Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 EE 1105 : Introduction to EE Freshman Seminar Lecture 10: Introduction to signals and systems

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Signals and Systems –Signal: Any time dependent physical quantity Constant – DC, Variable - AC Electrical, Optical, Mechanical –System: Object in which input signals interact to produce output signals. Linear System has some have fundamental properties that make it predictable: –Sinusoid in, sinusoid out of same frequency (when transients settle) –Double the amplitude in, double the amplitude out (when initial state conditions are zero)

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Signal Classification –Continuous Time vs. Discrete Time Telephone line signals, Neuron synapse potentials Stock Market, GPS signals –Analog vs. Digital Radio Frequency (RF) waves, battery power Computer signals, HDTV images Image Sources: Internet

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Unit Step Function u(t) Ramp function r(t)

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Below signal depends on independent variable t with parameters A, ω and . s= A Sin(ωt+  )=A Im{e j(ωt+  ) } A=Amplitude real ω =angular frequency  =phase Sin( ~ )=function ref:

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Signal Classification –Deterministic vs. Random FM Radio Signals Background Noise Speech Signals –Periodic vs. Aperiodic Sine wave Sum of sine waves with non- rational frequency ratio

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 System Classification –Linear vs. Nonlinear Linear systems have the property of superposition –If U →Y, U1 →Y1, U2 →Y2 then »U1+U2 → Y1+Y2 »A*U →A*Y Nonlinear systems do not have this property, and the I/O map is represented by a nonlinear mapping. –Examples: Diode, Dry Friction, Robot Arm at High Speeds. –Memoryless vs. Dynamical A memoryless system is represented by a static (non-time dependent) I/O map: Y=f(U). –Example: Amplifier – Y=A*U, A- amplification factor. A dynamical system is represented by a time-dependent I/O map, usually a differential equation: –Example: dY/dt=A*u, Integrator with Gain A. Mandelbrot set, a fractal image, result of a Nonlinear Discrete System Z n+1 =Z n ²+C Exact Equation, nonlinear Approximation around vertical equilibrium, linear

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 System Classification –Time-Invariant vs. Time Varying Time-invariant system parameters do not change over time. Example: pendulum, low power circuit Time-varying systems perform differently over time. Example: human body during exercise. –Causal vs. Non-Causal For a causal system, outputs depend on past inputs but not future inputs. Examples: most engineered and natural systems A non-causal system, outputs depend on future inputs. Example: computer simulation where we know the inputs a-priori, digital filter with known images or signals. –Stable vs. Unstable For a stable system the output to bounded inputs is also bounded. Example: pendulum at bottom equilibrium For an unstable system the ouput diverges to infinity or to values causing permanent damage. Example: short circuit on AC line.

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 An electronic amplifier is a device for increasing the power of a signal. It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude. There are various types of amplifier. Amplifier

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 A time shifter system shifts the function f(t) forward or backward by a specific time. The above system is a forward time shifter. It adds a delay (t 0) to the signal. t t Time shifter f(t)f(t – t 0 )

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 sampling is the reduction of a continuous-time signal to a discrete-time signal The sampling frequency must be higher than the frequency of the signal to be sampled. (minimum twice as high) Sampler ref:

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 An analog-to-digital converter (ADC, A/D) is a device that converts a continuous quantity to a discrete time digital representation. \ The system that does the opposite is called DAC Analog to Digital ref: DAC

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Conversion of Analog to digital is done in two step. Continuous analog  Sampled signal Sampled signal  Quantized digital signal A/DSampler ref:

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 A low-pass filter is a filter that passes low-frequency signals but attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency. ref: Low Pass Filter

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 A high-pass filter (HPF) is a device that passes high frequencies and attenuates (i.e., reduces the amplitude of) frequencies lower than its cutoff frequency. ref: Low Pass Filter

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 A band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. ref: Band Pass Filter

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels ref: Band –stop Filter

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 System Modeling Building mathematical models based on observed data, or other insight for the system. –Parametric models (analytical): ODE, PDE –Non-parametric models: graphical models - plots, look-up cause-effect tables –Mental models – Driving a car and using the cause-effect knowledge –Simulation models – Many interconnect subroutines, objects in video game

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Types of Models White Box –derived from first principles laws: physical, chemical, biological, economical, etc. –Examples: RLC circuits, MSD mechanical models (electromechanical system models). Black Box –model is entirely derived from measured data –Example: regression (data fit) Gray Box – combination of the two

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 White Box Systems: Electrical Defined by Electro-Magnetic Laws of Physics: Ohm’s Law, Kirchoff’s Laws, Maxwell’s Equations Example: Resistor, Capacitor, Inductor

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Physics of an Inductor Truncated hollow cylinder of permeability,  area, A, and length l m. Coil of N turns Flux linkage, Core flux,  Coil current, i

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Voltage Drop Across Inductor Note Passive Sign Convention

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Physics of a Capacitor Plate separation distance, g Plate area, A Current, i, and Charge, q. Dielectric material of permittivity, . Voltage across plates

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Physics of a Capacitor Current: Capacitance: Note Passive Sign Convention:

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Inductors in Series

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Capacitors in Parallel

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Inductors in Parallel

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Capacitors in Series

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 RLC Circuit as a System Kirchoff’s Voltage Law (KVL):

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 White Box Systems: Mechanical Newton’s Law: Mechanical-Electrical Equivalance: F (force) ~V (voltage) x (displacement) ~ q (charge) M (mass) ~ L (inductance) B (damping) ~ R (resistance) 1/K (compliance) ~ C (capacitance)

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 White-Box vs. Black-Box Models Newton-Euler Law: Image Sources: Internet

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Grey-Box Models Image Sources: Internet

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 White Box vs Black Box Models White Box ModelsBlack-Box Models Information SourceFirst PrincipleExperimentation AdvantagesGood Extrapolation Good understanding High reliability, scalability Short time to develop Little domain expertise required Works for not well understood systems DisadvantagesTime consuming and detailed domain expertise required Not scalable, data restricts accuracy, no system understanding Application AreasPlanning, Construction, Design, Analysis, Simple Systems Complex processes Existing systems Start to understand simple white continuous time models which are linear Eventually deal with grey-box or black-box models in real-life

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Application Areas for Systems Thinking Classical circuits & systems (1920s – 1960s) (transfer functions, state-space description of systems). First engineering applications: military - aerospace 1940’s-1960s Transitioned from specialized topic to ubiquitous in 1980s with EE applications to: –Electronic circuit design –Signal and image processing Networks (wired, wireless), imaging, radar, optics. –Control of dynamical systems Feedback control, prediction/estimation/identification of systems, robotics, micro and nano systems

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Diagram Representation of Systems Hierarchical Diagram: Organizations Undirected Graph: NetworksFlowchart: Procedures, Software

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 System Simulation Software Matlab Simulink – ulink/7.6/demos/sl_env_intro_web.htmlhttp:// ulink/7.6/demos/sl_env_intro_web.html National Instruments Labview – s/environment.htmhttp:// s/environment.htm

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 EE-Specific Diagrams Block Diagram Model: –Helps understand flow of information (signals) through a complex system –Helps visualize I/O dependencies –Equivalent to a set of linear algebraic equations. –Based on a set of primitives: Transfer FunctionSummer/Difference Pick-off point Signal Flow Graph (SFG): –Directed Graph alternative + + U2 U1U1+U2 U U U

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 EE-Specific Diagrams: Signal Flow Graph (SFG – Directed Graph) 2-port circuit SFG Multi-loop Control SFG Image Sources: Internet

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Integrator and Low Pass Filter from

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Differentiator and High Pass Filter from

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 EE 1106 Lab 9 Circuits

Dan O. Popa, Intro to EE, Freshman Seminar, Spring 2015 Acknowledgemengts: Dr. Bill Dillon, Dr. Kambiz Alavi, UTA Next Time: Homework 8 due 42