Frequency modulation

Frequency modulation ( FM) is a modulation method in which the carrier frequency is changed by the signal to be transmitted. Frequency modulation over the amplitude modulation allows a higher dynamic range of the information signal. Furthermore, it is less susceptible to interference. The procedure was as early as 1922 mathematically investigated by John Renshaw Carson and first put into practice by Edwin Howard Armstrong. The frequency of modulation is related to the angle of modulation, and phase modulation. In both of the phase angle T is influenced.

Do not confuse it with the designated as digital frequency modulation or as a Miller code channel coding, which is applicable for data recording, for example, in magnetic disks.

Modulation

A frequency modulated signal at high frequencies, can be generated using an oscillator circuit whose frequency-determining resonant circuit, a voltage-dependent capacitance, typically contains a capacitance diode, to which the modulation signal is applied as a signal voltage. Characterized the capacitance of the diode and hence the resonant frequency of the resonant circuit to change. FM at low frequencies is easier to produce with voltage-controlled oscillators. For the digital generation of a frequency modulated signal to a direct digital synthesis circuit (DDS ), or quadrature amplitude modulation (IQ ) modulation may advantageously be used.

Digital Modulation

• Frequency Shift Keying ( FSK), two defined signals
• Phase shift keying ( PSK ) carrier is shifted by 45 ° or 90 °

Demodulation

Prior to demodulation, the amplitude of the FM signal is kept constant ( "limited" ) to remove any amplitude variations, which may result from errors on the transmission path. This is possible because no information in the amplitude are included. Usually one uses for a chain of differential amplifiers.

The received FM signal is demodulated directly rare but displaced first to the superheterodyne principle to an intermediate frequency, this operation is referred to as a mixture. For example, the FM broadcasting is 100 MHz = = transmitted on the carrier frequency f with a frequency deviation of 75 kHz ΔfT. The relative amounts Hub

And does not allow easy demodulation. By reacting to the usual ones for FM receivers intermediate frequency of 10.7 MHz H is approximately tenfold and simplifies the circuit. Narrowband FM as Slow Scan Television is not demodulated without these pre- existing frequency change.

There are different types of FM demodulators. A discriminator converts the FM signal into a first amplitude or pulse modulation. In the early days they used to simple edge rectifiers, later Ratio detectors. Wherein Koinzidenzdemodulator a phase modulated signal is formed from the frequency-modulated signal that can be demodulated. A further possibility is the PLL demodulator. By phase comparison of the modulated signal with the local oscillator signal to obtain a voltage corresponding to the deviation, with which one adjusts the PLL oscillator. The control voltage is also the low-frequency output signal. PLL demodulation provides a high reception quality and safety, but it was costly to the dissemination of specially designed integrated circuits.

From the output voltage of the FM demodulator is often simultaneously acquires a control voltage to the one tracks the oscillator of the receiver ( short Automatic Frequency Control, AFC) in order to keep the signal at the center of the passband of the IF filter and thus the distortion is low.

Characteristics of frequency modulation

Is defined as the modulation caused by the change in the carrier frequency with ΔfT (also called frequency sweep, or short stroke ), η change with the phase angle of the carrier and the ratio of the frequency deviation to the modulation frequency fs as ΔfT modulation index:

Where fS is the highest useful signal to be transmitted (bandwidth of the wanted signal ).

For the bandwidth of the frequency-modulated signal is approximately the Carson formula:

( η at a modulation index greater than 1 ).

Here, all spectral lines are detected to within 10 % of the amplitude of the carrier. There are thus 90 % of the spectral lines within the calculated bandwidth (bandwidth medium transmission quality ). Taking into account the spectral lines to 1 % of the carrier amplitude, the result ( also referred to as the Carson formula ), the bandwidth for high quality transmission, in which 99% of the spectral lines are in the range by:

( η at a modulation index greater than 1 ).

As a concrete example of the characteristics detailed the frequency-modulated FM radio is specified: It is operated, = 75 kHz and a cutoff frequency of the audio signal of fS = 15 kHz for mono programs with a frequency deviation ΔfT. This results in the FM radio, a modulation index η = 5 and a required bandwidth B10 % = 180 kHz on the FM band. If the FM stereo radio, including the data signal of the Radio Data System (RDS ), the baseband width is fs = 60 kHz and the required FM bandwidth at about 400 kHz. Adjacent FM stereo transmitter must therefore send offset by at least 400 kHz, so as not to interfere with each other.

Illustrating the frequency modulation

The first diagram shows a frequency-modulated signal and a dashed line, the information signal. The support, the 15 - times the frequency of the signal, the signal is a simple cosine. It can be seen that, where the instantaneous value of the voltage of the signal is the lowest frequency of the modulated signal is also at its lowest. During the zero passage of the information signal, the modulated carrier has the same frequency as the unmodulated carrier. The frequency of the information signal is dependent on how often it occurs per second to a change in frequency of the carrier. The amplitude of the signal is depending on how large the change in frequency (stroke) is. The more times per second, changes the frequency of the carrier, the greater the frequency of the information signal. The larger the stroke, the greater the amplitude of the information signal. The greater the amplitude or frequency of the information signal, the greater the bandwidth required.

In the second diagram, the variation of the frequency of the carrier is shown as a function of the above signal, the unmodulated carrier in broken lines. The third diagram shows the phase angle in radians of the carrier. The unmodulated carrier is shown in dashed lines. The phasors of the carrier rotates continuously, so the graph is also increasing with unmodulated signal. The solid line represents the phase angle of the modulated signal dar. but is not proportional to the instantaneous value of the signal voltage. and shifted by 90 °.

Frequency spectrum for frequency modulation

In a frequency-modulated signal occur lateral vibration at a distance of the signal frequency of the carrier frequency. Theoretically arise infinitely many oscillations page. Practically page vibrations of less than 10 % of the amplitude of the unmodulated carrier can be neglected, it is the Carson formula gives for the bandwidth. The height of each lateral vibration and hence the power distribution in accordance with one determined on the basis of a Bessel function of the diagram with the modulation index.

The equation for the individual components of the frequency modulation is:

The factors should also be read from the Bessel diagram at a given. In particular, the carrier or page vibration couples can disappear. On the basis of this is also seen that when the power ratio between carrier and side oscillations is unfavorable.

Since with increasing signal frequency decreases with frequency modulation due to high frequencies with frequency modulation in contrast to the phase modulation can be transferred worse, since the side oscillation components are getting smaller. Therefore, it is often used for FM modulation in front of the pre-emphasis to the signal, to increase the high frequencies, which is reversed with a de-emphasis in the receiver.

Context of frequency modulation and phase modulation

Frequency modulation and phase modulation are related mathematically closely. A phase modulation of a sinusoidal carrier you can very simply. First, the unmodulated carrier:

The term denotes the instantaneous phase. is the carrier angular frequency, is a constant, the phase at the time. We can as a function of time write the instantaneous phase.

Now, the instantaneous phase is changed by the addition of a modulator, this creates the expression for a phase modulation:

It refers to the modulation strength and the modulating function or short the modulator. According to:

It is seen that a phase modulation is mathematically very simple terms.

Frequency modulation requires, however, that the frequency changes constantly. This can no longer be expressed by a term of the form, but we need to introduce the concept of instantaneous angular frequency. The instantaneous frequency So in general, the time derivative of the phase function. This is the core of the relationship between frequency and phase modulation. Consider from this point once the phase of the unmodulated carrier:

The time derivative of is:

The newly introduced concept of instantaneous frequency therefore also includes useful the case of constant frequency. Frequency modulation is now demanding that the instantaneous frequency behaves according to the following rule:. For the calculation of the waveform at any given time, however, we do not require the current frequency, but the phase function. If the frequency is the derivative of the phase, it is vice versa, the phase is the integral of frequency:

In the example:

Thus we obtain for the frequency modulation following expression:

A direct comparison with the expression for the phase modulation is:

The interpretation of this fact will become clear in the following example. Set, then we obtain for the modulations: and. The phase is therefore for the phase modulation is still, for the frequency modulation is obtained. The instantaneous frequency of the phase modulation and frequency modulation. In both cases, modulation of the phase takes place. However, at the frequency of modulation, the modulator acts not directly on the phase one, but it is only the integral of the modulator to be expected. The integral has a low-pass effect. The phase becomes less so at the frequency modulation with increasing frequency of the modulator. Conversely, the frequency shift in the phase modulation becomes lower modulator frequency is always lower.

In typical analog oscillators RC or LC elements occur differential equations in which, for example, currents are integrated. Consequently, it always comes with the simplest means to a frequency modulation. A change in the manipulated variable changes while controlling the frequency and the phase only indirectly. A phase modulation, however, is similarly very difficult as most no direct access to the phase function is possible. With digital oscillators, both are possible in a simple manner, as there is direct access to the phasor.

Modulation gain, noise-limited sensitivity

Compared with an amplitude modulation (AM) has an FM demodulator modulating a profit - he rated the noise is less than the useful signal. With too low carrier -to-noise ratio ( CNR of Engl. Carrier to Noise Ratio), the FM loses this modulation gain. It occurs due to phase jumps errors in the determination of the instantaneous frequency, which manifest themselves in short spikes in the signal. This loss of the modulation gain begins below 12 dB CNR and results below 5.5 ... 9 dB CNR ( FM threshold ) to a strong deterioration of the reception.

The " Fischchenbildung " with analogue SAT receiver, for example, due to this problem.

Applying the frequency modulation

Wireless technology

FM allows a good quality, low-interference wireless transmission of radio programs. It is also used for the TV sound and often the radio. While the AM signal can not be completely separated from the noise by a narrow-band filter, it is the FM receiver in spite of the wide-band filter is possible to improve the quality significantly:

• The demodulator ( ratio detector Koinzidenzdemodulator PLL - demodulator ) is hardly influenced by fluctuations in amplitude
• Amplitude fluctuations are additionally reduced by a signal limiter ( limiter )
• The transmission power is consistently high
• Frequency response errors in the demodulation only give low non-linear distortion
• Interference in the same frequency range do not generate NF- interference
• Fading phenomena have little impact - the reception field strength may vary

Through the first application of the FM VHF radio were encountered mainly in English-speaking technically incorrect to equate the terms FM and FM.

Audio / Video Technology

The video signal on video recorders and hi-fi sound with video recorders is recorded frequency modulated. Analog satellite television is also frequency modulated.

Measurement

By periodically changing the frequency of a measuring generator ( sweep ) within a certain range, the transmission characteristic of an electrical component can be determined (e.g., band pass ), or an entire system. In this case, the amplitude response is plotted as a function of frequency. This process is also referred to as wobbling.

Television Technology

The sound channel is always transmitted frequency modulated on a separate carrier for analog television. The carrier frequency is 5.5 MHz ( CCIR) and 6.5 MHz ( OIRT ) next to the picture carrier frequency. In the receiver, the difference frequency is obtained by mixture of image and sound carrier frequency and demodulated after filtering as the FM broadcast. The TV standard SECAM uses FM to transmit the color information.

FM system for hearing impaired people

For audio transmission of radio and TV sound, and in classrooms and conference rooms, special FM - audio-systems for hard of hearing people to use.

Digital technology

Binary information may be transmitted by frequency shift keying method, and the like coded and over larger distances (for example, via telephone lines ).

Printing Techniques

Frequency modulated screening: screening method that works with very small dots of equal size. The image reproduction is achieved by varying density scatter of the points. Light image areas have little pixels, deep image areas more. In contrast, the classical amplitude-modulated grid controls the image display by varying the dot sizes and screen angle. FM screens allow photo-realistic halftone reproduction and a more detailed playback, even on printers with low resolution. Moiré effects can be avoided. Also the resolution of the documents may be lower than with amplitude modulated grids with comparable quality of expression. A " troubled " image can arise in smooth surfaces, homogeneous grid areas or gradients.

Electronic Music

Main article: FM synthesis

Frequency modulation (FM ) allowed even at the earliest analogue modular synthesizers ( around 1960 ) the production of complex sounds right. When you switch to digital technology, it was found later that it is much cheaper to use phase modulation (PM). This leads to a significant tonal difference: one reason was already mentioned above - it's the dwindling with increasing frequency modulator in FM phase deviation which, however, remains constant at PM. Thus, PM in the strength of the harmonic components remains constant even after a change of frequency modulator, which simplifies handling. The difficult to control in FM frequency deviations do not occur in PM, since there is no access directly to the frequency. This makes the programming of sounds by means of PM compared with FM for the musician much easier. However, a signal generated by PM vibrato with decreasing frequency is weaker.

Only for historical reasons, the term FM continued to be used, eg for the controller from Yamaha ( DX7, etc.).

Frequency modulations in the acoustic

Frequency modulation often determines the character of ensembles and musical instruments. For speakers, however, it is undesirable.

Sound body

Ensembles that have an extensive surface (eg, bells, gongs, pipes, plates, sheets ), often result from frequency-modulated self-oscillations:

A metal sheet has a certain stiffness that it trying to bend it opposes. By waveform this stiffness can be increased in one direction ( corrugated iron ).

Spreads a bending wave on a flat sheet from, arise and disappear such wave structures periodically. A perpendicular to this higher frequency wave (further) self-oscillation is now exactly in this rhythm, a stiffer or softer medium before; the frequency of this self-oscillation is thus modulated due to the resulting different propagation velocity in the rhythm of the bending shaft.

An example to which this can demonstrate both static and dynamic, is a hand- variable bent strip of spring steel (eg a large blade ), which is posted here.

Musical Instruments

Tailpiece of stringed instruments are frequency-modulated by changing their length or their tension. The former is applied when vibrato and glissando in the strings and the sitar, the latter also with the sitar, but especially for guitars. The string tension is changed by dragging them on the fretboard to the side or by moving in electric guitars of the tailpiece (see Tremolo (guitar) ).

Strings also possess an amplitude-dependent natural frequency, the sound comes with low string tension or large vibration amplitude especially in gut stringed violins and string instruments to bear.

Among other flutes at the tone frequency from the blowing pressure is dependent; can also be produced by a frequency modulation, comprising, however, an additional amplitude modulation ( tremolo ).

Speaker

Frequency modulation occurs in speakers that reproduce both high frequencies and low frequencies with high amplitude; a frequency modulation of the high frequencies produced in this case by which the rhythm of the low frequency on the receiver on and wegbewegende membrane (Doppler effect). The effect is undesirable and can be avoided by a two- or multi- way speakers.

Short name of FM species

• F1 - frequency modulation; a single channel, the quantized or digital information includes ( without the use of a modulating sub-carrier )
• F2 - frequency modulation; a single channel, the quantized or digital information includes (using a modulating subcarrier )
• F3 - frequency modulation; contains a single channel, the analog information