Theory — Signals and Capacitors

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Reading signals on an oscilloscope, and how a capacitor sets timing. Try the examples, then test yourself.

Concept 1

Analogue vs digital & the oscilloscope

Key words

Analogue
a signal that changes smoothly through every value.
Digital
a signal with only two levels (high/low, 1/0).
Period (T)
the time for one full wave, in seconds.
Frequency (f)
how many waves per second, in hertz (Hz).
Frequency
f = 1T
frequency = 1 ÷ period
  • An analogue signal varies smoothly through every value; a digital signal has only two levels (high/low, 1/0).
  • On an oscilloscope, peak voltage = (vertical divisions to the peak) × Y-gain (V/div).
  • Period T = (horizontal divisions for one wave) × time-base (s/div). Then f = 1 ÷ T.
  • The same method works for a square wave (a digital signal) as for a sine: count the divisions for one complete cycle. Watch the units — convert ms → s before using f = 1 ÷ T.
A sine trace on an oscilloscope grid
One full wave spans a number of divisions across the screen.
Substitute & solve One complete wave spans 4.0 divisions. The time-base is set to 5.0 ms/division. Calculate the frequency.
Find the period
T = 4.0 × 5.0 = 20 ms
T = 0.020 s ms → s
f=1T
f=1 ÷ 0.020use seconds
f=50 Hz
We do — fill the gaps One wave spans 2.0 divisions. The time-base is 10 ms/division. Find the frequency.
1 Find the period: T = 2.0 × 10 = ms
2 Change ms → s: T = s
3 Formula: f = 1 ÷ T
4 Answer: f = 1 ÷ = Hz

Always change ms to s (÷ 1000) before you use f = 1 ÷ T.

See the full answer
T = 2.0 × 10 = 20 ms T = 0.020 s f = 1 ÷ 0.020 = 50 Hz

An analogue signal changes through every value, while a digital signal has only levels. The time for one full wave is the , and the number of waves each second is the .

Practice 1

A trace shows a peak 3.0 divisions high with the Y-gain at 2.0 V/division, and one wave spans 5.0 divisions with the time-base at 2.0 ms/division. State the peak voltage and calculate the frequency.

Answer
Peak voltage = 3.0 × 2.0 = 6.0 V T = 5.0 × 2.0 = 10 ms = 0.010 s f = 1 ÷ T = 1 ÷ 0.010 = 100 Hz

✅ You can now…

  • tell an analogue signal from a digital one.
  • read peak voltage, period and frequency from a scope trace.
Concept 2

Capacitance & timing

Key words

Capacitor
a component that stores charge.
Capacitance (C)
how much charge it stores, in farads (F).
Delay
the time the capacitor adds before the circuit switches.
  • A capacitor stores charge. It takes time to charge up through a resistor, so it introduces a delay.
  • A larger capacitance (or larger series resistance) lengthens the timing — the output takes longer to switch.
  • This is how a capacitor changes an output waveform's timing: it sets how long a timer (such as a 555 astable) stays high or low, which sets the frequency of the output.
Try it: the 555 Astable Simulator lets you change the capacitor and resistors and watch the on/off timing change.

A capacitor charge. It takes time to charge through a resistor, so it adds a . A bigger capacitor makes the timing .

Practice 2

In a timing circuit the capacitor is swapped from 10 µF to 100 µF, with the resistors unchanged. State and explain what happens to the time the output stays high.

Answer
The time increases (about ten times longer). A larger capacitance stores more charge, so it takes longer to charge up through the same resistor before the circuit switches state.

✅ You can now…

  • say what a capacitor does in a circuit.
  • explain how a bigger capacitor makes the output timing longer.
Interactive

Wave Reader challenge

Read peak voltage, period and frequency from oscilloscope traces, and work out capacitor timing changes. Count the grid divisions, use the readout, and type each answer in the unit shown. Score 8 / 10 to earn the 🌊 Wave Reader badge.

Your traces scored

Peak = divisions × Y-gain · Period = divisions × time-base · f = 1 ÷ T (use seconds). Answers within 2% are accepted.

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Check

Check your understanding

Answer the multiple-choice questions, then mark yourself with the RAG self-check.

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Tap Red / Amber / Green for how confident you feel.