Oscilloscope applications Revision Notes for AQA A-Level Physics

Oscilloscope applications

An oscilloscope (also known as a cathode ray oscilloscope or CRO) is a versatile measurement instrument that serves multiple purposes in physics and electronics. It functions as both a direct current and alternating current voltmeter, measures time intervals and frequencies, and displays alternating waveforms on a screen.

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The oscilloscope is one of the most versatile instruments in a physics laboratory. Its ability to display voltage changes over time makes it invaluable for analyzing both steady DC voltages and dynamic AC signals.

The oscilloscope screen

The screen of an oscilloscope displays a graph with voltage on the vertical axis (y-axis) and time on the horizontal axis (x-axis). When a voltage source is connected to the y-input terminals, the oscilloscope produces a trace showing how the voltage varies with time. This visual representation makes it particularly useful for analyzing both steady voltages and time-varying signals.

Controls and adjustments

Y-gain control

The y-gain control determines the voltage value assigned to each division on the vertical scale. This control adjusts the sensitivity of the vertical axis. When you select a higher y-gain value, you increase the number of volts represented by each grid division on the screen, which makes the oscilloscope less sensitive to small voltage changes. Conversely, selecting a lower y-gain value means fewer volts per division, providing greater sensitivity.

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Sensitivity and Measurement Accuracy

For accurate measurements taken from the screen, high sensitivity is necessary. A higher sensitivity produces a larger vertical displacement of the waveform, which reduces the percentage uncertainty in the measured value. The relationship between sensitivity and measurement accuracy is important: greater vertical displacement leads to smaller relative uncertainty.

Time base control

The time base control adjusts the time value assigned to each division on the horizontal axis. When the oscilloscope is switched on but no input voltage is connected, this control determines whether a horizontal line appears on the screen or a moving dot of light travels across it.

Similar to the y-gain control, the time base setting affects measurement precision. Each central division on both axes is subdivided into five smaller subdivisions, allowing for more precise readings.

Input control switch

The input control switch has three settings:

DC: Used for direct current or steady voltage measurements
AC: Used for alternating current or time-varying voltage measurements
GD: Stands for "ground" and disconnects any input from the oscilloscope

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Setting Up Your Reference Position

When using the oscilloscope, it is helpful to first switch to GD mode and adjust the horizontal line so that it aligns with the central horizontal axis of the screen. This provides a reference position before connecting the voltage source to be measured.

Measuring DC voltage

To measure the voltage of a battery or other DC source:

Set the input control switch to DC mode
Adjust the horizontal trace so it lies along the central horizontal axis (this is easier if you first switch to GD)
Connect the battery or DC source to the y-input terminals
Observe how the trace moves vertically
Count the number of divisions the trace has moved from the central axis
Calculate the voltage using the formula

$\text{emf} = \text{number of divisions} \times \text{y-gain}$

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Worked Example: Measuring a Battery's EMF

If the y-gain control is set to 2.0 V/div and the trace moves 3.3 divisions vertically, the battery's emf would be:

$\text{emf} = 3.3 \times 2.0 = 6.6 \text{ V}$

To minimize uncertainty in this type of measurement, the line should be kept at low intensity to make it as sharp and thin as possible. This allows for more precise determination of exactly how many divisions the voltage represents.

Measuring AC frequency

When measuring the frequency of an alternating signal:

Set the input control switch to AC mode
Connect a signal generator (or function generator) to the y-input
Set the signal generator to produce a sine wave function
Adjust the time base setting so that one complete cycle of the waveform occupies a reasonable portion of the screen

The oscilloscope will display a trace showing the characteristic sine wave pattern. To determine the frequency, you need to first find the period (the time for one complete cycle).

Count the number of divisions along the horizontal axis that correspond to exactly one cycle of the wave. The period $T$ can be calculated using:

$T = \text{number of divisions for one cycle} \times \text{time base setting}$

Once the period is known, the frequency $f$ can be calculated using the inverse relationship:

$f = \frac{1}{T}$

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Worked Example: Calculating Frequency from Period

Step 1: Measure the period

Time base setting: 0.2 ms/div
One cycle spans: 6.6 divisions

$T = 6.6 \times 0.2 = 1.32 \text{ ms}$

Step 2: Calculate the frequency

$f = \frac{1}{T} = \frac{1}{1.32 \times 10^{-3}} = 758 \text{ Hz}$

Uncertainty in frequency measurements

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Accounting for Measurement Uncertainty

Since each division contains five subdivisions along the central axis, the uncertainty in counting divisions is typically ±0.2 divisions. This translates to a percentage uncertainty in both the period and frequency measurements.

For the period, the percentage uncertainty is:

$\text{Percentage uncertainty} = \frac{0.2}{\text{number of divisions counted}} \times 100$

For the frequency, since $f = \frac{1}{T}$ , the percentage uncertainty in frequency equals the percentage uncertainty in period. Additionally, the absolute uncertainty in frequency can be calculated by applying the percentage uncertainty to the calculated frequency value.

Measuring AC peak-to-peak voltage

To accurately measure the peak-to-peak voltage of an alternating signal:

Use the y-position control to move the waveform vertically
Position the waveform so that the positive peak just touches a horizontal grid line
Use the x-position control to align the negative peak with the central vertical axis
Count the number of divisions from the positive peak to the negative peak
Calculate the peak-to-peak voltage using the formula

$\text{peak-to-peak voltage} = \text{number of divisions} \times \text{y-gain}$

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Worked Example: Measuring Peak-to-Peak Voltage

Measurements:

Y-gain setting: 0.1 V/div
Peak-to-peak span: 5.6 divisions

Step 1: Calculate the voltage

$\text{peak-to-peak voltage} = 5.6 \times 0.1 = 0.56 \text{ V}$

Step 2: Calculate the uncertainty

The uncertainty in this measurement arises from the ±0.2 division uncertainty in counting:

$\text{Percentage uncertainty} = \frac{0.2}{5.6} \times 100 = \pm 3.6\%$

Step 3: Find the absolute uncertainty

$3.6\%$ of $0.56$ V gives approximately $\pm 0.02$ V

Final result: $0.56 \pm 0.02$ V

Viewing other waveforms

Square waves

A square wave is an alternating voltage waveform that switches rapidly between two voltage levels, creating a rectangular pattern on the oscilloscope screen. Square waves play an important role in the operation of many electronic circuits and are commonly available as an output option from signal generators.

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Adjusting Intensity for Square Waves

When displaying square waves, the vertical sections of the trace may appear dimmer than the horizontal sections. This is because the electron beam moves more quickly through the vertical transitions and dwells longer on the horizontal sections. To measure the frequency accurately, you may need to adjust the intensity control on the oscilloscope to make the trace bright enough so that the vertical sections become clearly visible.

When measuring peak-to-peak voltage for square waves, it is often helpful to make the horizontal sections appear thinner by reducing the intensity. This allows for more precise determination of exactly which grid lines the top and bottom of the waveform align with, reducing measurement uncertainty.

The same formulas apply for square waves as for sine waves:

$T = \text{number of divisions for one cycle} \times \text{time base setting}$
$f = \frac{1}{T}$
$\text{peak-to-peak voltage} = \text{number of divisions} \times \text{y-gain}$

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Key Points to Remember:

An oscilloscope displays voltage versus time, with the y-gain controlling volts per division and the time base controlling time per division
For DC voltage measurements, set the control to DC mode and calculate voltage as: $\text{emf} = \text{divisions} \times \text{y-gain}$
For AC frequency measurements, count divisions for one complete cycle to find period $T$ , then use $f = \frac{1}{T}$
Peak-to-peak voltage is measured by counting divisions from positive to negative peak and multiplying by y-gain
Measurement uncertainty of ±0.2 divisions (due to five subdivisions per division) should be considered when calculating percentage uncertainty in all oscilloscope readings

Oscilloscope applications (AQA A-Level Physics): Revision Notes