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Home , Propagation constant, Scattering parameters

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]) 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 (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- 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 (in Farads per unit length). The conductance G of the material separating the two conductors is represented by a shunt 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: and

훾 = (푅 + 푗휔퐿)(퐺 + 푗휔퐶) Propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the and 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 strength or 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 . constant (Np/m) (rad/m) It becomes more complicated for lossy lines (different attenuation and propagation velocity for different , nonlinear phase, 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

• G describes how much of an electromagnetic wave is reflected by an impedance discontinuity in the . 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 푉− Γ = 푉+

Introduction to RF measurements and instrumentation 11 Daniel Valuch CERN BE/RF ([email protected]) Transmission line theory 101

• (SWR) is a measure of of loads to the characteristic impedance of a transmission line or . 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 (s-parameters)

• A square 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 /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: output 푉1 푆11 푆12 푉1 voltage as a function of − = + 푉2 푆21 푆22 푉2 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 ) 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]) (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. the measured voltage, 푅 0 푅 U0 reference reference voltage 2 푈 2 푃 푅 푈 = 2 = 푃0 푈0 푈0 푅 2 푃 푈 푈 푁 푑퐵 = 10 log10 = 10 log10 = 20 log10 푃0 푈0 푈0

Introduction to RF measurements and instrumentation 23 Daniel Valuch CERN BE/RF ([email protected]) Decibel (dB)

• dB is a very convenient unit for RF work

• Gain or attenuation is typically expressed in dB • The amplifier gas a voltage gain of 1000, or 60dB • Power can be expressed in dB 푃 • dBm – use 1 mW for P 푃 푑퐵푚 = 10 log 0 10 1푚푊 • Voltage can be expressed in dB 푈 푈 푑퐵휇푉 = 20 log10 • dBmV – use 1 mV for U0 1휇푉

Introduction to RF measurements and instrumentation 24 Daniel Valuch CERN BE/RF ([email protected]) Decibel (dB) – important numbers

Ratio linear Ratio power dB Ratio voltage dB 1 000 000 +60 +120 1 000 +30 +60 10 +10 +20 2 +3 +6 √2 (1.4142) +1.5 +3 1 0 0 1/√2 (0.7071) -1.5 -3 1/2 -3 -6 1/4 -6 -12 1/10 -10 -20 0.000 000 000 000 000 1 -160 -320

Introduction to RF measurements and instrumentation 25 Daniel Valuch CERN BE/RF ([email protected]) Decibel (dB)

• dB is a very convenient unit for RF work • Multiplication in linear scale converts to addition in logarithmic scale

RF source Amplifier Coaxial line Cavity out power gain attenuation input power

~

PmW = 20 mW AP = 2000 ACABLE = 0.5 PdBm = 13 dBm GP = 33 dB GCABLE = -3

Linear: Pcavity = PmW * AP * ACABLE = 0.020 W * 2000 * 0.5 = 20 W dB: Pcavity = PdBm + GP + GCABLE = 13 dBm + 33 dB – 3 dB = 43 dBm

Introduction to RF measurements and instrumentation 26 Daniel Valuch CERN BE/RF ([email protected]) Exercise 3 – Using the decibel

Power amplifier Superconducting Signal source 750W cavity

12m 3/8" -0.5dB 1m 3/8" -0.2dB 43m 7/8" -0.5dB 2m 3/8" -0.2dB 2

~ m

3

-

-

/

35

35

8

" "

dB FWD dB

dB RFLdB -

750W = 58.7dBm 0 .

Needs 10mW 2 (10.0dBm) for 750W dB Cavity probe transmission -48dB

Fund. coupler

Fwd/Rfl Cavity probe test points test points

Introduction to RF measurements and instrumentation 27 Daniel Valuch CERN BE/RF ([email protected]) Most common RF blocks/devices

• : Device that reduces the signal amplitude (power) without distorting the frequency content

• Important parameters: • Attenuation value (dB) • Power dissipation capacity (Watts) • Usable frequency range

• Special case - terminator

…..Introduction to RF measurements and instrumentation 29 Daniel Valuch CERN BE/RF ([email protected]) Most common RF blocks/devices

• Power divider: Device that splits power from one port into two, or multiple output ports. • Power combiner: Device that combines power from two, or multiple input ports into one output port.

• Important parameters: • Number of ports (2+) • Split ratio (usually equal) • Insertion loss above ideal (dB) • Power handling capacity (Watts) • Usable frequency range

…..Introduction to RF measurements and instrumentation 30 Daniel Valuch CERN BE/RF ([email protected]) Most common RF blocks/devices

• Directional coupler: device that couples out a given fraction (usually small) of the forward, or reflected power from a transmission line

• Important parameters: • Coupling (dB) • Directivity (dB) • Power handling capacity (Watts) • Usable frequency range

…..Introduction to RF measurements and instrumentation 31 Daniel Valuch CERN BE/RF ([email protected]) Most common RF blocks/devices

• Amplifier: Device that increases the signal amplitude (power) without distorting the frequency content

• Important parameters: • Gain (dB) • Max. output power (1 dB compression point) • Frequency range • Noise figure • In/out matching

…..Introduction to RF measurements and instrumentation 32 Daniel Valuch CERN BE/RF ([email protected]) RF connectors

• RF connectors are essential part of your measurement setup. • If not properly selected, installed and maintained they can become your worst nightmare

• Important parameters: • Characteristic impedance • Usable frequency range • Power handling capacity (Watts) • Number of mating cycles

Introduction to RF measurements and instrumentation 33 Daniel Valuch CERN BE/RF ([email protected]) RF connectors (most popular types in RF instrumentation)

SMA BNC Good for 6/18GHz Good <500MHz 100W @ low frequency Not suitable for power transmission Reliable connection for low power Fast connection for low power signals signals, high frequency and signals

N 7/16 Good for 4/8GHz Good for 1GHz 500W @ low frequency kW @ low frequency Robust and reliable, low loss connection Extremely robust and reliable, very low for medium power signals loss connection for high power signals

Introduction to RF measurements and instrumentation 34 Daniel Valuch CERN BE/RF ([email protected]) Connector care

• RF connectors are precision mechanical devices, proper care and handling is essential

Never do this!

Introduction to RF measurements and instrumentation 35 Daniel Valuch CERN BE/RF ([email protected]) Connector care

• Never turn the connectors bodies against each other. Instead insert, slide and turn the nut • Never force the connector when mounting, they have to slide with no resistance Step 1: Step 2: Step 3: align slide in, start to screw turn and tighten to torque

Introduction to RF measurements and instrumentation 36 Daniel Valuch CERN BE/RF ([email protected]) Connector care

• Never turn the connectors bodies against each other. Instead insert, slide and turn the nut • Never force the connector when mounting, they have to slide with no resistance

Flat wrenches N: 19, SMA: 5/16”

Pliers with parallel sliding jaws

Torque wrenches Recommended tools:

Introduction to RF measurements and instrumentation 37 Daniel Valuch CERN BE/RF ([email protected]) Connector care

• Always use protection!

Introduction to RF measurements and instrumentation 38 Daniel Valuch CERN BE/RF ([email protected]) And never, EVER, do this!!!!!!!!!!!!!!!

Introduction to RF measurements and instrumentation 39 Daniel Valuch CERN BE/RF ([email protected])