Frequency Modulation Concepts

Frequency Modulation

• Carrier amplitude remains constant
• Carrier frequency is changed by the modulating signal
• An increase in modulating signal amplitude results in an increase in carrier frequency
• The amount of change in carrier frequency produced by the modulating signal is known as frequency deviation (fd)
• In FM, the maximum deviation occurs at the peak positive and negative amplitude of the modulating voltage.
• In PM, the amount of carrier deviation is proportional to the rate of change of the modulating signal.
• In FM, frequency deviation is proportional only to the amplitude of the modulating signal, regardless of its frequency.

Modulation Index and Sidebands

• Any modulation process produces sidebands
• In FM and PM (as in AM), sum and difference sideband frequencies are produced.
• In addition, a large number of pairs of upper and lower sidebands are generated.
• The amplitudes depend upon the modulation index (m_f).
• Theoretically, the FM process produces an infinite number of upper and lower sidebands, therefore, theoretically infinitely large bandwidth.
• Practically, sidebands with the largest amplitudes are significant in carrying the information.
• Any sideband whose amplitude is less than 1 percent of the unmodulated carrier is considered insignificant.
• m_f = f_d / f_m, where f_d is the frequency deviation (sometimes denoted as δ) and f_m is the modulating frequency.
• In most communication systems using FM, maximum limits are put on both the frequency deviation and the modulating frequency. Example: Maximum permitted frequency deviation: 75 kHz; Maximum permitted modulating frequency: 15 kHz.
• When the maximum allowable frequency deviation and the maximum modulating frequency are used in computing the modulation index, m_f is known as the deviation ratio.

Bessel Functions

• The equation for the FM signal in terms of Bessel functions is: V_FM(t) = V_c cos(2πfct + m_f sin 2πfmt).
• Where f_c = carrier frequency and f_m = modulating frequency and mf = modulating index.
• The amplitudes of the sidebands are determined by the J_n coefficients.
• A table shows the values of Bessel functions for various modulation indices.

Amplitude Modulation

• The instantaneous voltage of a complex signal is described as V₂ = V_csin(2πfct) + V_m sin(2πfmt) sin(2πfct)

Converting PM to FM

• The deviation produced by frequency variations in the modulating signal must be compensated for
• Higher modulating frequencies produce a greater rate of change
• A low-pass RC network can be used.
• The result is an output that is the same as an FM signal → Indirect FM

FM Signal Bandwidth

• BW = 2f_mN where N is the number of sidebands.
• Carson's Rule bandwidth: BW = 2[f_d(max) + f_m(max)].
• Narrowband FM: Signals occupy no more spectrum space than an AM signal, BW = 2f_m.
• Wideband FM: m ≥ 1, BW = 2(m+1)f_m.

Noise Suppression Effects of FM

• Noise adds to a signal and interferes with it.
• FM has a constant modulated carrier amplitude.
• Spikes are clipped off at the receiver.
• Does not affect the information content of the FM signal.
• Solely within the frequency variations of the carrier.

Noise and Phase Shift

• Noise amplitude added to an FM signal introduces a small frequency variation (or phase shift).
• Noise is usually a short duration pulse containing many frequencies.
• Maximum phase shift occurs when the noise and signal phasors are at a right angle.
• δ = φ(f_m), where δ = frequency deviation produced by noise, φ = phase shift (radian), and f_m = frequency of modulating signal.

Preemphasis

• High-frequency components (low in amplitude) are amplified more than low-frequency components to compensate for noise obliteration.
• A simple high-pass filter circuit is used to achieve preemphasis
• Preemphasis occurs at 6 dB per octave. Note: Deemphasis has a 6-dB/octave slope in the opposite direction.

Frequency Modulator and Demodulator Circuits

• FM Modulators have two types: – Direct – varies the carrier oscillator according to the modulating signal – Indirect – utilizes a phase shifter.
• LC Oscillators, Varactors, Crystal Oscillators, and Voltage Controlled Oscillators are types of frequency circuits for FM modulators.
• C5 is a blocking capacitor to keep DC signal from the modulating circuits.
• RFC is high at carrier frequency to prevent the carrier from going into the modulating circuits
• Varactors are designed to optimize capacitance changes as widely and linearly as possible.
• The equation for capacitance is C_v = eA/d, where e is dielectric constant, A is area and d is dielectric thickness.

Receiver

• The electronic unit that selects the desired signal transmitted and extracts the original information signal.
• Tuning to accept the desired carrier signal.
• Detecting intelligence from the radio frequency signal.
• Providing adequate amplification.
• The receiver characteristics include sensitivity (amplifying weak signal), selectivity (rejecting unwanted signals), and stability (tuning consistency).

Receiver Characteristics

• Sensitivity - a measure of a receiver's ability to receive and amplify weak signals
• Selectivity - a measure of the receiver's ability to select one signal while rejecting all others at nearby frequencies
• Stability - the ability of a receiver to be fixed or tuned to a desired frequency.
• The TRF receiver (Tuned Radio Frequency) consists of bandpass filter, RF amplifier, demodulator, and audio amplifier as stages.
• The Superheterodyne Receiver uses a frequency conversion process called heterodyning to convert incoming radio signals into a fixed intermediate frequency (IF). This IF is then amplified before demodulation. The necessary components include RF filters, RF amplifier, mixer, IF amplifier, demodulator, and audio amplifier.
• The local oscillator (LO) is crucial, tuning the local oscillator frequency above or below the RF signal by an amount equal to the intermediate frequency.
• Receiver's intermediate frequency is 455 kHz for AM receivers and 10.7 MHz for FM receivers.
• Image frequency is any frequency other than the desired radio frequency carrier that, if allowed to enter a receiver and mix with the local oscillator, will produce a cross-product frequency that is equal to the intermediate frequency. The relationship is f_img = f_sig ± 2f_int, where f_img is the image frequency, f_sig is the desired signal frequency, and f_int is the intermediate frequency.
• Image frequency rejection ratio is often given in dB, with a higher value indicating better rejection of undesired signals.

Radio Wave Propagation Through Space

• Radio waves propagate through space until received by a receiving antenna.
• The signal strength decreases rapidly with distance.
• Other factors affecting propagation include signal frequency, atmospheric conditions, and the time of day.
• The characteristics of radio waves include reflection, refraction, and diffraction.

Optical Characteristics of Radio Waves

• Radio waves act very much as light waves.
• Reflection: Angle of incidence equals angle of reflection but is never complete due to imperfect conductor surfaces.
• Refraction: Bending of waves due to physical medium composition. The wave slows down as it passes through a medium resulting in a bending effect. The degree of bending depends on the index of refraction (n = speed in vacuum / speed in medium).
• Diffraction: Bending of the waves around an object, where Huygen's principle states that each point along a wave front can be considered as a source of another spherical wave.

Common Propagation Problems

• Fading: Variation in signal amplitude caused by signal path variations, distance differences, environmental differences, and relative motion of the transmitter and receiver. This fading can also be caused by obstacles, resulting in shadow fading.
• Multipath: The transmitted signal takes multiple paths, causing time delays that lead to phase shifts, often resulting in a 180 ° phase shift.
• Doppler Shift: Movement of the transmitter or receiver, causing changes in frequency.
• Fade Margin: Describes how much the received signal exceeds the minimum strength required for reliable communication and is computed in dB units using a formula.

Diversity System

• Minimizes fading by using multiple transmitters and receivers to compensate for fading. The variations include frequency diversity (using separate sets of transmitters and receivers operating at different frequencies), spatial diversity (using multiple antennas at a single station), and a combiner network (linearly mixing signals from multiple antennas to create a stronger composite signal) and/or selective switched systems (monitoring outputs and switching to the strongest signal).

Explore the key principles of frequency modulation (FM) and phase modulation (PM) in this quiz. Understand how carrier frequency changes with modulating signals and learn about modulation index and sidebands. Perfect for students seeking to grasp the fundamentals of FM and PM.