Electricity and physics lessons - Bastion Circuit Designer manual

A comprehensive engineering handbook and pedagogical physics curriculum integrated directly into the Bastion EDA environment.

Open-Source Curatorial References & Pedagogical Foundations

This curriculum and Bastion's built-in Physics & Electricity Academy (Ctrl+Shift+L) draw from premier open-source textbooks, physics references, and university courseware:

Tony R. Kuphaldt — Lessons In Electric Circuits (Vol. I DC, Vol. II AC, Vol. III Semiconductors, Vol. IV Digital) under the Design Science License (DSL).
OpenStax University Physics (Volume 2: Thermodynamics, Electricity, and Magnetism), licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).
HyperPhysics by Dr. Carl R. Nave (Department of Physics and Astronomy, Georgia State University).
MIT OpenCourseWare (OCW 6.002) — Circuits and Electronics by Prof. Anant Agarwal.

Curriculum Structure & Table of Contents

#	Topic	Category	Governing Physical Law	Primary Formula	Associated Components
1	Voltage & Electromotive Force	Fundamentals	Electric Potential Definition	\(V = \frac{W}{Q}\)	Voltage Sources, Batteries, VCC Rail
2	Current & Charge Drift Velocity	Fundamentals	Charge Conservation / Amperage	\(I = \frac{dQ}{dt} = n q A v_d\)	Ammeters, Series Loops
3	Circuit Ground & Reference Potential	Fundamentals	Gauss's Law / Earth Equipotential	\(V_{\text{GND}} = 0.0\text{ V}\)	Ground (GND), Earth, Chassis
4	Ohm's Law & Joule Heating	Fundamentals	Constitutive Resistive Relation	\(V = I \cdot R,\; P = I^2 R\)	Resistors, Trimpots, Heaters
5	Voltage Dividers & Thevenin Equivalence	Analysis	Conservation of Energy & Linearity	\(V_{\text{out}} = V_{\text{in}} \cdot \frac{R_2}{R_1 + R_2}\)	Potentiometers, Dividers
6	Capacitance, Dielectrics & RC Transients	Passives	Maxwell-Gauss / Displacement	\(i_C(t) = C \frac{dv}{dt},\; \tau = R C\)	Ceramic, Electrolytic Capacitors
7	Inductance, Faraday's Law & Back-EMF	Passives	Faraday-Lenz Electromagnetic Induction	\(v_L(t) = L \frac{di}{dt}\)	Inductors, Chokes, Flyback Coils
8	P-N Junctions & Diode Rectification	Semiconductors	Shockley Ideal Diode Equation	\(I_D = I_S \left(e^{\frac{V_D}{n V_T}} - 1\right)\)	1N4148, 1N4007, Rectifiers
9	Light Emitting Diodes & Optoelectronics	Semiconductors	Planck-Einstein Photoelectric Relation	\(E_g = \frac{h c}{\lambda},\; R_{\text{lim}} = \frac{V_S - V_F}{I_F}\)	LEDs, Optocouplers
10	Zener Breakdown & Voltage Regulation	Semiconductors	Quantum Zener Tunneling & Avalanche	\(V_Z = \text{const}\) (for \(I_Z \ge I_{ZK}\))	Zener Diodes, Clamps
11	Transistors: BJT Current & MOSFET Field	Semiconductors	Ebers-Moll & MOSFET Saturation	\(I_C = \beta I_B,\; I_D = \frac{1}{2} k_n' \frac{W}{L} (V_{GS} - V_{th})^2\)	2N3904 (NPN), 2N3906 (PNP), MOSFETs
12	Operational Amplifiers & Golden Rules	ICs & Analogs	Negative Feedback Virtual Short	\(V_+ = V_-,\; I_+ = I_- = 0\)	LM358, TL072, Op-Amps
13	The 555 Timer IC & Multivibrator Dynamics	ICs & Analogs	RC Threshold / Trigger Flip-Flop	\(f = \frac{1.44}{(R_1 + 2R_2)C}\)	NE555 Timer
14	Boolean Logic & CMOS Gates	Digital Logic	Switching Algebra & CMOS Pull-up/down	\(Y = \overline{A \cdot B},\; \overline{A + B}\)	74HC00, 74HC08, 74HC04
15	Microcontrollers & GPIO Interfacing	Digital Logic	CMOS Input/Output Driver Limits	\(I_{\text{GPIO}} \le 20\text{ mA},\; V_{IH} \ge 0.7 V_{CC}\)	ESP32, ATmega328P, RP2040
16	Oscilloscopes & Time-Domain Metrology	Instruments	Nyquist-Shannon Sampling Theorem	\(f_{\text{sample}} \ge 2 f_{\text{max}},\; BW \ge 5 f_{\text{signal}}\)	Virtual Scope, Probes
17	Multimeters & Shunt Measurement	Instruments	Galvanometer D'Arsonval & Burden Voltage	\(I = \frac{V_{\text{shunt}}}{R_{\text{shunt}}},\; R_{\text{in}} \ge 10\text{ M}\Omega\)	Virtual DMM, Voltmeter
18	Kirchhoff's Laws (KCL & KVL)	Analysis	Conservation of Charge & Energy	\(\sum I_{\text{node}} = 0,\; \sum V_{\text{loop}} = 0\)	Wires, Nets, Junctions

In-Depth Lesson Modules

Module 1: Voltage & Potential Difference

Open-Source Attribution: OpenStax University Physics Vol 2, Chapter 7; Kuphaldt, Vol I, Chapter 1.
Physical Concept: Electrostatic potential difference is the work required per unit charge to move a test charge between two points against an electrostatic field: \(V_{AB} = -\int_A^B \vec{E} \cdot d\vec{\ell}\) In lumped circuit theory, potential difference is measured in Volts (\(1\text{ V} = 1\text{ J}/\text{C}\)). It acts as the electrical "pressure" that induces drift current through conductive pathways.
Governing Equations: \(V = \frac{W}{Q},\quad \vec{E} = -\vec{\nabla} V\)
Engineering Rule of Thumb: Always decouple DC power rails with a \(100\text{ nF}\) ceramic capacitor placed immediately adjacent to every IC's \(V_{CC}\) pin to absorb transient high-frequency voltage sag caused by trace inductance.

Module 2: Electric Current & Charge Drift Velocity

Open-Source Attribution: Kuphaldt, Vol I, Chapter 2; OpenStax Vol 2, Chapter 9.
Physical Concept: Electric current is the net macroscopic rate of electrical charge transport through a cross-sectional area: \(I = \frac{dQ}{dt}\) Although individual conduction electrons drift remarkably slowly (drift velocity \(v_d \approx 10^{-4}\text{ m/s}\) in copper under typical fields), the electromagnetic wavefront propagates through the dielectric medium surrounding the conductor at approximately \(0.6c\) to \(0.7c\) (\(\sim 200{,}000\text{ km/s}\)).
Governing Equations: \(I = n \cdot q \cdot A \cdot v_d,\quad J = \sigma E = \frac{I}{A}\)
Engineering Rule of Thumb: For standard \(1\text{ oz/ft}^2\) (\(35\text{ }\mu\text{m}\)) copper PCB traces, budget approximately \(1\text{ mm}\) trace width per \(1\text{ A}\) of continuous direct current to maintain a trace temperature rise under \(10^\circ\text{C}\).

Module 3: Circuit Ground & Reference Equipotentials

Open-Source Attribution: Kuphaldt, Vol I, Chapter 3; Henry Ott, Electromagnetic Compatibility Engineering.
Physical Concept: Voltage is an inherently relative scalar quantity: voltage exists only between two spatial coordinates. "Ground" (GND) is an arbitrary but vital reference node designated by convention as \(0.0\text{ V}\). In high-frequency and low-noise electronics, ground is not a zero-impedance sink, but a return path through which all currents loop back to their energy sources.
Governing Equations: \(V_{\text{node}} = V_{\text{node}} - V_{\text{GND}},\quad Z_{\text{return}} = R_{\text{dc}} + j \omega L_{\text{loop}}\)
Engineering Rule of Thumb: Avoid ground loops. High-frequency return currents travel directly underneath the signal trace on the nearest continuous ground plane to minimize loop inductance (\(L_{\text{loop}}\)). Never split ground planes underneath fast digital or analog signal lines.

Module 4: Ohm's Law & Joule Heating

Open-Source Attribution: Kuphaldt, Vol I, Chapter 2; OpenStax Vol 2, Chapter 9.
Physical Concept: Ohm's Law describes the linear relationship between the electromotive potential drop across an ohmic conductor and the resulting current. Collisions between accelerated electrons and the metallic crystal lattice convert electric potential energy irreversibly into thermal kinetic energy (Joule heating).
Governing Equations: \(V = I \cdot R,\quad P = V \cdot I = I^2 R = \frac{V^2}{R}\)
Engineering Rule of Thumb: Never operate carbon film or SMD thick-film resistors at greater than \(50\%\) to \(60\%\) of their continuous rated power dissipation (e.g., limit a \(0.25\text{ W}\) 0805 resistor to \(\le 0.125\text{ W}\)) to ensure low thermal drift and prevent premature aging.

Module 5: Voltage Dividers & Thevenin Equivalence

Open-Source Attribution: Kuphaldt, Vol I, Chapter 6 & 10; MIT OCW 6.002.
Physical Concept: Two series resistors divide an input voltage in direct proportion to their resistances. However, connecting any finite load resistance \(R_L\) in parallel with \(R_2\) draws current and reduces the effective output voltage (loading effect). Thevenin's theorem models any linear two-terminal resistive network as a single ideal voltage source \(V_{th}\) in series with an equivalent resistance \(R_{th}\).
Governing Equations: \(V_{\text{out}} = V_{\text{in}} \cdot \frac{R_2}{R_1 + R_2},\quad R_{th} = R_1 \parallel R_2 = \frac{R_1 \cdot R_2}{R_1 + R_2}\)
Engineering Rule of Thumb: To prevent noticeable loading errors (\(<1\%\)), design voltage divider bleeders such that the divider resistance \(R_2\) is at least \(10\times\) to \(100\times\) smaller than the load impedance \(R_L\), or buffer the output with a unity-gain op-amp follower.

Module 6: Capacitors, Dielectrics & RC Transients

Open-Source Attribution: Kuphaldt, Vol I, Chapter 13; OpenStax Vol 2, Chapter 8.
Physical Concept: A capacitor stores electrostatic potential energy within the polarized electric field of its dielectric material. The instantaneous current through a capacitor is proportional to the time rate-of-change of voltage (\(i = C \frac{dv}{dt}\)). Consequently, the voltage across a capacitor cannot change instantaneously.
Governing Equations: \(Q = C \cdot V,\quad i_C(t) = C \frac{dv}{dt},\quad v_C(t) = V_{\text{final}} + (V_{\text{initial}} - V_{\text{final}}) e^{-t / \tau},\quad \tau = R \cdot C\)
Engineering Rule of Thumb: An RC transient circuit reaches \(63.2\%\) of its target step voltage in \(1\tau\), and effectively completes its charge/discharge cycle (\(>99.3\%\)) after \(5\tau\). For power decoupling, place low-ESR ceramic caps (\(0.1\text{ }\mu\text{F}\)) as close as physically possible to IC pins.

Module 7: Inductance, Faraday's Law & Back-EMF

Open-Source Attribution: Kuphaldt, Vol I, Chapter 14; OpenStax Vol 2, Chapters 13-14.
Physical Concept: Inductance is the property of an electric circuit that opposes any instantaneous change in current. By Faraday's Law of Induction and Lenz's Law, when current through an inductor collapses rapidly (\(\frac{di}{dt} \ll 0\)), the collapsing magnetic field induces an electromotive force (Back-EMF) that opposes the change, generating massive voltage spikes.
Governing Equations: \(v_L(t) = L \frac{di}{dt},\quad E_{\text{stored}} = \frac{1}{2} L I^2,\quad f_0 = \frac{1}{2\pi \sqrt{L C}}\)
Engineering Rule of Thumb: Always connect a reverse-biased flyback diode (such as a 1N4007 or Schottky diode) in antiparallel across inductive coils, relays, solenoids, and DC motors to clamp inductive kickback spikes and protect switching transistors from avalanche breakdown.

Module 8: P-N Junctions & Diode Rectification

Open-Source Attribution: Kuphaldt, Vol III (Semiconductors), Chapter 2; Streetman & Banerjee, Solid State Electronic Devices.
Physical Concept: The interface between p-type and n-type semiconductor regions forms a depletion layer devoid of free charge carriers. Under forward bias (\(V_D > V_F \approx 0.7\text{ V}\) for Silicon), the internal potential barrier is overcome, permitting exponential majority carrier diffusion. Reverse bias widens the barrier, restricting current to microscopic reverse saturation current \(I_S\).
Governing Equations: \(I_D = I_S \left(e^{\frac{q V_D}{n k_B T}} - 1\right) = I_S \left(e^{\frac{V_D}{n V_T}} - 1\right)\) (At room temperature \(T = 300\text{ K}\), thermal voltage \(V_T \approx 25.85\text{ mV}\)).
Engineering Rule of Thumb: Silicon diodes exhibit a nominal \(0.65\text{ V}\) to \(0.7\text{ V}\) forward drop at moderate currents. For high-efficiency or low-voltage solar/battery circuits, use Schottky barrier diodes (e.g. 1N5819) which feature a forward drop of only \(0.2\text{ V}\) to \(0.35\text{ V}\).

Module 9: Light Emitting Diodes & Optical Emission

Open-Source Attribution: Kuphaldt, Vol III, Chapter 3; OpenStax Vol 3 (Modern Physics).
Physical Concept: In direct-bandgap compound semiconductors (such as GaAs, GaN, InGaN), forward-biased injected electrons and holes recombine radiatively across the semiconductor bandgap \(E_g\), emitting photons whose wavelength \(\lambda\) is directly dictated by the Planck-Einstein relation: \(\lambda = \frac{h \cdot c}{E_g}\)
Governing Equations: \(R_{\text{series}} = \frac{V_{\text{source}} - V_F}{I_F},\quad \lambda (\text{nm}) \approx \frac{1240}{E_g (\text{eV})}\)
Engineering Rule of Thumb: Standard indicator LEDs operate safely between \(5\text{ mA}\) and \(20\text{ mA}\). Forward voltages vary predictably by photon emission energy: Red \(\approx 1.8\text{ V} - 2.0\text{ V}\), Green \(\approx 2.1\text{ V} - 2.4\text{ V}\), Blue/White \(\approx 3.0\text{ V} - 3.4\text{ V}\). Never connect an LED directly across a voltage source without current limiting.

Module 10: Zener Diodes & Breakdown Voltage Regulation

Open-Source Attribution: Kuphaldt, Vol III, Chapter 3; HyperPhysics.
Physical Concept: Heavily doped p-n junctions have an ultra-thin depletion region. Under reverse bias, the electric field reaches millions of volts per meter, allowing valence electrons to quantum-tunnel directly into the conduction band (Zener breakdown below \(\approx 5.6\text{ V}\)). Above \(5.6\text{ V}\), impact ionization avalanche multiplication dominates. Both mechanisms maintain an exceptionally constant reverse terminal voltage.
Governing Equations: \(V_Z \approx \text{const},\quad R_S = \frac{V_{\text{in(min)}} - V_Z}{I_{L(\text{max})} + I_{ZK}},\quad P_Z = V_Z \cdot I_Z\)
Engineering Rule of Thumb: Select \(5.1\text{ V}\) to \(5.6\text{ V}\) Zener diodes when high thermal stability is required; at \(\approx 5.6\text{ V}\), the negative temperature coefficient of Zener tunneling cancels the positive temperature coefficient of avalanche multiplication.

Module 11: Transistor Physics (BJT Current & MOSFET Field Effect)

Open-Source Attribution: Kuphaldt, Vol III, Chapters 4 & 5; MIT OCW 6.002.
Physical Concept:
- Bipolar Junction Transistors (BJT): Current-controlled devices where a minute base current \(I_B\) across the forward-biased base-emitter junction modulates a large collector current \(I_C = \beta I_B\).
- MOSFETs: Voltage-controlled devices where an electric field applied across an insulated gate oxide (\(SiO_2\)) inverts the underlying substrate channel, creating a conductive inversion layer without drawing continuous DC gate current.
Governing Equations: \(I_C = \beta \cdot I_B,\quad I_E = I_C + I_B,\quad I_D = \frac{1}{2} k_n' \frac{W}{L} (V_{GS} - V_{th})^2 \quad (\text{MOSFET Saturation})\)
Engineering Rule of Thumb: When using a BJT as a saturated digital switch, enforce a forced beta of \(\beta_{\text{forced}} \approx 10\) (\(I_B = \frac{I_C}{10}\)) to guarantee deep saturation and minimal \(V_{CE(\text{sat})} \approx 0.1\text{ V} - 0.2\text{ V}\). For logic-level MOSFETs, verify that \(R_{DS(\text{on})}\) is specified at your MCU's logic voltage (\(3.3\text{ V}\) or \(5.0\text{ V}\)).

Module 12: Operational Amplifiers & The Golden Rules

Open-Source Attribution: Kuphaldt, Vol III, Chapter 8; Franco, Design with Operational Amplifiers.
Physical Concept: An ideal operational amplifier has infinite open-loop differential gain (\(A_{OL} \to \infty\)), infinite input impedance (\(Z_{\text{in}} \to \infty\)), and zero output impedance (\(Z_{\text{out}} \to 0\)). When wrapped in a negative feedback loop, the high gain forces the inverting input to follow the non-inverting input.
The Two Golden Rules of Op-Amps:
1. Virtual Short: Under negative feedback without output saturation, \(V_+ = V_-\).
2. Zero Input Current: The inputs draw negligible current: \(I_+ = I_- = 0\).
Governing Equations: \(V_{\text{out}} = -\frac{R_f}{R_{\text{in}}} V_{\text{in}} \quad (\text{Inverting}),\quad V_{\text{out}} = \left(1 + \frac{R_f}{R_1}\right) V_{\text{in}} \quad (\text{Non-Inverting})\)
Engineering Rule of Thumb: Never leave unused op-amp sections floating; connect them as unity-gain voltage followers with the non-inverting input tied to a stable mid-rail potential to prevent oscillations and excessive power dissipation.

Module 13: 555 Timer Architecture & Astable / Monostable Dynamics

Open-Source Attribution: Kuphaldt, Vol IV (Digital), Chapter 10; Philips Semiconductors NE555 Datasheet.
Physical Concept: The 555 timer integrates a precision resistive voltage divider (\(3\times 5\text{ k}\Omega\) internal resistors dividing \(V_{CC}\) at \(\frac{1}{3} V_{CC}\) and \(\frac{2}{3} V_{CC}\)), two high-speed comparators, an SR set-reset latch, a discharge transistor, and a totem-pole output driver.
Governing Equations: \(t_{\text{high}} = 0.693 (R_1 + R_2) C,\quad t_{\text{low}} = 0.693 R_2 C,\quad f = \frac{1.44}{(R_1 + 2 R_2) C},\quad D = \frac{R_1 + R_2}{R_1 + 2 R_2}\)
Engineering Rule of Thumb: Always connect a \(10\text{ nF}\) (\(0.01\text{ }\mu\text{F}\)) capacitor from pin 5 (Control Voltage) to Ground to eliminate high-frequency noise that causes timing jitter on the upper \(\frac{2}{3} V_{CC}\) comparator reference.

Module 14: CMOS Digital Logic & Switching Boolean Algebra

Open-Source Attribution: Kuphaldt, Vol IV, Chapters 2 & 3; Harris & Harris, Digital Design and Computer Architecture.
Physical Concept: Complementary Metal-Oxide-Semiconductor (CMOS) logic uses matched pairs of p-channel (pull-up) and n-channel (pull-down) MOSFETs. Because either the pull-up network or pull-down network is off during static states, CMOS gates consume virtually zero static power, dissipating energy primarily during transitions when charging capacitive node loads (\(P_{\text{dyn}} = C \cdot V_{DD}^2 \cdot f\)).
Governing Equations: \(Y = \overline{A \cdot B} \quad (\text{NAND}),\quad Y = \overline{A + B} \quad (\text{NOR}),\quad P_{\text{dynamic}} = C_L \cdot V_{DD}^2 \cdot f\)
Engineering Rule of Thumb: Never leave unused CMOS input pins floating! Floating high-impedance CMOS inputs pick up ambient electromagnetic noise and hover in the linear switching region, turning on both PMOS and NMOS channels simultaneously and causing destructive shoot-through current. Tie unused inputs to \(V_{CC}\) or GND.

Module 15: Microcontroller GPIOs & Real-World Interfacing

Open-Source Attribution: Espressif ESP32 Technical Reference; Microchip ATmega328P Datasheet.
Physical Concept: Microcontroller General Purpose Input/Output (GPIO) pins incorporate internal protection clamping diodes, programmable weak pull-up/pull-down resistors (\(\approx 20\text{ k}\Omega - 50\text{ k}\Omega\)), and push-pull CMOS output stages. Interfacing requires adhering strictly to input logic thresholds (\(V_{IL}, V_{IH}\)) and absolute maximum continuous pin current ratings.
Governing Equations: \(V_{IL} \le 0.3 V_{CC},\quad V_{IH} \ge 0.7 V_{CC},\quad I_{\text{pin}} \le 20\text{ mA} \quad (\text{Max Safe}),\quad I_{\text{total\_MCU}} \le 150\text{ mA}\)
Engineering Rule of Thumb: \(3.3\text{ V}\) MCUs (like ESP32 or RP2040) are NOT \(5\text{ V}\) tolerant on their GPIO pins unless explicitly specified. Always use dedicated bi-directional level shifters (e.g. BSS138-based MOSFET converters) or resistive voltage dividers when interfacing with legacy \(5\text{ V}\) sensors or serial buses.

Module 16: Oscilloscopes & Time-Domain Metrology

Open-Source Attribution: Tektronix, XYZs of Oscilloscopes; Kuphaldt, Vol II (AC), Chapter 8.
Physical Concept: An oscilloscope measures and plots potential difference as a function of time (\(V(t)\)). Per the Nyquist-Shannon sampling theorem, an analog-to-digital converter (ADC) must sample at a rate greater than twice the highest frequency component of the signal (\(f_s > 2 f_{\text{max}}\)). Furthermore, to accurately capture fast square edges and harmonics, instrument bandwidth must exceed the signal frequency by at least \(5\times\).
Governing Equations: \(t_{\text{rise}} \approx \frac{0.35}{\text{Bandwidth}},\quad f_{\text{Nyquist}} = \frac{f_{\text{sample}}}{2}\)
Engineering Rule of Thumb: Standard \(10\times\) passive scope probes introduce \(\approx 10\text{ pF} - 15\text{ pF}\) of parasitic capacitance. For high-speed digital clocks (\(>20\text{ MHz}\)), keep probe ground leads as short as humanly possible (using a ground spring rather than a long ground alligator lead) to prevent inductive ringing from corrupting the measurement.

Module 17: Multimeters & Shunt Current Measurement

Open-Source Attribution: Kuphaldt, Vol I, Chapter 8; Keysight Digital Multimeter Measurement Handbook.
Physical Concept:
- Voltage Measurement: Voltmeter placed in parallel across nodes; features very high input impedance (\(R_{\text{in}} \ge 10\text{ M}\Omega\)) to prevent loading the circuit.
- Current Measurement: Ammeter placed in series within the loop; relies on a precision low-resistance shunt (\(R_{\text{shunt}}\)) and measures the resulting millivolt drop (\(V = I \cdot R_{\text{shunt}}\)). This introduces a small series voltage drop known as "burden voltage".
Governing Equations: \(I_{\text{meas}} = \frac{V_{\text{shunt}}}{R_{\text{shunt}}},\quad V_{\text{burden}} = I_{\text{meas}} \cdot R_{\text{shunt}}\)
Engineering Rule of Thumb: Never connect an ammeter across a power supply rail in parallel. Because an ammeter is virtually a zero-ohm short circuit, doing so will instantly blow the internal fuse or destroy the meter leads.

Module 18: Kirchhoff's Laws (KCL & KVL) & Nodal Analysis

Open-Source Attribution: Kuphaldt, Vol I, Chapter 6; MIT OCW 6.002.
Physical Concept:
- Kirchhoff's Current Law (KCL): Rooted in the fundamental physical law of Conservation of Electric Charge. The algebraic sum of all currents entering and leaving any node or closed boundary equals zero.
- Kirchhoff's Voltage Law (KVL): Rooted in the Conservation of Energy in conservative electrostatic fields. The directed sum of electrical potential differences around any closed circuit loop equals zero.
Governing Equations: \(\sum_{k=1}^n I_k = 0 \quad (\text{KCL at any node}),\quad \sum_{k=1}^m V_k = 0 \quad (\text{KVL in any closed loop})\)
Engineering Rule of Thumb: KCL and KVL are the foundation of Modified Nodal Analysis (MNA), the exact mathematical engine powering SPICE and Bastion's real-time 60fps physics solver! When debugging a non-functional net, check that node voltages satisfy KVL in every loop.

Study material: 58 lessons

Every lesson now goes beyond the short card (governing law, key equations, core concept, rule of thumb): it has several headed sections that explain the idea step by step, a worked example with numbers, a list of common mistakes, a Try it in Bastion list of things to build and measure in the simulator, self-check questions with answers, and links to related lessons. The material is stored as embedded JSON in src/Bastion.Core/Education/Content/ (one array of lessons per file); a lesson whose Id already exists in the built-in cards only adds its study material, any other lesson is added whole. A synchronised short card from the curriculum repository never erases the study material.

Category	Lesson	Level	Reading time
Fundamentals of Electricity	Voltage: Electric Potential & Electromotive Force	Beginner	about 2 min
Fundamentals of Electricity	Electric Current: Charge in Motion	Beginner	about 1 min
Fundamentals of Electricity	Ground: Common Reference & Return Path	Beginner	about 2 min
Fundamentals of Electricity	Power & Energy: Watts, Joules and Heat	Beginner	about 2 min
Fundamentals of Electricity	Batteries: Capacity, Internal Resistance & Discharge	Beginner	about 2 min
Circuit Laws & Analysis	Resistors, Resistance & Ohm's Law	Beginner	about 2 min
Circuit Laws & Analysis	Voltage Dividers & Ratio Attenuation	Beginner	about 2 min
Circuit Laws & Analysis	Kirchhoff's Laws: Conservation of Charge & Energy	Intermediate	about 1 min
Circuit Laws & Analysis	Series & Parallel Networks	Beginner	about 1 min
Circuit Laws & Analysis	Thevenin & Norton Equivalents	Intermediate	about 2 min
Circuit Laws & Analysis	Node-Voltage Analysis & How the Simulator Solves a Circuit	Advanced	about 2 min
Passive Components & Transients	Capacitors: Electric Fields & Time Constants	Intermediate	about 2 min
Passive Components & Transients	Inductors: Magnetic Storage & Back-EMF	Intermediate	about 1 min
Passive Components & Transients	AC Signals, RMS Values & Impedance	Intermediate	about 2 min
Passive Components & Transients	RC Filters, Cutoff Frequency & Bode Plots	Intermediate	about 1 min
Passive Components & Transients	Flyback Diodes & Switching Inductive Loads	Intermediate	about 2 min
Semiconductors & Active Devices	Diodes: The One-Way Semiconductor Valve	Beginner	about 2 min
Semiconductors & Active Devices	Light Emitting Diodes (LEDs) & Current Limiting	Beginner	about 1 min
Semiconductors & Active Devices	Zener Diodes: Voltage Clamping & References	Intermediate	about 1 min
Semiconductors & Active Devices	Transistors: Electronic Switches & Amplifiers	Intermediate	about 2 min
Semiconductors & Active Devices	Operational Amplifiers & Negative Feedback	Intermediate	about 2 min
Semiconductors & Active Devices	MOSFETs as Switches: Gate Drive & Rds(on)	Intermediate	about 2 min
Integrated Circuits & Digital Logic	Linear Regulators, Dropout & Heat	Intermediate	about 2 min
Integrated Circuits & Digital Logic	NE555 Timer: Voltage Comparators & Flip-Flops	Intermediate	about 2 min
Integrated Circuits & Digital Logic	Digital Logic Gates & Boolean Algebra	Beginner	about 1 min
Integrated Circuits & Digital Logic	Microcontrollers: Computing & GPIO Physics	Intermediate	about 2 min
Integrated Circuits & Digital Logic	Decoupling Capacitors & Power Integrity	Intermediate	about 2 min
Integrated Circuits & Digital Logic	Pull-ups, Open-Drain Outputs & Logic Levels	Intermediate	about 2 min
Integrated Circuits & Digital Logic	Serial Buses: UART, I2C and SPI	Intermediate	about 2 min
Integrated Circuits & Digital Logic	ADCs, Sampling & Quantization	Intermediate	about 2 min
Integrated Circuits & Digital Logic	PWM: Duty Cycle & Average Power	Intermediate	about 2 min
Integrated Circuits & Digital Logic	Switches, Contact Bounce & Debouncing	Beginner	about 2 min
Test Instruments & Measurement	Oscilloscopes: Waveforms & Signal Physics	Intermediate	about 2 min
Test Instruments & Measurement	Multimeters: Voltage vs Current Shunt Physics	Beginner	about 2 min
Test Instruments & Measurement	Thermal Design: Junction Temperature & Derating	Intermediate	about 2 min
Test Instruments & Measurement	Simulation Basics: Time Step, Accuracy & Why Results Differ from the Bench	Advanced	about 2 min
Microcontrollers & Embedded Systems	Inside a Microcontroller: Core, Clock, Memory and Peripherals	Beginner	about 4 min
Microcontrollers & Embedded Systems	Choosing a Board: AVR, ESP32, RP2040, STM32 and Linux Boards	Beginner	about 4 min
Microcontrollers & Embedded Systems	Bare-Metal GPIO: Registers, Bit Masks and Read-Modify-Write	Intermediate	about 4 min
Microcontrollers & Embedded Systems	MicroPython: Prototyping with a REPL	Beginner	about 3 min
Microcontrollers & Embedded Systems	RP2040: Dual Cores and PIO State Machines	Advanced	about 3 min
Microcontrollers & Embedded Systems	RTOS Basics: Tasks, the Scheduler and Priorities	Intermediate	about 4 min
Microcontrollers & Embedded Systems	RTOS Communication: Queues, Semaphores and Mutexes	Intermediate	about 3 min
Microcontrollers & Embedded Systems	The Project Ladder: Blink, Button, Sensor, Motor, Network	Beginner	about 3 min
PCB Design & Bench Practice	Reading Schematics and Building on a Breadboard	Beginner	about 4 min
PCB Design & Bench Practice	Resistor Colour Codes, Tolerances and Standard Values	Beginner	about 4 min
PCB Design & Bench Practice	Troubleshooting Circuits: A Systematic Method	Intermediate	about 4 min
PCB Design & Bench Practice	From Schematic to Fabrication: The PCB Design Flow	Intermediate	about 4 min
PCB Design & Bench Practice	PCB Layout Rules: Traces, Vias, Ground and Placement	Advanced	about 4 min
Microcontrollers & Embedded Systems	Interrupts: Reacting Instantly Without Polling	Intermediate	about 4 min
Microcontrollers & Embedded Systems	Non-Blocking Firmware: millis(), State Machines and Overflow-Safe Timing	Beginner	about 4 min
Microcontrollers & Embedded Systems	Connected Devices: Robust Wi-Fi, HTTP and JSON	Intermediate	about 4 min
Microcontrollers & Embedded Systems	Bluetooth Low Energy: Advertising, GATT Services and Characteristics	Intermediate	about 3 min
Microcontrollers & Embedded Systems	Low-Power Design: Deep Sleep, Wake-Up Sources and Duty Cycle	Intermediate	about 4 min
Microcontrollers & Embedded Systems	Embedded Rust: Ownership, no_std and embedded-hal	Advanced	about 4 min
Operating Systems & Computer Architecture	How a Computer Boots: From Reset Vector to a Running Kernel	Intermediate	about 4 min
Operating Systems & Computer Architecture	Virtual Memory: Page Tables, Frames and Memory-Mapped I/O	Advanced	about 4 min
Operating Systems & Computer Architecture	Traps, Interrupts and System Calls: How the Kernel Gets Control	Advanced	about 4 min

To add a lesson, append an object with the same fields as the existing ones (Id, Title, Category, GoverningLaw, KeyFormulas, Summary, DeepDive, EngineeringRuleOfThumb, AssociatedComponentIds, Keywords, Level, Sections, WorkedExample, CommonMistakes, TryInBastion, Quiz, RelatedLessonIds) to one of the files; Phase91AcademyAndInterfaceTests checks the structure (at least three sections, a worked example, two questions, links that resolve).

Accessing Lessons Inside Bastion Circuit Designer

Bastion provides 4 interconnected access points for educational physics and electricity theory:

Interactive Canvas Hover HUD Tooltips:
- Hover your mouse cursor over any component or net wire on the schematic canvas.
- Bastion displays a rich, translucent educational tooltip showing the component's name, governing physical law, formula, physical summary, and engineering rule of thumb.
- Can be toggled in View > Toggle Physics Canvas Tooltips.
Properties Inspector Card (Right Sidebar):
- Select any component on the canvas.
- The right sidebar displays the Physics & Electrical Theory card containing the governing equation, concept summary, rule of thumb, and a Read Full Physics Lesson... button.
Dedicated Physics & Electricity Academy Window (Ctrl+Shift+L):
- Open via Help > Physics & Electricity Lessons... or Tools > Physics & Electricity Academy... or pressing Ctrl+Shift+L.
- Search across topics or filter by category.
- View deep-dive physics, equation blocks, and open-source attributions.
- Click Place Associated Component to immediately instantiate related components onto your active canvas!
Multimodal AI Co-Pilot Pair Programming:
- Ask the AI Co-Pilot (AI Co-Pilot panel) any question about voltage, current, Ohm's law, op-amps, or circuit theory.
- The AI cites the authoritative open-source references, explains governing equations, and automatically opens the Academy topic for you!