- 2074 Chaitra · 8 marks
Single tone FM parameters
Short answer
Carrier frequency fc=ωc/2π=6×10⁸/(2π)≈95.5 MHz. Modulating frequency fm=1250/(2π)≈199 Hz. Modulation index β=5. Maximum deviation Δf=β fm≈995 Hz.
A single tone FM is represented by the voltage equation as v(t) = 12cos(6×10⁸t + 5sin1250t). Determine the following: a) Carrier frequency b) Modulating frequency c) Modulation index d) Maximum frequency deviation
v(t) = 12 cos(6×10⁸t + 5 sin 1250t)
Compare with the standard FM equation v(t) = Ac cos(ωct + β sin ωmt):
- ωc = 6×10⁸ rad/s
- ωm = 1250 rad/s
- β = 5
- Ac = 12 V
a) Carrier frequency
fc = ωc/2π = 6×10⁸ / 6.283 = 95.5 MHz
b) Modulating frequency
fm = ωm/2π = 1250 / 6.283 = 198.9 Hz (about 199 Hz)
c) Modulation index
β = 5
d) Maximum frequency deviation
Δf = β × fm = 5 × 198.9 = 994.7 Hz (about 995 Hz)
(Bandwidth by Carson's rule = 2(Δf + fm) = 2(994.7 + 198.9) = 2.39 kHz.)
✓ Answer checked by Claude Sonnet 5.5
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