Amplitude Modulation Calculator

• m = A_m / A_c (modulation index)
• s(t) = A_c[1 + m cos(2π f_m t)] cos(2π f_c t)
• V_max = A_c(1+m), V_min = A_c(1−m)
• A_USB = A_LSB = (m A_c)/2 (each sideband amplitude)
• Bandwidth ≈ 2 f_m

Optional power model (when a resistive load is provided): for a peak carrier voltage A_c across R, P_c = A_c² / (2R) and P_t = P_c(1 + m²/2).

1. Choose a mode, or keep Auto to infer a missing value.
2. Enter A_c, plus either A_m or m.
3. Add f_c and f_m to see bandwidth and sidebands.
4. Optionally enter load resistance to compute carrier and total power.
5. Press Calculate. Results appear above the form under the header.
6. Use Download CSV or Download PDF to save the results.

1) Modulation index and what it tells you

The modulation index m is the ratio of message amplitude to carrier amplitude: m = A_m/A_c. A value of 0.25 means the envelope varies ±25% around the carrier level. Many voice links target 0.5 to 0.9 to keep distortion low while improving loudness at the receiver.

2) Envelope limits and distortion threshold

This calculator reports V_max = A_c(1+m) and V_min = A_c(1−m). When m > 1, the minimum becomes negative, meaning the envelope crosses zero and an envelope detector can clip or invert sections. The “100% modulation” point (m = 1.0) is the practical upper limit for clean AM.

3) Sidebands and their amplitudes

A single-tone message at f_m produces two sidebands at f_c ± f_m. Each sideband’s peak voltage amplitude is (mA_c)/2, so a 10 V carrier with m = 0.6 yields 3.0 V peak in the upper and 3.0 V peak in the lower sideband components.

4) Bandwidth planning with message frequency

For standard double-sideband AM, occupied bandwidth is approximately 2f_m for the highest message frequency present. If your audio is limited to 5 kHz, plan about 10 kHz of RF bandwidth. If you widen audio to 10 kHz, bandwidth doubles to roughly 20 kHz, affecting channel spacing and filter design.

5) Power distribution across carrier and sidebands

If you enter a resistive load R, the tool estimates carrier power using P_c = A_c²/(2R) where A_c is peak carrier voltage across the load. Each sideband carries P_cm²/4, and total transmitted power is P_t = P_c(1 + m²/2). At m = 1, only one-third of power is in the sidebands.

6) Choosing levels for a clean measurement

For lab checks, start with a stable carrier amplitude and choose m between 0.2 and 0.8. Use a scope in “envelope view” to confirm the measured V_max and V_min match the computed values. If your generator reports RMS instead of peak, convert first to avoid power errors.

7) Practical example you can reproduce

Try A_c = 8 V, A_m = 6 V, f_c = 1 MHz, and f_m = 5 kHz. The calculator gives m = 0.75, V_max = 14 V, V_min = 2 V, and bandwidth ≈ 10 kHz. With a 50 Ω load, P_c ≈ 0.64 W and P_t ≈ 0.82 W.

8) Quick troubleshooting checklist

If results look wrong, verify you used consistent units for f_c and f_m, and confirm A_c is not zero. Overmodulation warnings usually mean the audio level is too high relative to the carrier. Reduce A_m or raise A_c until m returns to 1.0 or below.

Q1: What is a good modulation index for voice?
Many systems use 0.5–0.9. Lower values reduce noise improvement, while values near 1.0 maximize loudness without envelope distortion. Go above 1.0 only if you are not using simple envelope detection.

Q2: Why does AM bandwidth equal about 2f_m?
A message at f_m creates two sidebands at f_c ± f_m. The separation between the lowest and highest components is (f_c+f_m) − (f_c−f_m) = 2f_m.

Q3: What does “overmodulation” mean here?
It means m > 1, so the envelope crosses zero. An envelope detector can then create severe distortion because the carrier “reverses” within the envelope, producing clipped audio at the output.

Q4: Are the amplitudes peak or RMS?
The calculator treats A_c and A_m as peak amplitudes. If you have RMS values, convert first: V_peak = √2 · V_RMS for a sine wave. This matters for accurate power estimates.

Q5: Why is most AM power in the carrier?
The carrier is transmitted continuously even when the message is quiet. Sideband power scales with m², so at moderate m values the carrier dominates. At m = 1, sidebands together carry one-half of P_c.

Q6: What frequencies appear for a single-tone message?
You get a carrier at f_c, plus a lower sideband at f_c − f_m and an upper sideband at f_c + f_m. Their amplitudes are equal for standard AM.

Q7: How do I increase transmitted information power?
Increase m while keeping m ≤ 1, or use modulation schemes that reduce carrier power (like suppressed-carrier DSB or SSB). In classic AM, raising m boosts sideband power and improves received audio level.