Difference between revisions of "ECE 110/Concept List/S24"

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** Labels:
 
** Labels:
 
*** Label each mesh current, understanding that current sources, current measurements, and voltage measurements will require additional equations.
 
*** Label each mesh current, understanding that current sources, current measurements, and voltage measurements will require additional equations.
 +
 +
== 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
 +
 +
== Lecture 26 - 4/16 - Digital Logic 3 ==
 +
* Example going from maxterm representation to minterm representation to Karnaugh map to MSOP to MPOS to schematic
 +
* "Don't Care" conditions
 +
 +
== Lecture 27 - 4/18 - In-class work==
 +
* In-class work on HW 10
 +
 +
== Lecture 28 - 4/23 - Review ==
 +
* Please fill out the teacher-course evaluations!
 +
 +
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 +
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Latest revision as of 01:10, 24 April 2024

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

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.


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
  • MCM
    • Labels:
      • Label each mesh current, understanding that current sources, current measurements, and voltage measurements will require additional equations.

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

Lecture 26 - 4/16 - Digital Logic 3

  • Example going from maxterm representation to minterm representation to Karnaugh map to MSOP to MPOS to schematic
  • "Don't Care" conditions

Lecture 27 - 4/18 - In-class work

  • In-class work on HW 10

Lecture 28 - 4/23 - Review

  • Please fill out the teacher-course evaluations!


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