Difference between revisions of "ECE 110/Concept List/S24"
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* An $$RC$$ can be both a high-pass filter (resistor voltage) or a low-pass filter (capacitor voltage) | * An $$RC$$ can be both a high-pass filter (resistor voltage) or a low-pass filter (capacitor voltage) | ||
* The "cut-off frequency" of a filter is the frequency at which the magnitude of the transfer function is $$\frac{1}{\sqrt{2}}\mathbb{H}_{max}$$ - this is also known as the "half-power frequency" | * The "cut-off frequency" of a filter is the frequency at which the magnitude of the transfer function is $$\frac{1}{\sqrt{2}}\mathbb{H}_{max}$$ - this is also known as the "half-power frequency" | ||
+ | |||
+ | == Lecture 17 - 3/7 - Phasor Domain Recap == | ||
+ | * Review of impedance | ||
+ | * Review of DCSS with singularity functions | ||
+ | * Transfer functions between current and voltage | ||
+ | * Using a calculator to find ACSS | ||
+ | |||
+ | == Lecture 18 - 3/19 - First and Second-Order Filter Intro == | ||
+ | * High and low-pass filters using RC and LR circuits | ||
+ | * Modular filters using VCVS | ||
+ | * 2nd order circuits and transfer functions for LRC circuit | ||
+ | * Resonant Frequency | ||
+ | |||
+ | == Lecture 19 - 3/21 - Transfer Function Redux == | ||
+ | * Magnitude and phase diagrams | ||
+ | * General second-order equation | ||
+ | |||
+ | == Lecture 20 - 3/26 - Operational Amplifier Intro == | ||
+ | * Model using two resistors and a VCVS | ||
+ | * Without feedback, only really good as a comparator | ||
+ | * Feedback from output to inverting input makes circuit more useful | ||
+ | * Ideal op-amp assumptions are about the op-amp, not the circuit: $$A\rightarrow\infty$$, $$r_i\rightarrow\infty$$, $$r_o\rightarrow 0$$ | ||
+ | * Using ideal op-amp with a circuit with feedback from output to inverting input leads to a very useful circuit with implications of: | ||
+ | ** No voltage drop between the input terminals | ||
+ | ** No current entering the input terminals | ||
+ | ** Still possible to have current at the output terminal! | ||
+ | |||
+ | == Lecture 21 - 3/28 - Test 2 == | ||
+ | |||
+ | == Lecture 22 - 4/2 - More Op-Amp Circuits == | ||
+ | * Various configurations that are directly or nearly-directly from the circuit developed in Lecture 20: | ||
+ | ** Inverting | ||
+ | ** Non-inverting | ||
+ | *** Buffer / Voltage follower as a specific instance | ||
+ | ** Inverting summation | ||
+ | ** Difference | ||
+ | ** Can use with reactive elements as well | ||
+ | |||
+ | == Lecture 23 - 4/4 - Analyzing Circuits with Op-Amps == | ||
+ | * See if you can recognize typical circuits from Lecture 22 | ||
+ | * If you have an ideal op-amp with feedback from the output terminal to the inverting terminal, use implications to label voltages / currents wherever possible | ||
+ | * Generally use KCL at inverting node | ||
+ | * Reminder of passive high and low-pass | ||
+ | * Introduction to active high and low-pass | ||
+ | * Introduction to active band-pass | ||
+ | |||
+ | == Lecture 24 - 4/9 - Digital Logic 1 == | ||
+ | * Introduction to binary | ||
+ | * Introduction to boolean operators | ||
+ | * Basic operations: not, and, or, xor | ||
+ | * Truth tables | ||
+ | * DeMorgan's Laws | ||
+ | * Minterms and maxterms | ||
+ | |||
+ | == Lecture 25 - 4/11 - Digital Logic 2 == | ||
+ | * Digital logic gates and schematics | ||
+ | * Complexity | ||
+ | * Boolean algebra relationships and simplifications | ||
+ | * Manual logic function minimization | ||
+ | * Gray code motivation and construction | ||
+ | * Karnaugh maps | ||
+ | ** Structure | ||
+ | ** Use in finding minimum sum of products (MSOP) form | ||
+ | ** Use in finding minimum product of sums (MPOS) form | ||
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Revision as of 01:29, 15 April 2024
Contents
- 1 Lecture 1 - 1/11 - Course Introduction, Nomenclature
- 2 Lecture 2 - 1/16 - Electrical Quantities
- 3 Lecture 3 - 1/18 - Equivalents
- 4 Lecture 4 - 1/23 - Brute Force Method; Delta-Wye; Voltage Division Part 1
- 5 Lecture 5 - 1/25 - Voltage Division Part 2, Current Division, and Node Voltage Division Part 1
- 6 Lecture 6 - 1/30 - Node Voltage Method
- 7 Lecture 7 - 2/1 - Current Methods
- 8 Lecture 8 - 2/6 - Linearity and Superposition
- 9 Lecture 9 - 2/8 - Thévenin and Norton Equivalent Circuits
- 10 Lecture 10 - 2/13 - Capacitors and Inductors
- 11 Lecture 11 - 2/15 - Initial Conditions and Finding Equations
- 12 Lecture 12 - 2/20 - Test 1
- 13 Lecture 13 - 2/22 - First-Order Circuits (constant forcing functions)
- 14 Lecture 14 - 2/27 - ACSS and Phasors
- 15 Lecture 15 - 2/29 - More ACSS and Phasors
- 16 Lecture 16 - 3/5 - More Phasors; Filters
- 17 Lecture 17 - 3/7 - Phasor Domain Recap
- 18 Lecture 18 - 3/19 - First and Second-Order Filter Intro
- 19 Lecture 19 - 3/21 - Transfer Function Redux
- 20 Lecture 20 - 3/26 - Operational Amplifier Intro
- 21 Lecture 21 - 3/28 - Test 2
- 22 Lecture 22 - 4/2 - More Op-Amp Circuits
- 23 Lecture 23 - 4/4 - Analyzing Circuits with Op-Amps
- 24 Lecture 24 - 4/9 - Digital Logic 1
- 25 Lecture 25 - 4/11 - Digital Logic 2
Lecture 1 - 1/11 - Course Introduction, Nomenclature
- Circuit terms (Element, Circuit, Path, Branch and Essential Branch, Node and Essential Node, Loop and Mesh).
- Accounting:
- # of Elements * 2 = total number of voltages and currents that need to be found using brute force method
- # of Essential Branches = number of possibly-different currents that can be measured
- # of Meshes = number of independent currents in the circuit (or generally Elements - Nodes + 1 for planar and non-planar circuits)
- # of Nodes - 1 = number of independent voltage drops in the circuit
- Electrical quantities (charge, current, voltage, power)
Lecture 2 - 1/16 - Electrical Quantities
- Passive Sign Convention and Active Sign Convention and relation to calculating power absorbed and/or power delivered.
- Power conservation
- Kirchhoff's Laws
- Number of independent KCL equations = nodes-1
- Number of independent KVL equations = meshes
- Example of how to find $$i$$, $$v$$, and $$p_{\mathrm{abs}}$$ using conservation equations and how to check using extra conservation equations
- $$i$$-$$v$$ relationships of various elements (ideal independent voltage source, ideal independent current source, short circuit, open circuit, switch)
- Resistor symbol (and spring symbol)
Lecture 3 - 1/18 - Equivalents
- Resistance as $$R=\frac{\rho L}{A}$$
- $$i$$-$$v$$ relationship for resistors; resistance [$$\Omega$$] and conductance $$G=1/R$$ $$[S]$$
- $$i$$-$$v$$ for dependent (controlled) sources (VCVS, VCCS, CCVS, CCCS)
- Combining voltage sources in series; ability to move series items and put together
- Combining current sources in parallel; ability to move parallel items and put together
- Equivalent resistances
- series and parallel
- Examples/Req
Lecture 4 - 1/23 - Brute Force Method; Delta-Wye; Voltage Division Part 1
- Brute Force method
- Delta-Wye equivalencies (mainly refer to book)
- Voltage Division
Lecture 5 - 1/25 - Voltage Division Part 2, Current Division, and Node Voltage Division Part 1
- Voltage Re-Division
- Current Division and Re-Division
- Basics of NVM
Lecture 6 - 1/30 - Node Voltage Method
- Examples on Canvas
- NVM
- Labels:
- Very Lazy: label ground, then make every other node a new unknown. Voltage sources, voltage measurements, and current measurements will provide additional equations.
- Lazy: label ground, then label any node connected to ground if it has a voltage source or voltage measurement. Make every other node a new unknown. Voltage sources not connected to ground, voltage measurements not connected to ground, and current measurements will provide additional equations.
- Smart: label ground; once a node gets labeled, if there is a voltage source or a voltage measurement anchored at that node, use the source or measurement to label the other node it is attached to. Current measurements will provide additional equations.
- Really Smart: same as smart, only also use voltage drops across resistors with current measurements to relate node voltages.
- Labels:
Lecture 7 - 2/1 - Current Methods
- Examples on Canvas
- BCM
- Labels:
- Label each (essential) branch current, using as few unknowns as possible by incorporating current source and current measurement labels
- Labels:
- MCM
- Labels:
- Label each mesh current, understanding that current sources, current measurements, and voltage measurements will require additional equations.
- Labels:
Lecture 8 - 2/6 - Linearity and Superposition
- Definition of a linear system
- Examples of nonlinear systems and linear systems
- Nonlinear system examples (additive constants, powers other than 1, trig):
- $$\begin{align*} y(t)&=x(t)+1\\ y(t)&=(x(t))^n, n\neq 1\\ y(t)&=\cos(x(t)) \end{align*} $$
- Linear system examples (multiplicative constants, derivatives, integrals):
- $$\begin{align*} y(t)&=ax(t)\\ y(t)&=\frac{d^nx(t)}{dt^n}\\ y(t)&=\int x(\tau)~d\tau \end{align*} $$
- Superposition
- Redraw the circuit as many times as needed to focus on each independent source individually
- Use combinations of Phm's Law, Voltaeg Division, and Current Division, rather than setting up and solving multiple equations
- If there are dependent sources, you must keep them activated and solve for measurements each time - this likely means that superposition may not actually make solving things easier.
Lecture 9 - 2/8 - Thévenin and Norton Equivalent Circuits
- Thévenin and Norton Equivalents
- Circuits with independent sources, dependent sources, and resistances can be reduced to a single source and resistance from the perspective of any two nodes
- Equivalents are electrically indistinguishable from one another
- Several ways to solve:
- If there are only independent sources, turn independent sources off and find $$R_{eq}$$ between terminals of interest to get $$R_{T}$$. Then find $$v_{oc}=v_{T}$$ and recall that $$v_T=R_Ti_N$$
- If there are both independent sources and dependent sources, solve for $$v_{oc}=v_T$$ first, then put a short circuit between the terminals and solve for $$i_{sc}=i_N$$. Recall that $$v_T=R_Ti_N$$
- If there are only dependent sources, you have to activate the circuit with an external source.
Lecture 10 - 2/13 - Capacitors and Inductors
- Intro to capacitors and inductors
- Basic physical models
- Basic electrical models
- Energy storage
- Continuity requirements
- Finding circuit equation models
- DCSS equivalents
Lecture 11 - 2/15 - Initial Conditions and Finding Equations
- DCSS equivalents
- Finding values just before and just after circuit changes
- For $$t=0^+$$, can model inductor as independent current source and capacitor as independent voltage source
- Using Node Voltage Method to get model equations
Lecture 12 - 2/20 - Test 1
Test
Lecture 13 - 2/22 - First-Order Circuits (constant forcing functions)
- First-order switched circuits with constant forcing functions
- Sketching basic exponential decays
- Using the Node Voltage Method to get model equation
Lecture 14 - 2/27 - ACSS and Phasors
- Overview of Calculator Tips
- At the heart of complex analysis is an understanding of Complex Numbers
- Solving ACSS using just trig gets complex very quickly - we will use complex analysis to simplify the process - this is a motivation for phasors
- A phasor is a complex number whose magnitude represents the amplitude of a single-frequency sinusoid and whose angle represents the phase of a single-frequency sinusoid
- To use phasors to solve ACSS,
- Replace functions of t with their phasor representation
- Replace $$\frac{d}{dt}$$ with $$j\omega$$
- Solve for the output phasor as a function of the input phasor
Lecture 15 - 2/29 - More ACSS and Phasors
- Impedance: a ratio of phasors (though not a phasor itself)
- $$\mathbb{Z}=R+jX$$ where $$R$$ is resistance and $$X$$ is reactance
- Admittance $$\mathbb{Y}=\frac{1}{\mathbb{Z}}=G+jB$$ where $$G$$ is conductance and $$B$$ is susceptance
- For common elements:
- $$\mathbb{Z}_R=R$$
- $$\mathbb{Z}_L=j\omega L$$
- $$\mathbb{Z}_R=\frac{1}{j\omega C}$$
- Impedances add in series and admittances add in parallel
- Find transfer function $$\mathbb{H}(i\omega)$$ as a ratio of an output phasor and an input phasor
- Use transfer function to note that $$\mathbb{V}_{out}=\mathbb{H}(j\omega)\,\mathbb{V}_{in}$$ (input, output, or both could also be currents)
- If given numerical values, can use those to get actual magnitudes and phases for output and convert to time
Lecture 16 - 3/5 - More Phasors; Filters
- Once in the phasor domain, use KVL, KCL, NVM, MCM, BCM, and whatever else from resistive circuits to get relationships between input phasors and output phasors
- Note that $$\frac{d}{dt}$$ in the time domain is the same as multiplying a phasor by $$j\omega$$ in the frequency somin - this will allow us to use frequency techniques to back out differential equations
- An $$RC$$ can be both a high-pass filter (resistor voltage) or a low-pass filter (capacitor voltage)
- The "cut-off frequency" of a filter is the frequency at which the magnitude of the transfer function is $$\frac{1}{\sqrt{2}}\mathbb{H}_{max}$$ - this is also known as the "half-power frequency"
Lecture 17 - 3/7 - Phasor Domain Recap
- Review of impedance
- Review of DCSS with singularity functions
- Transfer functions between current and voltage
- Using a calculator to find ACSS
Lecture 18 - 3/19 - First and Second-Order Filter Intro
- High and low-pass filters using RC and LR circuits
- Modular filters using VCVS
- 2nd order circuits and transfer functions for LRC circuit
- Resonant Frequency
Lecture 19 - 3/21 - Transfer Function Redux
- Magnitude and phase diagrams
- General second-order equation
Lecture 20 - 3/26 - Operational Amplifier Intro
- Model using two resistors and a VCVS
- Without feedback, only really good as a comparator
- Feedback from output to inverting input makes circuit more useful
- Ideal op-amp assumptions are about the op-amp, not the circuit: $$A\rightarrow\infty$$, $$r_i\rightarrow\infty$$, $$r_o\rightarrow 0$$
- Using ideal op-amp with a circuit with feedback from output to inverting input leads to a very useful circuit with implications of:
- No voltage drop between the input terminals
- No current entering the input terminals
- Still possible to have current at the output terminal!
Lecture 21 - 3/28 - Test 2
Lecture 22 - 4/2 - More Op-Amp Circuits
- Various configurations that are directly or nearly-directly from the circuit developed in Lecture 20:
- Inverting
- Non-inverting
- Buffer / Voltage follower as a specific instance
- Inverting summation
- Difference
- Can use with reactive elements as well
Lecture 23 - 4/4 - Analyzing Circuits with Op-Amps
- See if you can recognize typical circuits from Lecture 22
- If you have an ideal op-amp with feedback from the output terminal to the inverting terminal, use implications to label voltages / currents wherever possible
- Generally use KCL at inverting node
- Reminder of passive high and low-pass
- Introduction to active high and low-pass
- Introduction to active band-pass
Lecture 24 - 4/9 - Digital Logic 1
- Introduction to binary
- Introduction to boolean operators
- Basic operations: not, and, or, xor
- Truth tables
- DeMorgan's Laws
- Minterms and maxterms
Lecture 25 - 4/11 - Digital Logic 2
- Digital logic gates and schematics
- Complexity
- Boolean algebra relationships and simplifications
- Manual logic function minimization
- Gray code motivation and construction
- Karnaugh maps
- Structure
- Use in finding minimum sum of products (MSOP) form
- Use in finding minimum product of sums (MPOS) form