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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A GUIDE TO NOISE IN MICROWAVE CIRCUITS A fulsome exploration of critical considerations in microwave circuit noise In A Guide to Noise in Microwave Circuits: Devices, Circuits, and Measurement, a team of distinguished researchers deliver a comprehensive introduction to noise in microwave circuits, with a strong focus on noise characterization of devices and circuits. The book describes fluctuations beginning with their physical origin and touches on the general description of noise in linear and non-linear circuits. Several chapters are devoted to the description of noise measurement -techniques and the interpretation of measured data. A full chapter is dedicated to noise sources as well, including thermal, shot, plasma, and current. A Guide to Noise in Microwave Circuits offers examples of measurement problems--like low noise block (LNB) of satellite television - and explores equipment and measurement methods, like the Y, cold source, and 7-state method. This book also includes: * A thorough introduction to foundational terms in microwave circuit noise, including average values, amplitude distribution, autocorrelation, cross-correlation, and noise spectra * Comprehensive explorations of common noise sources, including thermal noise, the Nyquist formula and thermal radiation, shot noise, plasma noise, and more * Practical discussions of noise and linear networks, including narrowband noise * In-depth examinations of calculation methods for noise quantities, including noise voltages, currents, and spectra, the noise correlation matrix, and the noise of simple passive networks Perfect for graduate students specializing in microwave and wireless electronics, A Guide to Noise in Microwave Circuits: Devices, Circuits, and Measurement will also earn a place in the libraries of professional engineers working in microwave or wireless circuits and system design.
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Veröffentlichungsjahr: 2021
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Table of Contents
Cover
Title Page
Copyright
Author Biographies
Preface
1 Introduction
Preliminary Remarks
History
References
2 Basic Terms
Average Values
Amplitude Distribution
Autocorrelation
Cross‐Correlation
Noise Spectra
Autocorrelation Function and Spectral Power Density
Band‐Limited Noise on the Spectrum Analyzer
References
3 Noise Sources
Thermal Noise
Nyquist Formula and Thermal Radiation
Validity and Experimental Confirmation of the Nyquist Formula
Thermal Noise Under Extreme Conditions
Shot Noise
Plasma Noise
Current Noise of Resistors and Contacts
Technical Resistors
Resistors Consisting of Semiconductor Material
Contact Noise
Generation–Recombination Noise
LF Noise from Transistors
References
4 Noise and Linear Networks
Narrowband Noise
Calculating with Phasors
Noise Source with Complex Internal Resistance
The Equivalent Noise Bandwidth
Network Components at Different Temperatures
Noise Generator and Attenuator
References
5 Nonlinear Networks
Mixing
Band‐Limited RF Noise at Input
Amplitude Clipping
The Detector as a Nonlinear Network
The Noise Spectrum Behind a Quadratic Detector
The Noise Spectrum Behind a Linear Detector
The Sensitivity Limit
Noise with Signal
The Phase Sensitive Rectifier
Trace Averaging
References
6 The Noise Factor
Amplifier and Noise Power
The Noise Factor F
Cascaded Amplifiers
The Noise Measure M
Definitions of Gain
Source and Load
Broadband and Spot Noise Factor
Noise Factor of a Passive Network
Antenna Temperature
The Reference Temperature T0 = 290 K
Noise Factor and Detection Limit
References
7 Noise of Linear Two‐Ports
Representation of Two‐Ports
Noise Modeling Using the Chain Matrix
References
8 Calculation Methods for Noise Quantities
Noise Voltages, Currents, and Spectra
Calculating with Current, Voltage, and Noise Waves
The Noise Correlation Matrix
The Correlation Matrix of Passive Components
The Noise of Simple Passive Networks
Transformation of Noise Sources in Different Network Representations
Correlation Matrix and IEEE Elements
FET‐Like Network with the Y‐Correlation Matrix
Noise Sources at Input with ABCD Correlation Matrix
References
9 Diodes and Bipolar Transistors
Semiconductor Diode
Bipolar Transistor
Small‐Signal Equivalent Circuit
Hawkins BJT Noise Model
Two Approaches for the Collector Noise Current Source
BJT Noise Model with Correlation Matrices
The Π‐Model
The T‐Model with Correlation Matrices
Transformation of the Y‐Sources to the Input
Modeling of a Microwave Transistor with Correlation Matrices
Simplest Π‐Model
Contour Diagram
Transistor in the Circuit
Using the Contour Diagram
References
10 Operational Amplifier
Operational Amplifier as Circuit Element
Noise Sources of the Operational Amplifier
Consideration of 1/
f
Noise
Operational Amplifier as an Active Low‐Pass Filter
References
11 Field Effect Transistors
JFET
Mode of Operation of the FET
The Channel Noise
Noise Sources at the Gate
The Correlation
Transformation to the Input
Simple Approximations
Field Effect Transistors for the Microwave Range (MESFET, HFET)
The Pucel Model
The Pospieszalski model
Discussion of the Results
Criteria for Noise Data
References
12 Theory of Noise Measurement
Measurements of Two‐Ports
The Equivalent Noise Resistance
Voltage and Current Source
Voltage and Current Source with Correlation
3 dB and Y‐Method
References
13 Basics of Measuring Technique
Principles of the RF‐Receiver
The Detection Limit
Diode as RF Receiver (Video Detector)
RF and Microwave Range Receiver
Dicke Radiometer
Correlation Radiometer in the Microwave Range
Network Analyzer as a Noise Measurement Device
References
14 Equipment and Measurement Methods
Noise Measurement Receiver
Spectrum Analyzer
The Y‐Method
Measurements in the Microwave Range
Selection Criteria of the Mixer
Image Rejection
Complete Noise Characterization
Analysis of Multi‐impedance Measurements
Cold Source Method
The 7‐State Method
On‐Wafer Measurement of Cold Source
On‐Wafer with Noise Generator According to the Y‐method
References
15 Noise Generators
Vacuum Diode
Gas Discharge
Semiconductor Diodes
Excess Noise Ratio (ENR)
Hot–Cold Sources
References
16 Impedance Tuners
Impedance Transformation with Simple Methods
Mechanical Components for the Microwave Range
Electronic Components
Precision Automatic Tuner
Attenuation of the Tuner
References
17 Examples of Measurement Problems
Transistor in a Test Fixture
The Low Noise Block (LNB) of Satellite Television
Verification of a Noise Measurement
References
18 Measurement and Modeling of Low‐Frequency Noise
Correlation Radiometer for Low Frequencies (f < 10 MHz)
The Low‐Frequency Noise of Transistors
Measurement Setup for LF Noise
Examples of LF Noise Measurements on GaAs‐HBT
Modeling of LF Noise
The Noise of the Microphone
References
19 Measurement Accuracy and Sources of Error
Accuracy of Measured Data
Error of Measurements
Inaccuracies of the Noise Measurement
Uncertainty of the ENR Calibration
Noise Source Mismatch
T0 = 290 K Is not TOFF
Mismatch in the System
Linearity of the Receiver
References
20 Phase Noise
Basics
Reciprocal Mixing
Description of Phase Noise
Spectral Power Density of Phase Fluctuations Sφ(f)
The Single Sideband Phase Noise L(f)
Spectral Power Density of Frequency Fluctuations SΔf(f)
Excursus on Frequency and Phase Modulation
The Allan Variance
Residual FM
Multiplication and Division
Amplitude Noise
Phase Noise and Jitter
References
21 Physics of the Oscillator
Oscillation Condition [1]
Simple Model of the Phase Disturbance [2]
Phase Slope, Resonator Quality, and Frequency Stability [3]
The Formula of Leeson [4]
Components of Oscillators
Influence of the Varactor Diode
Upward Mixing of LF Noise
The Influence of Microwave Noise on Phase Noise
References
22 Phase Noise Measurement
Basic Parameters
Spectrum Analyzer
Phase Detector Method
The Sensitivity of the Phase Detector
Example Calibration and Measurement
Keeping the Quadrature by a PLL
Delay Line as Frequency Discriminator
The Sensitivity of the Delay‐Line Method
Configuration and Calibration
Resonator as Frequency Discriminator
Detection Limit
Comparison of Measurement Systems
Cross‐Correlation Technique
Amplitude Noise
Problems with On‐Wafer Measurement
Residual Phase Noise
References
Appendix
Noise Signals and Deterministic Signals
Random Signals
Characteristic Values
The Probability Density Function
The Autocorrelation Function
Fourier Series
Sine–Cosine Spectrum
Amplitude–Phase Spectrum
Complex Fourier Series
The Fourier Integral
Energy and Power Signals
Example Transient Time Function
The Parseval Equation
Example Voltage Pulse
Fourier Transform and Power Spectral Density
Example Rectangular Pulse
Time‐Limited Noise Signal
Example of a Time‐Limited Wave Train
The Wiener–Khinchin Theorem
Cross Correlation
Cross‐Correlation After Splitting into Two Branches
Power Spectral Density Real and Complex
The Cross‐Spectral Density
Complex Representation of the Cross‐Spectral Density
Transmission of Noise by Networks
References
Glossary of Symbols
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Values of (
signal to interference and noise ratio
) for various app...
Table 1.2 Values of SINR for mobile communication.
Chapter 3
Table 3.1 Corner frequency
f
C
of some types of transistors.
Chapter 4
Table 4.1 Ratio of the equivalent noise bandwidth to the 3 dB bandwidth for ...
Chapter 7
Table 7.1 Manufacturer's specifications of the noise parameters: Infineon Te...
Chapter 8
Table 8.1 Matrices of simple networks.
Table 8.2 Two‐port equations with noise sources and transformation equations...
Chapter 9
Table 9.1 Transformation matrices
T
for converting the correlation matrices a...
Table 9.2 Values of the elements in Figure 9.22 derived from S‐parameter mea...
Table 9.3
H
‐parameters and noise sources from the BC546 data sheet.
Chapter 10
Table 10.1 Noise data as specified by the manufacturer.
Table 10.2 Compilation of the values for the noise analysis of OP27 in the c...
Table 10.3 Contributions of the components from Figure 10.9 to the total noi...
Table 10.4 Comparison of noise characteristics of operational amplifiers.
Chapter 11
Table 11.1 Manufacturer's specifications for different JFETs and the
R
EQ
and
Table 11.2 Elements of the PHEMT Avago VMMK 1225 equivalent circuit accordin...
Table 11.3 Values of the elements in Figure 11.17 optimized for
f
= 2–26 GHz....
Chapter 12
Table 12.1 Noise sources at the input of operational amplifiers.
Chapter 13
Table 13.1 Noise voltages of different sources at 50 Ω in
B
= 1 MHz.
Table 13.2 Detection limit of typical receivers.
Table 13.3 Comparison of the sensitivity of (13.19) with the factory specifi...
Chapter 14
Table 14.1 Noise bandwidth of typical filters.
Table 14.2 Level with the Y method.
Table 14.3 Standards for measuring the
S
‐parameters of a passive two‐port fro...
Chapter 15
Table 15.1 ENR values and corresponding noise temperatures.
Table 15.2 Frequency table of calibration data of an Keysight noise source (...
Chapter 18
Table 18.1 Noise sources of operational amplifiers according to data sheet.
Chapter 19
Table 19.1 ENR Specification of a Keysight 346B noise source.
Table 19.2 Error terms from the example of the LNA measurement in Figure 19....
Chapter 20
Table 20.1 Required phase noise levels for the demands of mobile phone stand...
Table 20.2 Frequency dependencies of the noise processes in a phase noise sp...
Table 20.3 Approximations of the curve
L
(f) to the formula (20.38).
Chapter 21
Table 21.1 Typical quality values of resonant circuits.
Table 21.2 Elements of the equivalent circuit for a varactor in HBT MMIC tec...
Chapter 22
Table 22.1 Phase noise: quantities to be measured.
Table 22.2 The effect of thermal noise.
Table 22.3 Phase noise measurement systems.
List of Illustrations
Chapter 1
Figure 1.1 Screenshot of the noise level of a LeCroy 70 GHz oscilloscope. (a...
Figure 1.2 Screenshot of a spectrum analyzer (a) and histogram (b).
Figure 1.3 Effect of reducing “noise from noise” by reducing video bandwidth...
Chapter 2
Figure 2.1 Amplitude distribution of the noise voltages
v
according to the G...
Figure 2.2 Probability
P
(
v
1
)
of the occurrence of noise voltages
|v| > v1
...
Figure 2.3 Twice the same noise voltage over time. The variance (2.3) is obt...
Figure 2.4 Normalized autocorrelation function
ρ
(
τ
)/
σ
2
versus...
Figure 2.5 White noise after passing through a bandpass filter is a blurred ...
Figure 2.6 ACF
ρ
(
τ
)
of band‐limited noise. It is periodic with the...
Figure 2.7 RC network with bandlimited noise sources
v
and
i
at 1 GHz. The n...
Figure 2.8 Superposition of the two noise currents in the load
Y
over the ph...
Figure 2.9 Spectral noise power density
S
(
f
)
of a microwave field effect tra...
Figure 2.10 Rayleigh distribution
RDF
(
v
)
of the envelope of a band‐limited n...
Chapter 3
Figure 3.1 Circuit for generating a noise voltage
v
C
at the capacitance
C
(1...
Figure 3.2 Planck factor
p
(
f
)
for
T
= 300 K (room temp.) and 77 K (
LN
2
temp....
Figure 3.3 Planck's radiation formula for
T
= 30 K (cold outer space) and th...
Figure 3.4 Isotropic antenna with matched termination exposed to thermal rad...
Figure 3.5 Spectral noise power density at
T
= 4 K. The vacuum fluctuations ...
Figure 3.6 A particle with charge
q
moves in the electric field of a vacuum ...
Figure 3.7 The induced current in the outer circuit
i
e
(
t
)
in the time domain...
Figure 3.8 Current pulses in a semiconductor. The ACF is calculated from a s...
Figure 3.9 ACF
ρ
i
(
τ
)
according to (3.34) of the current pulse in F...
Figure 3.10 Frequency spectrum of the spectral noise current density
S
(
f
)
of...
Figure 3.11 Spectral density of the voltage square
S
VC
of a SMD thick film r...
Figure 3.12 Noise index
A
(dB) of a chip resistor format 1608 (length 1.6 mm...
Figure 3.13 Measurement of the spectral density of the noise voltage square ...
Figure 3.14 Scheme of the exchange of electrons between conduction band and ...
Figure 3.15 Autocorrelation function of generation recombination noise (3.44...
Figure 3.16 Normalized spectral power density of GR noise
after (3.50). Th...
Figure 3.17 Overlay of GR‐spectra with different
f
g
(
τρ = 0.1 s − 0.1 ms
...
Figure 3.18 Spectral power density
S
IC
of the collector current of a GaInP/G...
Figure 3.19 Schematic representation of the transition from 1/
f
‐ to white no...
Chapter 4
Figure 4.1 (a) Phasor of a monochromatic signal. (b) Phasor of a narrowband ...
Figure 4.2 Vector diagram of current and voltage in a complex load resistanc...
Figure 4.3 Parallel resonant circuit as filter for a noise spectrum. The spe...
Figure 4.4 Equivalent circuit of a noise voltage source (a) and a noise curr...
Figure 4.5 Power transfer from a complex source to a complex load over an id...
Figure 4.6 The transfer characteristic of an RBW filter is replaced by the e...
Figure 4.7
R
1
,
R
2
,
R
3
at different temperatures forming a noisy one‐port. Th...
Figure 4.8 A noise power of the value
N
IN
= 1
is split into th...
Figure 4.9 Change in noise temperature due to losses at different temperatur...
Figure 4.10 Noise source with attenuator. The attenuator reduces the tempera...
Chapter 5
Figure 5.1 “Monochromatic noise bands” (vertical arrows) within
B
form pairs...
Figure 5.2 Probability distribution of the noise amplitudes behind a detecto...
Figure 5.3 Error of a noise measurement due to amplitude clipping with
R
C
in...
Figure 5.4 Output voltage at the load resistor 1 MΩ versus the RF power of a...
Figure 5.5 Transmission of signal
Vcos
(
ω
0
t
)
and noise
v
(
t
)
via bandpass...
Figure 5.6 Noise without signal. Spectra at quadratic rectification. Top: Na...
Figure 5.7 Noise with signal. Quadratic detection. Top: Narrowband noise and...
Figure 5.8 The triangular LF noise spectrum before the integrating low pass....
Figure 5.9 Fluctuations of a noise measurement (5.65) versus the video bandw...
Figure 5.10 Schematic of a phase sensitive detector. Mixed products
ω ≥ ω0
...
Figure 5.11 Comparison of PSD and quadratic detector for a very weak AC sign...
Chapter 6
Figure 6.1 Amplifier with gain
G
A
and bandwidth
B
. At the input, the resisto...
Figure 6.2 Output power
N
O
versus the temperature
T
S
of the source resistanc...
Figure 6.3 Ratio of noise power
10
log
(
N
O
/
N
O
1
)
versus the sourc...
Figure 6.4 Network as in Figure 6.1 but without noise. Noise source and sign...
Figure 6.5 (a) Power spectrum with signal at
f
0
and noise at amplifier input...
Figure 6.6 Two cascaded networks with
kT
0
B
at the input generate the noise p...
Figure 6.7 Amplifier with signal source at input and power meter at output.
Figure 6.8 Dependence of the different gains on the reflection coefficient o...
Figure 6.9 Flow chart of a source with complex internal resistance and a loa...
Figure 6.10 Fine structure of noise factor
F
and gain
G
of an amplifier vers...
Figure 6.11 Brightness temperature
T
B
versus frequency. The dipole receives ...
Figure 6.12 Parabolic antenna pointed at the sun. (a) Weak directionality, c...
Figure 6.13 12 GHz parabolic antenna pointed at the quiet sun.
T
A
increases ...
Figure 6.14 Calculated noise level
N
IN
(dBm) of a receiver (6.81) for the re...
Figure 6.15 Sensitivity limit (6.84) for RF (
B
= 1 MHz) and LF amplifiers (
B
Chapter 7
Figure 7.1 Placement of current and voltage sources in the different types o...
Figure 7.2 Schematic of the currents and voltages in the chain matrix.
Figure 7.3 Network in chain mode with correlated noise sources at the input....
Figure 7.4 Equivalent circuit with source
i
S
,
Y
S
, and correlation coefficien...
Figure 7.5 Example for mismatching of the BJT Infineon BFP405 at input (|
S
11
Figure 7.6 Smith chart of the source reflection coefficient
Γ
S
with cir...
Chapter 8
Figure 8.1 Noise of a lossy resonant circuit. Example data:
R
= 200 Ω at
T
=...
Figure 8.2 Spectral noise power density at the input plane
1, 1
′
of th...
Figure 8.3 Spectral noise power density
G
1
(
f
)
in the input reference plane o...
Figure 8.4 Two‐port in Y representation with additional noise current source...
Figure 8.5 Two‐port in s‐parameter form with incoming waves
a
1, 2
, outgoing ...
Figure 8.6
R
S
represents the mismatched source,
R
L
the matched load.
Figure 8.7 Derivation of the correlation matrix of a series resistor.
Figure 8.8 Two parallel conductances with noise current sources. At the inpu...
Figure 8.9 Two resistors in series with voltage sources. At the input the ge...
Figure 8.10 Noise figure for parallel and series connection of two resistors...
Figure 8.11 Two resistors in combination. Input and output as in Figure 8.10...
Figure 8.12 Noise figure of the circuit Figure 8.11 versus the generator res...
Figure 8.13 The noise contributions of the intrinsic elements
R
1
, G
2
transfo...
Figure 8.14 Two port in admittance representation.
Figure 8.15 Two‐port in admittance representation with noise current sources...
Figure 8.16 Two‐port with noise sources in the different representations.
Figure 8.17 Two‐port as chain matrix with noise sources at the input.
Figure 8.18 Noise equivalent circuit in admittance representation with the m...
Figure 8.19 Correlation coefficient in admittance representation according t...
Figure 8.20 The four noise parameters of the circuit Figure 8.18. In the Smi...
Figure 8.21 Noise equivalent circuit in chain representation with the main e...
Figure 8.22 Correlation coefficient for the chain representation Figure 8.19...
Figure 8.23 Complex correlation admittance for the circuit Figure 8.19.
Figure 8.24 Noise resistance
R
N
and conductance of the uncorrelated current
Chapter 9
Figure 9.1 The pn‐junction in reverse direction. n‐region positively biased....
Figure 9.2 Forward biased pn‐junction. n‐region is negatively biased.
Figure 9.3 Normalized noise temperature of the pn‐junction according to (9.1...
Figure 9.4 Schematic diagram of the npn‐bipolar transistor with currents of ...
Figure 9.5 Equivalent circuit of the npn‐BJT according to the Ebers‐Moll mod...
Figure 9.6
VI
‐characteristic according to (9.17);
α
F
= 0.95;
α
R
= ...
Figure 9.7 Simplest small signal equivalent circuit of a BJT.
Figure 9.8 Noise model of the BJT according to Hawkins.
Figure 9.9 Noise parameters of the BJT AT‐41400 according to data sheet [6] ...
Figure 9.10 Noise parameters according to the Hawkins model for the SiGe‐BJT...
Figure 9.11 Current dependence of the noise figure of the BFP 760 at
f
= 2.4...
Figure 9.12 Noise model of the BJT with the sources in the emitter and colle...
Figure 9.13 Π‐model of the BJT with noise sources in Y‐representation.
Figure 9.14 Base resistance
R
B
and intrinsic transistor are two cascaded net...
Figure 9.15 Intrinsic noise sources of the network (a) are converted to exte...
Figure 9.16 First step: The voltage source is ineffective (short circuited)....
Figure 9.17 Second step: The collector noise current source is ineffective (...
Figure 9.18 Transition from admittance (
Y
‐matrix) a to chain representation ...
Figure 9.19 Values of the correlation coefficient for the AT 41400 according...
Figure 9.20 Spectral power density of the current source
i
A
separated into t...
Figure 9.21 Correlation conductance for the AT 41400.
Figure 9.22 Small signal equivalent circuit of a microwave HBT. The intrinsi...
Figure 9.23 Intrinsic transistor from Figure 9.22 with noise sources.
Figure 9.24 Schematic structure of the noise equivalent circuit from individ...
Figure 9.25 S‐parameter of the InGaP/GaAs chip in Figure 9.22 calculated acc...
Figure 9.26 Noise parameters of the chip. Circles: Measurement; dashed: nois...
Figure 9.27 Comparison of
and
Γ
OPT
.
Figure 9.28 Noise equivalent circuit of a BJT in a simple model.
Figure 9.29 Noise figure of the BCW 60 at
f
= 1 kHz versus the collector cur...
Figure 9.30 Noise figure of the BCW 60 at
f
= 1 kHz versus the source resist...
Figure 9.31 Noise sources of the BJT 2N3392 [19] according to manufacturer's...
Figure 9.32 The uncorrelated noise sources
v
N
and
i
N
at the input of the two...
Figure 9.33 Results for 2N3392 @ 1 kHz calculated from the sources in Figure...
Figure 9.34 Contour diagram of the 2N3392 @1 kHz.
Figure 9.35 BJT BC546 with bias network and input circuit.
Figure 9.36 Noise parameters of the BJT BC546 in circuit Figure 9.35 as a fu...
Figure 9.37 Noise figure of the circuit Figure 9.35 versus the source resist...
Figure 9.38 Noise model of the BJT BC546 in common‐base circuit.
Figure 9.39 Comparison of the noise figure of the common‐emitter and common‐...
Figure 9.40 Contour diagram from the Hitachi 2SC 2545 data sheet.
Figure 9.41 Noise figure of the 2SC 2545 taken from the contour diagram.
I
C
...
Chapter 10
Figure 10.1 Circuit scheme of a non‐inverting operational amplifier.
Figure 10.2 Noise voltage and current sources at the input of BJT OP 27 and ...
Figure 10.3 Noise equivalent circuit of an operational amplifier.
R
S
: noisy ...
Figure 10.4 Equivalent noise voltage density
at the input versus the sourc...
Figure 10.5 Noise figure @ 10 kHz for BJT (OP27) and FET (OP111) technology ...
Figure 10.6 Noise equivalent circuit of the non‐inverting OP27 with intrinsi...
Figure 10.7 Modeling the LF noise of OP27 with (10.8).
Figure 10.8 Contribution of the 1/
f
range to the total noise voltage at the ...
Figure 10.9 Noise equivalent circuit of the AD743 as active low‐pass filter....
Chapter 11
Figure 11.1 Schematic of a field effect transistor with a pn‐diode as gate (...
Figure 11.2
IV
‐characteristics of a GaAs FET according to (11.8) and (11.10)...
Figure 11.3 Cuboid of conductive material for understanding the transconduct...
Figure 11.4 Noise model of the intrinsic FET in Y‐form (a) and in A‐form (b)...
Figure 11.5 Model of intrinsic FET extended by the source resistance and gen...
Figure 11.6 Noise figure of the circuit in Figure 11.5 versus the generator ...
Figure 11.7 Noise figure of the circuit in Figure 11.5 versus the generator ...
Figure 11.8 Frequency dependence of the noise figure at different
R
G
(11.40)...
Figure 11.9 Noise figure and transconductance of JFET 2N4416 versus the drai...
Figure 11.10 Noise voltage square of JFET 2N4416 in the 1/
f
range according ...
Figure 11.11 Noise figure of the JFET2N4416. Full line: Calculated according...
Figure 11.12 Equivalent circuit of a FET according to the Pucel model.
Figure 11.13 Coefficients of the Pucel model versus the drain current normal...
Figure 11.14 Lines: Calculated noise parameters according to the Pucel model...
Figure 11.15 Fukui (11.58) for the VMMK 1225.
Figure 11.16 The intrinsic transistor in the Pospieszalski model.
Figure 11.17 Extended equivalent circuit of VMMK1225 for noise analysis acco...
Figure 11.18 S‐parameters of VMMK1225
f
= 2–26 GHz. Full lines: Calculated w...
Figure 11.19 Splitting the equivalent circuit Figure 11.17 into the networks...
Figure 11.20 Pospieszalski model after Figure 11.19. Full Lines: Calculated
Figure 11.21 Noise sources at the input of the two‐port to derive the criter...
Figure 11.22 The criteria
κ
1 and
κ
2 versus the correlation coeffic...
Figure 11.23 Application of criteria (11.95) and (11.101) to manufacturer's ...
Figure 11.24 Wiatr's criterion
R
n
for the PHEMT LN240 (data sheet) is fulfil...
Chapter 12
Figure 12.1 Basic configuration for noise measurement of a two‐port, here a ...
Figure 12.2 Scheme for measuring the equivalent noise resistance.
Figure 12.3 Scheme for measuring the noise properties of an OPA in the 1/
f
r...
Figure 12.4 Wired OPA with the uncorrelated noise sources
e
N
and
i
N
.
Figure 12.5 Noise factor with variation of the imaginary part of the source ...
Figure 12.6 Noise minimum of the AT41400 with variation of
G
S
.
F
MIN
= 1.45 (...
Figure 12.7 Setup for complete noise characterization of a two‐port with noi...
Figure 12.8 Output power for the 3 dB method. Variation of the temperature
T
Chapter 13
Figure 13.1 Noise figures of input stages and transistor technologies.
Figure 13.2 12GHz receiving system directed toward the sun.
Figure 13.3 Ratio of sun signal to receiver noise. Measurement is possible f...
Figure 13.4 Video detector consisting of diode and matching element between ...
Figure 13.5 Equivalent circuit of a diode with load resistor
R
L
. Notation:
R
Figure 13.6 Screen display on an oscilloscope for tangential sensitivity. Th...
Figure 13.7 TSS of a Schottky diode for two frequencies versus the bias curr...
Figure 13.8 Block diagrams of test receivers in the RF and microwave range....
Figure 13.9 Noise power
N
OUT
at receiver output versus the temperature of th...
Figure 13.10 Time response of the noise voltage behind a rectangular bandpas...
Figure 13.11 Spectral power density of the time domain curve Figure 13.10 be...
Figure 13.12 Block diagram of Dicke's radiometer for measuring microwave rad...
Figure 13.13 Time curve of the noise power behind the switch.
Figure 13.14 Radiometer for mismatched sources.
Figure 13.15 Block diagram of a correlation radiometer. At the input there a...
Figure 13.16 Schema of a 3 dB‐hybrid 180°.
Figure 13.17 Schema of a noise measurement with signal generator and VNA.
Figure 13.18 Signal after passing through the DUT. A noise voltage is superi...
Figure 13.19 Phasor of the signal with superimposed noise Figure 13.18.
Figure 13.20 Comparison of the methods on a 6 GHz amplifier. Left: Standard ...
Chapter 14
Figure 14.1 Logarithmic Rayleigh distribution with linear average
and the ...
Figure 14.2 Example of the increasing noise level in the chain: DUT – preamp...
Figure 14.3 Calibration and measurement to determine
F
REC
,
G
DUT
, and
F
DUT
ac...
Figure 14.4 Level at the receiver versus the temperature of the noise genera...
Figure 14.5 Formation of the intermediate frequency
f
IF
from the two sideban...
Figure 14.6 Heterodyne receiver with mixer and local oscillator.
Figure 14.7 Conversion loss diagram of a commercial mixer in microwave range...
Figure 14.8 Heterodyne receiver with single sideband input filter.
Figure 14.9 Diagram of a mixer with internal suppression of the image band. ...
Figure 14.10 Orientation of the phasors in the two branches. In the A branch...
Figure 14.11 Rotation of the phasors representing positive and negative freq...
Figure 14.12 Cancelation of the mirror band (dashed) by the effect of the ph...
Figure 14.13 Source reflection coefficients
Γ
S
in the Smith chart (circ...
Figure 14.14 Measurement points versus
x
i
(14.33) ideally form a straight li...
Figure 14.15 Noise contributions of the components for the display
N
R
on the...
Figure 14.16 Two‐port noise measurement between source and receiver.
Figure 14.17 Noise measurement set‐up for transistor measurement is calibrat...
Figure 14.18 Arrangement for measuring a transistor with operating point set...
Figure 14.19 On‐wafer set‐up with NFA, switch and directional coupler in cal...
Figure 14.20 Set‐up with transistor as DUT.
Chapter 15
Figure 15.1 Equivalent circuit of a vacuum diode as noise source.
Figure 15.2 Vacuum diode GA560.
Figure 15.3 Waveguide noise source with absorber and attenuator.
T
NS
is adju...
Figure 15.4 Breakdown characteristics of avalanche and Zener diode.
Figure 15.5 Avalanche diode noise amplification.
Figure 15.6 Noise generator with avalanche diode and attenuator for matching...
Figure 15.7 Microwave noise source from Keysight in coaxial technology.
Figure 15.8 Hot load with a coaxial transmission line in a thermostat.
Figure 15.9 Cold load with a coaxial transmission line in a Dewar vessel wit...
Chapter 16
Figure 16.1 LC network for transformation from
R
= 50 Ω to
Z
IN
.
Figure 16.2 CL network for transformation from
R
= 50 Ω to Z
IN
.
Figure 16.3 Complex impedances
Z
IN
achieved with LC and CL networks with cap...
Figure 16.4 The load impedance
Z
L
is transformed into the impedance
Z
IN
with...
Figure 16.5 Transformation paths of
Re
(
y
1
) and
Im
(
y
1
) with variation of
l
1
. ...
Figure 16.6 Integrated impedance tuner using MEMS technology.
Figure 16.7 Structure of a mechanical tuner. The variable capacity is formed...
Figure 16.8 Impedance tuner for manual adjustment (a) and automatic tuner wi...
Figure 16.9 Electrical diagram of a mechanical tuner with capacitance, whose...
Figure 16.10 Tuner model with
R
= 1 Ω,
f
= 3 GHz. At a certain position, inc...
Figure 16.11 The attenuation of the tuner increases rapidly with increasing
Chapter 17
Figure 17.1 Photo of a transistor test fixture using microstrip technology. ...
Figure 17.2 Block diagram of a transistor test fixture using microstrip tech...
Figure 17.3 Scheme of LNB input.
Figure 17.4 Typical antenna system in the Mediterranean region.
Figure 17.5 Noise measurement on the model of an LNB with the noise source c...
Figure 17.6 Photo of a RC noise test structure using coplanar technology. Th...
Figure 17.7 Simple circuit diagram of the test structure in Fig. 17.6.
R
1
= ...
Figure 17.8 Comparison of
S
11
from direct measurement (symbols) and from the...
Figure 17.9 Verification of an on‐wafer system with the passive test structu...
Chapter 18
Figure 18.1 Input stage of the correlation spectrum analyzer for the 1/
f
ran...
Figure 18.2 Correlation spectrum analyzer input stages for measuring voltage...
Figure 18.3 Noise temperatures achievable with the CSA. The limitation resul...
Figure 18.4 The CSA can measure the thermal noise of resistors down to
R
< 1...
Figure 18.5 Spectral noise power density of the output current of transistor...
Figure 18.6 Noise figure of a microwave transistor in log frequency scale.
Figure 18.7 On‐wafer system for LF noise modeling of a transistor. The input...
Figure 18.8 LF noise spectra of a GaAs HBT in common emitter circuit as a fu...
Figure 18.9 Comparing
S
IB
@ 100 Hz of different technologies versus current ...
Figure 18.10 Equivalent circuit for the LF noise of an HBT. For Si‐BJT the c...
Figure 18.11 Example of modeling measured curves of LF noise.
Figure 18.12 Movably mounted capacitor plate of the area
A
C
. Molecules of ve...
Figure 18.13 Low frequency circuit of the condenser microphone.
Chapter 19
Figure 19.1
e
(
x
R
)
gives the deviation of the real (top) from the ideal chara...
Figure 19.2 Example of a series of measurements of the noise factor
F
.
Figure 19.3 Uncertainty of the ENR specification for an 18 GHz noise generat...
Figure 19.4 ENR curve of an 18 GHz noise generator with typical limits of va...
Figure 19.5 Noise measurement error due to mismatch of the noise source vers...
Figure 19.6 Error of a Y‐measurement due to the deviation of
T
C
from
T
0
= 29...
Figure 19.7 Scheme of the measurement of an amplifier at
f
= 10 GHz with det...
Figure 19.8 Error due to high receiver noise figure. Parameter is the gain o...
Figure 19.9 Output power for a transistor measurement with variation of
ΓS
...
Chapter 20
Figure 20.1 Ideal (left) and real signal (right) in time and frequency domai...
Figure 20.2 Left: Phasor of the signal voltage with superimposed noise volta...
Figure 20.3 Frequency shift due to Doppler effect according to (20.1) at
f
S
...
Figure 20.4 Detection problem of weak signals due to phase noise of LO.
Figure 20.5 Phase modulation error due to phase variations.
Figure 20.6 Reciprocal mixing. Below: No interference signal 3 present, 1 is...
Figure 20.7 Spectral energy distribution of the phase noise of an oscillator...
Figure 20.8 Phase noise spectrum
L
(
f
)
with the limit curve of the small angl...
Figure 20.9 Time diagram of measurement of frequency values
y
at distance
τ
...
Figure 20.10 Allan variance of the instability of an oscillator.
Figure 20.11 The frequency range between
f
L
and
f
U
of the phase noise spectr...
Figure 20.12 Phase and amplitude noise spectrum of a microwave synthesizer....
Figure 20.13 Square wave in the time domain. The edge distance is noisy.
Figure 20.14 Phase noise spectrum
L
(f) of an oscillator divided into frequen...
Chapter 21
Figure 21.1 Scheme of an oscillator consisting of amplifier and feedback.
Figure 21.2 Three‐point circuits of oscillators: Hartley (a) and Colpitts (b...
Figure 21.3 Resonant circuit with noise current source (a). Oscillator volta...
Figure 21.4 Feeding
q
at different phases of the oscillation. Maximum voltag...
Figure 21.5 Voltage and current waveform in the Clapp oscillator. Current fl...
Figure 21.6 Capacitive three‐point circuit with bipolar transistor and LC re...
Figure 21.7 Change in the LF noise spectrum of the amplifying element (a) wh...
Figure 21.8 Noise characteristics of relevant transistor technologies.
Figure 21.9 Transmission line resonator in coplanar technology. The bright r...
Figure 21.10 Quality values of line resonators in coplanar technology.
Figure 21.11 Equivalent circuit of a varactor diode.
Figure 21.12 Varactor diode in SMD technology (a) and in MMIC technology (b)...
Figure 21.13 Frequency dependence of quality factors of varactor diodes.
Figure 21.14 Resonant circuits tunable with varactor
f
= 20 GHz. (a) Lumped ...
Figure 21.15 (a) 19 GHz MMIC oscillator in HBT technology. (b) Measured phas...
Figure 21.16 Contribution of the base–emitter diode to the LF noise current ...
Figure 21.17 Spectral noise voltage density of the emitter resistance from m...
Figure 21.18 Emitter–collector transit time
τ
EC
of a GaAs HBT versus th...
Figure 21.19 Phase angle of the gain (∠
S
21
) of a GaAs HBT versus the collect...
Figure 21.20 Phase noise of a 19 GHz MMIC oscillator versus the collector cu...
Figure 21.21 Measured phase noise of the 19 GHz oscillator at
I
C
= 74 mA (no...
Figure 21.22 Scheme of a reflection oscillator. The frequency‐determining re...
Figure 21.23 Noise figure of an HBT with mismatch at the input. Typical situ...
Figure 21.24 Phase noise after (21.28) above the noise figure of the transis...
Chapter 22
Figure 22.1 Direct connecting an oscillator to a suitable spectrum analyzer....
Figure 22.2 Screen display of a spectrum analyzer in log scale.
Figure 22.3 Display of the upper sideband in log scale. Oscillator frequency...
Figure 22.4 Scheme of a spectrum analyzer..
Figure 22.5 RF signal switched between the levels 0 and 6 dBm.
Figure 22.6 Principle of a phase detector setup.
Figure 22.7 Determining the phase detector constant from
V
MAX
with slight de...
Figure 22.8 Setup with phase‐locked loop to ensure quadrature.
Figure 22.9 Reduction of phase noise near the carrier using a PLL.
Figure 22.10 Required PTR (0.5–5 MHz) to ensure that the PLL is locked. High...
Figure 22.11 PLL transfer function measured with noise generator. Here a red...
Figure 22.12 Scheme of the FM discriminator technique with delay line.
Figure 22.13 Frequency discriminator constant over the inverse line length. ...
Figure 22.14 Sensitivity of a system with delay line versus the length of th...
Figure 22.15 Detection limit of the phase noise of a
P
= 10 dBm oscillator (
Figure 22.16 Setup of the delay‐line method with all components required in ...
Figure 22.17 Calibrating the system with a frequency‐modulated source accord...
Figure 22.18 Setup with resonator as frequency discriminator.
Figure 22.19 Detection limit of the methods [1]: 1 Spectrum analyzer; 2 Dela...
Figure 22.20 Scheme of a cross correlation system for measuring phase noise....
Figure 22.21 Scheme of an amplitude noise measurement setup.
Figure 22.22 Scheme of calibration for measuring amplitude noise.
Figure 22.23 Typical levels of phase and amplitude noise of a synthesizer....
Figure 22.24 Section of the measuring setup with phase detector.
Figure 22.25 Schematic of an on‐wafer measurement of an MMIC oscillator with...
Figure 22.26 Reflection factor at the input of the measuring tip, caused by ...
Figure 22.27 Effect of the transmission line on phase noise at 1 MHz offset....
Figure 22.28 Calibrating the system Figure 22.29 with typical levels (dBm)....
Figure 22.29 Measurement of the residual phase noise of a 20 dB amplifier at...
Figure 22.30 Setup for measuring frequency‐converting objects. Two identical...
Figure 22.31 Residual phase noise of an amplifier. Plot −15 dBm: Linear oper...
Appendix
Figure A.1 (a) Measurement of a time‐varying process. (b) Mean value and flu...
Figure A.2 A sequence of
N
measurement points of a noise voltage scatters ar...
Figure A.3 (a) Period of a sine signal. (b) Probability density
p
(
y
)
of the ...
Figure A.4 (a) Period of a sawtooth curve (A.13). (b) Probability density
p(
...
Figure A.5 (a) White noise in the time domain (
μy = 0, σ = 1
...
Figure A.6 (a) Weakly noisy sine in the time domain. (b) Corresponding proba...
Figure A.7 (a) Highly noisy sine in the time domain. (b) Corresponding proba...
Figure A.8 Original white noise after passing a bandpass filter with center ...
Figure A.9 (a) Magnitude of narrowband noise in the time domain. (b) Corresp...
Figure A.10 (a) Sine function in the time domain. (b) Corresponding ACF.
Figure A.11 (a) Sawtooth calculated according to (A.19) with 12 harmonics. (...
Figure A.12 (a) Noisy sinusoidal signal in the time domain. (b) ACF of the s...
Figure A.13 (a) White noise in the time domain. (b) The ACF is
ρ(τ) = 0
...
Figure A.14 Example of a noise signal generated with (A.20). (a) Time domain...
Figure A.15 Transfer function of a low‐pass filter according to (A.21).
Figure A.16 White noise behind a low‐pass filter. (a) Time response for the ...
Figure A.17 Transfer curve of the bandpass filter according to (A.23).
Figure A.18 White noise after passing through the bandpass with center frequ...
Figure A.19 (a) Sampled signal in the time domain with period
T = 1 s
...
Figure A.20 Time dependence and Fourier coefficients as in Figure A.19, but ...
Figure A.21 Time dependence and Fourier coefficients as in Figure A.19, but ...
Figure A.22 Decrease in the amplitude of the Fourier coefficients with incre...
Figure A.23 Amplitude spectrum for an impulse train
T
= 10 seconds.
Figure A.24 Transient time function according to (A.45) as an example for th...
Figure A.25 Real and imaginary part of the Fourier transform of the time fun...
Figure A.26 Individual pulses of different durations in dB measure.
c
approx...
Figure A.27 Spectral distribution of the frequencies contained in the square...
Figure A.28 (a) Unlimited fluctuating time signal
y
2
(
t
)
. (b) Time segment of...
Figure A.29 Time‐limited signal (A.93).
Figure A.30 Fourier spectrum of the signal limited in time to the length
T
f...
Figure A.31 Typical curve of the two‐sided
S
(
f
)
and the one‐sided
G
(
f
)
power...
Figure A.32 The two white noise signals
y
1
(
t
)
and
y
2
(
t
)
(a) show no cross‐co...
Figure A.33 Frequency spectrum of the white noise after passing the bandpass...
Figure A.34 Time dependence of the two noise signals
y
1
(
t
)
and
y
2
(
t
)
behind ...
Figure A.35 (a) ACF of the signal from Figure A.34. (b) CCF of the two signa...
Figure A.36 (a) Time dependence of the noise signal behind the filter. (b) W...
Figure A.37 CCF of the two signals from Figure A.36. The center frequency
f
0
Figure A.38 Addition of the two signals
y
1
(
t
) +
y
2
(
t
)
. The f...
Figure A.39 Sinusoidal signal after passing through noisy amplifiers. (a) Lo...
Figure A.40 Normalized CCF of the signals from Figure A.39 after passing two...
Figure A.41 Transmission of an input voltage
v
1
by a linear network. (a) Tim...
Figure A.42 Superposition of two noise voltages in a network.
Guide
Cover Page
Table of Contents
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Title Page
Copyright
Author Biographies
Preface
Begin Reading
Appendix
Glossary of Symbols
Index
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IEEE Press
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A Guide to Noise in Microwave Circuits
Devices, Circuits, and Measurement
Peter Heymann
Matthias Rudolph
Copyright © 2022 by The Institute of Electricaland Electronics Engineers, Inc. All rights reserved.
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Author Biographies
Peter Heymann received his Dipl.‐Phys. and Dr. rer.‐nat. degrees in physics from the University of Greifswald, Greifswald, Germany, in 1963 and 1969, respectively. From 1963 to 1982, he worked on different projects in the field of wave plasma interaction, which include wave propagation, RF plasma sources and heating, and microwave and far infrared plasma diagnostics. Since 1982, he has been working on GaAs microwave electronics. In 1992, he joined the Ferdinand‐Braun‐Institut für Höchstfrequenztechnik, Berlin, Germany, where he was responsible for measurements, characterization, and modeling of active and passive components of microwave MMICs until his retirement in 2009.
Matthias Rudolph received his Dipl.‐Ing. degree from the Berlin Institute of Technology in 1996 and the Dr.‐Ing. degree from Darmstadt University of Technology in 2001. In 1996, he joined the Ferdinand‐Braun‐Institut (FBH), Leibniz‐Institut für Höchstfrequenztechnik, Berlin, Germany, where he was responsible for the modeling of III–V transistors and MMIC design. In 2009, he was appointed the Ulrich‐L.‐Rohde Professor at the Brandenburg University of Technology, Cottbus, Germany, and also heads the Low‐Noise Components Lab at FBH.
Preface
This book is intended for engineers working in practice and for students at technical college level. Knowledge of the mode of operation of electronic components and the most important mathematical methods of electrical engineering are supposed.
There is extensive literature on the fundamentals of electronic noise and the properties of semiconductor components. These basics are also covered here. In addition to these basics, we devote ourselves in detail to questions of measurement technology in the LF, RF, and microwave range. An attempt is made to show what is hidden behind the intelligence built into measuring instruments and in the omniscient design software.
The problems cannot be understood without mathematical details, especially because of the close interconnection with the statistics of fluctuating quantities. We present them as simply and clearly as possible. In all problems, starting from simple basics, each step is presented logically in a derivation. In doing so, we always try to maintain clarity and a reference to practice and to avoid any unnecessary abstract presentation.
Knowledge and results are based on the authors' work at the Ferdinand‐Braun‐Institut, Leibniz‐Institut für Höchstfrequenztechnik (FBH). The chapters are based on experience with measurement technology and modeling of microwave components in semiconductor technology.
These were acquired through many years of work at FBH. We thank Prof. Dr. G. Tränkle and Prof. Dr. W. Heinrich for their benevolent support and encouragement. Dipl.‐Ing. R. Dœrner and Dipl.‐Ing. S. Schulz have always provided valuable assistance with many technical problems.
Berlin and Cottbus2021
Peter Heymann
Matthias Rudolph
1Introduction
Preliminary Remarks
The spontaneous fluctuations of voltages or currents that we deal with are summarized under the term electronic noise. This is a historical term from the early days of radio technology. In those days, listeners were delighted when they had a more or less interference‐free reception. In the background, or when the receiver was slightly detuned, a disturbing noise could be heard. In the age of digital data transmission, this everyday acoustic noise has largely disappeared from radio and telephony. Noise need not always be of electronic origin. We can hear it, for example, from a mountain stream, when rain falls on a roof or when an air conditioning system is in operation. A clearly perceptible acoustic impression results from the summation of a plurality of randomly occurring individual processes.
Since the publication of the fundamental work “Noise” by A. van der Ziel in 1954 [1], a number of publications on the theory and practice of electronic noise have been published. In the books [2–8] the physical, mathematical aspect is in the foreground. For the practitioner of circuit design and measurement technology, the books [9–14] are more suitable.
The RF‐engineer we are addressing here knows noise as a visual impression at the screen of a spectrum analyzer or broadband oscilloscope. Even without an external signal, the display shows a statistical fluctuation, the “noise floor.” With an oscilloscope, this fluctuation can be seen in the time domain. When sweeping across the screen, the spot dithers irregularly around the baseline. In the spectrum analyzer it fluctuates around an average value. At first glance, the visual impression is the same. It is clear that such an irregularity, whose time dependence is obviously unrepeatable and unpredictable, can only be treated by means of the theory of fluctuation processes. It is indispensable to work with mean values, signal statistics, probability distributions, and correlation. In most cases, time averaging is used for analyses in the time domain, while in the frequency domain the ensemble average is used. Since the noise is ergodic, there is no difference between the two.
Before turning to the noise of amplifiers, receivers, and oscillators and its measurement, it is useful to understand what laws are hidden in this apparently completely chaotic process.
The reason for this is the atomistic structure of electricity. The electric current is not a continuous flow. It consists of the contributions of the individual elementary charges. Small irregular fluctuations are superimposed on the average value. This is also the case when the mean value is zero, i.e. no current flows. As a result of the thermal motion of the free electrons in the conductor, they generate a current pulse of the duration τ when flying over the distance of a free path. This current pulse corresponds to a voltage pulse at the ends of the structure. These are very short voltage pulses in short succession. In a doped semiconductor we have, e.g. n = 1017 electrons/cm3. The free time of flight is about τ = 10−12 seconds.
For a material die with a volume V of 10 μm edge length this results in z voltage impulses per second
The voltage pulses generated by the individual processes are superimposed to thermal noise at the terminals of the structure. The observation of the fluctuation of the voltage at an ohmic resistance in the time domain due to the thermal motion of the electrons is therefore an obvious entry into the physics of noise processes. However, this fluctuating voltage cannot be observed without special measurement technology. Although the oscilloscope is the appropriate instrument for the time domain, it is usually not sensitive enough. The spot on the screen of an older, analog oscilloscope with, e.g. 100 MHz bandwidth, shows, even in the most sensitive range (5 mV/div), a completely smooth curve. No matter which resistor we connect to the input. A voltage fluctuating in time can only be seen on a high performance oscilloscope with extreme bandwidth. However, this noise voltage visible there is also not generated by the thermal noise of a resistor at the input, but by the amplifier chain in the device itself. Nevertheless one has a direct picture of a typical noise process in the time domain. An example is shown in Figure 1.1. Figure 1.1a is the noise voltage on the screen of a LeCroy Wave Expert SE 70 in the y‐deviation 1 mV/div [15]. Figure 1.1b is the histogram of the voltage values together with the appropriate Gaussian distribution. This “elementary image” of the noise shows us some essential properties.
The mean value is zero. The amplitude distribution, the probability density function (PDF) follows the Gaussian curve. Thus one can define a standard deviation and thus an effective value of the noise voltage.
Before we deal with the origin of these vRMS = 2.8 mV and with the statistical quantities in detail, let us look at the screen of a spectrum analyzer. Unlike the oscilloscope, even the simplest model shows a noise floor. What at first glance looks the same on an oscilloscope and a spectrum analyzer turns out to be quite different on closer inspection. This is generally the case with noise observations. At the output of a communication system one has a disturbing noise floor. The contributions to this come from different sources and over a wide range of channels. If one wants to minimize them, one has to understand all the elementary processes and their interaction.
Figure 1.1 Screenshot of the noise level of a LeCroy 70 GHz oscilloscope. (a) Amplitude in the time domain. (b) Statistics of the voltage values. Gaussian distribution with vRMS = 2.8 mV.
Here we have a representation of the noise in the frequency domain. From the broadband noise spectrum we see a small section at the center frequency with the selected resolution bandwidth (RBW). This is not the “elementary picture” of noise as in Figure 1.1. The noise voltage in Figure 1.2 is characterized by two important networks. The IF filter with its RBW selects a narrow frequency range around the center frequency. The display is generated by a detector which displays the average value of the rectified noise voltage. The display is thus the result of data processing through a linear and a non‐linear network. This also results in a change in the distribution of the amplitudes. Instead of the Gaussian distribution, we see a Rayleigh distribution on a logarithmic scale in the histogram Figure 1.2b. There is another important difference to Figure 1.1: On the spectrum analyzer [16] we see the noise from the noise. The actual noise level is the average value corresponding to the Rayleigh distribution. What we see is the remaining fluctuation that can be averaged out by reducing the video bandwidth (VBW). By reducing the VBW in relation to the RBW, the standard deviation is reduced (Figure 1.3).
Figure 1.2 Screenshot of a spectrum analyzer (a) and histogram (b).
