ECE Lab #3: Device Characterization and Frequency Domain Analysis

Department of Electrical and Computer Engineering

Spring 2026

Overview

The purpose of Lab 3 is to:

1. Prelab Assignment

1.1 Reflective AI Exercise 1: Voltmeter Loading and Measurement Concepts

Objective: Demonstrate understanding of how a voltmeter's internal resistance interacts with the circuit under test, and how to distinguish between accuracy, precision, and resolution as distinct measurement concepts.

Part 1: Exploration

Using what you practiced in Lab 2, construct your own AI prompts to explore the following two areas:

Focus your prompts on how internal meter resistance creates a voltage divider with the circuit under test, and how resolution limits what a measurement can report.

Part 2: The Self-Test

Write your own quiz prompt targeting these two concepts. Your questions must involve predicting the effect of a voltmeter's internal resistance on a measured voltage in a resistive circuit, and distinguishing between accuracy, precision, and resolution in a real measurement scenario.

Apply the meta-prompt from A Mind Worth Questioning to evaluate and strengthen your draft, then run the quiz.

Part 3: Formal Reflection (150–250 words)

Your written synthesis must address all three of the following points:

Prelab Deliverable #1

Submit your Self-Test prompt-craft work via the course submission app. Upload up to two screenshots capturing your original draft prompt, the AI's critique, your revised prompt, and the quiz transcript. Your name must be visible in each image before uploading.

Prelab Deliverable #2

Submit your formal written reflection (150–250 words) via the course submission app.

1.2 Reflective AI Exercise 2: Signals in the Frequency Domain

Objective: Demonstrate understanding of how the shape of a time-domain waveform is determined by its frequency-domain harmonic content.

Part 1: Exploration

Example prompts are provided below. You may use them, adapt them, or write your own at the same level of specificity.

Focus Area 1: Fourier Series and Harmonic Content

"I am an electrical engineering student preparing for a lab on frequency-domain analysis. Can you explain what the Fourier Series tells us about a periodic waveform? Specifically, why does a square wave contain only odd harmonics, and what happens to the time-domain shape as higher harmonics are removed one by one?"

Follow up with:

"If I have a triangle wave and a square wave at the same fundamental frequency, how does their harmonic content differ? What does that difference look like in a frequency-domain plot?"

Focus Area 2: The Nyquist Criterion

"I am using a digital measurement instrument that samples at 100 kSa/s. Can you explain the Nyquist criterion and what it tells me about the highest frequency signal I can faithfully capture? What happens physically if I try to measure a signal above that limit?"

Follow up with:

"A square wave at 10 kHz contains harmonics at 30 kHz, 50 kHz, 70 kHz, and beyond. If my instrument samples at 100 kSa/s, which harmonics can I observe and which cannot? What will the captured waveform look like compared to the true signal?"

After completing both focus areas, connect them: if a square wave is bandwidth-limited by the Nyquist constraint of your instrument, what does that do to its time-domain shape in the captured waveform? Is what you see on screen the true signal?

Part 2: The Self-Test

Open Gemini and write your own quiz prompt targeting these two concepts. Your questions must involve predicting the harmonic content of a waveform from its time-domain shape, or applying the Nyquist criterion to predict what a captured waveform will look like when the sampling rate is insufficient.

Apply the meta-prompt from A Mind Worth Questioning to evaluate and strengthen your draft, then run the quiz.

Part 3: Formal Reflection (150–250 words)

Your written synthesis must address all three of the following points:

Prelab Deliverable #3

Submit your Self-Test prompt-craft work via the course submission app. Upload up to two screenshots capturing your original draft prompt, the AI's critique, your revised prompt, and the quiz transcript. Your name must be visible in each image before uploading.

Prelab Deliverable #4

Submit your formal written reflection (150–250 words) via the course submission app.

1.3 M2K Spectrum Analyzer

The M2K Spectrum Analyzer displays the frequency content of signals. To prepare for the lab, review the following resources:

Prelab Deliverable #5

Briefly explain how the Spectrum Analyzer in Scopy works. What key settings should be configured before making a frequency-domain measurement? Your answer should address frequency range, resolution bandwidth, windowing function, and averaging mode.

1.4 Noise in Measured Spectra

When a spectrum is measured using a real instrument, the result is never a perfectly clean set of spectral lines on a silent background. A noise floor is always present, and its level is not arbitrary: it is set by the physics and engineering of the measurement system. Understanding where this noise comes from is essential for interpreting measurements intelligently.

Quantization noise. The M2K oscilloscope is a digital instrument. Before any signal processing can occur, the continuous analog voltage at the input must be converted to a sequence of numbers by an analog-to-digital converter (ADC). An ADC with $N$ bits can represent $2^N$ distinct voltage levels. The M2K ADC uses 12 bits, giving $2^{12} = 4096$ levels. Any voltage that falls between two adjacent levels must be rounded to the nearest level; this rounding error is called quantization error.

If the input signal spans the full range of the ADC, the quantization step size is:

$$\Delta = \frac{V_\mathrm{FS}}{2^N}$$

where $V_\mathrm{FS}$ is the full-scale voltage range. The quantization error at any instant is bounded by $\pm\,\Delta/2$ and, for a well-designed ADC with a varying input signal, behaves approximately as white noise uniformly distributed over this range. This quantization noise power spreads across all frequencies up to the Nyquist limit, forming the noise floor visible in the spectrum.

For an ideal $N$-bit ADC, the theoretical signal-to-noise ratio (SNR) when the input is a full-scale sine wave is well approximated by:

$$\mathrm{SNR} \approx 6.02\,N + 1.76 \quad \text{(dB)}$$

This result is worth remembering: each additional bit of resolution improves the SNR by approximately 6 dB, which halves the noise amplitude. For the M2K with $N = 12$:

$$\mathrm{SNR} \approx 6.02 \times 12 + 1.76 \approx 74~\text{dB}$$

Spectrum Analyzer amplitudes are displayed in dBFS (decibels relative to full scale), where 0 dBFS corresponds to the maximum representable signal. The theoretical noise floor therefore sits at approximately $-74$ dBFS for a full-scale input. In practice, additional noise sources push the floor somewhat higher.

Other noise sources. Quantization noise is not the only contribution to the measured noise floor. Thermal noise (Johnson noise) arises from random electron motion in any resistive element at a temperature above absolute zero and is present in every electronic circuit. Non-ideal waveform generation in the signal generator can also introduce low-level harmonic distortion: spectral energy appears at harmonics that theory predicts to be zero (for example, even harmonics of an ideal square wave). Clock jitter, ground loops, and electromagnetic interference from nearby equipment can add further artefacts. When comparing measured spectra to theoretical predictions in Part 2, these effects must be considered alongside quantization noise.

Prelab Deliverable #6

The M2K ADC has a 12-bit resolution and a full-scale input range of $\pm\,2.5$ V (5 V total). Calculate the quantization step size $\Delta$ and the theoretical SNR for a full-scale sine wave input. Work on paper, showing all steps. Photograph your completed work and submit the image via the course submission app. Your name must be visible in the photo.

Prelab Deliverable #7

A square wave has odd harmonics only in theory. Explain two distinct reasons why even harmonics might still appear at non-zero amplitude in a measured spectrum.

Prelab Deliverable #8

If a measurement were repeated with a 16-bit ADC instead of a 12-bit ADC, by how many dB would the theoretical noise floor improve? How would this change the visibility of weak harmonics in the spectrum?

1.5 Fourier Series Predictions

Based on the material covered in Signals in Time and Signals in Frequency of the reader, predict the frequency-domain characteristics of different waveforms before making any measurements.

Prelab Deliverable #9a

For a 1 kHz sine wave (pure tone), state the expected frequency-domain content up to the 5th harmonic: which harmonics are present, their relative amplitudes, and the pattern of harmonic amplitude decay. Present your predictions in a table.

Prelab Deliverable #9b

For a 1 kHz square wave (50% duty cycle), state the expected frequency-domain content up to the 5th harmonic: which harmonics are present, their relative amplitudes, and the pattern of harmonic amplitude decay. Present your predictions in a table.

Prelab Deliverable #9c

For a 1 kHz triangle wave, state the expected frequency-domain content up to the 5th harmonic: which harmonics are present, their relative amplitudes, and the pattern of harmonic amplitude decay. Present your predictions in a table.

Prelab Deliverable #9d

For a 1 kHz sawtooth wave, state the expected frequency-domain content up to the 5th harmonic: which harmonics are present, their relative amplitudes, and the pattern of harmonic amplitude decay. Present your predictions in a table.

1.6 IV Curve Basics

Note

While this section and its deliverables are required, the IV curve observation activity in Part 3 of the lab procedure is optional. Completing it may be done during or outside the lab period and will count for 10 points of extra credit, with a maximum score of 100 points for the lab.

The current-voltage (IV) curve of a two-terminal component describes its terminal behavior across a range of applied voltages. Read Chapter 4 of the reader before attending lab. In Part 3 of the lab, the M2K is used in XY mode to display IV curves for several component types. The focus is on building visual intuition for how different devices behave; detailed post-lab analysis of the IV data is not required.

A diode is the simplest semiconductor device. It behaves as a one-way valve for electric current: it conducts readily in one direction (forward bias) and blocks current in the other (reverse bias). The terminal through which conventional current enters is called the anode; the terminal through which it exits is the cathode.

Circuit symbol of a diode with the anode on the left and cathode on the right. The anode is labeled with a plus sign and the cathode with a minus sign. A blue arrow above the symbol points from left to right, labeled Conventional current (forward bias), indicating the direction of current flow when the diode is forward biased.

Figure 1: Diode symbol. Current flows freely from anode to cathode in forward bias and is blocked in reverse bias.

When the anode voltage exceeds the cathode voltage by approximately 0.7 V (for a silicon diode), the diode turns on and current rises steeply. Below this threshold, essentially no current flows. In reverse bias, the diode blocks current until the breakdown voltage is reached. Figure 2 shows a typical IV characteristic.

Graph of the current-voltage characteristic of a silicon diode with voltage on the horizontal axis ranging from negative 7 to 1.3 volts and current on the vertical axis ranging from negative 18 to 22 milliamps. Three regions are shown. In the reverse bias region from negative 5.4 V to 0 V, current is nearly zero at approximately negative 0.05 milliamps. In the forward bias region, current remains negligible until about 0.7 V where a dashed threshold line is marked, then rises steeply to 20 milliamps at 0.9 V. In the breakdown region, a sharp vertical drop occurs at negative 5.5 V down to negative 15 milliamps, then the curve extends horizontally to the left. The three regions are labeled Forward bias, Reverse bias, and Breakdown on the graph.

Figure 2: Typical IV characteristic of a silicon diode. Current is negligible until the forward voltage reaches approximately 0.7 V, then rises steeply. In reverse bias, current is near zero until breakdown.

A Zener diode is designed to operate in the reverse breakdown region in a controlled way. Once the reverse voltage reaches the Zener voltage $V_Z$, the device holds that voltage approximately constant regardless of current, making it useful for voltage regulation. A 1N5222B Zener diode with $V_Z \approx 2.4$ V is used in this lab.

Graph of the current-voltage characteristic of a Zener diode with voltage on the horizontal axis ranging from negative 4.5 to 1.3 volts and current on the vertical axis ranging from negative 20 to 20 milliamps. Three regions are shown. In the reverse bias region from negative 2.3 V to 0 V, current is nearly zero at approximately negative 0.05 milliamps. In the forward bias region, current remains negligible until 0.7 V marked by a dashed threshold line, then rises steeply to 16 milliamps at 0.85 V, identical to a standard diode. In the Zener breakdown region, a sharp vertical drop occurs at negative 2.4 V, marked by a dashed line and labeled Vz approximately 2.4 V, then the curve extends horizontally left to negative 16 milliamps. The three regions are labeled Forward, Reverse, and Zener breakdown on the graph.

Figure 3: IV characteristic of a Zener diode. The forward region is the same as a standard diode. In reverse bias, current is negligible until the Zener voltage $V_Z$ is reached, at which point the device clamps the voltage.

LEDs are diodes; their IV curves in the forward region have the same shape as a standard silicon diode, but the forward voltage threshold is higher and varies by color. In this lab, red, green, and blue LEDs will be observed. The forward voltage at which each LED begins to emit visible light can be read directly from the IV curve.

Prelab Deliverable #10a

Read The I-V Menagerie in the reader before completing this deliverable. Sketch the expected IV curve for a 1 kΩ resistor, labeling the axes and any key features. Work on paper, photograph your sketch, and submit via the course submission app. Your name must be visible in the photo.

Prelab Deliverable #10b

Sketch the expected IV curve for a silicon diode (1N914). Label the approximate forward voltage threshold and indicate the reverse-bias blocking region. Work on paper, photograph your sketch, and submit via the course submission app. Your name must be visible in the photo.

Prelab Deliverable #10c

Sketch the expected IV curve for a Zener diode (1N5222B). Label the forward voltage threshold, the Zener voltage $V_Z$, and the breakdown region. Work on paper, photograph your sketch, and submit via the course submission app. Your name must be visible in the photo.

The following circuit measures the IV characteristics of electronic components using the M2K.

Circuit diagram for measuring diode IV characteristics using the M2K oscilloscope in XY mode. A triangular wave voltage source connects from ground up through a diode in series with a 1 kilohm resistor back to ground. Channel 1 measures the voltage across the diode: Ch1-plus taps the node between the source and the diode anode, and Ch1-minus taps the node between the diode cathode and the top of the resistor. Channel 2 measures the voltage across the resistor, which is proportional to current: Ch2-plus taps the node between the diode cathode and the resistor top, and Ch2-minus taps the bottom of the resistor at ground. Plotting CH1 on the X-axis against CH2 on the Y-axis in XY mode produces the diode IV characteristic curve.

Figure 4: Connection diagram for IV characteristics measurement. CH1 and CH2 are used in XY mode (review the XY mode introduced in Lab #2).

The circuit:

Prelab Deliverable #11

Based on this circuit, explain how the current through the device under test would be calculated from the measured voltages.

2. Lab Procedure

2.1 Part 1: Frequency Domain Analysis: Data Collection

IMPORTANT

Work Policy for Part 1: Data Collection

2.1.1 Initial Setup and Calibration

  1. Connect the M2K to the computer and launch Scopy.
  2. Allow the calibration process to complete before making any connections.
  3. Connect the waveform generator output (W1) to the oscilloscope input (CH1) as shown in Figure 5.

Circuit diagram showing the connection for single-ended signal measurement using the M2K. The W1 analog output signal generator connects to the Ch1-plus oscilloscope input. Ch1-minus and the W1 internal ground are both tied to circuit ground, forming a single-ended measurement loop where Channel 1 measures the W1 output signal directly referenced to ground.

Figure 5: Connection diagram for signal measurement.

Lab Deliverable #1(a)

Take a clear photograph of the connections and submit via the course submission app. Your name must be visible in the photo.

2.1.2 Sine Wave Analysis

  1. Configure the M2K signal generator to output a 1 kHz sine wave with 2 V peak-to-peak amplitude on channel W1 using the Math tab.

(a) Navigate to the Signal Generator tab and select the Math tab.

(b) Adjust the record length to 1 ms to show 1 period of a 1 kHz signal.

(c) Adjust the sample rate to 1 Msps (mega samples per second).

(d) Disable CH2 by clicking the purple circle at the bottom.

Scopy oscilloscope screenshot showing Part 1 of the steps to generate a sine wave using the Math channel. Three red highlighted boxes draw attention to key controls: one around the Signal Generator instrument in the left navigation panel; one around the Math tab in the upper right panel area with a formula input section showing fields for amplitude, frequency, and phase; and one around the CH2 channel indicator at the bottom of the display showing CH2 is active. The formula field at the bottom shows the expression sin(2 times pi times t times 1000) and the main display shows a single smooth sine wave cycle on Channel 2 in orange.

Figure 6: Part 1: Generating a sine wave in Scopy using the Math channel. Select Signal Generator from the left panel (red box), open the Math tab (top right red box), and enter the formula sin(2 times pi times t times 1000). Confirm CH2 is active at the bottom of the screen (red box).

(e) Scroll down and generate a 1 kHz sine wave with 2 Vpp by entering: $$f(t) = \sin(2 * pi * 1000 * t)$$

(f) Click Run to generate the sine wave on W1.

Scopy Signal Generator screenshot showing Part 2 of the steps to generate a sine wave. Three red highlighted boxes draw attention to key controls: one around the Signal Generator instrument in the left navigation panel confirming it is selected; one around the Stop/Run button in the upper right toolbar showing the generator is currently running; and one around the formula field at the bottom right showing the expression f(t) equals sin(2 times pi times 1000 times t) with an Apply button beside it. The main display shows a single smooth sine wave cycle on Channel 2 in orange over a 1 millisecond time window. The Amplitude field shows 1 V and Load shows infinity ohms.

Figure 7: Part 2: Confirm the sine wave is generating in Scopy. Verify Signal Generator is selected in the left panel (red box), the formula f(t) equals sin(2 times pi times 1000 times t) is entered with Apply clicked (bottom red box), and the Run button is active in the top right (red box).

  1. Open the oscilloscope and observe the time domain representation.

(a) Navigate to the Oscilloscope tab.

(b) Adjust the horizontal Time Base and vertical Voltage Division to view at least 6 cycles of the 1 kHz sine wave.

(c) Click Single to capture one sweep of data.

(d) Click Run to start continuous acquisition.

(e) Note the sample rate shown in the top left corner. For example, "1.6k Sample at 100 ksps" indicates 1600 data points captured at 100k samples per second.

  1. Export the captured sine wave in the time domain at 100 ksps.

(a) Adjust the sample rate to 100 ksps by changing the Memory Depth. Click Single to confirm the signal is well captured, as shown in Figure 8.

Scopy oscilloscope screenshot showing the steps to change the sample rate. Two red highlighted boxes draw attention to key controls: one around the sample rate indicator in the top toolbar displaying the current sample rate, and one around the Memory Depth field in the lower right settings panel set to 1600. The main display shows two overlapping sinusoidal waveforms in orange and blue, with multiple cycles visible across the screen indicating a higher frequency signal being captured.

Figure 8: Changing the sample rate in Scopy. The red boxes highlight the sample rate indicator in the top toolbar and the Memory Depth field in the right panel; adjust Memory Depth to change the effective sample rate for the capture.

(b) Click the Gear icon and use the Channels drop-down menu to select the channel to export. Only Channel 1 is required for the sine wave.

Scopy oscilloscope screenshot showing the first step to export channel data as a CSV file. Two red highlighted boxes draw attention to key controls: one around the gear settings icon in the upper right toolbar to open the export panel, and one around the Channels dropdown in the right settings panel set to Channels. Below the dropdown, Channel 1 checkbox is checked and Channel 2 checkbox is unchecked, indicating both should be selected before exporting. The main display shows two waveforms, an orange sinusoidal Channel 1 and a blue Channel 2, captured at 100 kilosamples per second.

Figure 9: Step 1 of exporting oscilloscope data as CSV: click the gear icon in the top right toolbar (red box), then select Channels from the Export dropdown (red box). Check both Channel 1 and Channel 2 before proceeding to export.

(c) Export all data files to the folder EEC1_Lab3_Data. Name the file sine_100ksps_time_ch1.csv. Follow the naming convention: <waveform>_<sample rate>_<domain>_<channel>.csv.

Scopy oscilloscope screenshot showing the final step to export channel data as a CSV file. A red highlighted box draws attention to the Export button at the bottom of the right settings panel, ready to be clicked. The Channels dropdown above it confirms the export target is set to Channels. The main display shows an orange sinusoidal Channel 1 waveform captured at 100 kilosamples per second.

Figure 10: Step 2 of exporting oscilloscope data as CSV: click the Export button (red box) to save the selected channel data to a CSV file.

(d) Examine the CSV file structure:

  1. Line 4 shows the number of samples captured.

  2. Line 5 shows the sample rate (100 ksps).

  3. Line 8 contains the column headers. Column 1 is the sample index (0 to 1599 for 1600 samples), Column 2 is the time axis, and Column 3 is the voltage.

Screenshot of lines 4 through 11 of the Scopy-exported CSV file sine_100ksps_time_ch1.csv. Line 4: number of samples 1600. Line 5: sample rate 100000. Line 6: tool Oscilloscope. Line 7: additional information blank. Line 8: column headers Sample, Time in seconds, CH1 in volts. Line 9: sample 0, time negative 0.00819 seconds, CH1 negative 1.05233 V. Line 10: sample 1, time negative 0.00818 seconds, CH1 negative 1.03563 V. Line 11: sample 2, time negative 0.00817 seconds, CH1 negative 1.00222 V.

Figure 11: sine_100ksps_time_ch1.csv (lines 4–11), showing Scopy CSV metadata and the first three data rows with sample index, time, and CH1 voltage.

  1. Open the Spectrum Analyzer and observe the frequency domain representation.

(a) Navigate to the Spectrum Analyzer tab.

(b) Disable the Channel 2 display.

(c) Click Single to capture the signal.

(d) Click Sweep to access the settings.

(e) Zoom in by left-clicking and dragging on the signal; right-click to zoom out.

Scopy Spectrum Analyzer screenshot showing the steps to display a signal in the frequency domain and zoom in. Three red highlighted boxes draw attention to key controls: one around the Spectrum Analyzer instrument in the left navigation panel confirming it is selected; one around the Single button in the upper right toolbar indicating a single capture mode; and one large box outlining the main frequency domain display area showing a broadband orange spectrum spanning from near 0 to 50 MHz with amplitude around negative 120 to negative 130 dBm. A fourth red box at the bottom right highlights the Sweep tab. The right panel shows sweep settings including Start 0 MHz, Stop 50 MHz, Center 25 MHz, Span 50 MHz, and Resolution BW of 12.21 kHz.

Figure 12: Steps to display a signal in the frequency domain using the Scopy Spectrum Analyzer. Select Spectrum Analyzer from the left panel (red box), click Single to capture (top right red box), and use the Sweep tab (bottom right red box) to configure the frequency range and zoom into the spectrum of interest.

  1. Adjust the Spectrum Analyzer settings:

(a) Set the frequency range to 0–20 kHz to observe the fundamental peak at 1 kHz. Click Single to capture under the new settings.

(b) Set the Resolution BW to provide clear visualization of the fundamental frequency. A smaller Resolution BW gives finer frequency resolution but increases acquisition time.

Scopy Spectrum Analyzer screenshot showing a 1 kHz sine wave in the frequency domain. A prominent sharp spike is visible at the far left of the spectrum near 1 kHz, rising approximately 60 dB above the broadband noise floor, which is characteristic of a single-frequency sine wave. The remaining spectrum shows a flat noise floor across the displayed range up to 20 kHz. Two red highlighted boxes draw attention to key sweep settings on the right panel: one around the Start and Stop frequency fields set to 0 Hz and 20 kHz respectively, and one around the Resolution BW field showing 2.44 Hz, indicating a narrow resolution bandwidth was selected to resolve the sharp 1 kHz peak clearly.

Figure 13: 1 kHz sine wave in the frequency domain, showing a sharp spectral peak at 1 kHz rising well above the noise floor. The sweep is configured from 0 to 20 kHz with a narrow Resolution BW of 2.44 Hz to resolve the peak clearly.

(c) Navigate to the CH1 settings.

(d) To reduce noise, change Type to Peak Hold, Window to Hamming, and Averaging to 10. Additional information on these settings is available at: https://wiki.analog.com/university/tools/m2k/scopy/spectrumanalyzer.

(e) Click Run to remeasure and average the signal.

(f) Click Snapshot to store the result.

(g) Click Single to compare stored signals from different settings.

(h) Experiment with the Type, Window, and Averaging settings to obtain a smooth curve, and use those settings throughout the remainder of the lab. Hint: try setting Type to Peak Hold Continuous.

Scopy Spectrum Analyzer screenshot showing a 1 kHz sine wave in the frequency domain with two overlaid traces. The orange trace shows the instantaneous spectrum with a noisy, jagged noise floor. The green trace shows the averaged spectrum computed over 10 sweeps, producing a smoother, lower noise floor that more clearly reveals the sharp 1 kHz peak at the left of the display. A red highlighted box on the right settings panel draws attention to the Channel 1 averaging controls, showing Type set to Peak Hold, Window set to Hamming, and Average set to 10 with a Snapshot button below. A red highlighted box at the bottom left highlights the CH1 channel indicator confirming Channel 1 is active.

Figure 14: 1 kHz sine wave in the frequency domain with averaging enabled. The orange trace shows the instantaneous spectrum while the green trace shows the Peak Hold average over 10 sweeps, producing a smoother noise floor and clearer spectral peak. Averaging settings are configured in the Channel 1 panel on the right.

  1. Once the best settings have been identified, export the frequency domain data.

(a) Click Run to display a single curve with the optimal settings. The signal should appear less noisy than in Figure 13.

(b) Click the Gear icon and select Export.

(c) Name the file sine_freq_ch1.csv. The export collects data on both CH1 and CH2; only the CH1 column is relevant for the sine wave. Examine the file:
1. Line 7 stores the channel settings (for example, "Peak hold Continuous, Hamming, 10" for Channel 1).

  2. Column 4 in the data table contains Channel 2 data. Since Channel 2 is not connected, this column is not relevant.

Screenshot of lines 4 through 13 of the Scopy-exported CSV file sine_freq_ch1.csv. Line 4: number of samples 16384. Line 5: sample rate 0. Line 6: tool Spectrum Analyzer. Line 7: additional information Peak Hold Continuous, Hamming, 10, Sample, Hamming, 1. Line 8: column headers Sample, Frequency in Hz, Amplitude CH1 in dBFS, Amplitude CH2 in dBFS. Line 9: sample 0, frequency 0 Hz, CH1 negative 55.4537 dBFS, CH2 negative 71.5743 dBFS. Line 10: sample 1, frequency 1.2207 Hz, CH1 negative 55.4537 dBFS, CH2 negative 71.5743 dBFS. Line 11: sample 2, frequency 2.44141 Hz, CH1 negative 92.5079 dBFS, CH2 negative 98.1707 dBFS. Line 12: sample 3, frequency 3.66211 Hz, CH1 negative 94.1632 dBFS, CH2 negative 99.0241 dBFS. Line 13: sample 4, frequency 4.88281 Hz, CH1 negative 93.6439 dBFS, CH2 negative 98.5005 dBFS.

Figure 15: sine_freq_ch1.csv (lines 4–13), showing Scopy Spectrum Analyzer CSV metadata and the first five data rows with sample index, frequency, and amplitude readings for CH1 and CH2 in dBFS.

Screenshot of the EEC1_Lab3_Data folder showing two CSV files. The first file is sine_100ksps_time_ch1, a Comma Separated Values Source File of 35 KB. The second file is sine_freq_ch1, a Comma Separated Values Source File of 496 KB.

Figure 16: The EEC1_Lab3_Data folder at this stage, containing the time-domain and frequency-domain CSV exports.

  1. Measure and record the amplitude at the fundamental frequency.

(a) Navigate to the Markers settings in Figure 17.

(b) Enable a marker and click Peak to mark the highest peak at the fundamental frequency.

(c) Turn on the Marker Table to view the precise frequency and magnitude of the peak. The video at https://wiki.analog.com/university/tools/m2k/scopy/spectrumanalyzer provides instructions on using the Peak and Amplitude buttons.

2.1 Part 1: Frequency Domain Analysis: Data Collection
Waveform Harmonic Frequency (Hz) Measured Amplitude (dBFS)
Sine 1

Lab Deliverable #2(a)

Capture a screenshot of the oscilloscope (time domain) showing the sine wave and submit via the course submission app. Your name must be visible in the image before uploading.

Lab Deliverable #2(b)

Capture a screenshot of the Spectrum Analyzer (frequency domain) showing the sine wave with a marker placed at the fundamental frequency and submit via the course submission app. Your name must be visible in the image before uploading.

Scopy Spectrum Analyzer screenshot showing the steps to place a marker on a spectral peak. Three red highlighted boxes draw attention to key controls: one around the marker diamond icon placed directly on the sharp 1 kHz peak in the main display, one around the marker selection buttons in the upper right panel showing five numbered marker slots, and one around the Marker Table toggle at the bottom right of the settings panel switched on. The marker table at the bottom of the screen shows Marker 1 on Channel 1 at a frequency of 1.001 kHz with a magnitude of negative 28.7500 dBFS and type Peak.

Figure 17: Placing a frequency marker in the Scopy Spectrum Analyzer. Select a marker slot from the upper right panel (red box), click Peak to snap the marker to the nearest spectral peak (red box), then enable the Marker Table (bottom right red box) to read the exact frequency and amplitude values below the display.

  1. Optional: View the FFT and oscilloscope simultaneously.

(a) Navigate to the Oscilloscope tab.

(b) Click the Gear icon and enable the FFT.

(c) Do not submit this FFT as the frequency domain screenshot; the Spectrum Analyzer settings are not available in the Oscilloscope tab. This view is provided for quick visual comparison only.

Scopy screenshot showing the steps to view both the FFT spectrum and oscilloscope time-domain signal simultaneously. Three red highlighted boxes draw attention to key controls: one around the Oscilloscope instrument in the left navigation panel confirming it is selected; one around the gear settings icon in the upper right toolbar; and one around the XY and FFT toggle switches in the upper right settings panel with FFT enabled. The display is split into two panes: the upper pane shows the frequency-domain FFT spectrum in orange spanning 0 to 50 kHz, and the lower pane shows the time-domain oscilloscope traces with orange Channel 1 and blue Channel 2 sinusoidal waveforms. A frequency marker label is visible in the lower pane at approximately 1 kHz.

Figure 18: Viewing the FFT spectrum and oscilloscope time-domain signal simultaneously in Scopy. Select Oscilloscope from the left panel (red box), click the gear icon (top right red box), and enable FFT in the settings panel (red box) to display both views at the same time.

2.1.3 Harmonic Synthesis Experiment

The following section provides less procedural detail than Section 2.1.2 and focuses primarily on demonstrating the expected output.

  1. Configure the signal generator to output the sum of the first three odd harmonics of a square wave.
  2. A square wave is composed of a fundamental sine wave and a series of odd harmonics with decreasing amplitudes. Letting $N$ denote the harmonic number (1, 3, 5, 7, …), the amplitude of each harmonic is $1/N$. A square wave is represented by:

$$f(t) = \frac{4}{\pi} \sum_{N = 1,\ 3,\ 5,\ \ldots}^{\infty} \frac{1}{N} \sin(2\pi \cdot N f_{0} \cdot t)$$

  1. W1: construct a 1 kHz square wave with 50% duty cycle and 2 V peak-to-peak amplitude.

Two side-by-side plots illustrating a square wave in time and frequency domains. Left plot titled Square Wave in Time Domain: a blue square wave alternating between amplitude positive 1 and negative 1 over four time units, with sharp vertical transitions at every half-unit interval showing a 50 percent duty cycle. Right plot titled Square Wave in Frequency Domain: a red stem plot showing five discrete spectral components at odd multiples of the fundamental frequency. The fundamental frequency f0 has magnitude 1, the third harmonic 3f0 has magnitude 0.33, the fifth harmonic 5f0 has magnitude 0.20, the seventh harmonic 7f0 has magnitude 0.14, and the ninth harmonic 9f0 has magnitude 0.11, demonstrating that a square wave contains only odd harmonics with amplitudes decreasing as 1 over the harmonic number.

Figure 19: A square wave in the time domain (left) and frequency domain (right). The spectrum shows the fundamental frequency $f_0$ and odd harmonics ($3f_0$, $5f_0$, etc.) with decreasing amplitudes, illustrating the discrete frequency content of periodic signals.

  1. For W2, construct an approximation of the square wave using the first three odd harmonics at $f_0$, $3f_0$, and $5f_0$.

    (a) 1st harmonic: fundamental at 1 kHz with 2 Vpp.

$$f(t) = \sin(2 *\cdot* pi * 1000 * t)$$

Scopy oscilloscope screenshot showing the first harmonic of a synthesized square wave. The main display shows two overlaid waveforms: an orange square wave on Channel 1 and a blue sinusoidal waveform on Channel 2 representing the fundamental frequency first harmonic generated via the Math channel. A red highlighted box draws attention to the formula field in the lower right Math panel showing the expression f(t) equals sin(2 times pi times 1000 times t) with the Apply button beside it. The sine wave closely follows the rising and falling portions of the square wave, illustrating how the fundamental frequency component alone approximates the overall shape.

Figure 20: First harmonic of the synthesized square wave. The orange trace shows the original square wave on Channel 1 and the blue trace shows the Math channel output of sin(2 times pi times 1000 times t), representing the fundamental frequency component alone.

Lab Deliverable #3(a)

Capture a screenshot of the oscilloscope showing the fundamental frequency alone (W2) alongside the original square wave (W1). Submit via the course submission app. Your name must be visible in the image before uploading.

  (b) 3rd harmonic: add the 3rd harmonic at $3 \cdot f_0$ with amplitude $2 \cdot (1/3)$ Vpp.

$$f(t) = \sin(2 * pi * 1000 * t) + \frac{\sin(2 * pi * 3000 * t)}{3}$$

Scopy oscilloscope screenshot showing the first and third harmonics of a synthesized square wave combined. The main display shows two overlaid waveforms: an orange square wave on Channel 1 and a blue synthesized waveform on Channel 2 representing the sum of the first and third harmonics. Compared to the first harmonic alone, the blue waveform more closely approximates the square wave shape, with a flatter top, steeper transitions, and slight ripple visible near the edges. A red highlighted box draws attention to the formula field in the lower right Math panel showing the expression f(t) equals .909 times (sin(2 times pi times 1000 times t) plus sin(2 times pi times 3000 times t) divided by 3) with the Apply button beside it.

Figure 21: First and third harmonics of the synthesized square wave combined. Adding the third harmonic at one-third amplitude produces a closer approximation to the square wave, visible as a flatter top and steeper edges on the blue trace compared to the first harmonic alone.

Lab Deliverable #3(b)

Capture a screenshot of the oscilloscope showing the fundamental plus 3rd harmonic (W2) alongside the original square wave (W1). Submit via the course submission app. Your name must be visible in the image before uploading.

  (c) 5th harmonic: add the 5th harmonic at $5 \cdot f_0$ with amplitude $2 \cdot (1/5)$ Vpp.

$$f(t) = \sin(2 * pi * 1000 * t) + \frac{\sin(2 * pi * 3000 * t)}{3} + \frac{\sin(2 * pi * 5000 * t)}{5}$$

Scopy oscilloscope screenshot showing the first, third, and fifth harmonics of a synthesized square wave combined. The main display shows two overlaid waveforms: an orange square wave on Channel 1 and a blue synthesized waveform on Channel 2. Compared to the first and third harmonics combined, the blue waveform more closely approximates the square wave with an even flatter top, sharper transitions, and slightly more pronounced ripple near the edges. A red highlighted box draws attention to the formula field in the lower right Math panel showing the expression f(t) equals .909 times (sin(2 times pi times 1000 times t) plus sin(2 times pi times 3000 times t) divided by 3 plus sin(2 times pi times 5000 times t) divided by 5) with the Apply button beside it.

Figure 22: First, third, and fifth harmonics of the synthesized square wave combined. Each additional odd harmonic at decreasing amplitude brings the blue synthesized trace closer to the ideal square wave shape, with a flatter top and sharper transitions than the two-harmonic approximation.

Lab Deliverable #3(c)

Capture a screenshot of the oscilloscope showing the fundamental plus 3rd plus 5th harmonic approximation (W2) alongside the original square wave (W1). Submit via the course submission app. Your name must be visible in the image before uploading.

  1. Observe both the time domain and frequency domain representations of the square wave on W1 and the synthesized wave on W2.

Scopy Spectrum Analyzer screenshot showing two overlaid frequency-domain spectra from 1 kHz to 20 kHz. The orange trace shows the original square wave spectrum and the purple trace shows the synthesized wave spectrum. Both display a series of sharp spectral peaks at odd harmonics. Five yellow and orange diamond markers label the first five odd harmonic peaks: M1 at approximately 2 kHz (fundamental), M2 at approximately 4 kHz (third harmonic), M3 at approximately 6 kHz (fifth harmonic), M4 at approximately 8 kHz (seventh harmonic), and M5 at approximately 10 kHz (ninth harmonic). Peak amplitudes decrease progressively from approximately negative 28 dB at the fundamental to approximately negative 48 dB at the ninth harmonic. Additional unlabeled peaks from higher odd harmonics are visible continuing to the right above the noise floor at approximately negative 90 dBFS.

Figure 23: Frequency-domain spectra of the original square wave (orange) and the synthesized wave (purple) overlaid in the Scopy Spectrum Analyzer. Markers M1 through M5 identify the first five odd harmonics at 1 kHz, 3 kHz, 5 kHz, 7 kHz, and 9 kHz, with amplitudes decreasing as expected for a square wave Fourier series.

  1. Export the following CSV files. Export both CH1 and CH2 for the time domain data files.

(a) synth_100ksps_time_ch1_ch2.csv

(b) synth_freq_ch1_ch2.csv

2.1 Part 1: Frequency Domain Analysis: Data Collection
Waveform Harmonic Frequency (Hz) Measured Amplitude (dBFS)
Synthesis 1
Synthesis 3
Synthesis 5

Lab Deliverable #3(d)

Capture a screenshot of the Spectrum Analyzer showing both the original square wave and the synthesized wave overlaid in the frequency domain, and a screenshot of the oscilloscope showing both signals in the time domain. Submit both screenshots via the course submission app. Your name must be visible in each image before uploading.

Lab Deliverable #3(e)

Write one to two sentences describing how the synthesized waveform compares to the original square wave, referencing both the time domain and frequency domain observations. Submit via the course submission app.

2.1.4 Square Wave Analysis

  1. Change the signal generator output to a 1 kHz square wave with 50% duty cycle and 2 V peak-to-peak amplitude.

Scopy Signal Generator screenshot showing the steps to generate a square wave. Two red highlighted boxes draw attention to key controls: one around the Signal Generator instrument in the left navigation panel confirming it is selected, and one around the Waveform settings panel in the upper right showing the waveform type set to Square, Amplitude set to 2 V, Offset set to 0, Frequency set to 1 kHz, Phase set to 0, and Duty Cycle set to 50 percent. The main display shows a single orange square wave cycle with a flat high level at approximately 1.4 V and flat low level at approximately negative 0.6 V over a 1 millisecond time window.

Figure 24: Generating a square wave in the Scopy Signal Generator. Select Signal Generator from the left panel (red box), then configure the Waveform settings (red box) with waveform type Square, Amplitude 2 V, Frequency 1 kHz, and Duty Cycle 50 percent.

  1. Observe both the time domain and frequency domain representations.

(a) If the FFT view is enabled in the Oscilloscope tab, click Run to update the FFT display.

(b) Export the captured square wave in the time domain at 100 ksps. Name the file square_100ksps_time_ch1.csv.

(c) In the Spectrum Analyzer, adjust the CH1, Sweep, and Marker settings to smooth the frequency domain signal and identify the fundamental frequency and harmonics.
3. Measure and record the amplitude of each harmonic up to the 9th harmonic.
4. Export the frequency domain data. Name the file square_freq_ch1.csv.

2.1 Part 1: Frequency Domain Analysis: Data Collection
Waveform Harmonic Frequency (Hz) Measured Amplitude (dBFS)
Square 1
2
3
4
5
6
7
8
9

Lab Deliverable #4(a)

Capture screenshots of both the time domain and frequency domain displays of the square wave and submit via the course submission app. Your name must be visible in each image before uploading.

2.1.5 Triangle Wave Analysis

  1. Generate a 1 kHz triangle wave with 2 V peak-to-peak amplitude.
  2. Observe and record both the time and frequency domain representations.
  3. Export the following CSV files. Only CH1 is required for the time domain data.

(a) triangle_100ksps_time_ch1.csv

(b) triangle_freq_ch1.csv

2.1 Part 1: Frequency Domain Analysis: Data Collection
Waveform Harmonic Frequency (Hz) Measured Amplitude (dBFS)
Triangle 1
2
3
4
5
6
7
8
9

Lab Deliverable #5(a)

Capture screenshots of both the time and frequency domain displays for the triangle wave and submit via the course submission app. Your name must be visible in each image before uploading.

2.1.6 Sawtooth Wave Analysis

  1. Repeat the measurement procedure with a 1 kHz rising ramp sawtooth wave.
  2. Export the following CSV files. Only CH1 is required for the time domain data.

(a) sawtooth_100ksps_time_ch1.csv

(b) sawtooth_freq_ch1.csv

2.1 Part 1: Frequency Domain Analysis: Data Collection
Waveform Harmonic Frequency (Hz) Measured Amplitude (dBFS)
Sawtooth 1
2
3
4
5
6
7
8
9

Lab Deliverable #6(a)

Capture screenshots of both the time and frequency domain displays for the sawtooth wave and submit via the course submission app. Your name must be visible in each image before uploading.

2.1.7 Data Export Summary

  1. Confirm that both time domain and frequency domain data have been exported for all five waveforms: sine, square, synthesis, triangle, and sawtooth.
  2. The EEC1_Lab3_Data folder should contain 10 files at this point.

Screenshot of the EEC1_Lab3_Data folder showing ten CSV files, all of type Comma Separated Values Source File. The files and their sizes are: sine_100ksps_time_ch1 at 35 KB, sine_freq_ch1 at 496 KB, square_100ksps_time_ch1 at 35 KB, square_freq_ch1 at 496 KB, synth_100ksps_time_ch1_ch2 at 49 KB, synth_freq_ch1_ch2 at 496 KB, triangle_100ksps_time_ch1 at 36 KB, triangle_freq_ch1 at 496 KB, sawtooth_100ksps_time_ch1 at 36 KB, and sawtooth_freq_ch1 at 496 KB. The time-domain files are significantly smaller than the frequency-domain files.

Figure 25: Contents of the EEC1_Lab3_Data folder, showing the ten CSV data files collected for sine, square, synthesized, triangle, and sawtooth waveforms in both time and frequency domains.

  1. Confirm that all files are correctly labeled before proceeding to the post-lab analysis.

2.2 Part 3: IV Curve Observation (Optional)

Note

Part 3 is optional. It may be completed during or outside the lab period after Part 1 is finished. Prelab Deliverables 10 and 11 provide the required background. Completing this part will count for 10 points of extra credit, with a maximum score of 100 points for the lab.

In Part 3, the XY mode of the M2K oscilloscope is used to observe the IV curves of a resistor, a diode, a Zener diode, and three LEDs. The purpose is to see these characteristics directly and to develop intuition for how each device behaves at its terminals. Screenshots of each curve are required; no CSV export or post-lab MATLAB analysis is needed for this part.

IMPORTANT

All measurements in Part 3 must be completed independently. Discussion with classmates is permitted; data sharing is not.

2.2 Part 3: IV Curve Observation (Optional)
Part Name Type Quantity
Resistor 1 kΩ 2
LED Blue 1
LED Red 1
LED Green 1
Diode 1N914 1
Zener Diode 1N5222B 1

2.2.1 Circuit Setup for IV Measurements

The circuit in Figure 26 will be used for all IV characteristic measurements.

Circuit diagram for measuring the IV characteristics of a generic Device Under Test using the M2K oscilloscope in XY mode. A triangular wave voltage source connects from ground up through the Device Under Test in series with a 1 kilohm reference resistor back to ground. Channel 1 measures the voltage across the Device Under Test: Ch1-plus taps the node between the source and the Device Under Test, and Ch1-minus taps the node between the Device Under Test and the top of the reference resistor. Channel 2 measures the voltage across the reference resistor, which is proportional to current through the Device Under Test: Ch2-plus taps the node between the Device Under Test and the resistor top, and Ch2-minus taps the bottom of the resistor at ground.

Figure 26: Circuit connection for IV curve measurement for a Device Under Test (DUT).

Lab Deliverable #8(a)

Take a clear photograph of the measurement circuit setup and submit via the course submission app. Your name must be visible in the photo. The DUT socket does not need to be populated when taking the photograph; indicate where the DUT will be inserted.

2.2.2 Resistor IV Curve

  1. Place a 1 kΩ resistor as the device under test (DUT).
  2. Configure the signal generator to produce a slow triangle wave (approximately 10 Hz) that sweeps from $-5$ V to $+5$ V.
  3. Use the Math function to display the derived current trace.

(a) Navigate to the Oscilloscope tab. Adjust the Channel 1 Time Base to 50 ms and the Voltage Division value to 1 V.

(b) Add a channel by clicking the + sign at the bottom and enter the current equation for the series resistor. The variable t1 represents the differential voltage signal from CH2.

(c) Enable the measurement tool to view the channel details.

Scopy oscilloscope screenshot showing the steps to display a derived current signal using the Math channel feature. Four red highlighted boxes draw attention to the key controls: one around the Oscilloscope instrument in the left navigation panel; one around the Math button in the upper right tab area; one around the numeric keypad used to enter a scaling formula; and one around the Add Channel button at the bottom right. The formula field shows the expression Ky equals negative 1 divided by 1000, scaling the Channel 2 voltage across the 1 kilohm reference resistor into a current value in milliamps. The main display shows a triangular waveform on Channel 1 in red.

Figure 27: Steps to display a derived current signal in Scopy. Click Math (top right), enter the scaling formula Ky equals negative 1 divided by 1000 to convert the CH2 voltage across the 1 kilohm sense resistor into current, then click Add Channel to overlay the current trace on the oscilloscope display.

(d) Navigate to the M1 channel settings by clicking the M1 setting button at the bottom.

(e) Adjust the Voltage Division value of M1 to 1 mV.

  1. Set the oscilloscope to XY mode, with CH1 ($V_\mathrm{DUT}$) on the X-axis and the calculated current ($V_S / R_S$) on the Y-axis. Verify that the resulting IV curve is a straight line through the origin, consistent with Ohm's law for the 1 kΩ resistor.
  2. Observe and capture a screenshot of the IV curve.

Lab Deliverable #8(b)

Capture a screenshot of the resistor IV curve from the oscilloscope and submit via the course submission app. Confirm the curve is consistent with Ohm's law. Your name must be visible in the image before uploading.

2.2.3 Diode IV Curves

  1. Replace the resistor with a standard diode (1N914 or similar) and repeat the IV curve measurement. If the IV curve does not resemble the expected diode characteristic shown in Figure 2, rotate the diode.

  2. Repeat the IV measurement with a Zener diode (1N5222B). If the IV curve does not resemble the expected Zener characteristic shown in Figure 3, rotate the diode. Observe both forward and reverse characteristics. Note the voltage at which current begins to flow in each direction.

Lab Deliverable #8(c)

Capture screenshots of the IV curves for both the standard diode and the Zener diode and submit via the course submission app. For each, note the approximate forward voltage and, for the Zener, the breakdown voltage. Your name must be visible in the image before uploading.

2.2.4 LED Characterization

IMPORTANT

Do not exceed the current ratings of the LEDs. LEDs can typically tolerate a direct current in the range of a few milliamperes. Never use an LED without a current-limiting resistor. The 1 kΩ resistor in this circuit limits the LED current to a safe level.

  1. Perform IV curve measurements for red, green, and blue LEDs.

(a) If the IV curve does not resemble the expected diode characteristic shown in Figure 2, rotate the LED.

(b) Observe and note why the LED appears to flicker during the measurement.
2. Note the forward voltage at which each LED begins to emit visible light. Zoom in by left-clicking and dragging on the signal; right-click to zoom out.
3. Observe any differences in the IV characteristics between the different colored LEDs.
4. Create a folder on the computer named EEC1_Lab3_Data for the frequency domain data collected in Part 2.

2.2 Part 3: IV Curve Observation (Optional)
Color Forward Voltage (V)
Red
Green
Blue

Lab Deliverable #8(d)

Capture screenshots of the IV curves for all three LEDs and submit via the course submission app. Record the approximate forward voltage at which each LED begins to emit visible light in the table provided. Your name must be visible in the image before uploading.

Self-Verification Checklist

Before leaving the lab, verify that you have collected all the necessary information to complete your post-lab report:

3. Post-Lab Analysis Report

Objective: Use the SignalLab MATLAB class to connect theoretical signal models with the measurements collected during the lab session. This part is completed individually outside of the scheduled lab period and submitted via the course submission app.

Background: Chapters 5 and 6 of the reader establish that periodic waveforms have discrete frequency spectra whose harmonic amplitudes follow predictable decay patterns depending on waveform shape. The SignalLab class encapsulates these theoretical models and provides methods for generating periodic signals, computing their spectra, and measuring signal properties directly in MATLAB.

The four waveforms measured in Part 1 (sine, square, triangle, sawtooth) will each be compared to their theoretical counterpart. The goal is to examine where agreement between theory and measurement is strong, where it breaks down, and why.

Getting SignalLab Class

  1. Download SignalLab.m (https://aknoesen.github.io/ECE-Emerge/SignalLab.m)
  2. Place the file in your working MATLAB folder, or add its location permanently to the MATLAB path:
addpath('C:/path/to/folder/containing/SignalLab')
savepath
  1. Verify MATLAB can find the class:
which SignalLab

MATLAB should respond with the full path to SignalLab.m. If it does not, check that the file is in the correct folder.

  1. A complete usage guide (SignalLab_Guide) is found here (https://aknoesen.github.io/ECE-Emerge/SignalLab_Guide.html)

Starter Script

The following script sets up the signal parameters and loads your first measured CSV file. Use it as your starting point and extend it to complete Tasks 2a through 2e.

%% Lab 3 Part 2 -- Frequency Domain Analysis
%  Complete each task below using SignalLab.
%  Refer to the SignalLab Guide for command syntax.

% --- Signal parameters (same for all waveforms) ---
Fs = 100000;   % sampling rate: 100 kSps
f0 = 1000;     % fundamental frequency: 1 kHz
A  = 1;        % amplitude: 1 V

sine_s = SignalLab(A, f0, Fs);

% --- Load a measured CSV file ---
% Update the filename and path to match your saved files.
% Your files should be named: sine_100ksps_time_ch1.csv, etc.

data   = readmatrix("sine_100ksps_time_ch1.csv");
sine_t_meas = data(:, 2);   % time vector (s)
sine_x_meas = data(:, 3);   % measured voltage (V)

% --- Generate the matching theoretical signal ---
duration          = length(sine_t_meas) / Fs;
[sine_t_theory, sine_x_theory]  = sine_s.generate(duration);

% --- Example: time-domain comparison for sine ---
figure;
plot(sine_t_meas,   sine_x_meas, "b-",  "LineWidth", 1.2);
hold on;
plot(sine_t_theory, sine_x_theory,   "r--", "LineWidth", 1.2);
hold off;
xlabel("Time (s)");  ylabel("Amplitude (V)");
legend("Measured", "Theoretical");
title("Sine Wave -- Measured vs Theoretical");
grid on;

% -------------------------------------------------------
% YOUR WORK STARTS HERE
% Repeat the pattern above for square, triangle, sawtooth
% and complete Tasks 2b through 2e.
% -------------------------------------------------------

WARNING

Always create your SignalLab object before calling setWave. The constructor resets all settings to their defaults. The correct order is: create the object, configure the waveform type, then generate the signal.

s = SignalLab(A, f0, Fs);     % 1. create
s = s.setWave("square");      % 2. configure
[t, x] = s.generate(dur);     % 3. generate

Tasks

Lab Deliverable #7(a)

Load the four time-domain CSV files collected in Part 1 into MATLAB. Plot the measured time-domain signal for each waveform. Each plot must include labeled axes (time in seconds, amplitude in volts) and a descriptive title. Arrange all four plots in a single figure using subplot. Upload the figure as an image via the course submission app. Your name must be visible in the image before uploading.

(MATLAB Grader) Submit the generateTheoretical function via the MATLAB Grader link in Canvas.

Lab Deliverable #7(b)

Using your generateTheoretical function and your measured CSV files, overlay the theoretical and measured time-domain signals for each of the four waveforms on the same axes. Use distinct colors or line styles and include a legend. For each waveform, write one to two sentences comparing the two signals. Arrange all four comparison plots in a single figure using subplot. Upload the figure as an image via the course submission app. Your name must be visible in the image before uploading.

(MATLAB Grader) Submit the theoreticalHarmonics function via the MATLAB Grader link in Canvas.

Lab Deliverable #7(c)

Using theoreticalHarmonics and the frequency-domain CSV files exported from the M2K Spectrum Analyzer during the lab session, produce one plot per waveform (four total) showing the theoretical and M2K-measured spectra on the same axes over 0–10 kHz. Label all axes and include a legend. Upload all four plots as images via the course submission app. Your name must be visible in each image before uploading.

(MATLAB Grader) Submit the harmonicTable function via the MATLAB Grader link in Canvas.

Lab Deliverable #7(d)

Using the output of harmonicTable and the amplitude values you recorded in the in-lab harmonic tables, complete three comparison tables — one each for the square, triangle, and sawtooth wave — with columns for harmonic number, theoretical amplitude, and measured amplitude. In each table, mark any harmonic predicted to be zero and note whether a non-zero amplitude was observed. Take a screenshot of each completed table and upload via the course submission app. Your name must be visible in each image before uploading.

Lab Deliverable #7(e)

Write a paragraph of 5–8 sentences analysing how well the measured square wave spectrum agrees with the theoretical prediction. Where is the agreement closest and where does it break down? Identify at least two physical or instrumental factors that could account for any observed discrepancies. Draw on Chapters 5 and 6 of the reader to support your explanation. Submit via the course submission app.

Lab Deliverable #7(f)

Write a paragraph of 5–8 sentences analysing how well the measured triangle wave spectrum agrees with the theoretical prediction. Where is the agreement closest and where does it break down? Identify at least two physical or instrumental factors that could account for any observed discrepancies. Draw on Chapters 5 and 6 of the reader to support your explanation. Submit via the course submission app.

Lab Deliverable #7(g)

Write a paragraph of 5–8 sentences analysing how well the measured sawtooth wave spectrum agrees with the theoretical prediction. Where is the agreement closest and where does it break down? Identify at least two physical or instrumental factors that could account for any observed discrepancies. Draw on Chapters 5 and 6 of the reader to support your explanation. Submit via the course submission app.

You are encouraged to use an AI assistant to help structure your analysis or to clarify concepts such as Fourier analysis and frequency content. Ask it to explain, check your reasoning, or suggest a framework; then apply that framework to your own data. The analysis you submit must be your own work: use AI as a thinking partner, not as a substitute for your own conclusions.

Lab Deliverable #7(h)

Code review paragraph (see AI-Assisted Coding Guide Section 6). In 3–5 sentences, written in your own words: (a) name the AI tool you used for your MATLAB analysis and describe how you used it — did you iterate on the prompt, and if so, what changed between attempts? (b) identify one specific thing you verified or would change in the generated code, and explain why; (c) state whether the output matched your physical expectations and how you checked.

Submission Instructions

IMPORTANT

Deliverables marked (MATLAB Grader) must be submitted through the MATLAB Grader link in Canvas. Deliverables marked (course submission app) must be submitted through the course submission app. All plots, images, data tables, and calculations must be clearly labeled.

Version 3.2