Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #9 Linear Circuit-Fourier- Digital Dr. Han Le ECE Dept.
Han Q Le©
ECE 3336 Introduction to Circuits & Electronics
Lecture Set #9Linear Circuit-Fourier-Digital
Dr. Han LeECE Dept.
Han Q Le©
Introduction to Circuits & Electronics
Input Output
It does something useful:- information- power
Han Q Le©
Concept of System in Electronics
R
Cinput vin[t] output vout[t]i(t)
R
C
output vout[t]i(t)input vin[t]
Low pass
High pass
System(circuits)
Input Output
Control
xk(t) yj(t)
k=1,..., mj=1,..., p
Han Q Le©
Linear (Time-Invariant) System
System(circuits)
Input Output
Control
xk(t) yj(t)
k=1,..., mj=1,..., p
tbxtax 21 tbytay 21 Input Output
This is called “linear”
Time-invariant DOES NOT mean time-constant. It means that it does not matter when you input the signals (today or 1,000,000 yr BC), you’ll get the same output
Han Q Le©
The most significant application of electronic systems is signal processing:
• generating: signal synthesis: converting information (logic) into electrical signal (voltage or current), encoding
• conditioning (transforming): signal shaping, filtering, amplifying
• transmitting: sending signal to other parts of the circuit, or over transmission media: conductor, air (EM waves), fiber optics (for long distance)
• receiving: transforming the signal, converting into information
Han Q Le©
Applications of mathematical techniques
Fourier transform
Harmonic function
Complex number
&analysisPhasors
Signal and AC circuit problems• RLC or any time-varying linear
circuits. Applicable to linear portion of circuits that include nonlinear elements
• Signal processing• signal analysis (spectral
decomposition)• filtering, conditioning (inc
amplification)• synthesizing
Han Q Le©
Outline
• Time-varying circuits and signals• Introduction to mathematical techniques:
– Harmonic functions– Complex analysis– Phasors– Fourier analysis and transform
• Applications of mathematical techniques to physical problems and circuits
Han Q Le©
refv
sv
Automatic Fan Control: The Analog WayWe have +-15 V and 5 V DC power input.
+15 V
-15 V
Temperature sensor input(low=0.5 V; high=4 V)
User preset (controllable) voltage input.
Voltage comparator
refout vvgv s
Han Q Le©
Automatic Fan Control: The Digital WayWe have +-15 V and 5 V DC power input.
Temperature sensor
User preset digital:
10101101
refout vvgv s
Micro-processor
However, the physical world is analog; the digital core is still based on the analog circuit principle. And outside the digital core, it is still an analog periphery.
The digital core
Han Q Le©
Digital Electronics• Signal processing is fundamentally mathematical operation
• In the past, electronic circuits were used to do signal processing mathematics directly on the signal voltage or current (analog).
• With digital electronic, voltage and current no longer represents the signal directly, they represent the numerical (digital) value of the signal
• Electronic circuits (ICs) are designed to perform numerical (digital) mathematical operations: microcontrollers, digital signal processors, FPGA, microprocessors…
Han Q Le©
• Electronics become “mathematical operation”-oriented at the functional design level
• However, fundamental electrical circuit behavior is still essential at the physical implementation level
Logical layer(Digital design)
Physical layer (Analog
implementation)
Han Q Le©
The basics• Voltage or current signal is time-dependent (otherwise,
there is no information transmitted)• Solving time-dependent differential equations for circuits
involving R, L, C is difficult & tedious• But if the signal is a pure harmonic of single frequency, we
can use phasor transform, which is easy• As it turns out, even if the signal is not a harmonic, Fourier
theorem tells us that it can be break down as a sum (or integral) of harmonics
• Hence, we can use phasor method, along with Fourier theorem to solve for any signal