Mapping a Smoke Detector
One tiny circuit, four completely different diagrams.
Read case study →Guiding questionHow can electronic systems be incorporated into product design?
Where A3.4 gave you the vocabulary, B3.4 asks you to specify: which sensor, which output, how much current, which protocol, and what happens when the battery runs low. This is the level at which designers actually work with electronics. You are rarely the person soldering, but you are frequently the person who decided the product needed to know the temperature, and every one of those decisions has consequences in cost, power and size.
The calculations here are the most predictable marks in the topic. Ohm's law and electrical power are not difficult, and once you are comfortable rearranging them you have a reliable source of marks in Paper 2 that does not depend on how well you write. Beyond the exam, this material is unusually practical. If you have ever wanted to build something that responds to the world, the input, process and output framework plus a sensible sensor choice is most of what you need to start, and I would genuinely encourage you to try it outside of class.
Building on A3.4, this topic applies electronic systems to real product design: using test equipment, calculating V/I/R/P, working with resistors and capacitors, drawing flow and system diagrams, selecting sensors and outputs, and comparing wireless protocols. The Input–Process–Output model provides the organising framework throughout.
Students must be able toAnalyse simple electronic products and circuits to identify the main component parts that enable them to perform a specific function.
The Input–Process–Output (IPO) model is the fundamental framework for understanding any electronic system. It breaks a complex product into three stages:
Electronics are now embedded in almost every product category: home appliances (refrigerators, washing machines, microwaves), entertainment (TVs, game consoles), communication (smartphones, computers), automotive (engine control units, GPS, advanced driver assistance), and personal wearables (smartwatches, fitness trackers). When analysing a product, the first task is to identify which components serve which stage of the IPO model.
输入-处理-输出(IPO)模型是理解任何电子系统的基本框架。它将复杂产品分解为三个阶段:
电子系统现已嵌入几乎所有产品类别:家用电器(冰箱、洗衣机、微波炉)、娱乐设备(电视、游戏机)、通信工具(智能手机、计算机)、汽车(发动机控制单元、GPS、高级驾驶辅助)和可穿戴设备(智能手表、健身追踪器)。分析产品时,第一步是识别哪些组件属于IPO模型的哪个阶段。
Students must be able toDescribe how to use basic electronic measuring apparatus, including multi-meters on voltage, current and resistance ranges, and oscilloscopes to observe waveforms.
Choosing the right instrument (and connecting it correctly) is as important as the measurement itself. Using a current meter in parallel, for example, will short-circuit the component and may destroy the meter.
Digital multimeter (DMM), the most versatile handheld instrument:
Digital storage oscilloscope (DSO): visualises voltage waveforms over time (voltage on Y-axis, time on X-axis). Indispensable for diagnosing: ringing (damped oscillations indicating impedance problems), distorted rising edges (slow component or excessive capacitance), and amplitude problems (incorrect voltage levels indicating a faulty supply). A multimeter cannot reveal any of these: it only shows a single numerical value.
Function generator: produces test signals (sine, square, triangle waves) at a chosen frequency. Frequently used alongside a DSO: the generator provides a known input, the DSO captures the circuit's response.
Clamp meter: measures current without breaking the circuit by clamping around the conductor. For AC it uses a current transformer; for DC it uses the Hall effect (detecting the magnetic field produced by the current).
Other instruments: Megohmmeter (tests insulation resistance at high voltage: a downward trend indicates insulation breakdown); Wattmeter (measures real power P = VI); LCR meter (measures inductance, capacitance and resistance using AC test signals); Logic analyser (captures multiple digital signals simultaneously to debug timing and decode communication protocols such as I²C, SPI, UART).
选择正确的仪器并正确连接与测量本身同样重要。例如,将电流表并联连接会使元件短路,并可能损坏仪表。
数字万用表(DMM)——最通用的手持仪器:
数字存储示波器(DSO)——随时间可视化电压波形(Y轴为电压,X轴为时间)。用于诊断:振铃(阻抗问题导致的阻尼振荡)、上升沿失真(元件缓慢或电容过大)和幅度异常(电压电平不正确,提示电源故障)。万用表无法揭示这些问题——它只能显示单一数值。
函数发生器——产生指定频率的测试信号(正弦波、方波、三角波)。常与示波器配合使用:发生器提供已知输入,示波器捕捉电路响应。
钳形表——无需断路即可测量电流,通过夹住导线来检测其周围的磁场。交流使用电流互感器;直流使用霍尔效应。
其他仪器:兆欧表(在高电压下测试绝缘电阻——数值下降趋势表明绝缘劣化);功率计(测量实际功率P = VI);LCR表(用交流信号测量电感、电容和电阻);逻辑分析仪(同时捕捉多路数字信号,调试时序并解码通信协议)。
| Instrument | Measures | Connection | Key limitation |
|---|---|---|---|
| DMM | V, I, R | V: parallel / I: series / R: removed | Only static values: no waveform |
| DSO | Waveform over time | Parallel (high impedance probe) | Can miss very slow DC drift |
| Clamp meter | Current only | Clamp around wire (no break) | Cannot measure very low currents |
| Megger | Insulation resistance | High-voltage DC applied | Cannot test live circuits |
| LCR meter | L, C, R | Component removed from circuit | AC test signal only |
| Logic analyser | Digital signals (timing) | Probes on multiple pins | No analog voltage detail |
Plan the switches, wiring and components for a real macropad, then generate downloadable code to build it with an ESP32: a genuine circuit to point a multimeter at once it's built. Try it →
Students must be able toCalculate power, voltage, current and resistance in a circuit, considering V = IR and P = VI by rearranging equations and substituting values.
Ohm's law: the voltage across a component equals the current through it multiplied by its resistance.
V = I × R → I = V / R → R = V / I
Power formulas: electrical power is the rate of energy conversion. Three equivalent forms:
P = V × I = I² × R = V² / R
Use whichever form avoids an intermediate calculation step. If you know V and R but not I, use P = V²/R directly rather than calculating I first.
Single-phase vs three-phase power:
IEC 60309 industrial plug colour coding: yellow = 100–130 V, blue = 200–250 V, red = 380–480 V. Colour coding prevents incorrect connection of equipment to incompatible voltages.
欧姆定律:元件两端的电压等于通过它的电流乘以其电阻。
V = I × R → I = V / R → R = V / I
功率公式:电功率是能量转换的速率。三种等效形式:
P = V × I = I² × R = V² / R
选择能减少计算步骤的公式。若已知V和R但不知I,直接用P = V²/R,而无需先计算I。
单相电与三相电:
IEC 60309工业插头颜色编码:黄色=100–130V,蓝色=200–250V,红色=380–480V。颜色编码防止设备连接到不兼容的电压。
Worked examples
| Given | Find | Formula | Result |
|---|---|---|---|
| V = 12 V, R = 470 Ω | I | I = V / R | I = 12 / 470 = 25.5 mA |
| V = 12 V, I = 25.5 mA | P | P = V × I | P = 12 × 0.0255 = 0.306 W |
| V = 12 V, R = 470 Ω | P (direct) | P = V² / R | P = 144 / 470 = 0.306 W |
Enter any two of V, I and R — or one of them plus P — and the rest solve automatically, with the working shown below.
Students must be able toCalculate resistance and capacitance in series and parallel in a circuit.
Resistors in series: total resistance is the sum of all resistors. Current is the same through each.
R_total = R₁ + R₂ + R₃ + …
Resistors in parallel: total resistance is always less than the smallest individual resistor. Voltage is the same across each; current splits between branches.
1 / R_total = 1/R₁ + 1/R₂ + 1/R₃ + … (for equal R: R_total = R / n)
RC circuits: a resistor (R) and capacitor (C) together create time-dependent behaviour. The capacitor charges through the resistor; the time constant τ = R × C (in seconds when R is in Ω and C is in Farads) determines how quickly voltage rises or falls.
Low-pass filter: resistor in series, capacitor in parallel with the output. Passes low-frequency (slow) signals; attenuates high-frequency (fast) signals. The capacitor charges slowly, smoothing rapid fluctuations.
High-pass filter: capacitor in series, resistor in parallel with the output. Blocks low-frequency signals (capacitor blocks DC and very slow signals); passes high-frequency signals.
Contact bounce (chatter) elimination: when a mechanical switch closes, the contacts bounce and produce multiple rapid 1s and 0s before settling. A low-pass RC filter smooths this leading edge, so the logic gate receives a clean single transition rather than a burst of false triggers.
串联电阻——总电阻为所有电阻之和。每个电阻通过的电流相同。
R_total = R₁ + R₂ + R₃ + …
并联电阻——总电阻始终小于最小的单个电阻。每个电阻两端电压相同;电流在各支路间分配。
1 / R_total = 1/R₁ + 1/R₂ + 1/R₃ + … (相等时:R_total = R / n)
RC电路——电阻(R)和电容(C)共同产生时间依赖的行为。电容通过电阻充电;时间常数τ = R × C(R单位Ω,C单位F时,τ单位为秒)决定电压上升或下降的速度。
低通滤波器:电阻串联,电容与输出并联。通过低频(慢速)信号;衰减高频(快速)信号。电容缓慢充电,平滑快速波动。
高通滤波器:电容串联,电阻与输出并联。阻断低频信号(电容阻断直流和极慢信号);通过高频信号。
消除触点弹跳(抖动):机械开关闭合时,触点在稳定前会多次弹跳,产生一系列快速的1和0。低通RC滤波器平滑这一前沿信号,使逻辑门接收到干净的单一跳变,而非一连串误触发。
Worked examples (resistor networks)
| Configuration | Calculation | Result |
|---|---|---|
| Series: 100 Ω + 220 Ω + 330 Ω | 100 + 220 + 330 | 650 Ω |
| Parallel: 100 Ω ∥ 100 Ω | R / n = 100 / 2 | 50 Ω |
| Parallel: 47 Ω ∥ 47 Ω | 47 / 2 | 23.5 Ω |
| Combination: 100 Ω + (50 Ω ∥ 50 Ω) | 50/2 = 25; 100 + 25 | 125 Ω |
For combination circuits, always resolve the parallel branches first, then add the series elements, just as you would apply BODMAS to arithmetic.
Students must be able toConstruct flow diagrams (using appropriate symbols) to model a programmable system that controls an electronic device.
A flow diagram (flowchart) maps the sequence of steps in an algorithm using standardised symbols. In electronics, flowcharts are used to plan and communicate how a microcontroller will respond to inputs.
Standard flowchart symbols:
Flow diagrams are useful before writing code because they separate the logic of what the system must do from the syntax of how to code it. A well-drawn flowchart can be translated directly into any programming language.
流程图使用标准化符号描述算法的步骤序列。在电子学中,流程图用于规划和传达微控制器如何响应输入。
标准流程图符号:
在编写代码之前先画流程图非常有用,因为它将系统的逻辑(做什么)与编程语法(如何编写)分开。一张绘制良好的流程图可以直接翻译成任何编程语言。
Students must be able toConstruct diagrams for simple circuits that use resistors, capacitors, switches, relays, diodes, transistors, operational amplifiers, integrated circuits, and input and output devices.
Designers use different diagram types depending on the level of detail needed and the audience for the drawing:
All four types are used in IB assessment. Block and flow diagrams are expected at a conceptual level; circuit and logic diagrams require correct use of standard symbols.
设计师根据所需的详细程度和目标受众使用不同类型的图:
IB评估中使用所有四种类型。框图和流程图在概念层面上考查;电路图和逻辑图需要正确使用标准符号。
One tiny circuit, four completely different diagrams.
Read case study →Students must be able toDetermine the use of sensors to collect and input information into a digital system, including accelerometer (motion), ultrasonic (distance or proximity), photoresistor (light), voltage (moisture), hygrometer (humidity and air temperature), pressure (barometric), microphone (sound) and infrared (radiation or heat).
Sensors are the input stage of the IPO model: they convert a physical quantity into an electrical signal that a microcontroller can read. The choice of sensor must match the physical quantity being measured and the output format the processor expects (analog voltage, or digital signal).
传感器是IPO模型的输入阶段——它们将物理量转换为微控制器可读取的电信号。传感器的选择必须匹配被测物理量以及处理器所需的输出格式(模拟电压或数字信号)。
| Sensor | Detects | Output | Typical application | 中文 |
|---|---|---|---|---|
| Accelerometer | Motion, vibration, tilt | Analog / digital | Phone orientation, fall detection | 加速度计 |
| Ultrasonic | Distance / proximity | Digital (pulse timing) | Parking sensors, robotics | 超声波传感器 |
| Photoresistor (LDR) | Light level | Analog voltage | Automatic street lights | 光敏电阻 |
| Moisture / voltage | Soil or liquid conductivity | Analog | Plant watering systems | 湿度/电压传感器 |
| Hygrometer | Humidity and air temperature | Analog / digital | HVAC, weather stations | 湿度计 |
| Barometric pressure | Atmospheric pressure | Analog / digital | Weather apps, altimeters | 气压传感器 |
| Microphone | Sound | Analog (AC) | Voice control, noise monitoring | 麦克风 |
| Infrared / PIR | Heat, radiation, motion | Digital | Intruder detection, touchless switches | 红外/热释电传感器 |
| Hall effect | Magnetic field strength | Analog / digital | Speed sensors, position sensing | 霍尔效应传感器 |
| Gas sensor | Chemical concentration | Analog | CO detectors, air quality monitors | 气体传感器 |
Students must be able toCreate simple circuits that use microcontrollers as a programmable integrated circuit (PIC) with appropriate software to carry out a predetermined task.
An embedded system is a dedicated computer system designed to perform a specific function within a larger product. Unlike a general-purpose computer, it runs one fixed program stored in its memory.
The heart of the process stage is a microcontroller (MCU), also referred to as a programmable integrated circuit (PIC). A microcontroller integrates on a single chip:
Educational platforms such as Arduino (AVR/ARM microcontrollers) and Raspberry Pi (single-board computer) make it accessible to prototype embedded systems. In industry, dedicated MCUs (e.g., STM32, PIC, ATmega) are chosen for their size, power consumption and cost.
嵌入式系统是专为在更大产品中执行特定功能而设计的专用计算机系统。与通用计算机不同,它运行存储在内存中的固定程序。
处理阶段的核心是微控制器(MCU),也称为可编程集成电路(PIC)。微控制器在单芯片上集成了:
Arduino(AVR/ARM微控制器)和Raspberry Pi(单板计算机)等教育平台让嵌入式系统原型开发变得更加容易。在工业中,专用MCU(如STM32、PIC、ATmega)因其尺寸、功耗和成本而被选用。
Students must be able toDescribe digital systems in terms of the binary number system, Boolean algebra, logic gates (AND, OR and NOT), combinational logic circuits and sequential logic circuits, and construct truth tables for a digital circuit.
All digital systems represent data using binary: a base-2 number system using only 0 and 1 (off and on). Multiple binary digits (bits) represent larger values: 8 bits = 1 byte, capable of representing 256 values (0–255).
Boolean algebra defines how binary values are combined using logical operations. Three fundamental gates:
A truth table lists every possible combination of inputs and the corresponding output. For n inputs there are 2ⁿ rows.
Combinational logic: the output depends only on the current inputs. No memory: the same input always produces the same output. Examples: AND, OR, NOT, NAND, NOR, XOR gates.
Sequential logic: the output depends on current inputs AND previous states. Uses memory elements (flip-flops). Examples: counters, registers, state machines: the basis of most microcontrollers.
所有数字系统都使用二进制表示数据——一种仅使用0和1(关和开)的二进制数系统。多个二进制位(比特)表示更大的值:8位=1字节,能表示256个值(0–255)。
布尔代数定义了如何使用逻辑运算组合二进制值。三种基本门:
真值表列出所有可能的输入组合及其对应输出。n个输入有2ⁿ行。
组合逻辑:输出仅取决于当前输入。无记忆——相同输入始终产生相同输出。例:与、或、非、与非、或非、异或门。
时序逻辑:输出取决于当前输入和之前状态。使用记忆元件(触发器)。例:计数器、寄存器、状态机——大多数微控制器的基础。
Truth tables (AND, OR, NOT)
| A | B | A AND B | A OR B | NOT A |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 0 |
Students must be able toDetermine appropriate output devices to communicate information or physically control an environment, including motors (including servos and pumps), LCD display, buzzer and relay.
Output devices are the third stage of the IPO model: they convert the processed electrical signal into a physical action or visible/audible communication.
输出设备是IPO模型的第三阶段——将处理后的电信号转换为物理动作或可见/可听的通信。
| Output device | Function | Notes | 中文 |
|---|---|---|---|
| DC motor | Continuous rotary motion | Speed controlled by PWM; direction by H-bridge circuit | 直流电机 |
| Servo motor | Precise angular positioning (0–180°) | Position set by PWM pulse width; used in robotic arms, steering | 伺服电机 |
| Pump | Fluid movement | Essentially a motor with an impeller; used in irrigation, aquariums | 泵 |
| LCD display | Text and numeric information | Communicates data to the user; requires no moving parts | LCD显示屏 |
| Piezo buzzer | Audible alert or tone | Simple alarm; frequency can be varied to produce different tones | 压电蜂鸣器 |
| Relay | Switches a separate high-power circuit using a low-power control signal | Electrically isolates the control circuit from the load circuit; used to switch mains voltage from a 5V microcontroller output | 继电器 |
When selecting an output device, consider three things: the type of action needed (motion, information, sound), the voltage and current required by the device, and whether the microcontroller can drive it directly or needs an amplifying component (transistor, relay, or motor driver IC).
A microcontroller's digital output pin can only be fully on or fully off; it has no way to produce an intermediate voltage directly. PWM works around this by switching the pin on and off very rapidly and varying the proportion of time it spends on, called the duty cycle. A device that responds to average power rather than to the instant-by-instant signal, such as a motor or an LED, behaves as if it were receiving a steady intermediate voltage.
A 0% duty cycle is equivalent to fully off, 100% is fully on, and 50% behaves roughly like half power. This is exactly how DC motor speed and servo position are controlled in the output device table above: a DC motor's average rotational speed scales with duty cycle, while a servo reads the pulse width of each cycle (not the average) to determine the angle it should hold.
Students must be able toCompare the protocol embedded systems used to communicate with other systems (Wi-Fi vs Bluetooth vs 5G).
Embedded systems often need to communicate with other devices or networks. The choice of wireless protocol depends on range, speed, power consumption and the infrastructure available.
Bluetooth: designed for low-power, short-range device-to-device communication. Operates at 2.4 GHz using frequency hopping to reduce interference. Typical range: ~10 m. Uses a layered protocol stack: the Controller layer (Radio, Link Manager, Voice CODEC) communicates with the Host layer (GAP, GATT, ATT, SMP, RFCOMM) via the HCI interface. GAP (Generic Access Profile) governs device discovery and connection setup. Used in: wireless earbuds, keyboards, fitness trackers, medical devices.
Wi-Fi: high-speed, medium-range local area network access. Connects devices to a router (and thus the internet). Higher power consumption than Bluetooth. Range: ~50 m indoors. Used in: laptops, smart home devices, IP cameras.
5G: fifth-generation cellular technology. Offers ultra-high data speeds, ultra-low latency, and the ability to connect massive numbers of devices simultaneously. Does not require a local router: connects directly to the cellular network. Used in: autonomous vehicles, smart cities, large-scale IoT deployments.
Case study (Australia's 3G shutdown, October 2024): Many 4G phones were designed to fall back to 3G for voice calls because 4G voice required a separate technology called VoLTE (Voice over LTE). When Australia's ACMA shut down the 3G network, non-VoLTE phones lost all voice capability, including emergency calls. Even medical alarms and personal emergency response devices stopped working. The lesson for embedded systems designers: never assume that legacy infrastructure will remain available. Design for forward compatibility and include graceful upgrade paths.
嵌入式系统通常需要与其他设备或网络通信。无线协议的选择取决于范围、速度、功耗和可用基础设施。
蓝牙——专为低功耗、短距离设备间通信设计。在2.4 GHz频段使用跳频技术减少干扰。典型范围:约10米。使用分层协议栈:控制器层(无线电、链路管理器、语音编解码器)通过HCI接口与主机层(GAP、GATT、ATT、SMP、RFCOMM)通信。GAP(通用访问配置文件)负责设备发现和连接建立。应用于:无线耳机、键盘、健身追踪器、医疗设备。
Wi-Fi——高速、中距离局域网络访问。将设备连接到路由器(进而连接互联网)。功耗高于蓝牙。室内范围约50米。应用于:笔记本电脑、智能家居设备、IP摄像头。
5G——第五代蜂窝技术。提供超高数据速度、超低延迟,以及同时连接大量设备的能力。不需要本地路由器——直接连接到蜂窝网络。应用于:自动驾驶汽车、智慧城市、大规模物联网部署。
案例研究——澳大利亚3G网络关闭(2024年10月):许多4G手机被设计为回落到3G进行语音通话,因为4G语音需要一种名为VoLTE(基于LTE的语音通话)的独立技术。当澳大利亚通信与媒体管理局关闭3G网络后,非VoLTE手机失去了所有语音功能——包括紧急呼叫。甚至医疗警报和个人紧急响应设备也停止工作。对嵌入式系统设计师的启示:永远不要假设遗留基础设施将持续可用。应为前向兼容性而设计,并提供优雅的升级路径。
| Protocol | Range | Speed | Power | Infrastructure needed | Best for |
|---|---|---|---|---|---|
| Bluetooth | ~10 m | Moderate | Very low | None (peer-to-peer) | Wearables, peripherals, medical sensors |
| Wi-Fi | ~50 m | High | Moderate | Router / access point | Smart home, streaming, internet access |
| 5G | Kilometres | Ultra-high | Higher | Cellular network | Autonomous vehicles, smart cities, IoT at scale |
Ten questions covering the key learning objectives. Select one answer per question, then click "Check all answers" to see your score and the explanations.
Voltage: The voltmeter probes are connected in parallel across the two points being measured. No circuit interruption is required: the meter has very high internal resistance so that almost no current flows through it and the circuit is not disturbed. The black probe connects to COM; the red probe to the V terminal.
Current: The meter must be connected in series: the circuit must be broken and the meter inserted into the break so that the full circuit current flows through it. The power must be switched off before breaking the circuit, then restored for the reading. The black probe connects to COM; the red probe to the A (or mA) terminal. Caution: connecting a current meter in parallel will short-circuit the component.
Resistance: The component to be measured must be removed from the circuit entirely. If left in circuit, parallel current paths will give a false reading. The dial is set to Ω; the meter sends its own small test current from its internal battery through the component and calculates resistance from the resulting voltage drop. The reading is meaningless if other components remain connected in parallel.
a) Contact bounce: When a mechanical switch closes, the spring contacts do not make a single clean connection. Instead, they bounce or vibrate against each other for several milliseconds before settling. This produces a rapid series of 1s and 0s at the logic gate input rather than a single clean 0-to-1 transition. Because different signal paths through a circuit have different propagation delays, inputs to a logic gate may not arrive simultaneously: the gate's output can briefly flicker to an incorrect state before settling to its correct value. A counter circuit, for example, might increment multiple times from a single intended button press.
b) RC circuit solution: A resistor-capacitor (RC) circuit is placed between the switch output and the logic gate input. When the switch closes, the capacitor does not charge instantly: it charges through the resistor at a rate determined by the time constant τ = R × C. The output voltage rises smoothly from 0 V toward the supply voltage rather than jumping immediately. This smooth rise filters out the rapid spikes caused by bouncing. By the time the voltage crosses the logic gate's switching threshold, the contacts have settled and a clean transition is presented to the gate.
c) Low-pass filter: A low-pass filter configuration is appropriate: resistor in series, capacitor in parallel with the output. A low-pass filter passes slow (low-frequency) signals and attenuates fast (high-frequency) signals. The intended switch closure is a slow event (the user presses the button over tens of milliseconds); the bounce spikes are fast events (milliseconds). The RC filter smooths away the fast spikes while still allowing the slow, intended transition to reach the logic gate. A high-pass filter would do the opposite: it would block the intended slow signal and pass the fast bounce spikes, which is exactly what must be avoided.
a) What a DSO shows that a multimeter cannot: A DSO visualises voltage as a waveform over time, displaying voltage on the vertical axis and time on the horizontal axis. It captures the shape, frequency, period, and timing of a signal. A multimeter (even a high-quality digital model) only displays a single numerical value (RMS voltage, average current, or resistance). It cannot reveal signal shape, timing relationships, or transient events.
b) Three signal abnormalities a DSO can reveal:
c) Why use both: The multimeter excels at steady-state DC measurements (precise voltage levels, continuity checking, and resistance values) quickly and portably. The DSO excels at dynamic, time-varying signals: capturing transients, measuring frequency and duty cycle, and debugging communication timing. The instruments complement each other: use the multimeter first to verify that power supply voltages are correct and there are no short circuits, then use the DSO to verify signal integrity and timing. A function generator paired with the DSO allows a technician to inject a known test signal and observe the circuit's response: a powerful combination for diagnosing filters, amplifiers and logic circuits.
a) Series:
R_total = 100 + 220 + 330 = 650 Ω
b) Two equal resistors in parallel (100 Ω ∥ 100 Ω):
R_total = R / n = 100 / 2 = 50 Ω
Verification: 1/R_total = 1/100 + 1/100 = 0.02; R_total = 1/0.02 = 50 Ω ✓
c) Two equal resistors in parallel (47 Ω ∥ 47 Ω):
R_total = 47 / 2 = 23.5 Ω
d) Combination (100 Ω in series with 50 Ω ∥ 50 Ω):
Step 1 (resolve the parallel branch first): R_parallel = 50 / 2 = 25 Ω
Step 2 (add the series resistor): R_total = 100 + 25 = 125 Ω
| Configuration | Result |
|---|---|
| Series: 100 + 220 + 330 | 650 Ω |
| Parallel: 100 ∥ 100 | 50 Ω |
| Parallel: 47 ∥ 47 | 23.5 Ω |
| Combination: 100 + (50 ∥ 50) | 125 Ω |
a) Why 4G/5G phones stopped working: Many phones marketed as 4G-capable were designed to fall back to the older 3G network for voice calls, because carrying voice natively over 4G requires a separate technology (VoLTE) that not all devices included. When Australia's ACMA shut down the 3G network, this fallback path disappeared. The ACMA then blocked service to all non-VoLTE 4G phones. These phones lost voice calling, SMS and emergency services entirely (despite having functional 4G data radios) because their voice system had no network to connect to.
b) VoLTE and why it was critical: VoLTE (Voice over Long-Term Evolution) is a technology that carries voice calls as data packets over the 4G LTE network, rather than switching to a separate circuit-switched voice network (3G or 2G). VoLTE provides clearer HD voice quality, faster call connection times, and the ability to use mobile data simultaneously during a call. It was critical because without it, a 4G phone had no way to make or receive any call, including Triple Zero (000) emergency calls, once 3G was decommissioned.
c) Lessons for embedded systems designers:
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