AC Circuits

About this book

Chad Davis’s AC Circuits, first edition dated November 11, 2017, develops alternating-current analysis in seven modules. It connects waveform definitions, complex arithmetic, impedance, power, filters, transformers, diodes, and operational amplifiers. The text assumes DC-circuit foundations and uses worked examples to link calculations with circuits. Track reference directions, units, and the conditions of an idealized model before substituting values. A correct symbolic result must still correspond to the specified source, frequency, loading, and measurement convention.

Chapter-by-chapter summaries

1. AC signal overview

Sinusoids are described by amplitude, frequency, phase, and offset. Peak, peak-to-peak, average, and root-mean-square values are different measurements. RMS expresses a heating-equivalent relationship under the applicable conditions and its conversion factor depends on waveform shape. Compare sine, square, and triangular examples using definitions rather than applying a sine-wave factor universally. Keep angular frequency distinct from frequency in hertz. A phase comparison requires a common time reference, and a stated voltage without its measurement convention can be ambiguous.

2. Mathematical background

Complex numbers represent magnitude and phase compactly, supporting addition, multiplication, and division through appropriate rectangular and polar forms. A phasor is a frequency-specific representation, not a complete arbitrary transient. Convert forms carefully and preserve angle units. Verify a calculation through an independent representation and interpret the result as a sinusoid. The chapter’s mathematical tools simplify work only when their assumptions match the signal; combining unrelated frequencies as if they were one phasor obscures the actual time dependence.

3. RLC analysis, power, and transfer

Impedance and admittance extend familiar circuit laws to sinusoidal steady state. Series and parallel RLC circuits differ in how voltages, currents, and frequency dependence combine. Real, reactive, and apparent power measure different relationships, while maximum-power transfer depends on the source and load model. Check low- and high-frequency limits before trusting a computed value. Distinguish resonance from an unlimited real response. Use consistent RMS or peak conventions in power calculations and state which one the formula assumes.

4. Passive filters

Low-pass, high-pass, band-pass, and band-stop networks select frequency ranges through their transfer characteristics. Cutoff, bandwidth, attenuation, and phase do not describe interchangeable features. Define input, output, source, and load because loading changes the transfer function. Compare predicted limiting gains with the circuit’s physical behaviour. A filter category describes a response pattern, not perfect removal of every unwanted component. Evaluate the magnitude and phase at frequencies relevant to the application rather than relying only on a named topology.

5. Transformers

Transformer relationships connect voltages, currents, turns, and impedance under an ideal model. A voltage change does not create energy, and the current relationship must be interpreted with the power balance. Reflected impedance changes how a source sees a load. Keep winding polarity and reference conventions explicit. Compare ideal predictions with the assumptions they require. The module provides analytical foundations; practical devices introduce losses and limits that cannot be inferred from a turns ratio alone.

6. Diodes and AC-to-DC conversion

The constant-drop approximation supports introductory analysis of diode logic, protection arrangements, and rectifiers. First determine the assumed diode state, solve the corresponding circuit, and check whether the result is consistent with that state. Rectification changes waveform shape; it does not automatically provide smooth regulated DC. Distinguish conduction threshold assumptions from a full device characteristic. Trace current paths across parts of an input cycle and explain how they generate the output rather than memorizing a waveform without its circuit reasoning.

7. Operational amplifiers

Comparator operation differs from linear amplification with suitable negative feedback. Ideal input and output assumptions are useful only in the appropriate operating regime. A virtual-short relationship is not a universal property of every op-amp circuit. Identify feedback, solve for the intended operating point, and check consistency with output limits. Superposition can simplify a linear model but must be applied to the represented circuit correctly. The final module integrates earlier circuit reasoning with active devices whose practical behaviour also depends on supply and component specifications.

Study instructions

1. Label waveform convention, frequency units, polarity, and current references before calculating.
2. Solve examples in rectangular and polar form where helpful and check limiting cases.
3. For filters, derive the transfer relationship including the stated source and load.
4. For nonlinear or active-device examples, verify that the assumed operating state is consistent with the solution.

Questions for reflection

• Why does an RMS conversion depend on waveform shape?
• When is phasor analysis insufficient?
• Why does negative feedback not guarantee an unlimited linear output?

Sources and coverage

This original reading guide follows the linked source edition’s chapter, module, unit, or lesson structure. Consult the source for full arguments, cases, worked examples, exercises, illustrations, and references. First edition, November 11, 2017. The guide covers all seven modules; the source includes additional examples, references, and appendices. Read the source edition.