Systems and Control; Electronic Concepts and Ohm's Law

Introduction to Systems and Control

Welcome to Unit 2 Option A: Electronic and Microelectronic Control Systems! Electronics might seem daunting at first with all its symbols, numbers, and formulas, but every electronic device—from your smartphone to an automated greenhouse—follows the exact same logical principles. In this chapter, we will break down electronic systems into easy, bite-sized concepts, master Ohm's Law, and explore how to design safe, working circuits.

Don't worry if maths and physics aren't your favourite topics—we will walk through every calculation step by step!

1. Systems Architecture: Input \(\rightarrow\) Process \(\rightarrow\) Output

Every electronic control system, no matter how simple or complex, is organized into three main building blocks:

Input \(\rightarrow\) Process \(\rightarrow\) Output

A. Input Devices (Transducers)

An input transducer takes physical energy from the real world (such as light, heat, pressure, or moisture) and converts it into an electrical signal (voltage or current).
Examples: Light Dependent Resistors (LDRs), thermistors, pressure pads, and push-button switches.

B. Process Devices

The process block is the "brain" of the system. It receives the electrical signal from the input, then manipulates, compares, amplifies, or times it before deciding what action to take.
Examples: Potential divider circuits, transistors (acting as electronic switches/amplifiers), 555 timers, logic gates, and microcontrollers.

C. Output Devices (Actuators / Output Transducers)

An output transducer or actuator takes the processed electrical energy and converts it back into a useful form of energy such as light, sound, or physical movement.
Examples: Light Emitting Diodes (LEDs), buzzers, relays, solenoids, electric motors, and 7-segment displays.

Everyday Analogy: Think of an automatic night light. The LDR senses the darkness (Input), the transistor or potential divider circuit detects that the voltage has reached a trigger level (Process), and the LED lights up to illuminate the room (Output).

Key Takeaway: All electronic systems follow the flow Input \(\rightarrow\) Process \(\rightarrow\) Output. Inputs convert physical energy to electrical signals, processes make decisions or amplify signals, and outputs turn electrical energy into light, sound, or movement.

2. Fundamental Electrical Quantities and Units

To understand how electronic circuits function, you must know the three core electrical quantities:

1. Potential Difference / Voltage (\(V\))
Voltage is the measure of electrical "push" or the energy transferred per unit of charge between two points in a circuit.
Standard Unit: Volts (\(\text{V}\)).

2. Current (\(I\))
Current is the rate of flow of electric charge around a closed circuit.
Standard Unit: Amperes or Amps (\(\text{A}\)). In low-power electronics, current is frequently measured in milliamperes (\(\text{mA}\)).
Conversion rule: \(1\,\text{A} = 1000\,\text{mA}\). To turn \(\text{mA}\) into \(\text{A}\), divide by \(1000\) (e.g., \(20\,\text{mA} = 0.02\,\text{A}\)).

3. Resistance (\(R\))
Resistance is the opposition to the flow of electric current through a material or component.
Standard Unit: Ohms (\(\Omega\)). Larger resistances are given in kilo-ohms (\(\text{k}\Omega\)) or mega-ohms (\(\text{M}\Omega\)).
Conversion rules:
\(1\,\text{k}\Omega = 1000\,\Omega = 10^3\,\Omega\)
\(1\,\text{M}\Omega = 1\,000\,000\,\Omega = 10^6\,\Omega\)

Water Pipe Analogy: Imagine water flowing through a garden pipe:
- Voltage (\(V\)) is the water pressure pushing the water through.
- Current (\(I\)) is the volume of water flowing past each second.
- Resistance (\(R\)) is a constriction or squeeze in the pipe that slows down the flow.

Key Takeaway: Always check your units before calculating! Formulae require base units: Volts (\(\text{V}\)), Amperes (\(\text{A}\)), and Ohms (\(\Omega\)).

3. Ohm's Law and Circuit Resistance

What is Ohm's Law?

Ohm's Law states that the current passing through a conductor between two points is directly proportional to the potential difference across those two points, provided the temperature remains constant.

The Core Formulae:

\(V = I \times R\)
\(I = \frac{V}{R}\)
\(R = \frac{V}{I}\)

Memory Trick: The Formula Triangle
Picture a triangle with \(V\) on top, and \(I\) and \(R\) side by side on the bottom. Cover the letter you want to find:
- Cover \(V\) \(\rightarrow\) you see \(I \times R\)
- Cover \(I\) \(\rightarrow\) you see \(\frac{V}{R}\)
- Cover \(R\) \(\rightarrow\) you see \(\frac{V}{I}\)

Step-by-Step Ohm's Law Example:

Question: A \(9\,\text{V}\) battery is connected across a \(450\,\Omega\) resistor. What current flows through the circuit?
- Step 1: Identify values: \(V = 9\,\text{V}\), \(R = 450\,\Omega\)
- Step 2: Choose formula: \(I = \frac{V}{R}\)
- Step 3: Calculate: \(I = \frac{9\,\text{V}}{450\,\Omega} = 0.02\,\text{A}\) (or \(20\,\text{mA}\))

Resistors in Series and Parallel

Resistors in Series:
When resistors are connected end-to-end along a single path, their resistances add together directly:
\(R_{\text{total}} = R_1 + R_2 + R_3 + \dots\)
Example: A \(100\,\Omega\) resistor and a \(220\,\Omega\) resistor in series give \(R_{\text{total}} = 100\,\Omega + 220\,\Omega = 320\,\Omega\).

Resistors in Parallel:
When resistors are connected across shared nodes providing alternative paths, the total resistance decreases:
\(\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots\)
For two resistors in parallel, you can use the product-over-sum formula:
\(R_{\text{total}} = \frac{R_1 \times R_2}{R_1 + R_2}\)
Example: Two \(100\,\Omega\) resistors in parallel:
\(R_{\text{total}} = \frac{100 \times 100}{100 + 100} = \frac{10\,000}{200} = 50\,\Omega\).

Key Takeaway: Adding resistors in series increases total resistance; placing resistors in parallel provides extra paths and decreases total resistance.

4. Essential Circuit Calculations

A. LED Protective (Current-Limiting) Resistors

An LED (Light Emitting Diode) is delicate. If connected directly to a power supply, it will draw too much current and instantly burn out. We must place a current-limiting resistor in series with it.

Because the LED creates a fixed forward voltage drop (\(V_{\text{LED}}\), typically \(1.8\,\text{V}\text{–}2.2\,\text{V}\)), the protective resistor only has to drop the remaining voltage from the supply.

The LED Resistor Formula:
\(R = \frac{V_{\text{supply}} - V_{\text{LED}}}{I_{\text{LED}}}\)

Worked Example:
An LED requires a forward operating current of \(20\,\text{mA}\) and has a forward voltage drop of \(2.0\,\text{V}\). Calculate the required series resistor when running from a \(9\,\text{V}\) supply.
- Step 1: Convert current to Amps: \(I_{\text{LED}} = 20\,\text{mA} = 0.02\,\text{A}\)
- Step 2: Find voltage across resistor: \(V_{\text{resistor}} = V_{\text{supply}} - V_{\text{LED}} = 9\,\text{V} - 2.0\,\text{V} = 7.0\,\text{V}\)
- Step 3: Calculate resistance: \(R = \frac{7.0\,\text{V}}{0.02\,\text{A}} = 350\,\Omega\)

B. Potential Divider (Voltage Divider)

A potential divider consists of two resistors in series across a power supply. It divides the input voltage into a smaller output voltage (\(V_{\text{out}}\)), which is commonly used to produce a sensing signal for transistors or microcontrollers.

The Potential Divider Formula:
\(V_{\text{out}} = V_{\text{in}} \times \left(\frac{R_2}{R_1 + R_2}\right)\)
Note: \(R_1\) is the top resistor (connected to the positive supply rail), and \(R_2\) is the bottom resistor (connected to \(0\,\text{V}\) / ground). \(V_{\text{out}}\) is taken across \(R_2\).

Worked Example:
A \(12\,\text{V}\) supply is connected across \(R_1 = 4\,\text{k}\Omega\) and \(R_2 = 2\,\text{k}\Omega\). What is \(V_{\text{out}}\)?
- Step 1: Substitute values: \(V_{\text{out}} = 12\,\text{V} \times \left(\frac{2\,\text{k}\Omega}{4\,\text{k}\Omega + 2\,\text{k}\Omega}\right)\)
- Step 2: Simplify: \(V_{\text{out}} = 12\,\text{V} \times \left(\frac{2}{6}\right) = 12\,\text{V} \times \frac{1}{3} = 4\,\text{V}\)

Key Takeaway: For an LED, always subtract the forward voltage drop (\(V_{\text{LED}}\)) before applying Ohm's Law. In a potential divider, \(V_{\text{out}}\) is proportional to the bottom resistor (\(R_2\)).

5. Component Conventions, Polarity, and Colour Codes

Component Polarity

Some components are polarized, meaning they must be connected the correct way around to work safely:

- Diodes and LEDs: Have an Anode (positive terminal, longer leg on LEDs) and a Cathode (negative terminal, shorter leg / flat edge on LED casing). Current flows only from Anode to Cathode.
- Electrolytic Capacitors: Have marked negative stripes on their casing and a shorter negative lead. Connecting them backward can destroy them.

Flyback / Protection Diodes

When an inductive load such as a relay coil or motor is switched off, the collapsing magnetic field creates a huge, sudden reverse voltage spike called back-EMF. This high voltage spike can instantly destroy sensitive driver transistors.

- To prevent this, a diode is connected in reverse-bias (pointing towards the positive rail) directly across the coil/motor.
- During normal operation, the diode does nothing (it blocks current).
- When the device is switched off, the diode safely conducts the back-EMF spike, protecting the transistor.

Resistor 4-Band Colour Code

Fixed resistors use coloured bands to indicate their resistance value in ohms (\(\Omega\)):

- Band 1: 1st Significant Digit
- Band 2: 2nd Significant Digit
- Band 3: Multiplier (\(10^n\))
- Band 4: Tolerance (Gold = \(\pm 5\%\), Silver = \(\pm 10\%\))

The Colour Values:
0 = Black, 1 = Brown, 2 = Red, 3 = Orange, 4 = Yellow, 5 = Green, 6 = Blue, 7 = Violet, 8 = Grey, 9 = White

Example: A resistor with bands Yellow – Violet – Red – Gold:
- Yellow = \(4\)
- Violet = \(7\)
- Red = Multiplier of \(10^2\) (multiply by \(100\))
- Gold = \(\pm 5\%\) tolerance
- Value: \(47 \times 100 = 4700\,\Omega = 4.7\,\text{k}\Omega\) (\(\pm 5\%\)).

Key Takeaway: Protection diodes must be wired in reverse-bias across inductive loads. Diodes and electrolytic capacitors are polarized and must be oriented correctly.

6. Common Exam Pitfalls to Avoid

Examiners frequently highlight the same simple mistakes in Technology and Design papers. Keep these in mind to secure top marks:

1. Unit Prefix Errors: Forgetting to convert \(\text{mA}\) into \(\text{A}\) (divide by \(1000\)) or \(\text{k}\Omega\) into \(\Omega\) (multiply by \(1000\)). An unadjusted \(\text{mA}\) value will throw your final answer off by a factor of \(1000\)!

2. Forgetting LED Forward Voltage: In LED resistor calculations, students often divide the entire supply voltage by current: \(R = \frac{V_{\text{supply}}}{I}\). You must subtract the forward voltage drop: \(R = \frac{V_{\text{supply}} - V_{\text{LED}}}{I_{\text{LED}}}\).

3. Mixing Up \(R_1\) and \(R_2\) in Potential Dividers: Remember that \(R_2\) is always the resistor across which \(V_{\text{out}}\) is measured (usually the bottom resistor to \(0\,\text{V}\)). If the position of a sensor (like an LDR) moves to the top position, the formula rules change accordingly.

4. Wiring Protection Diodes in Forward Bias: If you draw the protection diode across a relay in forward-bias, it creates an immediate short circuit across your power supply. Ensure the cathode (bar side) points to the positive rail.

5. Non-Standard Symbols: Always use standard British/BS circuit diagram symbols rather than rough sketches or informal drawings.

Chapter Quick Review

- System Structure: Input (Transducer) \(\rightarrow\) Process (Control/Amplify) \(\rightarrow\) Output (Actuator).
- Ohm's Law: \(V = I \times R\), \(I = \frac{V}{R}\), \(R = \frac{V}{I}\).
- Series Resistance: \(R_{\text{total}} = R_1 + R_2 + \dots\)
- Parallel Resistance: \(\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2}\)
- LED Resistor: \(R = \frac{V_{\text{supply}} - V_{\text{LED}}}{I_{\text{LED}}}\)
- Potential Divider: \(V_{\text{out}} = V_{\text{in}} \times \left(\frac{R_2}{R_1 + R_2}\right)\)
- Back-EMF Protection: Place a diode in reverse-bias across inductive coils (relays/motors).