This document provides information about an Advanced Physics course offered at Mbeya University of Science and Technology. The course code is NS 6141 and it covers dimensions of physical quantities, atomic theory, and radioactivity. It will be taught on Fridays from 7:30-9:45am in the Sports Hall by instructor Charles Kadala. Students will be assessed based on two class tests, assignments, and an end of semester exam. The document also provides details on the concepts that will be covered related to dimensions of physical quantities, including defining, explaining, deriving formulas for, and checking formulas using dimensions.
This document discusses frequency concepts in continuous and discrete time signals. For continuous time signals, frequency is defined as cycles per second and relates to the periodic nature of sinusoidal signals. Discrete time signals are periodic only if the frequency is a rational number. The fundamental period is the smallest value that makes the signal periodic. As frequency increases for both continuous and discrete signals, the number of oscillations increases but the period decreases.
Fourier Series for Continuous Time & Discrete Time SignalsJayanshu Gundaniya
- Fourier introduced Fourier series in 1807 to solve the heat equation in a metal plate. The heat equation is a partial differential equation describing the distribution of heat in a body over time.
- Prior to Fourier's work, there was no known solution to the heat equation in the general case. Fourier's idea was to model a complicated heat source as a superposition of simple sine and cosine waves.
- This superposition or linear combination of sine and cosine waves is called the Fourier series. It allows any periodic function to be decomposed into the sum of simple oscillating functions. Although originally introduced for heat problems, Fourier series have wide applications in mathematics and physics.
Numerical methods in Transient-heat-conductiontmuliya
This file contains slides on Numerical methods in Transient heat conduction.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Finite difference eqns. by energy balance – Explicit and Implicit methods – 1-D transient conduction in a plane wall – stability criterion – Problems - 2-D transient heat conduction – Finite diff. eqns. for interior nodes – Explicit and Implicit methods - stability criterion – difference eqns for different boundary conditions – Accuracy considerations – discretization error and round–off error - Problems
This document defines and provides examples of various types of signals and systems. It discusses continuous and discrete time signals, even and odd signals, deterministic and random signals, periodic and aperiodic signals. It also defines linear and nonlinear systems, time invariant systems, causal and non-causal systems, memory and memoryless systems, and stable and unstable systems. Examples are provided for each type of signal and system defined.
This document discusses the physical layer and media in networking. It covers:
- The physical layer is responsible for carrying information between nodes by converting data to signals and transmitting them across a medium.
- Data must be transformed into electromagnetic signals to be transmitted. Both analog and digital signals can be used for transmission.
- Periodic analog signals like sine waves are commonly used. They are defined by amplitude, frequency, and phase. Composite signals can be decomposed into sums of sine waves.
- The bandwidth of a signal is the range of its component frequencies. Frequency spectrum refers to the specific frequencies present in a signal.
This document provides information about an Advanced Physics course offered at Mbeya University of Science and Technology. The course code is NS 6141 and it covers dimensions of physical quantities, atomic theory, and radioactivity. It will be taught on Fridays from 7:30-9:45am in the Sports Hall by instructor Charles Kadala. Students will be assessed based on two class tests, assignments, and an end of semester exam. The document also provides details on the concepts that will be covered related to dimensions of physical quantities, including defining, explaining, deriving formulas for, and checking formulas using dimensions.
This document discusses frequency concepts in continuous and discrete time signals. For continuous time signals, frequency is defined as cycles per second and relates to the periodic nature of sinusoidal signals. Discrete time signals are periodic only if the frequency is a rational number. The fundamental period is the smallest value that makes the signal periodic. As frequency increases for both continuous and discrete signals, the number of oscillations increases but the period decreases.
Fourier Series for Continuous Time & Discrete Time SignalsJayanshu Gundaniya
- Fourier introduced Fourier series in 1807 to solve the heat equation in a metal plate. The heat equation is a partial differential equation describing the distribution of heat in a body over time.
- Prior to Fourier's work, there was no known solution to the heat equation in the general case. Fourier's idea was to model a complicated heat source as a superposition of simple sine and cosine waves.
- This superposition or linear combination of sine and cosine waves is called the Fourier series. It allows any periodic function to be decomposed into the sum of simple oscillating functions. Although originally introduced for heat problems, Fourier series have wide applications in mathematics and physics.
Numerical methods in Transient-heat-conductiontmuliya
This file contains slides on Numerical methods in Transient heat conduction.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Finite difference eqns. by energy balance – Explicit and Implicit methods – 1-D transient conduction in a plane wall – stability criterion – Problems - 2-D transient heat conduction – Finite diff. eqns. for interior nodes – Explicit and Implicit methods - stability criterion – difference eqns for different boundary conditions – Accuracy considerations – discretization error and round–off error - Problems
This document defines and provides examples of various types of signals and systems. It discusses continuous and discrete time signals, even and odd signals, deterministic and random signals, periodic and aperiodic signals. It also defines linear and nonlinear systems, time invariant systems, causal and non-causal systems, memory and memoryless systems, and stable and unstable systems. Examples are provided for each type of signal and system defined.
This document discusses the physical layer and media in networking. It covers:
- The physical layer is responsible for carrying information between nodes by converting data to signals and transmitting them across a medium.
- Data must be transformed into electromagnetic signals to be transmitted. Both analog and digital signals can be used for transmission.
- Periodic analog signals like sine waves are commonly used. They are defined by amplitude, frequency, and phase. Composite signals can be decomposed into sums of sine waves.
- The bandwidth of a signal is the range of its component frequencies. Frequency spectrum refers to the specific frequencies present in a signal.
Thermal diffusivity describes how quickly heat diffuses through a material. It is calculated as the thermal conductivity divided by the density and specific heat. Fick's laws of diffusion quantitatively describe steady-state and non-steady-state diffusion. For a heat pulse experiment passing through a brass tube, the temperature was measured at two points over time. Fourier analysis was used to determine the amplitude and phase of the temperature waves. The ratio of amplitudes and difference in phases was used to calculate the thermal diffusivity, found to be 0.231 cm^2/s, close to the actual value for brass of 0.3 cm^2/s.
This document discusses the four Fourier representations used to represent signals: Fourier series, discrete-time Fourier series, Fourier transform, and discrete-time Fourier transform. It explains why the frequencies of the sinusoids used in the representations are discrete or continuous depending on whether the signal is periodic or non-periodic. It also discusses why the integration/summation intervals and normalization factors differ between the four representations.
The International Journal of Engineering and Science (The IJES)theijes
The document discusses applying the Hansen-Bliek-Rohn method to solve the total least squares problem with interval data input. It begins with an introduction to total least squares and interval arithmetic. It then presents how to compute the mean and variance for statistical data expressed as intervals. Next, it discusses the general linear model for least squares and properties of the covariance matrix. It introduces using component-wise distance as a condition number for the weight matrix. In the following sections it will apply the Hansen-Bliek-Rohn method to a numerical example to solve the resulting interval linear system.
This document summarizes a physics assignment on key concepts including space, time, motion, frames of reference, and the Michelson-Morley experiment. It defines these concepts and describes the experimental setup and calculations used in the Michelson-Morley experiment. The experiment found no fringe shift, inconsistent with the expected results if the Earth moved through the hypothesized luminiferous ether. This led to the conclusion that the speed of light is constant regardless of motion through the ether, questioning the concept of the stationary ether.
The document provides information about a signals and systems course taught by Mr. Koay Fong Thai. It includes announcements about course policies, assessments, and schedule. Students are advised to ask questions, work hard, and submit assignments on time. The use of phones and laptops in class is strictly prohibited. The course aims to introduce signals and systems analysis using various transforms. Topics include signals in the time domain, Fourier transforms, Laplace transforms, and z-transforms. Reference books and a lecture schedule are also provided.
Time Table Scheduling Problem Using Fuzzy Algorithmic ApproachWaqas Tariq
Abstract In this paper we develop an algorithm to generate a course Time table using fuzzy algorithmic approach satisfying certain constraints. With an example we show that how these constraints are satisfied.
Signals and Systems-Fourier Series and TransformPraveen430329
This document discusses analysis of continuous time signals. It begins by introducing Fourier series representation of periodic signals using trigonometric and exponential forms. It describes properties of Fourier series such as linearity, time shifting, and frequency scaling. It then introduces the Fourier transform which transforms signals from the time domain to the frequency domain. Common Fourier transform pairs are listed. The Laplace transform is also introduced which transforms signals from the time domain to the complex s-domain. Key properties of the Laplace transform include linearity, scaling, time shifting, and the initial and final value theorems. Conditions for the existence of the Laplace transform are also provided.
Master Thesis on Rotating Cryostats and FFT, DRAFT VERSIONKaarle Kulvik
This thesis studied the vibrational and rotational aspects of the Cryo I Helsinki cryostat using Fourier analysis methods. Extensive Fourier analysis was performed to model the vibrations mathematically. The goal was to lower noise levels to improve cryostat operations. The second part of the work tested the homogeneity of a superconducting magnet. Significant preparation was required to build testing equipment for evaluating the magnet.
This document summarizes key concepts relating to stellar spectra and temperatures:
1. Stars are classified based on their spectra into spectral types running from O to M, which broadly corresponds to temperature, from hottest to coolest.
2. Different elements and ions absorb or emit light at characteristic wavelengths, allowing spectra to reveal a star's composition and physical properties.
3. Stellar radiation can be approximated as blackbody radiation of an effective temperature, though real stars deviate somewhat. Color indices like B-V relate to temperature.
4. The Hertzsprung-Russell diagram plots stellar properties like luminosity versus temperature/spectral type, revealing patterns of stellar evolution.
Experiment 4
Newtonian Cooling
EGME 306A
Group 2
ABSTRACT
The objective of this experiment is to understand the relationship between the change of temperature of an object and its surroundings. The Newtonian Cooling says that the temperature of an object is proportional to the temperature of the surrounding. The reason for the experiment is to make an experiment that measures temperature using a transducer of our own choice, understand the heat transfer and determine the coefficient of the heat transfer.
TABLE OF CONTENTS
Abstract ……………………………………………………………………………2
Table of Contents…………………………………………………………………..3
Introduction and Theory……………………………………………………….......4-9
Procedures………………………………………………………………………..10-11
Summary of Important Results…………………………………………………….12
Sample Calculations and Error Analysis…………………………………………...13
Discussion and Conclusion…………………………………………………………14
References…………………………………………………………………………..15
Appendix…………………………………………………………………………16-19
INTRODUCTION AND THEORY
In this experiment, a mass of lead in a crucible will be heated to its melting point and a transducer will be inserted in the lead. The heating is then ceased and the data of temperature versus time are accumulated by some data-acquisition system of your choice.
It is known from thermodynamics that when two bodies at different temperatures are in contact, heat will flow from the hotter body to the cooler one in a process known as Heat Transfer. The rate of this heat flow depends upon the temperature difference and thermal resistances in much the same way that electric current depends upon the potential difference (voltage) and electrical resistances. In solids, heat transfer occurs by molecular motion in a process called conduction, whereas in fluids, such as air and water, heat is transferred by fluid motion in a process called convection. In addition, heat is also transferred by electromagnetic radiation in transparent substances, or in a vacuum.
Consider a solid object in contact with air. If the surface temperature of the body, , is higher than the air temperature, , then there will be heat transferred from the object to the air. Newton proposed that the rate of this heat transfer, q, is proportional to the surface area of the object, A, and the temperature difference, :
(IV-1)
where the constant of proportionality, h, is called the heat transfer coefficient. Equation (IV-1) is known as the Newton’s rate equation.
In Newton’s time, the actual mechanism whereby this heat transfer occurred was not well understood. Today, however, it is known that heat transfer from a surface involves convection and radiation, and that these two mechanisms occur in parallel. As a result, the total rate of heat transfer from the surface, q, is the sum of the parts due to convection, , and radiation,. Thus, from Eq. (IV-1),
(IV-2)
where,
= convective heat transfer coefficient ...
The document provides instructions for a 5-hour theoretical physics competition with 3 questions. It details formatting requirements for working out the questions, including labeling pages with question number, page number, and total pages used. It also provides instructions for arranging the completed pages in proper order at the end. The first theoretical question is about vibrational modes in a linear crystal lattice model and includes parts on deriving the equation of motion, solving for mode frequencies and wave numbers, calculating average phonon energy, determining total crystal energy, and relating heat capacity to temperature. The second question considers a "rail gun" device constructed by a young man to launch himself across a strait to reach his love within 11 seconds. It involves deriving acceleration, calculating
ABSTRACTThe objective of this experiment is to understa.docxannetnash8266
ABSTRACT
The objective of this experiment is to understand the relationship between the change of temperature of an object and its surroundings. The Newtonian Cooling says that the temperature of an object is proportional to the temperature of the surrounding. The reason for the experiment is to make an experiment that measures temperature using a transducer of our own choice, understand the heat transfer and determine the coefficient of the heat transfer.
TABLE OF CONTENTS
Abstract ……………………………………………………………………………2
Table of Contents…………………………………………………………………..3
Introduction and Theory……………………………………………………….......4-9
Procedures………………………………………………………………………..10-11
Summary of Important Results…………………………………………………….12
Sample Calculations and Error Analysis…………………………………………...13
Discussion and Conclusion…………………………………………………………14
References…………………………………………………………………………..15
Appendix…………………………………………………………………………16-19
INTRODUCTION AND THEORY
In this experiment, a mass of lead in a crucible will be heated to its melting point and a transducer will be inserted in the lead. The heating is then ceased and the data of temperature versus time are accumulated by some data-acquisition system of your choice.
It is known from thermodynamics that when two bodies at different temperatures are in contact, heat will flow from the hotter body to the cooler one in a process known as Heat Transfer. The rate of this heat flow depends upon the temperature difference and thermal resistances in much the same way that electric current depends upon the potential difference (voltage) and electrical resistances. In solids, heat transfer occurs by molecular motion in a process called conduction, whereas in fluids, such as air and water, heat is transferred by fluid motion in a process called convection. In addition, heat is also transferred by electromagnetic radiation in transparent substances, or in a vacuum.
Consider a solid object in contact with air. If the surface temperature of the body, , is higher than the air temperature, , then there will be heat transferred from the object to the air. Newton proposed that the rate of this heat transfer, q, is proportional to the surface area of the object, A, and the temperature difference, :
(IV-1)
where the constant of proportionality, h, is called the heat transfer coefficient. Equation (IV-1) is known as the Newton’s rate equation.
In Newton’s time, the actual mechanism whereby this heat transfer occurred was not well understood. Today, however, it is known that heat transfer from a surface involves convection and radiation, and that these two mechanisms occur in parallel. As a result, the total rate of heat transfer from the surface, q, is the sum of the parts due to convection, , and radiation,. Thus, from Eq. (IV-1),
(IV-2)
where,
= convective heat transfer coefficient
= effective radiative heat transfer coefficien.
This document provides a tutorial on the Fast Fourier Transform (FFT). It begins by explaining that the FFT is a faster version of the Discrete Fourier Transform (DFT) that takes a discrete signal in the time domain and transforms it into the discrete frequency domain. It then reviews other transforms taught in previous courses and explains how the DFT relates to the Discrete-Time Fourier Transform (DTFT). The document provides MATLAB examples demonstrating how to use the FFT function to compute the DFT of signals and understand the results. It concludes by discussing how to properly analyze a signal's spectrum using the FFT with MATLAB.
1. Fourier transforms can be used to analyze aperiodic signals by extending the period to infinity, turning the aperiodic signal into a periodic one. This allows the computation of Fourier coefficients using the continuous-time Fourier transform (CTFT).
2. The CTFT of an aperiodic signal results in a continuous function of frequency rather than discrete frequencies. Key examples are computed, such as the CTFT of an impulse function being 1 for all frequencies and the CTFT of a constant function being an impulse at zero frequency.
3. The CTFT represents the frequency content of a signal and is useful for analyzing aperiodic real-world signals. Examples demonstrate how the CTFT can be used to analyze signals like sinusoids
This document discusses standing waves, which occur when two waves of equal amplitude and wavelength traveling in opposite directions interfere. It defines nodes as points of no motion and antinodes as points of maximum amplitude. The distance between a node and antinode is always λ/4, where λ is the wavelength. Key equations are provided for calculating the wavelength, frequency, and location of nodes and antinodes for standing waves on strings. Examples are given for standing waves on guitar strings and how changing the tension affects the fundamental frequency.
This document discusses principles of communication and representation of signals. It begins with an introduction to the communication process and challenges involved. Signals exist in the time and frequency domains, and Fourier analysis using the Fourier series and Fourier transform helps characterize signals in the frequency domain. Periodic signals can be represented by a Fourier series which decomposes the signal into a sum of complex exponentials at discrete frequencies that are integer multiples of the fundamental frequency. Examples are provided to illustrate calculation of Fourier coefficients and representation of periodic signals in the exponential and trigonometric forms of the Fourier series. Spectral plots from a spectrum analyzer are also presented for various waveforms.
This document discusses various MRI pulse sequences. It begins by describing the basic spin echo (SE) sequence, noting that the two main parameters are TR and TE. It then discusses how varying these parameters can produce T1-weighted, T2-weighted, or proton density weighted images. The document next summarizes fast spin echo and gradient echo sequences. It concludes by discussing advanced gradient echo techniques like steady-state sequences and how they can provide very fast imaging, as well as discussing factors that influence image quality and artifacts.
This experiment studied standing waves on strings by measuring the relationship between wave velocity, string tension, and other factors. Three parts were conducted: 1) measuring the period of a simple pendulum at various lengths to determine the effect of length on period, 2) finding the period of a physical pendulum at different angles, and 3) examining coupled pendulums in different normal modes. The results were analyzed to calculate the acceleration due to gravity and percent error. While the data followed expected trends, some discrepancies were due to imperfect measurements and friction. Overall, the experiment demonstrated how string properties influence wave properties.
Bounds for overlapping interval join on MapReduceShantanu Sharma
This document summarizes a paper on mapping interval join problems to MapReduce. It presents algorithms for assigning intervals to reducers in different scenarios: unit-length and equally-spaced intervals, variable-length but equally-spaced intervals, and a general case of variable-length intervals. The algorithms aim to respect reducer capacity while ensuring overlapping intervals are assigned to a common reducer. Proofs are given that the algorithms achieve near-optimal upper bounds on data replication compared to theoretical lower bounds.
This document contains slides on transient heat conduction from a lecture. It discusses lumped system analysis where the internal conduction resistance is negligible compared to the surface convection resistance. For lumped systems, the temperature at any point in the solid varies only with time. It introduces the Biot and Fourier numbers which are used to determine if lumped system analysis can be applied for a given solid geometry and time. The temperature distribution equation for lumped systems is presented.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Thermal diffusivity describes how quickly heat diffuses through a material. It is calculated as the thermal conductivity divided by the density and specific heat. Fick's laws of diffusion quantitatively describe steady-state and non-steady-state diffusion. For a heat pulse experiment passing through a brass tube, the temperature was measured at two points over time. Fourier analysis was used to determine the amplitude and phase of the temperature waves. The ratio of amplitudes and difference in phases was used to calculate the thermal diffusivity, found to be 0.231 cm^2/s, close to the actual value for brass of 0.3 cm^2/s.
This document discusses the four Fourier representations used to represent signals: Fourier series, discrete-time Fourier series, Fourier transform, and discrete-time Fourier transform. It explains why the frequencies of the sinusoids used in the representations are discrete or continuous depending on whether the signal is periodic or non-periodic. It also discusses why the integration/summation intervals and normalization factors differ between the four representations.
The International Journal of Engineering and Science (The IJES)theijes
The document discusses applying the Hansen-Bliek-Rohn method to solve the total least squares problem with interval data input. It begins with an introduction to total least squares and interval arithmetic. It then presents how to compute the mean and variance for statistical data expressed as intervals. Next, it discusses the general linear model for least squares and properties of the covariance matrix. It introduces using component-wise distance as a condition number for the weight matrix. In the following sections it will apply the Hansen-Bliek-Rohn method to a numerical example to solve the resulting interval linear system.
This document summarizes a physics assignment on key concepts including space, time, motion, frames of reference, and the Michelson-Morley experiment. It defines these concepts and describes the experimental setup and calculations used in the Michelson-Morley experiment. The experiment found no fringe shift, inconsistent with the expected results if the Earth moved through the hypothesized luminiferous ether. This led to the conclusion that the speed of light is constant regardless of motion through the ether, questioning the concept of the stationary ether.
The document provides information about a signals and systems course taught by Mr. Koay Fong Thai. It includes announcements about course policies, assessments, and schedule. Students are advised to ask questions, work hard, and submit assignments on time. The use of phones and laptops in class is strictly prohibited. The course aims to introduce signals and systems analysis using various transforms. Topics include signals in the time domain, Fourier transforms, Laplace transforms, and z-transforms. Reference books and a lecture schedule are also provided.
Time Table Scheduling Problem Using Fuzzy Algorithmic ApproachWaqas Tariq
Abstract In this paper we develop an algorithm to generate a course Time table using fuzzy algorithmic approach satisfying certain constraints. With an example we show that how these constraints are satisfied.
Signals and Systems-Fourier Series and TransformPraveen430329
This document discusses analysis of continuous time signals. It begins by introducing Fourier series representation of periodic signals using trigonometric and exponential forms. It describes properties of Fourier series such as linearity, time shifting, and frequency scaling. It then introduces the Fourier transform which transforms signals from the time domain to the frequency domain. Common Fourier transform pairs are listed. The Laplace transform is also introduced which transforms signals from the time domain to the complex s-domain. Key properties of the Laplace transform include linearity, scaling, time shifting, and the initial and final value theorems. Conditions for the existence of the Laplace transform are also provided.
Master Thesis on Rotating Cryostats and FFT, DRAFT VERSIONKaarle Kulvik
This thesis studied the vibrational and rotational aspects of the Cryo I Helsinki cryostat using Fourier analysis methods. Extensive Fourier analysis was performed to model the vibrations mathematically. The goal was to lower noise levels to improve cryostat operations. The second part of the work tested the homogeneity of a superconducting magnet. Significant preparation was required to build testing equipment for evaluating the magnet.
This document summarizes key concepts relating to stellar spectra and temperatures:
1. Stars are classified based on their spectra into spectral types running from O to M, which broadly corresponds to temperature, from hottest to coolest.
2. Different elements and ions absorb or emit light at characteristic wavelengths, allowing spectra to reveal a star's composition and physical properties.
3. Stellar radiation can be approximated as blackbody radiation of an effective temperature, though real stars deviate somewhat. Color indices like B-V relate to temperature.
4. The Hertzsprung-Russell diagram plots stellar properties like luminosity versus temperature/spectral type, revealing patterns of stellar evolution.
Experiment 4
Newtonian Cooling
EGME 306A
Group 2
ABSTRACT
The objective of this experiment is to understand the relationship between the change of temperature of an object and its surroundings. The Newtonian Cooling says that the temperature of an object is proportional to the temperature of the surrounding. The reason for the experiment is to make an experiment that measures temperature using a transducer of our own choice, understand the heat transfer and determine the coefficient of the heat transfer.
TABLE OF CONTENTS
Abstract ……………………………………………………………………………2
Table of Contents…………………………………………………………………..3
Introduction and Theory……………………………………………………….......4-9
Procedures………………………………………………………………………..10-11
Summary of Important Results…………………………………………………….12
Sample Calculations and Error Analysis…………………………………………...13
Discussion and Conclusion…………………………………………………………14
References…………………………………………………………………………..15
Appendix…………………………………………………………………………16-19
INTRODUCTION AND THEORY
In this experiment, a mass of lead in a crucible will be heated to its melting point and a transducer will be inserted in the lead. The heating is then ceased and the data of temperature versus time are accumulated by some data-acquisition system of your choice.
It is known from thermodynamics that when two bodies at different temperatures are in contact, heat will flow from the hotter body to the cooler one in a process known as Heat Transfer. The rate of this heat flow depends upon the temperature difference and thermal resistances in much the same way that electric current depends upon the potential difference (voltage) and electrical resistances. In solids, heat transfer occurs by molecular motion in a process called conduction, whereas in fluids, such as air and water, heat is transferred by fluid motion in a process called convection. In addition, heat is also transferred by electromagnetic radiation in transparent substances, or in a vacuum.
Consider a solid object in contact with air. If the surface temperature of the body, , is higher than the air temperature, , then there will be heat transferred from the object to the air. Newton proposed that the rate of this heat transfer, q, is proportional to the surface area of the object, A, and the temperature difference, :
(IV-1)
where the constant of proportionality, h, is called the heat transfer coefficient. Equation (IV-1) is known as the Newton’s rate equation.
In Newton’s time, the actual mechanism whereby this heat transfer occurred was not well understood. Today, however, it is known that heat transfer from a surface involves convection and radiation, and that these two mechanisms occur in parallel. As a result, the total rate of heat transfer from the surface, q, is the sum of the parts due to convection, , and radiation,. Thus, from Eq. (IV-1),
(IV-2)
where,
= convective heat transfer coefficient ...
The document provides instructions for a 5-hour theoretical physics competition with 3 questions. It details formatting requirements for working out the questions, including labeling pages with question number, page number, and total pages used. It also provides instructions for arranging the completed pages in proper order at the end. The first theoretical question is about vibrational modes in a linear crystal lattice model and includes parts on deriving the equation of motion, solving for mode frequencies and wave numbers, calculating average phonon energy, determining total crystal energy, and relating heat capacity to temperature. The second question considers a "rail gun" device constructed by a young man to launch himself across a strait to reach his love within 11 seconds. It involves deriving acceleration, calculating
ABSTRACTThe objective of this experiment is to understa.docxannetnash8266
ABSTRACT
The objective of this experiment is to understand the relationship between the change of temperature of an object and its surroundings. The Newtonian Cooling says that the temperature of an object is proportional to the temperature of the surrounding. The reason for the experiment is to make an experiment that measures temperature using a transducer of our own choice, understand the heat transfer and determine the coefficient of the heat transfer.
TABLE OF CONTENTS
Abstract ……………………………………………………………………………2
Table of Contents…………………………………………………………………..3
Introduction and Theory……………………………………………………….......4-9
Procedures………………………………………………………………………..10-11
Summary of Important Results…………………………………………………….12
Sample Calculations and Error Analysis…………………………………………...13
Discussion and Conclusion…………………………………………………………14
References…………………………………………………………………………..15
Appendix…………………………………………………………………………16-19
INTRODUCTION AND THEORY
In this experiment, a mass of lead in a crucible will be heated to its melting point and a transducer will be inserted in the lead. The heating is then ceased and the data of temperature versus time are accumulated by some data-acquisition system of your choice.
It is known from thermodynamics that when two bodies at different temperatures are in contact, heat will flow from the hotter body to the cooler one in a process known as Heat Transfer. The rate of this heat flow depends upon the temperature difference and thermal resistances in much the same way that electric current depends upon the potential difference (voltage) and electrical resistances. In solids, heat transfer occurs by molecular motion in a process called conduction, whereas in fluids, such as air and water, heat is transferred by fluid motion in a process called convection. In addition, heat is also transferred by electromagnetic radiation in transparent substances, or in a vacuum.
Consider a solid object in contact with air. If the surface temperature of the body, , is higher than the air temperature, , then there will be heat transferred from the object to the air. Newton proposed that the rate of this heat transfer, q, is proportional to the surface area of the object, A, and the temperature difference, :
(IV-1)
where the constant of proportionality, h, is called the heat transfer coefficient. Equation (IV-1) is known as the Newton’s rate equation.
In Newton’s time, the actual mechanism whereby this heat transfer occurred was not well understood. Today, however, it is known that heat transfer from a surface involves convection and radiation, and that these two mechanisms occur in parallel. As a result, the total rate of heat transfer from the surface, q, is the sum of the parts due to convection, , and radiation,. Thus, from Eq. (IV-1),
(IV-2)
where,
= convective heat transfer coefficient
= effective radiative heat transfer coefficien.
This document provides a tutorial on the Fast Fourier Transform (FFT). It begins by explaining that the FFT is a faster version of the Discrete Fourier Transform (DFT) that takes a discrete signal in the time domain and transforms it into the discrete frequency domain. It then reviews other transforms taught in previous courses and explains how the DFT relates to the Discrete-Time Fourier Transform (DTFT). The document provides MATLAB examples demonstrating how to use the FFT function to compute the DFT of signals and understand the results. It concludes by discussing how to properly analyze a signal's spectrum using the FFT with MATLAB.
1. Fourier transforms can be used to analyze aperiodic signals by extending the period to infinity, turning the aperiodic signal into a periodic one. This allows the computation of Fourier coefficients using the continuous-time Fourier transform (CTFT).
2. The CTFT of an aperiodic signal results in a continuous function of frequency rather than discrete frequencies. Key examples are computed, such as the CTFT of an impulse function being 1 for all frequencies and the CTFT of a constant function being an impulse at zero frequency.
3. The CTFT represents the frequency content of a signal and is useful for analyzing aperiodic real-world signals. Examples demonstrate how the CTFT can be used to analyze signals like sinusoids
This document discusses standing waves, which occur when two waves of equal amplitude and wavelength traveling in opposite directions interfere. It defines nodes as points of no motion and antinodes as points of maximum amplitude. The distance between a node and antinode is always λ/4, where λ is the wavelength. Key equations are provided for calculating the wavelength, frequency, and location of nodes and antinodes for standing waves on strings. Examples are given for standing waves on guitar strings and how changing the tension affects the fundamental frequency.
This document discusses principles of communication and representation of signals. It begins with an introduction to the communication process and challenges involved. Signals exist in the time and frequency domains, and Fourier analysis using the Fourier series and Fourier transform helps characterize signals in the frequency domain. Periodic signals can be represented by a Fourier series which decomposes the signal into a sum of complex exponentials at discrete frequencies that are integer multiples of the fundamental frequency. Examples are provided to illustrate calculation of Fourier coefficients and representation of periodic signals in the exponential and trigonometric forms of the Fourier series. Spectral plots from a spectrum analyzer are also presented for various waveforms.
This document discusses various MRI pulse sequences. It begins by describing the basic spin echo (SE) sequence, noting that the two main parameters are TR and TE. It then discusses how varying these parameters can produce T1-weighted, T2-weighted, or proton density weighted images. The document next summarizes fast spin echo and gradient echo sequences. It concludes by discussing advanced gradient echo techniques like steady-state sequences and how they can provide very fast imaging, as well as discussing factors that influence image quality and artifacts.
This experiment studied standing waves on strings by measuring the relationship between wave velocity, string tension, and other factors. Three parts were conducted: 1) measuring the period of a simple pendulum at various lengths to determine the effect of length on period, 2) finding the period of a physical pendulum at different angles, and 3) examining coupled pendulums in different normal modes. The results were analyzed to calculate the acceleration due to gravity and percent error. While the data followed expected trends, some discrepancies were due to imperfect measurements and friction. Overall, the experiment demonstrated how string properties influence wave properties.
Bounds for overlapping interval join on MapReduceShantanu Sharma
This document summarizes a paper on mapping interval join problems to MapReduce. It presents algorithms for assigning intervals to reducers in different scenarios: unit-length and equally-spaced intervals, variable-length but equally-spaced intervals, and a general case of variable-length intervals. The algorithms aim to respect reducer capacity while ensuring overlapping intervals are assigned to a common reducer. Proofs are given that the algorithms achieve near-optimal upper bounds on data replication compared to theoretical lower bounds.
This document contains slides on transient heat conduction from a lecture. It discusses lumped system analysis where the internal conduction resistance is negligible compared to the surface convection resistance. For lumped systems, the temperature at any point in the solid varies only with time. It introduces the Biot and Fourier numbers which are used to determine if lumped system analysis can be applied for a given solid geometry and time. The temperature distribution equation for lumped systems is presented.
Similar to Satellite Tracking and Communication Lecture (20)
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
6. • Exercises
– They are introduced during the contact hours.
– Exercises are typical for exam problems
• Assignments
– Groups will be formed before in week 1.6
– Group assignment will be issued in week 1.6
– Due dates are menNoned in the assignment text
– Assignment reports do yield credits
• Maneesh Verma deals with all assignments and
exercises for satellite communicaNons, for
satellite tracking Bart Root is your guide.
06/10/17 TU Del3 class ae3535-16 6
7. • Preference for MATLAB during exercises/assignments
• Structure of a report
• Explain the problem and the soluNon
• Include MATLAB results
• Explain task distribuNon in your group (if applicable)
• Explain how you validated your results?
• HandwriSen reports are fine as long as we can read them
• Copied and pasNng from lecture notes, the internet and other
sources is not allowed
• Convert your report to an unsigned PDF file
• Submit your reports to brightspace, there are individual
and groups folders for assignment or exercise, consult
your TA.
06/10/17 TU Del3 class ae3535-16 7
8. 06/10/17 TU Del3 class ae3535-16 8
Week Topics
1.1 IntroducNon to radio technology in spaceflight, Nme and
frequency domain, Fourier transformaNon, FFT
1.2 ProperNes of the Fourier transform, schemaNcs transmiSer
and receiver, superheterodyne receiver, intermodulaNon,
so3ware defined receiver (SDR)
1.3 LC networks, admiSance of inductors and capacitors, RC
constant, LC circuit, π filters, LCR circuits, Q factor,
transmission lines, antenna’s
1.4 Impedance matching, modulaNon, propagaNon, signal and
noise, link margin
1.5 Digital modulaNon, radio astronomy, GNSS
1.6 PracNcal
1.7 PracNcal
10. • Satellites, rockets, parts of rockets, etc,
all is nowadays tracked by radio
• Visual contact:
– maybe for several kilometer, and only for
verificaNon purposes
– In the past we relied on opNcal tracking
• Radio-range depends on:
– Frequencies used
– Antenna characterisNcs
– Transmit power and receiver sensisiNvity
– Antenna horizon and field of view
• CommunicaNon and navigaNon are
closely related, in fact, there is hardly
any difference
06/10/17 TU Del3 class ae3535-16 10
Baker-Nunn camera
S-band tracking system
17. Normally signals appear in the time domain:
v(t) with t ∈ [0,T]
where T is the length of a record. If we assume that:
v(t +T) = v(t)
then the function is said to be periodic. Furthermore
if v(t) has a finite number of oscillations in [0,T] then
we can develop v(t) in a series:
v(t) = Ai
i=0
N/2
∑ cos(ωit)+ Bi sin(ωit)
which is known as a Fourier series and where Ai and Bi
denote the Euler coefficients.
06/10/17 TU Del3 class ae3535-16 17
22. • EssenNally y=FFT(x) carries out a Fourier transform
• FFT algorithm input
– Real vector x(0..N-1) with N datasamples
– The record starts at 0 and is filled to N-1
• FFT algorithm output
– Euler coefficients are stored in the form of complex numbers
– Stored in y(i) are:
y(0) = A0 + I.B0 , y(1) = A1+ I.B1 , …, y(N/2) = AN/2 + I.BN/2
– I is a complex number:
– Be careful with scaling factors, check this always with a test funcNon of
which you now the Euler coefficients in advance
– Suitable test funcNons are for instance linear sin and cos expressions
• FFT algorithms exploit symmetries of sin and cos funcNons, please
use MATLAB because it is thoroughly debugged.
• Be aware that indices in MATLAB vectors start at 1 (and not 0)
I = −1
06/10/17 TU Del3 class ae3535-16 22
43. A F A F O
antenna
informaNon
A: amplifiers, F: band pass filters, O: local oscillator
“InformaNon” changes either the frequency, the phase
or the amplitude of the oscillator
The band pass filters are required to eliminate,
unwanted, parasiNc frequencies such as overtones
which are taboo on the output
Never operate a transmiSer without an antenna,
because it is likely to kill the output amplifier
The use of transmiSers is bound to regula2ons, only
certain frequencies, power, and bandwidth can be used
for designated applicaNons.
06/10/17 TU Del3 class ae3-535 43
Transmission
line
44. antenna
L L C
A A
SPKR
D
A: amplifier
D: demodulator
C
D
Input Output
The voltage level
a3er demodulaNon
proporNonal to amplitude
input signal
06/10/17 TU Del3 class ae3-535 44
72. R
C
SPST
VC +VR = 0 with C =
Q
V
and I =
dQ
dt
Q(t)
C
+ I(t)R = 0 ⇒
Q(t)
C
+
dQ(t)
dt
R = 0
Q(t) = −RC
dQ
dt
⇒ Q(t) = Q(t0 )e−t/τ
with τ=RC so that V(t) =V(t0 )e−t/τ
When a complex notation is used
R.ejωt
+
ejωt
jωC
= 0 ⇒ ω =
j
RC
06/10/17 TU Del3 class ae3-535 72
73. ZC =
1
jωC
and ZL = jωL
ZLC = ( 1
ZL
+ 1
ZC
)−1
= ∞ ⇒
ω =
1
LC
C L
I
known
parallel resistance
consequence
The only thing you need to know is the impedance of inductors and capacitors,
The parallel resistance should be infinite for a LC circuit without dissipaNon
In that case ω should be as given, it is maintained when there are no losses
06/10/17 TU Del3 class ae3-535 73
76. C
L R
Energy loss in a LCR circuit
Z−1
= ZL
−1
+ ZC
−1
+ R−1
To obtain the dissipation P:
V = Hejωt
so that T =
2π
ω
P =
1
T
V2
Z0
T
∫ dt =
H2
R
1+
(ω2
LC −1)2
R2
ω2
L2
P0 = P(ω0 ) =
H2
R
and ω0 =
1
LC
Search now the ω where P(ω0 ) =
1
2
2 P(ω)
since this results in the bandwidth
(ω2
LC −1)2
R2
=ω2
L2
⇔ (ω −ω0 )(ω +ω0 ) =
ω
RC
≈ ω0Δω
By definition Q =
ω
Δω
=ω0RC =
RC
LC
= R
C
L
(Quality factor)
06/10/17 TU Del3 class ae3-535 76
83. 06/10/17 TU Del3 class ae3-535 83
In a transmission line signal propagation is described by
the so-called telegraphers equations (Oliver Heaviside, 1880)
∂V(x,t)
∂x
= −L
∂I(x,t)
∂t
− R.I(x,t)
∂I(x,t)
∂x
= −C
∂V(x,t)
∂t
−G.V(x,t)
For an ideal line we can set R = 0 and G = 0, we find:
∂V(x,t)
∂x
= −L
∂I(x,t)
∂t
and
∂I(x,t)
∂x
= −C
∂V(x,t)
∂t
so that
∂2
V(x,t)
∂t2
−u2 ∂2
V(x,t)
∂x2
= 0 and
∂2
I(x,t)
∂t2
−u2 ∂2
I(x,t)
∂x2
= 0
where u =1 LC is the propagation speed in the transmission line
85. Standing wave soluNon
Let us try separation of variables
V(x,t) =V(x)exp( jωt) and I(x,t) = I(x)exp( jωt)
in this case one case show that:
d2
V(x)
dx2
+ ω2
LC.V(x) = 0 and
d2
I(x)
dx2
+ ω2
LC.I(x) = 0
we define wave number k =ω LC =
ω
u
d2
V(x)
dx2
+ k2
V(x) = 0 and
d2
I(x)
dx2
+ k2
I(x) = 0
Result: one dimensional Helmholtz wave equation
86. General soluNon standing waves
06/10/17 TU Del3 class ae3-535 86
V(x) =V1 e− j.k.x
+V2 ej.k.x
I(x) =
V1
z0
e− j.k.x
−
V2
z0
ej.k.x
z0 =
L
C
V
x
(characterisNc impedance)
Coaxial cables usually come with an impedance between 50Ω
and 100Ω, twin lines 300 to 450Ω. Coax: asymmetric, Twin:
symmetric
93. • The decibel is defined as:
• Normally Pref = 1
– dBW is used for power relaNve to 1 WaS
– dBm is used for power relaNve to 10-3 WaS
– dBi is the gain relaNve to an isotropic antenna
– dBd is the gain relaNve to a dipole
– dBc is takes relaNve to a carrier
• MathemaNcs:
– Adding dB’s is the same as mulNplicaNon
– SubtracNng dB’s : divide values
dB=10log10
P
Pref
!
"
#
$
%
&
107. • Dipole
• Half dipole, quarter dipole, etc
• MulN-element yagi antennas
• Helical antenna’s
• Patch antenna’s
• Parabolic antenna’s
• AcNve antenna’s (means that a remote receiving
antenna in a noise free environment comes with
an LNA to counteract transmission line losses)
06/10/17 TU Del3 class ae3-535 107
108. • Antenna gain reveals that the antenna is somehow
direcNonal.
• Your ears and your voice are direcNonal antennas
• Rather than that all radiated power goes out in every
direcNon, a direcNonal antenna takes care of radiaNng
the transmiSed power along a paSern.
• Antenna gains are expressed as dBi and these are
relaNve to a theoreNcal isotropic antenna that has
unit gain.
• DirecNonal antennas has a front-back raNo in dB
• When you receive a signal a similar thing happens, the
incoming energy is focused onto one point
06/10/17 TU Del3 class ae3-535 108
119. This lecture
• Impedance matching
• IntroducNon to modulaNon
• Signal propagaNon
• Signal and noise
• Link margin calculaNon
• Reference material:
– Electronics, A system approach, 6th ediNon Neil Storey
– Week 1.3: Chapters 1-9
– Week 1.4 and 1.5: Chapter 29
121. Impedance matching
• Impedances:
– Transceiver : design of power amplifier (50 Ω)
– Transmission line : type of line that is used (50 Ω)
– Antenna : type of antenna that is used (we hope it is 50 Ω)
– In the ideal case all impedances should be the same
• The reality is:
– The antenna does not match to the transmission line
– TransmiSed signal is reflected back to the transmiSer,
– Reflected signal could damage the transmiSer
• For RF circuits we measure a standing wave raNo (SWR)
– We opNmize the SWR and it should become 1
– There are various ways to accomplish an impedance match
06/10/17 TU Del3 class ae3-535 121
134. FM beRer than AM?
• Yes:
– FM less suscepNble to variaNons in recepNon strength
– FM is therefore more resilient to noise
– FM does not require highly linear amplifiers
• No:
– Requires more bandwidth, FM is typically used at
frequencies >100 MHz where there is enough
bandwidth
– DemodulaNon circuits are more difficult (PLL’s etc) (is
not a real issue nowadays)
06/10/17 TU Del3 class ae3-535 134
147. Physics of noise at the receiver
06/10/17 TU Del3 class ae3-535 147
In reality we deal with electronic components which
have a certain temperature T, all components emit
electromagnetic radiation:
P = kT B with k =1.38064854×10−23
J K−1
and B bandwidth
The Bolzmann constant comes from
k =
R
N
where R is a gas constant and N Avogadro's number
For semiconductors etc the thermal voltage is:
VT =
kT
q
where q is the charge of an electron
P is the Power contained in the noise
148. Physics of noise: spectral density
06/10/17 TU Del3 class ae3-535 148
Spectral density is specified in dBm/Hz, but how?
For T=290K (room temperature) we find
Pdbm =10log10 (
kT
10−3
) = −174 dBm/Hz
for a bandwidth of 1 MHz we get -114dBm,
note that the dBm calculation refers to 1mW
and that we can add to multiply or subtract
to divide due to the definition of the decibel.
152. Link margin calcula2on
06/10/17 TU Del3 class ae3-535 152
TransmiSer Receiver
PT PR
Free space loss
PR = PT − L +GT +G R with L =
4πd
λ
⎛
⎝
⎜
⎞
⎠
⎟
2
or in dB
L = −20log10 (λ)+ 20log10 (d)+ 21.98 where 21.98 =10log10 ((4π)2
)
M = PR − Nr is the so called link margin, preferable it is > 0
Nr = kT B + Nd
Nd : You got it from the noise floor measurement
153. Example link margin calcula2on
• Transmit power : 10mW which is 10dBm
• Receiver noise: -100dBm (noise floor measurement)
• Distance = 1000m, Frequency=5.8GHz, FSL = 107.7dB
• Gains transmiSer: 0dB, receiver: 0dB (ant./line etc)
• Margin: 10-107.7-(-100) = 2.3dB > 0 dB (ok);
– Obstacles (wet leaves, etc) would aSentuate the signal
– They introduce noise or even completely block the signal
– Any reflector in the Fressnel ellipse affects the quality
• Various opNons to improve the situaNon:
– Increase the antenna gain
– Choose beSer antenna posiNons (no trees, hills, buildings)
06/10/17 TU Del3 class ae3-535 153
155. Signal, noise, bandwidth
06/10/17 TU Del3 class ae3-535 155
dB
f
Signal 1 Signal 2
noise
Clearly signal 1 is below the noise level, and signal 2 is above it, and intuiNvely
you would think that signal 1 could not be received while signal 2 could, however,
this is not per se true. In week 1.5 we will conNnue with this topic
SNR
177. We start with
S
N
=100.1×SNRdb
C ≤ Blog2 1+
S
N
⎛
⎝
⎜
⎞
⎠
⎟ and
S
N
B =
Eb
No
C
C
B
= log2 1+
Eb
No
C
B
⎛
⎝
⎜
⎞
⎠
⎟ ⇒ 2C B
−1=
Eb
No
C
B
η =
C
B
⇒
2η
−1
η
=
Eb
No
⇒
η→0
lim
2η
−1
η
⎛
⎝
⎜
⎞
⎠
⎟ = ln(2) = 0.693...
As a result we find that min
Eb
No
⎛
⎝
⎜
⎞
⎠
⎟
dB
= -1.592... dB
179. Digital receiver sensi2vity model
The relation between carrier (signal) to noise ratio and the
spectral density of energy is B
C
N
=
Eb
N0
fb where fB is the
bit rate and B the bandwidth,
EB
N0
is the energy per symbol
to noise ratio spectral density. As a result the receiver sensitivity
sensitivity σ becomes:
σ =10log10 (B)+10log10
C
N
⎛
⎝
⎜
⎞
⎠
⎟−174dBm + NF
which is equivalent to:
σ =−174dBm + NF +
Eb
N0
⎛
⎝
⎜
⎞
⎠
⎟
dB
+10log10 ( fB )
Where NF is the noise floor of the receiver, it says something
about the quality of the receiver.
189. GPS signal structure
• What informaNon is relevant for the user?
– L1 : contains C/A codes and the P (or Y) codes
– L2 : contains P (or Y) codes
– C/A codes bandwidth is 1.023 MHz, data rate = 50 bps
– P(Y) code bandwidth is 10.23 MHz, data rate = 50 bps
• Codes are unique for each GPS space vehicle (S/V)
– Code repeNNon length C/A = 1023, or 1 milliseconds at 1.023 mbps
– Code length P(Y) = 6.19 x 1012, or 7 days at 10.23 mbps,
– The full P(Y)-code cycle is length is however much longer
• New GPS signals are planned in the near future, the
above overview is not meant to represent the new
situaNon
• Also: GNSS = GPS + Galileo + Glonass + Beidou
06/10/17 TU Del3 class ae3-535 189
190. PRN or Gold code
XOR 0 1
0 0 1
1 1 0
D
Ck
Q
Flip
Flop
FF1 FF4 FF5 FF6 FF7 FF8 FF2 FF3
preset
clock
PRN code
XOR
A
B
C
01001110101…
XOR truth table
Q=D a3er
acNve flank
of Ck
hSps://www.maximintegrated.com/en/app-notes/index.mvp/id/1890
193. GPS Receiver
• EssenNally it is a superheterodyne receiver except that
you would not be able to hear anything because:
– All S/V PRN signals are on top of one another
– The signals are below the noise level of the receiver
• So how would this work? SNR < 1 seems a bit strange.
• Digital code correlaNon solves this problem:
– Generate PRN code replica’s (C/A and NAV are always
accessible, P-codes were open, Y-codes are classified)
– Degrees of freedom during correlaNon are the code phase
offset and the frequency of the signal.
– Conclusion, there are at least two tracking loops in a GPS
receiver, one aligns the codes, the other aligns the
frequency
06/10/17 TU Del3 class ae3-535 193
196. 06/10/17 TU Del3 class ae3-535 196
By correlating the received signal with a replica code
you introduce a so-called processing gain:
db(Gain) = 10 log10
bandwidth of the PRN code
bandwidth of the data rate
!
"
#
$
%
&
db(Gain) =10 log10
2MHz
100Hz
!
"
#
$
%
& = 43db
which lifts the signal above the noise level
Processing gain due to correla2on
For more details: D. Doberstein, Fundamentals of GPS receivers, appendix A, Springer Verlag 2012
197. GPS naviga2on
• Transmit Nme of GPS signal is known (atom clock)
• Received from the GPS S/V’s are (X,Y,Z,T)satellite
• Observed: Code-phase difference between the local
oscillator (iniNally not synchronized) and the
transmiSed code
• This informaNon is called pseudo-range informaNon
(comes with a 1msec ambiguity)
• Pseudo range = c . (Treceived – Tsend) + Biasreceiverclock
• Phase range à integrate the Doppler effect (This is
what scienNsts/engineers call the carrier phase)
06/10/17 TU Del3 class ae3-535 197
200. Exercise on digital modula2on
• Problem descripNon
– Assume a 2.4 GHz QPSK signal,
– Channel spacing is 40 MHz for 802.11n wifi
– Assume SNRs between -15 and +15dB
– BER = 1/2*erfc(sqrt(2*Eb/No)*sin(pi/4))
• Exercise:
– The channel capacity is a funcNon of the SNR, How is
the BER is affected by the SNR? Make a graph.
– At what SNR is your wifi connecNon sNll comfortable?
– EsNmate the spectral efficiency parameter, and the
minimum Eb/No that is possible.
06/10/17 TU Del3 class ae3-535 200
208. What do you get?
• Moteino board, plugged onto a breadboard
• Jumper wires and USB cables
• Sign-up with name and student ID and return the
hardware a3er period Q2
• You can leave your experiment on the 9th floor, e.g. in
my office,
• You can take the boards with you as long as safe
transportaNon is demonstrated
• Preferred way of transportaNon: a carton box
• Any boards that leaves the faculty needs to be
registered
06/10/17 TU Del3 class ae3-535 208
219. • Experiment
– Find an area that is mostly free of obstrucNon
– Measure the RSSI offset close to the beacon.
– Measure the RSSI values at a distance up to 100 meter
from the beacon
– Evaluate the free space loss term in the link budget.
• ReporNng
– Answer all quesNons related to the FSL experiment
– Include a plot the measured free space loss
– Match the plot with a FSL equaNon
• Maximum: 3 points out of 10
06/10/17 TU Del3 class ae3-535 219
222. Experiment to simulate a satellite to groundstaNon link
• Experiment
– You need two set-ups of the Arduino IDE
– No baSery powered experiments are allowed, only laptop and USB
– One moteino is the satellite, the other moteino is the ground staNon
– The satellite performs measurements of the NTC and/or LDRs.
– Ground staNon collects the measurements
– LEDs are the actuators on the satellite
– Make a funcNonal diagram first, consult a supervisor to check the design
– Get it to work and demonstrate the end-result to the TA
• ReporNng
– Include the schemaNc, calculate the current by pin in the moteino board
– The full experiment should be described in the report.
• Maximum: 2 points out of 10
223. • What we always expect
– A group report should be submiSed as one unsigned PDF file
– No separate MATLAB or Python code files or plots
– Clearly state which problem (1 to 4) you are reporNng
– All names and study numbers should be included
– DistribuNon of tasks should be included in the report
– Deadline: November the 14th 2017.
• Mandatory
– Free space loss experiment: 3 points
– Exercises previous weeks: 3 points
• OpNonal
– ModulaNon performance : 2 points
– SimulaNon ground staNon satellite: 2 points