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Introduction to RF Measurements and Instrumentation

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Introduction to RF Measurements and Instrumentation Introduction to RF measurements and instrumentation Daniel Valuch, CERN BE/RF, [email protected] Purpose of the course • Introduce the most common RF devices • Introduce the most commonly used RF measurement instruments • Explain typical RF measurement problems • Learn the essential RF work practices • Teach you to measure RF structures and devices properly, accurately and safely to you and to the instruments Introduction to RF measurements and instrumentation 2 Daniel Valuch CERN BE/RF ([email protected]) Purpose of the course • What are we NOT going to do… But we still need a little bit of math… Introduction to RF measurements and instrumentation 3 Daniel Valuch CERN BE/RF ([email protected]) Purpose of the course • We will rather focus on: Instruments: …and practices: Methods: Introduction to RF measurements and instrumentation 4 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101 • Transmission lines are defined as waveguiding structures that can support transverse electromagnetic (TEM) waves or quasi-TEM waves. • For purpose of this course: The device which transports RF power from the source to the load (and back) Introduction to RF measurements and instrumentation 5 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101 Transmission line Source Load Introduction to RF measurements and instrumentation 6 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101 • The telegrapher's equations are a pair of linear differential equations which describe the voltage (V) and current (I) on an electrical transmission line with distance and time. • The transmission line model represents the transmission line as an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line: Distributed resistance R of the conductors (Ohms per unit length) Distributed inductance L (Henries per unit length). The capacitance C between the two conductors is represented by a shunt capacitor (in Farads per unit length). The conductance G of the dielectric material separating the two conductors is represented by a shunt resistor between the signal wire and the return wire (in Siemens per unit length). Source and more reading: https://en.wikipedia.org/wiki/Transmission_line Introduction to RF measurements and instrumentation 7 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101 • Solution of telegrapher's equations: 푉 푥 = 푉+푒−훾푥 + 푉−푒+훾푥 1 퐼 푥 = 푉+푒−훾푥 − 푉−푒+훾푥 푍0 • Introduction of an important concept: forward and reflected waves Forward wave 푉+푒−훾푥 Reflected wave 푉−푒+훾푥 Introduction to RF measurements and instrumentation 8 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101 • Introduction of an important transmission line parameters: Propagation constant and characteristic impedance 훾 = (푅 + 푗휔퐿)(퐺 + 푗휔퐶) Propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a circuit, or a field vector such as electric field strength or flux density. The propagation constant itself measures the change per 훾 = 훼 + 푗훽 unit length, but it is otherwise dimensionless. Propagation constant of a lossless line is purely imaginary. Only phase of the waves changes with distance along the Attenuation Phase constant line and the change is linear with distance and frequency. constant (Np/m) (rad/m) It becomes more complicated for lossy lines (different attenuation and propagation velocity for different frequencies, nonlinear phase, dispersion etc…). Introduction to RF measurements and instrumentation 9 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101 • Introduction of an important transmission line parameters: Propagation constant and characteristic impedance Characteristic impedance 푅 + 푗휔퐿 of a uniform transmission line is the ratio of the amplitude of 푍 = a single voltage wave to its current wave propagating along 0 퐺 + 푗휔퐶 the line. Characteristic impedance is determined by the geometry and materials of the transmission line and, for a uniform line, is not dependent on its length. The unit of characteristic impedance is Ohm. Since most transmission lines also have a reflected wave, the characteristic impedance is generally not the impedance that is measured on the line. Introduction to RF measurements and instrumentation 10 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101 • Reflection coefficient G describes how much of an electromagnetic wave is reflected by an impedance discontinuity in the transmission medium. Forward wave 푉+ Reflected wave 푉− 푍퐿 − 푍0 Γ퐿 = 푍퐿 + 푍0 • It is equal to the ratio of the amplitude of the reflected wave to the incident wave, with each expressed as phasors 푉− Γ = 푉+ Introduction to RF measurements and instrumentation 11 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101 • Standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. SWR is defined as the ratio of the partial standing wave's amplitude at an antinode (maximum) to the amplitude at a node (minimum) along the line. 푃 1 + 푅퐹퐿ൗ 푃퐹푊퐷 푉 1 + Γ 푆푊푅 = 푉푆푊푅 = 푚푎푥 = 푃 푉푚푖푛 1 − Γ 1 − 푅퐹퐿ൗ 푃퐹푊퐷 Note: V = Voltage standing wave ratio Introduction to RF measurements and instrumentation 12 Daniel Valuch CERN BE/RF ([email protected]) Exercise 1 – transmission line theory • Calculate the reflection coefficient and the voltage standing wave ratio for the following configurations: = 50 W = 50 W Load 푍퐿 Γ퐿 푉푆푊푅 terminated = 50 W = short 51 W short = 50 W = open open 100 pF capacitor = 50 W 100 pF at 100 MHz 푍퐿 − 푍0 푉푚푎푥 1 + Γ Γ퐿 = 푉푆푊푅 = = 푍퐿 + 푍0 푉푚푖푛 1 − Γ Introduction to RF measurements and instrumentation 13 Daniel Valuch CERN BE/RF ([email protected]) Exercise 1 – transmission line theory • Calculate the reflection coefficient and the voltage standing wave ratio for the following configurations: = 50 W = 50 W Load 푍퐿 Γ퐿 푉푆푊푅 terminated 50 W 0 1.00 = 50 W = short 51 W 51 W 0.01 1.02 short 0 W -1 ∞ ∞ 1.00 ∞ = 50 W = open open 377 W 0.765 7.54 100 pF capacitor -0.81 - -j15.9 W ∞ = 50 W 100 pF at 100 j0.57 MHz 푍퐿 − 푍0 푉푚푎푥 1 + Γ Γ퐿 = 푉푆푊푅 = = 푍퐿 + 푍0 푉푚푖푛 1 − Γ Introduction to RF measurements and instrumentation 14 Daniel Valuch CERN BE/RF ([email protected]) RF network parameters • Most popular method to characterize parameters of linear RF networks is by means of scattering parameters (s-parameters) • A square matrix describes coupling between all of the device’s ports Introduction to RF measurements and instrumentation 15 Daniel Valuch CERN BE/RF ([email protected]) s-parameters Forward direction Backward direction Incident S21 Transmitted a1 b2 Reflected Reflected b1 DUT b2 S11 S22 Transmitted S12 b1 a2 푏 푆 푆 푎 1 = 11 12 1 푏2 푆21 푆22 푎2 Introduction to RF measurements and instrumentation 16 Daniel Valuch CERN BE/RF ([email protected]) s-parameters Forward direction Backward direction Incident S21 Transmitted a1 b2 Reflected Reflected b1 DUT b2 S11 S22 Transmitted S12 b1 a2 푅푒푓푙푒푐푡푒푑 푏1 푅푒푓푙푒푐푡푒푑 푏2 푆11 = = |푎2 = 0 푆22 = = |푎1 = 0 퐼푛푐푖푑푒푛푡 푎1 퐼푛푐푖푑푒푛푡 푎2 푇푟푎푛푠푚푖푡푡푒푑 푏2 푇푟푎푛푠푚푖푡푡푒푑 푏1 푆21 = = |푎2 = 0 푆12 = = |푎1 = 0 퐼푛푐푖푑푒푛푡 푎1 퐼푛푐푖푑푒푛푡 푎2 Introduction to RF measurements and instrumentation 17 Daniel Valuch CERN BE/RF ([email protected]) s-parameters • Simplified approach for lower frequencies: Use voltages/currents instead of waves Forward direction Backward direction Incident S Transmitted + 21 - V1 a1 b2 V2 - Reflected V1 b1 DUT S11 Common notation: + what goes into the port - what leaves the port Introduction to RF measurements and instrumentation 18 Daniel Valuch CERN BE/RF ([email protected]) s-parameters • How do we work out the signals from the s- parameters? − + Example: amplifier output 푉1 푆11 푆12 푉1 voltage as a function of − = + 푉2 푆21 푆22 푉2 gain and input stimulus: − + 푉2 = 푆21푉1 − + + 푉1 = 푆11푉1 + 푆12푉2 Example: amplifier gain − + + calculated from input 푉2 = 푆21푉1 + 푆22푉2 stimulus and output voltage: − 푉2 푆21 = + 푉1 Introduction to RF measurements and instrumentation 19 Daniel Valuch CERN BE/RF ([email protected]) s-parameters • A typical notation: 푆푖푗 To port From port A typical two port device: S11 reflection at the input (input return loss) S21 forward transmission (gain, attenuation) S22 reflection at the output (output return loss) S12 reverse transmission Introduction to RF measurements and instrumentation 20 Daniel Valuch CERN BE/RF ([email protected]) Exercise 2: S-parameters S21 é ù 1 é ù 1 -1 × 0 × ê ú Z0 ê ú S11 ë × × û ë × × û G = 1/10 é ù G = 2 é ù 0 1 0 0 1 2 ê 10 ú 1 2 ê ú ê ú ë 2 0 û 1 0 ëê 10 ûú é - jwt ù é ù ê 0 e ú 0 0 1 2 - jwt ê ú ëê e 0 ûú 1 2 ë 1 0 û Introduction to RF measurements and instrumentation 21 Daniel Valuch CERN BE/RF ([email protected]) Decibel (dB) • Decibel: universal unit of measurement to express ratio of two quantities in logarithmic scale • Primary definition uses ratio of “power quantities” 푃 Where: 푁 푑퐵 = 10 log P is e.g. the measured power, 10 푃 0 P0 reference power N their ratio in dB Introduction to RF measurements and instrumentation 22 Daniel Valuch CERN BE/RF ([email protected]) Decibel (dB) • Derivation for state or field quantities • E.g. case of power expressed by means of voltage and impedance 2 2 Where: 푈 푈0 푃 = 푃 = U is e.g.
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