# Circuits 1

**Main Reference Book**

Tim Hanshaw, “** Real Analog: An Introduction to Electrical Circuits**”, free online access

**Additional Reference**

Roland E. Thomas, Albert J. Rosa, and Gregory J. Toussaint

“** The Analysis and Design of Linear Circuits**”, Wiley, 7th Edition, 2012

(Prior or more recent versions of this book are also acceptable)

**Course Goals**

- An introduction to electrical circuit analysis, design and evaluation.
- Emphasis on definitions of basic variables, passive circuit components and the ideal operational amplifier.
- DC analysis of circuits and dc circuit theorems are stressed.
- AC signals are introduced.
- Computer analysis software integrated throughout the course.

**Course Modules**

**Module 1 – Circuit Fundamentals**

- Define voltage and current in terms of electrical charge
- State common prefixes and the symbols used in scientific notation
- State the passive sign convention from memory
- Determine the power absorbed or generated by an circuit element, based on the current and voltage provided to it
- Write symbols for independent voltage and current sources
- State from memory the function of independent voltage and current sources
- Write symbols for dependent voltage and current sources
- State governing equations for the four types of dependent sources
- State Ohm’s Law from memory
- Use Ohm’s Law to perform voltage and current calculations for resistive circuit elements
- Identify nodes in an electrical circuit
- Identify loops in an electrical circuit
- State Kirchhoff’s current law from memory, both in words and as a mathematical expression
- State Kirchhoff’s voltage law from memory, both in words and as a mathematical expression
- Apply Kirchhoff’s voltage and current laws to electrical circuits

**Module 2 – Circuit Reduction**

- Identify series and parallel combinations of circuit elements
- Determine the equivalent resistance of series resistor combinations
- Determine the equivalent resistance of parallel resistor combinations
- State voltage and current divider relationships from memory
- Determine the equivalent resistance of electrical circuits consisting of series and parallel combinations of resistors
- Sketch equivalent circuits for non-ideal voltage and current meters
- Analyze circuits containing non-ideal voltage or current sources
- Determine the effect of non-ideal meters on the parameter being measured

**Module 3 – Nodal and Mesh Analysis**

- Use nodal analysis techniques to analyze electrical circuits
- Use mesh analysis techniques to analyze electrical circuits

**Module 4 – Systems and Network Theorems**

- Define signals and systems
- Represent systems in block diagram form
- Identify system inputs and outputs
- Write input-output equations for systems
- State the defining properties of linear systems
- Determine whether a system is linear
- State conditions under which superposition can be applied to circuit analysis
- Analyze electrical circuits using the principle of superposition
- Define the i-v characteristic for a circuit
- Represent a resistive circuit in terms of its i-v characteristic
- Represent a resistive circuit as a two-terminal network
- Determine Thévenin and Norton equivalent circuits for circuits containing power sources and resistors
- Relate Thévenin and Norton equivalent circuits to i-v characteristics of two-terminal networks
- Determine a load resistance which will maximize the power transfer from a circuit

**Module 5 – Operational Amplifiers**

- State ideal operational amplifier modeling rules
- State constraints on the operational amplifier output voltage
- Represent operational amplifiers as dependent voltage sources
- Be able to identify standard operational amplifier pin connections
- Analyze electrical circuits containing ideal operational amplifiers and resistors
- Sketch op-amp based circuits which perform the following operations:
- Inverting voltage amplification
- Non-inverting voltage amplification
- Summation (addition)
- Differencing (subtraction)
- Buffering

- Describe the operation of a comparator
- Briefly describe the effect of the following non-ideal op-amp parameters, relative to ideal op-amp performance:
- Finite input resistance
- Finite output resistance
- Finite op-amp gain

**Module 6 – Energy Storage Elements**

- Qualitatively state the effect of energy storage on the type of mathematics governing a system
- Write the mathematical expression for a unit step function
- Sketch the unit step function
- Sketch shifted and scaled versions of the unit step function
- Write the mathematical expression for a decaying exponential function
- Use a unit step function to restrict an exponential function to times greater than zero
- Write the circuit symbol for a capacitor
- State the mechanism by which a capacitor stores energy
- State the voltage-current relationship for a capacitor in both differential and integral form
- State the response of a capacitor to constant voltages and instantaneous voltage changes
- Write the mathematical expression describing energy storage in a capacitor
- Determine the equivalent capacitance of series and parallel combinations of capacitors
- Write the circuit symbol for an inductor
- State the mechanism by which an inductor stores energy
- State the voltage-current relationship for an inductor in both differential and integral form
- State the response of an inductor to constant voltages and instantaneous current changes
- Write the mathematical expression describing energy storage in an inductor
- Determine the equivalent inductance of series and parallel combinations of inductors