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RF Measurement Techniques�

1

Manfred Wendt – CERN

based on the training classes given at the CERN Accelerator School (CAS) and Joint University Accelerator School (JUAS)

​

U.S. Particle Accelerator School 2024

Design and Engineering of Modern Beam Diagnostics

Hampton (VA), U.S.A., January 29 – February 2, 2024

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Contents

  • Introduction
  • RF measurement methods and beam signals
  • Transmission-lines
  • The Smith chart
  • Scattering (S) parameters
  • The vector network analyzer (VNA)
  • Backup slides: �If you want to know more…

​

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Introduction – An Electro-Magnetic Beam Monitor

  • EM beam pickup, e.g. for
    • Beam intensity monitoring
      • Beam pickup based on toroidal transformer, wall-current monitor
    • Beam position / orbit and/or tune monitoring
      • Beam pickup based on button-style or other electrostatic, stripline, resonant cavity, periodic RF coupler, etc. electrodes
  • Transmission-lines
    • Usually, coaxial cables to transmit the signals from the beam pickup to the read-out electronics
      • Also used for calibration, trigger and clock signals
  • RF signal processing
    • Analog components for signal shaping and conditioning
      • Amplifier, attenuator, filter, hybrid coupler, RF diode & limiter, signal splitter & combiner, transformers & balun, etc.

RF & Analog Signal Conditioning

coaxial signal cable

v

bunched beam�(with EM-field)

metallic beam pipe (vacuum)

EM beam�pickup

 

 

 

Digital Signal Processing�& DAQ

control

system

(LAN)

ADC

RF Measurement�Techniques apply

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Introduction – A simple RF system

Free space�wavelength:

 

 

RF frequencies typically utilized �in accelerator applications

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RF Measurement Methods (1)

There are different options to observe RF signals �Here some typical measurement tools:

  • Oscilloscope: to observe signals in time-domain
    • periodic signals
    • burst and transient signals with arbitrary waveforms
    • application: direct observation of signals from a beam pick-up, �from a test generator, or from other sources
    • visualizes the shape of a waveform, etc.
    • limited performance for the evaluation of non-linear effects.

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Cathode Ray Tube (CRT) Oscilloscope

fortunately, or unfortunately,�this good ol times are gone…

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Today: Digital Storage Oscilloscope (DSO)

  • Signal processing based on fast ADCs and DACs
    • Similar “look and feel” as analog oscilloscopes, but better performance
      • 8…12-bit multi-GS/s ADCs, still, be aware of aliasing effects!
      • Fast sampling oscilloscope require sufficient memory resources.
  • AWG or pulse generator & digital oscilloscope: Time-domain (TD) test setup
    • Device under test (DUT) characterization and trouble shooting
      • Impulse, step, or arbitrary waveform (e.g., beam signal) as stimulus signal
      • High impedance probe for measurements on the printed circuit board (PCB)

​

Device Under Test (DUT)

…and digital signal generator�(AWG: arbitrary waveform generator)

50 GS/s, 10-bit AWG (Tektronix)

100 GHz bandwidth�240 GS/s oscilloscope�(LeCroy)

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RF Measurements Methods (2)

  • Spectrum analyzer: to observe signals in a “frequency-domain like” fashion
    • sweeps in equidistant steps through a given frequency range
    • application: observation of spectrum from the beam, or from a signal generator or RF source, or the spectrum emitted from an antenna to locate EMI issues in the accelerator tunnel, etc.
      • Also, DUT characterization in the laboratory, e.g., noise figure measurement on amplifiers (requires a noise source), intermodulation measurements on amplifiers (requires two RF generators).
    • Requires periodic signals
    • Assumes time-invariance of the measurement object (DUT) throughout the frequency sweep
    • Large dynamic range!

​

  • RF detection (Schottky) diode (RF power meter)
    • Supplies a rectified (video) output signal proportional to the RF signal level
    • Delivers no frequency or phase information but operates over a very broad frequency range few MHz to many GHz, and up to 90 dB dynamic range.

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RF Measurements Methods (3)

  • Vector signal analyzer (VSA), sometimes called FFT analyzer
    • Acquires the RF signal, after down-conversion to an intermediate (IF) signal, �in time-domain by fast sampling
      • Please note, all modern spectrum analyzers of today are VSAs!
    • Further numerical treatment in digital signal processors (DSPs)
    • Spectrum calculated using Fast Fourier Transform (FFT)
    • Combines features of an oscilloscope and a spectrum analyzer:
      • Signals can be observed directly in time-domain, or in a frequency-domain like fashion
    • Contrary to the SA, also the spectrum of non-periodic signals �and transients can be measured
    • Application: Observation of tune sidebands, transient behavior of a phase locked loop, single pass beam signal spectrum, etc.
    • Digital oscilloscopes and FFT analyzers share similar technologies, i.e., fast sampling and digital signal processing, and therefore can provide similar measurement options
      • The digital oscilloscope directly digitizes the RF signal�→ limited dynamic range, large instantaneous bandwidth
      • The FFT analyzer digitizes the down-converted IF signal�→ large dynamic range, but a (still) limited instantaneous bandwidth

​

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RF Measurements Methods (4)

  •  

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Beam Signals

  •  

 

i(t)

1

2

3

4

0

 

 

Fourier trans. or

spectrum analyzer

I(f)

 

0

1

2

3

4

 

 

 

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Beam Signals (cont.)

  • Normalized representation on a logarithmic amplitude (magnitude, modulus) scale
    • Typical magnitude spectrum
      • As is would be observed with a spectrum analyzer

​

​

​

​

​

​

​

    • Spectrum of repetitive bunches of same intensity
      • Fourier series expansion

​

​

  • Beam bunches have different distribution functions and length
    • Electron bunches are typically 100…1000x shorter compared to proton bunches
    • Ion bunches can be 10…1000x longer than relativistic proton bunches
    • Longitudinal particle distribution vary depending on particle type and “RF gymnastics”:
      • Gaussian (electrons), parabolic, Tsallis q-Gaussian, cos2, etc. (hadrons)

 

 

 

 

 

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“dB” [dee-bee], or not to be…

  • dezi-Bel: 1 dB = 0.1 B (Bel)
    • Logarithmic scaling to compare large, e.g., power ratios:

​

    • or large ratios of other quantities, e.g.:

​

 

 

 

dB ratio

P1/P2

V1/V2

n x 10 dB

10n

10n/2

40 dB

10000

100

20 dB

100

10

10 dB

10

~3.16

6 dB

~4

~2

3 dB

~2

~1.41

0 dB

1

1

-3 dB

~0.5

~0.71

-20 dB

0.01

0.1

 

 

The 3 dB ratio (half power) is a �common specification for the bandwidth

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“dB” is not “dBm”

  •  

 

 

dBm

P

V (RMS)

30 dBm

1 W

7.07 V

20 dBm

100 mW

2.24 V

10 dBm

10 mW

707 mV

6 dBm

4.0 mW

446 mV

0 dBm

1.0 mW

224 mV

-20 dBm

10 μW

22.4 mV

-60 dBm

1.0 nW

224 μV

-120 dBm

1.0 fW

224 nV

- 174 dBm

4.0e-21 W

0.446 nV

 

 

noise power in a bandwidth BW = 1 Hz at room temperature

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RF Signals & Modulation, without Math!

  • RF signals are continuous wave (CW),sinusoidal signals
    • Often, a high frequency carrier is modulated with low frequency information
    • Modulation appears “naturally” in ring accelerators as:
      • Modulation is also provided through the LLRF system to the accelerating structures

​

FM: Synchrotron oscillations

AM: Betatron oscillations

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A (too) simple Radio Receiver

  • …or: How does a ”traditional” analog radio works?
    • It was, and still is, difficult to make precisely tunable narrowband, band-pass filters �for high frequencies (~100 MHz)!!
    • high frequency low-noise amplifiers are expensive!
    • high frequency demodulators are not trivial.

​

    • direct detection of radio and RF signals is challenging!

broadband�low-noise RF amp�e.g., 87-108 MHz

tunable�narrowband�band-pass filter

RF amp

demodulator

audio amp

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The Super-Heterodyne Receiver

 

broadband�low-noise RF amp�e.g., 87-108 MHz

IF narrowband�band-pass filter�e.g., 10.7 MHz ± 90 kHz

IF amp

demodulator,�e.g., FM PLL or�AM diode detector

audio amp

 

tunable�local oscillator (LO)�e.g., 97.7-118.7 MHz

 

 

 

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The RF Mixer as Down-Converter

 

RF

LO

IF

 

 

 

 

 

upper sideband

lower sideband

 

 

 

 

 

 

 

 

 

 

 

 

courtesy T. Schilcher

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Simplified Spectrum Analyzer

  • based on the super-heterodyne principle

Today, the IF, demodulation, video and display sections �of a spectrum analyzer are realized digitally

    • Requires an analog-digital converter (ADC) with sufficient dynamic range

Switchable BW of the�IF filter and video BPF�(analog or digital)�allows to improve the�signal-to noise (S/N)-ratio

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Modern Spectrum (RF Signal) Analyzer

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Transmission-lines

  •  

dl

outer�conductor

inner�conductor

dl

L’

C’

equivalent�circuit of a

​

​

lossless

TEM transmission-line

 

coaxial�cable

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Transmission-lines (1)

Waveguides (TE10)

Coaxial cables (TEM)

with and w/o connectors

 

 

 

SMA

MCX

BNC

N-type

7/8”

1/4”

1/2”

RG58

VNA

SiO2

semi-rigid�& flex

RG-type�coaxial cables

 

corrugated�coaxial cables,�foamed PE & air

Low-loss, high-power�air coaxial�transmission-line

PCB microstrip-line (TEM)

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Transmission-lines (2)

  •  

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Transmission-lines (3)

  •  

 

 

 

 

 

load

 

RF source

 

 

 

transmission-line,�here: TEM coaxial

 

with losses no losses

 

 

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Telegrapher’s Equation for TEM transmission-lines

A more general approach:

 

 

 

 

 

 

 

 

 

 

 

 

 

in steady state:

 

 

 

 

 

voltage and current along a transmission-line:

propagation constant

 

characteristic impedance

attenuation�constant

phase�constant

 

 

wave�number

phase�velocity

 

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Transmission-lines – Coaxial Cables

  •  

 

 

 

 

 

 

 

 

 

 

For inner and outer conductor in copper:

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TL: Signal visualization in time-domain

  • Circuit simulator applet:�https://www.falstad.com/circuit/
    • Load file: IdealTL_DCswitched_Z050-RL.txt
      • Change the load resistor value:�RL = 50, 100, 25 Ω
      • Operate the switch and observe the signals at the beginning, and at the end of the transmission-line.
    • Load file: �IdealTL_pulsed_Z050-RL.txt
      • Change the load resistor value:�RL = 50, 100, 25 Ω
      • Observe the signal waveforms!�Can you predict the values?!
        • (Press Run/STOP and hover with the mouse over the waveform)

​

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TL: Operating with sinusoidal signals (FD)

  •  

 

 

waves

E-fields

voltages

impedances

 

 

 

 

sine-wave�generator

(source)

 

 

 

 

 

 

transmission-line

load

 

 

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TL: Voltage Standing Wave Ratio (VSWR)

  • The voltage standing wave ratio (VSWR) expresses the ratio between the maximum and minimum voltage of a standing wave along a transmission-line

​

​

​

    • The VSWR is a function of the frequency.

​

​

​

  • The return loss (RL) is another way �to express reflection effects

 

 

 

​

​

Return Loss [dB]

​

​

0.0

1.00

∞

0.00

1.00

0.1

1.22

20.0

0.01

0.99

0.2

1.50

14.0

0.04

0.96

0.3

1.87

10.5

0.09

0.91

0.4

2.33

8.0

0.16

0.84

0.5

3.00

6.0

0.25

0.75

0.6

4.00

4.4

0.36

0.64

0.7

5.67

3.1

0.49

0.51

0.8

9.00

1.9

0.64

0.36

0.9

19.00

0.9

0.81

0.19

1.0

∞

0

1.00

0.00

 

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Reflection (VSWR) Measurement

  •  

V

 

 

 

 

 

 

 

 

 

 

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Electrical Networks (1)

  • The electromagnetic behavior or RF circuits and systems, like any other electrical / electronics circuit or system can be described by Maxwell’s equations

​

​

    • These equations need to be solved, taking all the boundaries and materials into account
  • However, this is far too complicated and inconvenient for most practical situations!
    • simplified electrical network description based on approximative lumped or distributed elements
      • With given characteristics and values of each circuit element represented by a symbol in an electrical network, following the laws of Ohm and Kirchhoff. Here some examples:

 

lumped, passive,�non-linear

 

 

lumped, active,�non-linear

 

npn transistor

distributed, passive,�linear

 

 

lumped, passive, linear

 

 

 

 

 

 

 

 

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Electrical Networks (2)

  •  

2-port network

 

 

 

 

1

1’

2

2’

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Electrical Networks (3)

  •  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

linear two-port

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Principle of Scattering (S)-Parameters

  •  

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Generalized S-Parameters

  •  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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  •  

 

 

 

 

1

1’

1-1’ reference plane�(port 1)

 

R

L

C

 

 

 

DUT�(device under test)

1-port RF network (DUT) example

  • S-Parameters allow to characterize the DUT with the measurement equipment located at some physical distance
  • All high frequency effects of distributed elements are included with respect to the reference plane

​

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  •  

 

 

 

 

 

 

 

1

1’

port 1

DUT

2

2’

 

 

 

 

 

port 2

 

 

 

 

 

 

    • Independent �parameters:

​

​

​

    • Dependent �parameters:

 

 

 

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  • Analysis of the reverse S-parameters:

​

​

​

​

​

​

    • Examples of 2-ports DUT: filters, amplifiers, attenuators, transmission-lines (cables), etc.
    • ALL ports ALWAYS need to be terminated�in their characteristic impedance!

 

 

 

 

1

1’

port 1

DUT

2

2’

 

 

 

 

 

port 2

 

 

 

 

 

 

 

 

 

    • Independent �parameters:

​

​

​

    • Dependent �parameters:

 

 

 

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  •  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

port 1

port 2

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  •  

 

 

 

 

 

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The Scattering Matrix

  •  

 

one-port

​

two-port

​

three-port

​

four-port

​

 

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  •  

 

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  •  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SFG example: 3 dB attenuator

port 1

port 2

 

 

 

 

 

 

 

 

port 1

port 2

 

 

 

 

 

 

signal flow graph (SFG):

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  • Ideal amplifier (gain stage)

​

​

​

​

​

  • Low-noise RF transistor

​

​

​

    • Avago VMMK-1218
    • E-pHEMT GaAs FET
      • The S-parameters are different at other frequencies �and operational conditions
      • The transistor requires impedance matching networks at in- and output

 

 

port 1

port 2

 

 

 

 

 

port 1

port 2

 

 

 

 

 

 

 

 

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  •  

 

 

port 1

port 2

port 3

 

 

 

 

 

 

 

 

 

 

 

port 1

 

 

port 2

 

 

port 3

 

 

 

 

 

port 1

port 2

 

 

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  • Ideal directional coupler

​

​

​

​

​

​

    • Operating at the center frequency
    • Figures of merit (ideal, lossless):
      • Coupling factor
      • Insertion loss
      • Coupling loss
    • Coupler with losses, imperfections, etc.
      • Isolation
      • Directivity

​

 

 

port 1

port 2

port 4

port 3

input

isolated

transmitted

coupled

 

 

 

 

 

 

https://en.wikipedia.org/wiki/Power_dividers_and_directional_couplers

double-symmetry

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S-Parameters in Practice

  •  

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SnP Touchstone S-Parameter Files

  •  

 

! header

# format

 

 

 

Touchstone v1.1 example file

  • v2.0 is different, file ext. *.ts

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  •  
    • Each EM-mode must then be represented �by a distinct modal port.
      • This is very important in EM-simulation �to ensure the absorption of the energy for all modes!
    • The number of modal ports needed �generally, increases with frequency, �as more waveguide modes can propagate.

​

​

​

 

 

 

 

 

 

 

 

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How to measure S-Parameters?

  •  

DUT

2-port

DUT = Device Under Test

4-port

Directional Coupler

 

 

 

 

 

 

 

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The Vector Network Analyzer (VNA)

  • 2-port VNA
    • Simplified block schematic

​

DUT

A/D

DAQ CTRL�Sig Proc�Display

RF�source

LO�source

X-switch

Port 1

Port 2

cable

cable

 

 

 

 

 

 

 

 

IF

directional�couplers

term

directional�couplers

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Fun with the VNA!

  • The “look and feel” between VNAs vary between manufacturers and models
    • Concepts and operation is still very similar

​

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VNA Calibration (1)

  • Calibration is not necessary for pure frequency or phase measurements
  • Before calibrating the VNA measurement setup, �perform a brief measurement and chose appropriate VNA settings:
    • Frequency range (center, span or start, stop)
    • Number of frequency points
      • Can be sometimes increased by rearranging the VNA memory (# of channels)
    • IF filter bandwidth
    • Output power level
  • Calibrate the setup, preferable with an electronic calibration system �if more than 2 ports are used!
    • Each port and combination needs to be�calibrated, with the cables attached
    • Choose the appropriate connector type and sex
    • The instrument establishes a correction matrix�and displays the ”CAL” status.

​

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VNA Calibration (2)

  • Calibration improves the measurement performance
    • Return loss improvement by typically 20 dB. Enables mdB accuracy measurements!
    • Full 2-port or 4-port calibration with manual calibration kits is prone to errors, �better use electronic calibration systems.
    • Change VNA settings will cause the instrument to inter- and extrapolate, �and the calibration status becomes uncertain.
  • Cables are included in the calibration
    • However, changing coaxial connector types not.
    • Special VNA cables allows the adaption of different connector types and sex, �without requiring a re-calibration of the setup!

​

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RF Measurement Instrument Features

  •  

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Synthetic Pulse TD Measurements (1)

  •  

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Synthetic Pulse TD Measurements (2)

FD

TD

TD

FD

unlimited frequency range

truncated frequency range

smoothing window �functions

 

 

TDR impulse response

TDR step response

TD gate�markers

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Example: SPS “Shoe-box” BPM Analysis

Measurement (VNA)

Simulation (CST)

Horizontal pickup

Vertical pickup

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Backup Slides

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  •  

 

 

 

complex impedance plane

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EE Reminder: Circuit Vocabulary

  • Resistance, impedance, reactance are inverse proportional to conductance, susceptance, admittance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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The Smith Chart (1)

  •  

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The Smith Chart (2)

  •  

 

 

 

 

 

 

 

 

 

 

 

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The Smith Chart (3)

  •  

 

 

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The Smith Chart (4)

  •  

 

 

 

 

 

 

 

 

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The Smith Chart (5)

  •  

 

 

 

 

 

 

 

mismatch losses

available source power

 

 

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The Smith Chart – “Important Points”

  •  

Short Circuit

 

 

inductive

capacitive

 

 

 

 

Matched Load

 

 

Open Circuit

 

 

 

 

 

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The Smith Chart – Basic Example

  •  

 

 

 

 

 

 

reactive

resistive

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Remarks on transmission-lines and the Smith chart

  •  

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Beam Coupling Impedance

  •  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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  • Formulas:
    • Normalized electrical length:
    • Lumped impedance formula

​

​

    • Log formula

​

    • Improved log formula

​

​

    • Transmission coefficient

​

​

    • Circular beam pipe impedance

 

 

 

 

 

 

 

 

VNA�S21 meas.

P1 P2

stretched wire

 

 

 

 

-10dB

-10dB

REF

absorbing foam

 

-10dB

-10dB

DUT

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Refresher: Some TL Equations (1)

  •  

 

 

 

 

  • Propagation constant
    • for a TEM transmission-line

​

​

​

​

      • attenuation constant

​

​

​

      • phase constant

​

​

 

 

 

 

The characteristic impedance can be�calculated from 2D electrostatic equations

 

 

 

 

 

Equivalent circuit�TEM TL segment

 

 

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Refresher: Some TL Equations (2)

  •  

 

 

 

 

 

in media

Characteristic impedance of free space

 

 

 

in free space

guide wavelength (in media)

 

 

 

 

 

 

 

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Lossless Transmission-lines

  •  

 

 

 

 

 

 

 

 

 

 

    • Popular applications
      • Quarter-wave line:

​

      • Terminated (matched) line:

​

      • Open line:

​

      • Shorted line:

​

 

 

 

 

 

 

 

 

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Lossless Transmission-lines

  •  

​

​

​

​

​

lossless TL open

“capacitive”

“inductive”

“capacitive”

“inductive”

lossless TL shorted

“inductive”

“capacitive”

“inductive”

“capacitive”

 

 

inductive

capacitive

 

 

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Navigation in the Smith Chart (1)

  •  
      • a straight line is equivalent to a circle with infinite radius
      • a circle is defined by 3 points
      • a straight line is defined by 2 points

​

​

​

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Navigation in the Smith Chart (2)

​

Up

Down

Red circles

Series L

Series C

​

Blue circles

Shunt L

Shunt C

Shunt L

Shunt C

Series C

Series L

 

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Navigation in the Smith Chart (3)

Red arcs

​

Blue arcs

​

Con-centric circle

Transmission line going Toward load �Toward generator

 

 

Toward load

Toward generator

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The Smith Chart – Basic Example (1)

  •  

 

 

 

 

 

 

reactive

resistive

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The Smith Chart – Basic Example (2)

  • …and for different component values and circuit combinations

 

 

 

 

 

 

 

 

 

 

 

 

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The Smith Chart – TL Transformer (1)

  •  

 

backward�transmission

coefficient S12

forward�transmission

coefficient S21

 

 

 

 

 

 

 

 

 

 

 

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The Smith Chart – TL Transformer (2)

  •  

 

 

 

 

 

 

 

 

 

 

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The Smith Chart – TL Transformer (3)

  •  

 

 

 

when adding a transmission-line

to some terminating impedance we rotate

clockwise through the Smith-Chart

 

 

 

 

 

 

 

 

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Examples for Symmetry and Reciprocity

  • Without prof: The S-matrix is always symmetric for reciprocal networks.

1’

1

2’

2

 

 

 

symmetry

1’

1

2’

2

 

 

 

 

 

divider-network

 

 

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Numerical lossless / lossy Examples

  •  

1’

1

2’

2

 

 

 

 

 

 

​

​

​

​

​

​

​

​

​

​

 

 

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Numerical lossless / lossy Examples

  •  

1’

1

2’

2

 

 

 

 

 

​

​

​

​

​

​

​

​

​

​

 

 

 

 

 

 

 

 

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Numerical lossless / lossy Examples

  •  

1’

1

2’

2

 

 

 

 

 

​

​

​

​

​

​

​

​

​

​

 

 

 

 

 

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T-Parameters

  •  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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ABCD-Parameters

  •  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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