Frequency Modulation

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Application of the Frequency Modulation

1.0 Introduction

Edwin H. Armstrong, known as one of the founding fathers of radio technology, invented the super hetero dyne radio receiver in 1918 and frequency modulation (FM) in 1933. These two concepts, along with his regenerative circuit technique developed in 1912, formed the basis of radio frequency electronics as we know it today. In the United States, FM radio stations broadcast between radio frequencies of 88 MHz to 108 MHz with a channel bandwidth of 200 kHz. FM radio was first deployed in monaural in 1940; and in 1960, FM stereo was introduced.

Before defining frequency modulation, it is pertinent to understand what modulation means as applied to radio communications. Modulation is the process of converting low frequency signals into high frequency signals, so that they can be radiated and recovered at a remote location.Frequency modulation is a form of analog angle modulation in which the baseband information-carrying signal, typically called the message or information signal m(t), varies the frequency of a carrier wave. Audio signals transmitted by FM radio are the most common. However, FM radio can also transmit digital data with the low bandwidth digital information known as Radio Data System (RDS) in Europe and Radio Broadcast Data System (RBDS) in the U.S.

In telecommunications and signal processing, frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. This contrasts with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency remains constant.
In analog frequency modulation, such as FM radio broadcasting of an audio signal representing voice or music, the instantaneous frequency deviation, the difference between the frequency of the carrier and its center frequency, is proportional to the modulating signal.

Digital data can be encoded and transmitted via FM by shifting the carrier’s frequency among a predefined set of frequencies representing digits – for example one frequency can represent a binary 1 and a second can represent binary 0. This modulation technique is known as frequency-shift keying (FSK). FSK is widely used in modems and fax modems, and can also be used to send Morse codes. Radio teletype also uses FSK.

Frequency modulation is widely used for FM radio broadcasting. It is also used in telemetry, radar, seismic prospecting, and monitoring newborns for seizures via EEG, two-way radio systems, music synthesis, magnetic tape-recording systems and some video-transmission systems. In radio transmission, an advantage of frequency modulation is that it has a larger signal-to-noise ratio and therefore rejects radio frequency interference better than an equal power amplitude modulation (AM) signal. For this reason, most music is broadcast over FM radio.Frequency modulation has a close relationship with phase modulation; phase modulation is often used as an intermediate step to achieve frequency modulation. Mathematically both of these are considered a special case of quadrature amplitude modulation (QAM).

The simplest approach to generating FM signals is to apply the message signal directly to a voltage-controlled oscillator (VCO).

A voltage message signal, m(t), is applied to the control voltage of the VCO, and the output signal, XFM(t), is a constant amplitude sinusoidal carrier wave whose frequency is ideally a linear function of its control voltage. When there is no message or the message signal is zero, the carrier wave is at its center frequency, fc. When a message signal exists, the instantaneous frequency of the output signal varies above and below the center frequency and is expressed by

fi(t) = fc + Kvcom(t)

Where Kvco is the voltage-to-frequency gain of the VCO expressed in units of Hz/V, and the quantity, Kvco*m(t), is the instantaneous frequency deviation. The instantaneous phase of the output signal is equal to 2π multiplied by the integral of the instantaneous frequency where the initial condition of the phase is assumed to be zero for simplicity.

A few observations can be made from the FM output signal. First, the amplitude of an FM signal is constant regardless of the message signal, giving it a constant envelope property with an output power equal to A2c /2 into a 1 Ω resistor. Secondly, the frequency-modulated output, xFM(t), has a nonlinear dependence to the message signal, m(t), making it difficult to analyze the properties of an FM signal. To estimate the bandwidth of an FM signal, a single tone messagesignal is used as shown below

m(t) = Am cos(2π fmt)

where Am is the amplitude of the message signal and fm is the frequency of the message signal.

1.1 Sinusoidal baseband signal

Mathematically, a baseband modulated signal may be approximated by a sinusoidal continuous wave signal with a frequency fm. This method is also named as Single-tone Modulation. The integral of such a signal is:

wave signal

In this case, the expression for y(t) above simplifies to:

wave signal formula

where the amplitude of the modulating sinusoid is represented by the peak deviation.

The harmonic distribution of a sine wave carrier modulated by such a sinusoidal signal can be represented with Bessel functions; this provides the basis for a mathematical understanding of frequency modulation in the frequency domain.

1.2 Modulation index

As in other modulation systems, the modulation index indicates by how much the modulated variable varies around its unmodulated level. It relates to variations in the carrier frequency:

formula of signal

where Fm  is the highest frequency component present in the modulating signal xm(t), and is the peak frequency-deviation—i.e. the maximum deviation of the instantaneous frequency from the carrier frequency. For a sine wave modulation, the modulation index is seen to be the ratio of the peak frequency deviation of the carrier wave to the frequency of the modulating sine wave.If  , the modulation is called narrowband FM, and its bandwidth is approximately  .Sometimes modulation index h

For digital modulation systems, for example Binary Frequency Shift Keying (BFSK), where a binary signal modulates the carrier, the modulation index is given by:

wave signal

where Ts  is the symbol period, and Fm=1/2ts  is used as the highest frequency of the modulating binary waveform by convention, even though it would be more accurate to say it is the highest fundamental of the modulating binary waveform. In the case of digital modulation, the carrier   is never transmitted. Rather, one of two frequencies is transmitted, either Fc+F or Fc , depending on the binary state 0 or 1 of the modulation signal.

If  , the modulation is called wideband FM and its bandwidth is approximately  . While wideband FM uses more bandwidth, it can improve the signal-to-noise ratio significantly; for example, doubling the value of  , while keeping   constant, results in an eight-fold improvement in the signal-to-noise ratio. (Compare this with Chirp spread spectrum, which uses extremely wide frequency deviations to achieve processing gains comparable to traditional, better-known spread-spectrum modes).

With a tone-modulated FM wave, if the modulation frequency is held constant and the modulation index is increased, the (non-negligible) bandwidth of the FM signal increases but the spacing between spectra remains the same; some spectral components decrease in strength as others increase. If the frequency deviation is held constant and the modulation frequency increased, the spacing between spectra increases.

Frequency modulation can be classified as narrowband if the change in the carrier frequency is about the same as the signal frequency, or as wideband if the change in the carrier frequency is much higher (modulation index >1) than the signal frequency. For example, narrowband FM is used for two way radio systems such as Family Radio Service, in which the carrier is allowed to deviate only 2.5 kHz above and below the center frequency with speech signals of no more than 3.5 kHz bandwidth. Wideband FM is used for FM broadcasting, in which music and speech are transmitted with up to 75 kHz deviation from the center frequency and carry audio with up to a 20-kHz bandwidth.

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