Frequency modulation in detail
In this article, I will explain Frequency modulation in detail. Since frequency modulation has many advantages compared to amplitude modulation, so frequency modulation is widely used in transmission of signals.
In addition to the earlier amplitude modulation than other analog modulation, frequency modulation FM in communications technology a high priority. The information as to the modulation signal, in this case acts upon the frequency of the carrier signal and the amplitude of which can be changed. The FM is part of the angle modulation and is closely related to the phase modulation. The most prominent area of application for FM is the FM radio reception and event technology, it is the wireless microphones.
A simple method for generating the FM due to the interference components in the frequency-determining circuit of the carrier oscillator of the information signal. In the case of an LC oscillator, a parallel resonant circuit, so the capacity of a variable-capacitance diode (varicap), a condenser microphone can be added to or. Another possibility is the use of voltage controlled square wave or sawtooth generators which generate a synthetic sine signal with special diode circuits.
In a condenser microphone, the sound pressure changes the diaphragm spacing in the capsule and varies according to their capacitance value. The pn junction capacitance of a diode, a blocking zone is maintained at a DC bias voltage that has capacitive properties due to their charge distribution. An additional diode voltage applied to this information, the actual modulating signal changes the barrier width, without reducing them all. Again, the capacitance value of the information signal is directly dependent.
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The figure shows an oscillator circuit which operates in cooperation with the varicap as an FM modulator. The transistor is a basic fundamental circuit because the base has over 1 nF capacitor for the direct signal ground reference. The LC-generator corresponds to a Colpitts oscillator split-C and the positive feedback path through 2.2 k to the emitter. If we recall the AC equivalent circuit where seen between operating voltage and ground for the signal, a short circuit exists, it can be seen that the capacitance diode is connected in parallel to the LC resonant circuit and its frequency determined.
The graph represents the modulation characteristic; they were taken without AF signal by varying the diode reverse voltage. The linear working range between 15 and 26 V corresponds to a frequency of 35 kHz, which can be used for modulation.The FM modulation signal
For the circuit shown above, the oscillator or carrier frequency is approximately 125 kHz with a diode reverse voltage of 21V. If the entire linear characteristic region are utilized to modulate the amplitude of the low frequency signal can be up to 5 volts. When positive peak remains a diode reverse voltage of 16 V and the negative peak value of 26 V. The resulting two associated stroke frequencies of 108 kHz and 142 kHz are read from the characteristic curve.
It will be appreciated, a direct correlation between the low frequency amplitude and the frequency deviation. In modulating the volume of audio signals determines the frequency deviation. The following diagram illustrates these relationships for a large and small low-frequency signal amplitude. In FM modulation signal are continuously through all frequencies between the two limits. NF in the zero-crossing occurs, the unmodulated carrier frequency.
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Oscilloscope view is not realistic for the following frequency ratios between HF and LF were chosen in order to be able to show how represents an amplitude or frequency change of the AF signal in the FM signal. The carrier frequency is constant. The modulation index is proportional to the signal amplitude.
The left column shows that increases with increasing NF-amplitude represented by the blue curve, the frequency deviation. The stroke DELTA.F is the difference between the highest and lowest instantaneous frequency of the FM signal. The highest frequencies in the FM signal to be assigned to the low frequency range of the positive amplitude and the lowest value of the peak value of the negative half wave signal. The right column shows that when a constant amplitude signal, the frequency of change of frequency between maximum and minimum instantaneous frequency of the FM signal is directly related to the NF frequency. With an ever-flowing exchange rate between two limit values, the FM signal can not be described by a sine or cosine function.
the frequency deviation of the FM signal.
maximum and minimum instantaneous frequency of the FM signal.Frequency deviation
The FM signal is a symmetrical frequency range lying to the carrier frequency is run. With the two basic parameters of the frequency of the frequency deviation is calculated. It can be specified as peak deviation, which can be particularly clearly measured in a rectangular LF signal, since in this case only the two corner frequencies occur in the FM signal. For sinusoidal signals of the Effective Stroke can also be specified, which is smaller by a factor of v 2.Degree of modulation
In analogy to the amplitude modulation, a modulation degree can also be defined for the FM. It is to be understood as a measure of the relative change of the carrier signal f T. The modulation depth is not important and should not be confused with the important modulation index.Modulation index
The relationship between frequency deviation and signal frequency is called the modulation index and is a major in the frequency modulation size. As indicated above, the modulation index is proportional to the AF amplitude. To distinguish the degree of modulation of the characteristic letter , Greek eta, screw cap.Bandwidth
The following Fourier spectra that the bandwidth of an FM signal can be very large. It is greater than twice the frequency deviation in each case. In practice, one expects a finite bandwidth. All spectral components remain therein outboard of the FM spectrum with amplitudes less than 10% of the maximum amplitude involved. To the FM stereo FM signal transmission in the broadcasting sector, the bandwidth must be calculated according to the equation 2. With her first spectral less than 5% are neglected, so that the distortion in the received signal remains below 1%.
In FM radio (mono), the hub 75 kHz and low frequency signals are transmitted with a maximum of 15 kHz. The transmitter bandwidth is calculated according to equation 1 to equation 2 to 180 kHz and 210 kHz. A similar amplitude modulation would require only 30 kHz bandwidth. A frequency modulated signal having modulation at indices 1 a much higher bandwidth than a comparable amplitude modulation. Another side deals with the FM stereo broadcasting on the FM broadcast band.The Fourier spectrum of an FM
The spectra were created rinrm simulation program and the present there adjustable FM source. The Fourier analysis was carried out with the same frequency but different settings modulation indices.
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With a modulation index m= 0.5 is similar to the spectrum of the amplitude modulation. Symmetrically to the beam line, there are two spectral lines at a distance of information or modulation frequency. This frequency spacing does not match the frequency deviation, because it remains constant, while the stroke is greater amplitude dependent. The line frequency for the AF information is not available. In contrast to the AM to FM in line with the amplitude of the carrier to the modulation index changes. These small modulation indices can be calculated from the ratio n of the sum of the amplitude of the carrier line of the side lines value.
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With a modulation index m> 0,5 occur symmetrically to the carrier frequency to another side frequencies. They are available in fixed intervals of ± 2 × f N f, ± 3 × f N f ... ± n · f and Nf are called higher-order side frequencies. Their distance to each other is equal to the signal frequency. The frequency is also not readable in the spectrum. The amplitudes of the side lines vary depending on the modulation index. For m = 2.4 the amplitude of the carrier line is zero, and is no longer available in the FM signal. From the spectrum of the modulation index can not be determined. The bandwidth of the FM signal increases with a larger modulation index.
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If the modulation index is increased further, so does the number of side lines of higher order to continue. The amplitudes vary, but are generally smaller. The support line is absent once again present at m = 5.5. The modulation frequencies can be selected here, higher modulation indices for an undistorted FM signal not to.
The two stroke frequencies f min = f T and f max = f DELTA.F T + DELTA.F can only occur in the spectrum if they are random an integer multiple of the frequency information.Bessel functions and FM spectrum
The quite different behavior of the carrier amplitude and the frequency of pairs of side depending on modulation index is derived from the course of the Bessel functions. It is to understand a good knowledge of higher mathematics and the solution of differential equations ahead. But here is the result and the interaction with the FM frequency spectra are shown.
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From the course of the curve of the amplitude value J0 of the carrier frequency can be read depending on the modulation index. For m = 2.4, the carrier line is the first time no longer in the FM signal. Then they will return to again reach zero at 5.5 and later at 8.65.
The higher functions J1 from the amplitude values of the corresponding side line pairs are determined depending on the modulation index. Extend the Bessel functions in the negative, the amplitude values of the lateral line pair are also shown positive in the Fourier spectrum. Would you also represent the phase diagram, we find there a phase shift of 180 °.
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The graph shows the relation between the Bessel function and an FM spectrum. The spectrum was generated in the simulation program to the carrier frequency of 1 kHz and an amplitude of 1 V. The modulation was effected with a sinusoidal signal at f = 100 Hz with a modulation index m= 3.Advantages of frequency modulation
Disadvantages of frequency modulation
Furthermore, NF-high frequencies at the angle modulation (FM) can be transferred worse, since the phase shift is inversely proportional to the NF and thus the amplitude of the oscillation page pairs are smaller.