calibrated out, due to randomness. • Systematic Errors – CAN be reduced via calibration – Transmission and Reflection Frequency Response Errors – Source and Load Match Errors – Directivity and Isolation (Crosstalk) Errors Slide 112 0

Error Vectors or err b me as nt ur em icie en t eff co ra w VN A m l tua b UT pe r rfo c an e b Once the error vector is known (Mag. & Phase) It can be vectorially added to the raw VNA measurement Resultant is the actual DUT performance! D ac x Slide 113 0

Error Vectors Slide 114 0

Error Vectors Slide 115 0

How to Calibrateb 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 method b Other calibration techniques • LRL, LRM, TRM, Offset Short. . . b Exercise Good Techniques for best results • Practice/Care/Knowledge/Clean Parts Slide 116 0

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. Slide 117 0

ALL MEASUREMENT ARE REFERENCED TO A STARTING POINT ART HERE ST PHASE MEASUREMENTS BEGIN BY UNDERSTANDING WHERE THE REFERENCE PLANE IS POINT IS THE REFERENCE PLANE Slide 118 0

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. Slide 119 0

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. Slide 120 0

Corrected S-parameters Slide 121 0

Calibration - (Open, Short Load, Thru) The most common calibration type is the OSL. b Open • Infinite Impedance • Voltage Maximum • O degree Phase Reflection • Reflection Magnitude = 1 b Short • Zero Ohms Impedance • Voltage Null • 180 degrees Phase Reflection • Reflection magnitude = 1 b Load (Broadband) b Through • Test ports connected together for transmission calibration measurement • • 50 Ohms (match) Reflection Magnitude = 0 Slide 122 0

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 Slide 123 0

VNA Measurement Uncertainties 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 Slide 124 0

Uncertainty Curve Slide 125 0

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 2300 -361 b Application Note 11410 -00270 Slide 126 0

Measurement Uncertainty Exercise Slide 127 0

Common Microwave Devices Slide 128 0

What do our Customers manufacture? § § § Amplifiers Mixers Power Dividers Power Splitters Combiners § § § Couplers Circulators Isolators Attenuators Filters Slide 129 0

Amplifier b b An Amplifier is an active RF component used to increase the power of an RF signal. Four fundamental properties of amplifiers are: • • Input/Output Matches Gain Noise figure Linearity - 1 d. B Compression point Small signal in Big signal out Slide 130 0

Match and Gain b Use the Transmission/Reflection Measurement mode of the VNA to measure these parameters: • • • Input match – S 11 Output match – S 22 Gain – S 21 Slide 131 0

Noise b We are interested in specific manmade signal b But there are some unwanted signals combined with our desired signal. b Thermal Noise Slide 132 0

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 Slide 133 0

Noise Figure b Noise can be expressed in Noise Figure which is the logarithmic equivalent of Noise Factor. Si/Ni NF = 10 log So/No Slide 134 0

Noise Figure Measurement Slide 135 0

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 Slide 136 0

1 -d. B Compression Point Input signal (d. Bm) Slide 137 0

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 Compression • Swept Power Gain Compression Slide 138 0

Swept Frequency Gain Compression Slide 139 0

Swept Power Gain Compression Slide 140 0

Third-order Intercept Point (TOIP) Slide 141 0

TOIP Third-order intercept point (TOIP) Slide 142 0

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? Slide 143 0

Intermodulation (Continued) Frequencies causing problem l Overdriven amplifier or receiver l Slide 144 0

IMD/TOI Measurement Setup Slide 145 0

IMD Measurements Slide 146 0

TOI Measurement Slide 147 0

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/loss Port Match Isolation Intermodulation Distortion (IMD) Slide 148 0

Conversion Gain/Loss, Isolation & Port Matches Slide 149 0

Mixer IMD Measurement Slide 150 0

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 Output 1 Output 2 Slide 151 0

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 Slide 152 0

Combiner b. A Combiner is a passive RF device used to add together, in equal proportion, two or more RF signals. Slide 153 0

Coupler l l Directional coupler Bidirectional coupler A C B Slide 154 0

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. Slide 155 0

Applications of hybrids Combining two signal sources Slide 156 0

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. Slide 157 0

Multi-port Devices Slide 158 0

Attenuator b An Attenuator is a RF component used to make RF signals smaller by a predetermined amount, which is measured in decibels. Slide 159 0

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 (d. B). b It is essential that the measurement instrument has sufficient dynamic range to accurately characterize an attenuator. Slide 160 0

Attenuator Measurements Slide 161 0

Attenuator Measurements Slide 162 0

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 frequency Low pass filters transmit energy below a certain frequency Band pass filters transmit energy of a certain bandwidth Band stop filters transmit energy outside a specific frequency band Slide 163 0

Filter Measurements Slide 164 0