---
title: 'Hardware Fundamentals: A Learning Path from Circuit Computation to Measurement'
url: https://doc.liz6.com/en/hardware/00-learning-path
locale: en
area: hardware
tags:
- Electronics
date: 2026-09-12
modified: 2026-09-12
description: For readers who can perform algebraic operations and wish to understand electronic circuits. Start by using low-voltage DC models on paper or in simulation to recognize quantities, reference directions, and meter connection methods; for experiments with real components, begin with a low-voltage power supply that has clear current limiting. MCU development boards, wireless protocols, and charging schemes are subsequent branches.
---

# Hardware Fundamentals: A Learning Path from Circuit Computation to Measurement

For readers who can perform algebraic operations and wish to understand electronic circuits. Start by using low-voltage DC models on paper or in simulation to recognize quantities, reference directions, and meter connection methods; for experiments with real components, begin with a low-voltage power supply that has clear current limiting. MCU development boards, wireless protocols, and charging schemes are subsequent branches.

## What you will build

You will be able to predict how node voltages change when a load is connected, verify a simple circuit using measurements, and distinguish between static relationships, dynamic processes, and model assumptions.

## Required reading and checkpoints

1. [Basic Physical Quantities and Laws](01-basic-electricity/01-basic-physical-quantities-and-laws.md) → [DC Circuit Analysis](01-basic-electricity/02-dc-circuit-analysis.md).

   Recalculate the voltage divider with 12 V and two 10 kΩ resistors: 6 V unloaded, 4 V with a 10 kΩ load connected. Self-check: Explain the same result using nodal equations and Thevenin equivalent, clearly marking current directions and units.

2. [Resistors](02-passive-components/01-resistor.md) → [Measurement Instruments and Tools](10-practices-and-tools/01-measurement-instruments-and-tools.md).

   Connect theoretical values with component tolerances and meter input impedance. Self-check: First estimate whether connecting the measurement will alter the object being measured, then explain the difference between observations and ideal values; do not consider success achieved merely by matching a digital reading.

3. [Logic Gates and Boolean Algebra](05-digital-circuits/01-logic-gates-and-boolean-algebra.md) → [Logic Levels and Interface Physical Layers](06-interfaces-and-communication/01-logic-levels-and-interface-physical-layers.md).

   Move from Boolean values to real high/low levels and input/output relationships. Self-check: Draw the voltage ranges, directions, and common reference for two interfaces, and explain why logical compatibility may still result in electrical incompatibility.

## Optional branches

For the analog direction, start with [Fundamentals of Amplifier Circuits](04-analog-circuits/01-fundamentals-of-amplifier-circuits.md); for the embedded direction, start with [MCU Selection and Development Ecosystem](09-embedded-systems/01-mcu-selection-and-development-ecosystem.md). When encountering feedback, response, and oscillation, switch to [Control Theory](../theory/02-control-theory/index.md) to establish dynamic models first, then return to device circuits; choose wireless and power supply protocols based on usage scenarios.

## Completion task

Submit a calculation table, connection diagram, and simulation or measurement records for the voltage divider before and after loading, explaining sources of error. If no physical hardware is connected, explicitly state "simulation results." Subsequently, choose either the analog circuit or embedded direction; for first-time learning, there is no need to read all semiconductor physics and protocols in full.

Skipping long proofs and implementation details is allowed during the first reading, but you must complete the self-checks for each phase. If you find yourself "knowing the terminology but unable to explain the results," return to the current example, change one condition, and then proceed to the next article; there is no need to read the entire table of contents beforehand.