AC Waveforms, Frequency, and RMS Values

What Is an AC Waveform?

Alternating current (AC) reverses direction periodically. The most common shape in power systems and electronics is the sine wave, produced naturally by rotating generators. Unlike direct current (DC), which flows steadily in one direction, AC rises to a positive peak, falls back through zero, drops to a negative peak, and returns to zero—completing one cycle.

The oscilloscope lets you see this cycle drawn on a screen. The horizontal axis represents time; the vertical axis represents voltage. By reading the grid, you can extract every important AC measurement directly.

Key AC Measurements

Peak Voltage (V_pk)

Peak voltage is the maximum voltage reached during one cycle, measured from zero to the top (or bottom) of the waveform. On the oscilloscope screen, count the vertical divisions from the center line to the crest of the wave, then multiply by the volts/division setting.

Peak-to-Peak Voltage (V_pp)

Peak-to-peak voltage spans from the negative peak to the positive peak. It equals twice the peak voltage:

V_pp = 2 × V_pk

This value is easy to read directly on the scope because you measure the full vertical height of the waveform.

Period (T)

The period is the time for one complete cycle, measured in seconds (or milliseconds, microseconds). On the oscilloscope, count the horizontal divisions that one full cycle occupies and multiply by the time/division (time-base) setting.

Frequency (f)

Frequency is the number of cycles per second, measured in hertz (Hz). Frequency and period are reciprocals:

f = 1 / T

US utility power operates at 60 Hz, meaning 60 complete cycles every second.

RMS Voltage—Why It Matters

Peak voltage overstates how much work AC actually does. A sine wave spends most of its time at values below its peak. The root-mean-square (RMS) value is the equivalent DC voltage that would deliver the same power to a resistive load.

For a pure sine wave:

V_rms = V_pk × 0.7071 (equivalently, V_pk ÷ √2)

Working backward:

V_pk = V_rms × 1.414 (equivalently, V_rms × √2)

The familiar 120 V on a household outlet is an RMS value. Its peak voltage is approximately 120 × 1.414 = 170 V.

A true-RMS digital multimeter (DMM) measures RMS directly by computing the mathematical RMS of the actual waveform. Average-responding meters display a scaled average that equals RMS only for a perfect sine wave—always use a true-RMS meter for AC measurements in the field.

Using the Oscilloscope Safely

Before touching any equipment:

• Inspect probe leads for cracked insulation or damaged connectors. Damaged probes must be replaced before use.
• Keep the function generator output at the low voltages used in this lab (typically a few volts). Never connect oscilloscope probes directly to building wiring without appropriate high-voltage probes and instructor authorization.
• Set probe attenuation (1× or 10×) to match the oscilloscope input setting; a mismatch causes readings to be off by a factor of 10.
• Ensure the oscilloscope chassis ground (through the BNC connector) is connected to the circuit's reference ground. Connecting the probe ground clip to a live conductor can cause a short circuit and shock hazard.

Oscilloscope Controls You Will Use

| Control | What It Does |

|---|---|

| Volts/Div | Sets the vertical scale; each grid square equals this many volts |

| Time/Div | Sets the horizontal (time-base) scale; each square equals this much time |

| Trigger Level | Stabilizes the waveform display; adjust until the trace is steady |

| Probe Comp | Square-wave output used to calibrate probe; adjust until corners are flat |

Procedure Overview

1. Calibrate the probe using the built-in probe compensation output. Adjust the probe trimmer until the square wave has flat tops—this ensures accurate frequency response.

2. Connect the function generator to channel 1 using the BNC-to-banana adapter and probe leads.

3. Adjust time-base and volts/div until two complete, stable cycles fill the screen.

4. Read V_pk: count divisions from center to crest; multiply by volts/div.

5. Read period (T): count divisions for one full cycle; multiply by time/div.

6. Calculate f = 1/T and V_rms = V_pk × 0.7071.

7. Verify with the true-RMS DMM: connect across the function generator output; record the displayed RMS value and compare to your calculation.

Recording and Comparing Results

For each of the three frequency/amplitude settings, record V_pk, T, calculated f, and calculated V_rms in your lab log. Then record the DMM RMS reading. Small discrepancies (within ±5%) are normal due to generator output impedance, probe loading, and rounding. Larger discrepancies suggest a setting error—recheck probe attenuation and volts/div before assuming instrument fault.