EEEN 462 - Frequency Modulation Quiz

Frequency modulation (FM) varies the frequency of the carrier wave in proportion to the amplitude of the message signal. The amplitude of the carrier remains constant, which provides FM with superior noise immunity compared to amplitude modulation (AM).

This fundamental characteristic makes FM ideal for high-fidelity audio transmission, such as in FM radio broadcasting, where signal quality is critical.

The standard mathematical expression for an FM wave is:

Where:

• A_c is the carrier amplitude
• f_c is the carrier frequency
• β is the modulation index
• f_m is the modulating frequency

This equation shows how the message signal (represented by the sine term) affects the phase of the carrier wave, resulting in frequency modulation.

The modulation index (β) in FM is defined as:

Where:

• Δf is the peak frequency deviation (the maximum shift from the carrier frequency)
• f_m is the highest modulating frequency

This dimensionless parameter determines whether the FM signal is narrowband (β < 1) or wideband (β > 1). It also influences the number of significant sidebands and the bandwidth of the FM signal.

Carson's Rule provides a practical estimate for the bandwidth of an FM signal:

Where:

• Δf is the peak frequency deviation
• f_m is the highest modulating frequency

This approximation accounts for approximately 98% of the total power in the FM signal. For example, in commercial FM radio broadcasting:

• Δf = 75 kHz
• f_m = 15 kHz
• Bandwidth ≈ 2(75 + 15) = 180 kHz

FM's superior noise immunity comes from these key factors:

• Most noise is amplitude noise, which affects AM signals directly since information is encoded in amplitude variations
• FM receivers use limiters to remove amplitude variations before demodulation
• Information in FM is encoded in frequency variations, which are less affected by noise
• FM systems can trade bandwidth for improved signal-to-noise ratio

This noise immunity is why FM is used for high-fidelity audio broadcasting, while AM is more susceptible to static and interference.

A Phase-Locked Loop (PLL) FM demodulator consists of three essential components:

• Phase Detector: Compares the input FM signal with the VCO output
• Loop Filter: Filters the phase detector output
• Voltage-Controlled Oscillator (VCO): Produces a signal whose frequency is controlled by the filtered error voltage

The VCO is crucial because:

• It generates the local oscillator signal that tracks the input FM signal
• Its control voltage becomes the demodulated output signal
• It allows the PLL to lock onto and follow the frequency variations of the input

While FM offers superior noise immunity and audio quality, it comes with a significant trade-off:

• FM signals require much more bandwidth than AM signals
• A typical AM radio channel uses 10 kHz bandwidth, while an FM channel requires 200 kHz
• This bandwidth expansion is necessary to achieve the noise immunity benefits
• The large bandwidth limits the number of FM stations that can be accommodated in the radio spectrum

For example:

• AM Broadcast: 530-1700 kHz (1170 kHz range) → 117 channels (10 kHz each)
• FM Broadcast: 88-108 MHz (20 MHz range) → 100 channels (200 kHz each)

Commercial FM broadcasting uses the following standards:

• Peak frequency deviation: ±75 kHz
• Maximum modulating frequency: 15 kHz
• Modulation index: β = Δf/f_m = 75/15 = 5
• Channel bandwidth: 200 kHz (with 100 kHz guard bands)

This standard was established by the FCC in the United States and adopted internationally. The ±75 kHz deviation provides an optimal balance between audio quality and bandwidth efficiency for music broadcasting.

A key characteristic of FM is constant transmitted power:

• Total power in FM remains constant regardless of modulation
• This is expressed mathematically as: P_total = A_c²/2
• As modulation increases, power is redistributed from the carrier to sidebands
• This contrasts with AM, where total power increases with modulation

The constant power in FM enables:

• More efficient power amplifier design (Class C amplifiers)
• Better utilization of transmitter power
• No risk of overmodulation distortion like in AM

FM is widely used in many applications, but not for traditional AM broadcasting:

• FM Applications:
  • Commercial FM radio (88-108 MHz)
  • Television audio transmission
  • Aircraft VHF communication (108-137 MHz)
  • Two-way radio systems (police, emergency services)
  • Microwave and satellite communications
• AM Applications:
  • AM radio broadcasting (530-1700 kHz)
  • Aviation navigation systems (NDBs)
  • Some types of data transmission

The 530-1700 kHz band is exclusively used for AM broadcasting, which uses amplitude modulation rather than frequency modulation.