 # Real Analog - Circuits 1 "Real Analog" is a comprehensive collection of free educational materials that seamlessly blend hands-on design projects with theoretical concepts and circuit analysis techniques. Developed for university "Circuits" classes by practicing engineers and experienced educators, Real Analog is centered on a newly-written 12-chapter textbook and features:

• Exercises designed to reinforce textbook and lecture topics
• Homework assignments for every chapter
• Multiple design projects that reinforce and extend theoretical concepts
• Worksheets and videos to help students complete design projects outside of the lab.

Design projects use Digilent's Analog Discovery and Analog Parts Kit that together include everything needed to build and test a wide variety of analog circuits - the Analog Discovery includes a dual-channel oscilloscope, waveform generator, power supplies, digital I/O channels and more, and the Analog Parts Kit includes a breadboard, jumper wires, more than 20 integrated circuits from Analog Devices, and a wide variety of sensors, resistors, capacitors, discrete semiconductors, and other components.

Real Analog, the Analog Discovery and Analog Parts Kit form the core of a world-class engineering educational program that can be used by themselves or in support of existing curricular materials. Students with their own design kits learn more, learn faster, retain information longer, and have a more enjoyable experience - now every student can take charge of their education for less than the cost of a textbook!

Note: To see the previous version of Circuits 1 for the Electronics Explorer, click here.

In this chapter, we introduce all fundamental concepts associated with circuit analysis. Electrical circuits are constructed in order to direct the flow of electrons to perform a specific task. In other words, in circuit analysis and design, we are concerned with transferring electrical energy in order to accomplish a desired objective.

Course overview, basic circuit parameters, passive sign convention
Power generation & absorption, power sources, resistance
Review, Kirchoff's current law, Kirchoff's voltage law
Circuit analysis examples, series & parallel circuit elements

DMM Usage: Measuring voltage, current, and resistance using a hand-held digital multimeter. Using breadboards to implement circuits
Resistors 1: Physical resistors. Nominal resistance values from color codes. Resistance measurement using ohmeters or measured voltage and current.
Dependent Sources: MOSFETs and BJTs as dependent sources.

Applications: Concept applications: dusk-to-dawn light and temperature measurement.

Independent Power Supplies, Ammeters, and Voltmeters
Dependent Sources and MOSFETs
Resistors and Ohms Law - Resistance Variations
Resistors and Ohms Law - Voltage-Current Characteristics
Dusk-to-Dawn Light
Resistive Network Power Dissipation
Input Resistance
Temperature Measurement System

Chapter 1 exercise solutions
Chapter 1 homework problems
Background material for lab 1.4.4: Resistive Temperature Sensors
In this chapter, we introduce analysis methods based on circuit reduction. Circuit reduction consists of combining resistances in a circuit to a smaller number of resistors, which are (in some sense) equivalent to the original resistive network. Reducing the number of resistors, of course, reduces the number of unknowns in a circuit.

Circuit reduction
Circuit reduction examples, practical application: temperature measurement

Potentiometers: Variable resistors

Resistors 2: Resistance of networks of resistors. Using time-varying voltage sources to plot voltage-current characteristics of resistors.
Non-ideal effects: Non-ideal voltage sources and voltage measurements. Analog Discovery power supply limitations.

Temperature Measurement System
Series and Parallel Resistances and Circuit Reduction
Series and Parallel Resistances and Circuit Reduction
Non-Ideal Power Sources
Practical Voltage and Current Measurement

Chapter 2 exercise solutions
Chapter 2 homework problems
In cases where circuit reduction is not feasible, approaches are still available to reduce the total number of unknowns in the system. Nodal analysis and mesh analysis are two of these.

Overview of nodal & mesh analysis, nodal analysis
Mesh analysis
Constrained loops, additional mesh analysis examples

Nodal and Mesh Analysis: Analysis and implementation of circuits with multiple sources. Using multiple sources on the Analog Discovery to create sources outside its nominal +/- 5V range.

Nodal Analysis
Nodal Analysis
Nodal Analysis
Mesh Analysis
Mesh Analysis
Mesh Analysis

Chapter 3 exercise solutions
Chapter 3 homework problems
In this chapter, we introduce the concept of a systems level approach to circuit analysis. In this type of approach, we represent the circuit as a system with some inputs and outputs. We then characterize the system by the mathematical relationship between the system inputs and the system outputs. This relationship is called the input-output relation for the system.

Linear systems and superposition, Thévenin and Norton's Theorems
Thévenin and Norton's Theorems & examples, source transformations, maximum power transfer
Derivation of maximum power transfer, Thévenin theorem examples, operational amplifiers

Superposition: Validation of superposition in cases of (a) multiple discrete sources, and (b) single sources with multiple components.
Two-Terminal Networks : Measuring voltage-current characteristics of two-terminal networks. Measurement techniques used are introduced in Resistors I and Resistors II videos.
Thevenin's theorem: Experimental validation of Thevenin's theorem. Measurement techniques used are introduced in Resistors I and Resistors II videos.

Superposition
Superposition
Two-terminal Characteristics
Thévenin's Theorem
Maximum Power Transfer

Chapter 4 exercise solutions
Chapter 4 homework problems
Operational amplifiers (commonly abbreviated as op-amps) are extremely useful electronic devices. Some argue, in fact, that operational amplifiers are the single most useful integrated circuit in analog circuit design. Operational amplifier-based circuits are commonly used for signal conditioning, performing mathematical operations, and buffering.

Derivation of maximum power transfer, Thévenin theorem examples, operational amplifiers
Operational amplifier examples, dependent Sources

Operational amplifiers: Constructing operational amplifier based circuits.
Inverting Voltage Amplifier
Summing Amplifier
Non-inverting Voltage Amplifier
Difference Amplifier
Temperature Measurement System Design

Chapter 5 exercise solutions
Chapter 5 homework problems
This chapter begins with an overview of the basic concepts associated with energy storage. This discussion focuses not on electrical systems, but instead introduces the topic qualitatively in the context of systems with which the reader is already familiar. The goal is to provide a basis for the mathematics, which will be introduced subsequently.

Introduction to dynamic systems, basic time-varying signals
Capacitors
Inductors, introduction to first-order circuits, RC circuit natural response

Physical inductors and capacitors: Inductor and capacitor construction. Nominal capacitance and inductance values from part labels. Electrolytic capacitors.
Capacitor voltage-current relations: Measuring voltage-current relations for capacitors. Non-ideal effects: leakage currents.
Inductor V-C Relations: Measuring voltage-current relations for inductors. Non-ideal effects: inductor resistance.

Time-varying Signals
Capacitor Voltage-current Relations
Leakage Currents and Electrolytic Capacitors
Inductor Voltage-current Relations
Non-ideal Inductor Effects

Chapter 6 exercise solutions
Chapter 6 homework problems
First order systems are, by definition, systems whose input-output relationship is a first order differential equation. A first order differential equation contains a first order derivative but no derivative higher than first order - the order of a differential equation is the order of the highest order derivative present in the equation.

Inductors, introduction to first-order circuits, RC circuit natural response
RL circuit natural response, general first-order system natural response, first-order circuit examples
Forced response of first-order circuits, active first-order system examples, step response of first-order circuits
Steady-state response & DC gain, step response examples
First-order circuit step response, introduction to second-order systems

RC Circuit Natural Response: We create an RC circuit natural response in two ways: by (1) converting the source to an open circuit and (2) converting the source to a short-circuit.
RC Circuit Forced Response: The step responses of both passive and active first-order RC circuits are measured. Loading effects on the two circuits are examined.
Passive RC Circuit Natural Response
Passive RL Circuit Natural Response
Inverting Differentiator
Passive RC Circuit Step Response
Passive RL Circuit Step Response
Active RC Circuit Step Response

Chapter 7 exercise solutions
Chapter 7 homework problems
Second order systems are, by definition, systems whose input-output relationship is a second order differential equation. A second order differential equation contains a second order derivative but no derivative higher than second order.

First-order circuit step response, introduction to second-order systems
Second-order circuit natural response, sinusoidal signals & complex exponentials
Second-order system natural response, mathematical form of solutions, qualitative interpretation
Second-order system step response, governing equation, mathematical expression, estimating step response, examples

Second Order Circuit Step Response: Measuring the step response of a series RLC circuit. The measured peak value of the response is compared to analytical expectations.

Series RLC Circuit Step Response
Parallel RLC Circuit Response
RLC Circuit Response

Chapter 8 exercise solutions
Chapter 8 homework problems
In this chapter, we will provide a very brief introduction to the topic of state variable modeling. The brief presentation provided here is intended simply to introduce the reader to the basic concepts of state variable models, since they are a natural - and relatively painless - extension of the analysis approach we have used in Chapters 7 and 8.

Introduction to state-variable modeling, simulating system response using MATLAB®

State Variable Models: The step response of the state variables of a series RLC circuit are measured. The measurements are compared to the simulated response obtained by using MATLAB®.

State Variable Model of Series RLC Circuits
Second Order Circuit Response

Chapter 9 exercise solutions
Chapter 9 homework problems
In this chapter we will study dynamic systems which are subjected to sinusoidal forcing functions.

Introduction to steady-state sinusoidal analysis, system response to complex units, phasor representation of sinusoids
Phasor diagrams, phasor representations of circuit elements
Frequency domain system characterization, frequency response

Measuring Gain & Phase: Measuring steady-state sinusoidal responses of circuits and estimating gain and phase differences between sinusoidal signals.
Impedance Measurement: Gain and phase measurement in terms of impedance.

Impedance
Passive RL Circuit Response
Passive RC Circuit Response
Inverting Voltage Amplifier
Non-inverting Voltage Amplifier

Chapter 10 exercise solutions
Chapter 10 homework problems
In this chapter we discuss representation of signals in terms of their frequency content. We will also represent the frequency content of the input and output signals and the frequency response of the system in graphical format. This leads us to think in terms of using a system to create a signal with a desired frequency content - this process is called filtering.

Frequency response examples, frequency response plots & signal spectra, filters
Checking frequency response results, time-to-frequency domain relations for first-order filters, Bode plots

Introduction to Frequency Response: Using frequency response to estimate a circuit's behavior. A low-pass filter is used as an example to filter noise out of a sinusoidal signal.
Practical Filters: Examples of low-pass filters are presented. The properties of passive vs. active filters are compared, especially relative to the effects of applying a "load" to the filter.
Bode Plots: Bode plots and their creation using the Analog Discovery Network Analyzer.

Signals with Multiple Frequency Components
Passive RL Filter
Passive RC Filter
Active Low Pass Filte
Signal Conditioning - Audio Application
Signal Conditioning - Vibration Measurement
Passive Low Pass Filter
Non-inverting Low Pass Filter
Non-inverting Low Pass Filter

Chapter 11 exercise solutions
Chapter 11 homework problems
In this chapter we will address the issue of power transmission via sinusoidal (or AC) signals. This topic is extremely important, since the vast majority of power transmission in the world is performed using AC voltages and currents.

Sinusoidal steady-state power, instantaneous & average power, reactive power, complex power, power factor
Review: AC power analysis (average & complex power, power triangles, RMS values, power factor), power factor correction

AC Power & Power Factor: An example of the role of power factor in the transmission of AC power. Power factor correction is used to improve the efficiency of power transmission.

Apparent Power and Power Factor

Chapter 12 exercise solutions
Chapter 12 homework problems