It is a modulation system where the amplitude of the carrier is made constant (fixed) while the frequency is made to change according to the changes in the modulation signal (AF). In a sinusoidal wave, the instantaneous value (constantenous) for voltage / current is expressed as:
X = A sin (ωt + Q)
Information:
- X : instantaneous value (for voltage / current)
- A : wave amplitude (max value)
- ω : angular velocity (rad/s)
- Q : phase angle
If one of the 3 parameters (A, ω, Q) is changed, modulation will occur, just like AM and FM modulation, which was as follows:
- Frequency calculation
- Voltage calculation
- Modulation index calculation
- Deviation calculation
- Power calculation
- Band width calculation
Frequency Modulation Illustration
Transistor Band Code
For High or Mid Frequency:
2 SA ..xx
2 SC ..xx
For Low Frequency (AF):
2 SB ..xx
2 SD ..xx
Transistor Code Description
Frequency Calculation
The magnitude of the instantaneous frequency (f) on an FM wave is formulated:
f = fc (1 + k Em cos ωmt)\
f = fc + k Em cos ωmt*fc
Information:
- f = instantaneous frequency (Hz)
- fc = carrier frequency (Hz)
- k = constant of proportionality
- Em*cos ωmt = instantaneous voltage of AF wave (volt)
The maximum value of the above equation is obtained if:
- cos ωmt = 1, so f = fc + k Em fc
- k value Em fc = maximum deviation = ʆ/Δf
Understanding the FM Radio Frequency Spectrum
It is determined by the modulation index (mf) obtained from the First Bassel Function equation. The spectrum consists of the carrier frequency (fc) and the harmonic frequencies (sideband frequencies).
The form of the Bassel frequency model 1 is made in the form of a Bassel function table, where the amplitude in the frequency spectrum is determined by the coefficients (Jn).
Still part of the single sine wave modulation carrier signal, the resulting frequency spectrum can be calculated using the Bassel Function of the first kind, it is a function of the number of sidebands and the modulation index. The carrier signal and sideband amplitude are illustrated to find out the difference in the modulation index of the FM signal. In practice, the modulation index value, the carrier signal amplitude becomes zero, and all the signal power is in the sidebands.
Bassel Function Table
Frequency Spectrum
Example:
A 10 watt unmodulated carrier is frequency modulated by a sinusoidal signal so that the maximum frequency deviation is 4 kHz if the modulating signal frequency is 2 kHz. Then determine!
- Its modulation index (mf)
- Describe the frequency spectrum
Answer:
Answer Determines Spectrum