Introduction to Systems: Stock Forms and Calculations

In the world of Systems, we don't usually start with raw materials like a log of wood or a sheet of metal. Instead, we use electronic components. Just like a builder uses standard-sized bricks, electronic designers use stock forms. These are standard shapes and sizes of components that manufacturers make in bulk. Understanding these forms, how they are valued, and how to calculate the quantities you need is essential for designing circuits that actually work without costing a fortune!

1. Stock Forms of Components

Electronic components generally come in two main "stock forms" based on how they are attached to a Printed Circuit Board (PCB):

Through-Hole Technology (THT)

These components have long metal "legs" (leads). To use them, you drill a hole in the PCB, push the legs through, and solder them on the other side.
Why use them? They are great for prototypes (the first versions of a design) because they are large enough to handle and solder by hand.

Surface-Mount Technology (SMT)

These are tiny components that are soldered directly onto the surface of the PCB. There are no holes required.
Why use them? They are much smaller, allowing devices like smartphones to be incredibly thin. They are usually fitted by Computer-Aided Manufacture (CAM) machines in large-scale mass production.

Quick Review: If you are making a one-off project in class, you will likely use through-hole components. If you are looking at the inside of a modern laptop, you will see SMT.

2. Component Values, Ratings, and Tolerances

Manufacturers don't make every single possible value of a resistor or capacitor. Instead, they follow standard sets of values to keep production efficient.

The E12 Series

The E12 series is a set of 12 standard "base" values for components (like resistors) within every decade (multiples of 10). These values are:
1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2
By using these and multiplying them by 10, 100, or 1,000, we get all the common resistors we use (e.g., \(470 \Omega\) or \(4.7 k\Omega\)).

Tolerance

No component is perfect. Tolerance is the "give or take" amount. It tells you how much the actual value might differ from what is written on the label.
Example: A resistor labeled \(100 \Omega\) with a \(10\%\) tolerance might actually be anywhere between \(90 \Omega\) and \(110 \Omega\).
Common mistake: Students often forget that a higher tolerance percentage means a less accurate component.

Resistor Colour Code Bands

Because resistors are small, their values are printed using coloured bands.

  • The first two or three bands represent digits.
  • The next band is the multiplier (what you multiply the digits by).
  • The final band (usually gold or silver) represents the tolerance.

3. Quantity Calculations: Ohm’s Law

To calculate how many components you need or what "rating" they should have, you must master Ohm's Law. This formula shows the relationship between Voltage (\(V\)), Current (\(I\)), and Resistance (\(R\)).

The Formula: \(V = I \times R\)

  • \(V\) (Voltage): Measured in Volts (the "pressure" pushing electricity).
  • \(I\) (Current): Measured in Amps (the flow of electricity).
  • \(R\) (Resistance): Measured in Ohms (\(\Omega\)) (how much the circuit slows the flow).

Example Calculation:
If a circuit has a voltage of \(9V\) and you want a current of \(0.02A\), what resistor do you need?
Rearrange the formula: \(R = V / I\)
\(R = 9 / 0.02 = 450 \Omega\).
Note: You would then check the E12 series to find the closest standard resistor!

4. Calculating Resistors in Series and Parallel

Sometimes you need a specific resistance that isn't available as a single component. You can combine resistors to get the value you need.

Resistors in Series

When resistors are placed end-to-end in a single line, you simply add their values together.
Formula: \(R_{total} = R_1 + R_2 + R_3 ...\)

Resistors in Parallel

When resistors are placed side-by-side (like rungs on a ladder), the total resistance decreases because there are more paths for the electricity to take.
Formula: \(\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ...\)

Key Takeaway: Adding resistors in series makes the total resistance bigger. Adding them in parallel makes the total resistance smaller.

5. Units and Prefixes

In your exam, values are often given with prefixes (like "kilo" or "milli"). You must be able to convert these to use them in formulas.

Common Prefixes:

  • Mega (M): \(\times 1,000,000\) (e.g., \(1 M\Omega = 1,000,000 \Omega\))
  • Kilo (k): \(\times 1,000\) (e.g., \(1 k\Omega = 1,000 \Omega\))
  • milli (m): \(\div 1,000\) (e.g., \(10 mA = 0.01 A\))
  • micro (\(\mu\)): \(\div 1,000,000\) (e.g., \(100 \mu F = 0.0001 F\))

Top Tip: Always convert your units back to the "base" unit (Amps, Volts, Ohms) before doing any multiplication or division to avoid decimal errors!

Summary Checklist

1. Stock Forms: Do you know the difference between Through-hole (manual) and SMT (automated)?
2. E12 Series: Can you identify that these are standard, preferred values?
3. Tolerance: Do you understand that no component is exactly its labeled value?
4. Calculations: Can you use \(V = I \times R\) and calculate total resistance in series and parallel?
5. Units: Are you comfortable converting \(mA\) to \(A\) or \(k\Omega\) to \(\Omega\)?