AM vs FM: Differences in Bandwidth, Power, Noise & Applications (with MCQs)

Amplitude modulation (AM) and frequency modulation (FM) are the two classic analog modulation methods. AM is still used for medium-wave and short-wave broadcasting and in aircraft (VHF airband) radio; FM is used for FM broadcasting, TV sound in older systems and two-way radios. “Differences between AM and FM”, “why FM is less noisy” and bandwidth/power calculations are standard in BTCL, Bangladesh Betar, BCS (EEE/ETE) and university exams. This post compares them with an animation, formulas, solved examples and MCQs.

⚡ Key takeaways

• AM: carrier amplitude follows the message; BW = 2f_m; total power P_t = P_c(1 + μ²/2).
• FM: carrier frequency follows the message; Carson’s rule BW ≈ 2(Δf + f_m); total power is constant.
• FM has much better noise immunity, because noise mainly changes amplitude and a limiter removes it, but FM needs more bandwidth.
• Modulation index: AM μ = A_m/A_c (should be ≤ 1); FM β = Δf/f_m (can be greater than 1).
• Commercial FM: Δf = 75 kHz, f_m ≤ 15 kHz → BW ≈ 180 kHz (200 kHz channels).

📑 Contents

1. Basics of AM and FM
2. Animation: waveforms and noise
3. AM formulas
4. FM formulas
5. AM vs FM comparison table
6. Solved problems
7. Practice MCQs
8. বাংলায় দ্রুত রিভিশন

1. Basics of AM and FM

Modulation shifts a low-frequency message (audio, 20 Hz–20 kHz) onto a high-frequency carrier so it can be radiated by a practical antenna, multiplexed with other stations, and sent over long distances. A sinusoidal carrier c(t) = A_c cos(2πf_ct + φ) has three parameters that can be changed:

• Amplitude → amplitude modulation (AM)
• Frequency → frequency modulation (FM)
• Phase → phase modulation (PM). FM and PM are together called angle modulation.

2. Animation: Where Is the Information?

Animation 1 – In AM the envelope carries the message, so amplitude noise directly corrupts it. In FM the information is in the zero-crossing rate (frequency); amplitude spikes are removed by the limiter.

3. AM Formulas

s_AM(t) = A_c[1 + μ cos(2πf_mt)] cos(2πf_ct)

• Modulation index: μ = A_m/A_c = (V_max − V_min)/(V_max + V_min). If μ > 1 (over-modulation), the envelope is distorted.
• Spectrum: carrier at f_c, and sidebands at f_c ± f_m, each with amplitude μA_c/2.
• Bandwidth: BW = 2f_m (DSB-FC). SSB needs only f_m.
• Power: P_t = P_c(1 + μ²/2); sideband power = P_cμ²/2.
• Transmission efficiency: η = μ²/(2 + μ²). The maximum is 33.3 % at μ = 1, so at least two-thirds of the power is wasted in the carrier.
• Current relation: I_t = I_c√(1 + μ²/2).

4. FM Formulas

s_FM(t) = A_c cos[2πf_ct + β sin(2πf_mt)], f_i(t) = f_c + k_f m(t)

• Frequency deviation: Δf = k_fA_m (the maximum shift from f_c).
• Modulation index: β = Δf/f_m. Narrow-band FM (β ≪ 1) has BW ≈ 2f_m, like AM; wide-band FM (β > 1) has many sidebands.
• Carson’s rule: BW ≈ 2(Δf + f_m) = 2f_m(β + 1). This contains about 98 % of the power.
• Spectrum: sidebands at f_c ± nf_m with amplitudes given by Bessel functions J_n(β). The carrier amplitude can even become zero (at β ≈ 2.405).
• Power: constant = A_c²/2R, independent of modulation; modulation only redistributes power among the sidebands.
• Noise improvement: above threshold, the output SNR improves in proportion to β² (figure of merit = 3β²/2 for tone modulation, against 1/3 for AM with μ = 1), so doubling the deviation gives about 6 dB more SNR. Pre-emphasis in the transmitter and de-emphasis in the receiver boost high-frequency SNR further. Below a threshold carrier-to-noise ratio, FM performance falls sharply (threshold effect).
• Capture effect: when two FM signals share a frequency, the receiver locks onto the stronger one.

5. AM vs FM Comparison Table

Parameter	AM	FM
Varied parameter	Carrier amplitude	Carrier frequency
Modulation index	μ = Am/Ac (0 to 1)	β = Δf/fm (can be > 1)
Bandwidth	2fm (≈ 10 kHz for broadcast)	2(Δf + fm) (≈ 180–200 kHz)
Number of sidebands	Two (one pair)	Theoretically infinite
Transmitted power	Depends on μ; carrier wastes ≥ 2/3	Constant; all power useful
Noise immunity	Poor (noise adds to amplitude)	Good (limiter removes amplitude noise)
Sound fidelity	Lower (audio ≈ 5 kHz)	High (audio up to 15 kHz, stereo)
Broadcast band	MW 531–1602 kHz (9 kHz spacing in ITU Regions 1 & 3), SW	VHF 88–108 MHz
Propagation	Ground wave / sky wave → long range	Line of sight → limited range
Circuit complexity	Simple, cheap (envelope detector)	More complex (discriminator, PLL)
Typical uses	MW/SW broadcast, aircraft voice radio	FM radio, two-way radio, analog TV sound

6. Solved Problems

Problem 1 (AM power). A carrier of 1000 W is amplitude-modulated with μ = 0.8. Find the total power, the sideband power and the efficiency.

P_t = 1000(1 + 0.8²/2) = 1320 W; P_SB = 320 W; η = 320/1320 = 24.2 %

Problem 2 (AM index from envelope). An AM envelope varies between 12 V and 4 V. Find μ.

μ = (12 − 4)/(12 + 4) = 0.5

Problem 3 (FM bandwidth). Commercial FM: Δf = 75 kHz, maximum f_m = 15 kHz.

β = 75/15 = 5; BW ≈ 2(75 + 15) = 180 kHz

Problem 4 (narrow-band FM). Δf = 5 kHz, f_m = 3 kHz → BW ≈ 2(5 + 3) = 16 kHz, typical of two-way voice radio.

7. Practice MCQs

1. Bandwidth of a DSB-FC AM signal with f_m = 5 kHz is: (a) 5 kHz (b) 10 kHz (c) 15 kHz (d) 2.5 kHz

✔ (b) 2f_m = 10 kHz.

2. Maximum transmission efficiency of AM (DSB-FC) is: (a) 25 % (b) 33.3 % (c) 50 % (d) 100 %

✔ (b) 33.3 % at μ = 1.

3. Carson’s rule bandwidth is: (a) 2f_m (b) 2Δf (c) 2(Δf + f_m) (d) Δf + f_m

✔ (c) 2(Δf + f_m).

4. In FM, the total transmitted power: (a) Increases with β (b) Decreases with β (c) Remains constant (d) Becomes zero

✔ (c) Remains constant.

5. Over-modulation in AM occurs when: (a) μ = 0 (b) μ < 1 (c) μ = 1 (d) μ > 1

✔ (d) μ > 1.

6. FM is less affected by noise mainly because: (a) It uses a lower frequency (b) Information is in frequency, and a limiter removes amplitude noise (c) It uses less bandwidth (d) It uses higher power

✔ (b).

7. Frequency deviation of commercial FM broadcast is: (a) 15 kHz (b) 25 kHz (c) 75 kHz (d) 200 kHz

✔ (c) ±75 kHz.

8. AM carrier power 400 W, μ = 1. Total power is: (a) 400 W (b) 500 W (c) 600 W (d) 800 W

✔ (c) 400 × 1.5 = 600 W.

9. Pre-emphasis in FM boosts: (a) Low audio frequencies (b) High audio frequencies (c) Carrier (d) Noise

✔ (b) High audio frequencies, before transmission.

10. Which detector is used for AM broadcast receivers? (a) Foster–Seeley (b) Ratio detector (c) Envelope (diode) detector (d) PLL

✔ (c) Envelope detector.

8. বাংলায় দ্রুত রিভিশন

📝 পরীক্ষার আগে এক নজরে

• AM: বাহক তরঙ্গের বিস্তার (amplitude) পরিবর্তন হয়; ব্যান্ডউইথ = 2f_m।
• FM: বাহক তরঙ্গের কম্পাঙ্ক পরিবর্তন হয়; কারসন সূত্র BW = 2(Δf + f_m)।
• AM-এ মোট শক্তি P_t = P_c(1 + μ²/2); সর্বোচ্চ দক্ষতা ৩৩.৩% (μ = 1)।
• FM-এ মোট শক্তি স্থির; নয়েজ কম, শব্দের মান ভালো, কিন্তু ব্যান্ডউইথ বেশি লাগে।
• বাণিজ্যিক FM: Δf = ৭৫ kHz, f_m = ১৫ kHz, β = ৫, BW ≈ ১৮০ kHz; ব্যান্ড ৮৮–১০৮ MHz।
• AM মিডিয়াম ওয়েভে গ্রাউন্ড/স্কাই ওয়েভে দূরে যায়; FM দৃষ্টিসীমার (line of sight) মধ্যে সীমিত।

Related Posts

• Advantages of FM over AM for Sound
• Why Modulation and Demodulation?
• Constellation Diagram: BPSK, QPSK & QAM
• Different Types of Noise and Signals
• Mostly Asked Communication Systems MCQs

References: George Kennedy, Electronic Communication Systems; B. P. Lathi, Modern Digital and Analog Communication Systems; ITU Radio Regulations. Images and animations: original work by Totalecer.