Amplitude modulation
The amplitude modulation (AM) is a modulation method in which the amplitude of a frequency total signal (consisting of the carrier frequency and sidebands ) to be transmitted, depending on the low-frequency ( modulating ) the useful signal is changed.
Low-frequency useful signals such as speech or music often can not be transferred directly over desired transmission media, such as a radio channel. To transfer the payload must be moved to a different frequency range, which can be accomplished for example by AM. By moving several useful signals can be transmitted simultaneously and without mutual interference.
- 7.1 Coherent demodulation
- 7.2 Incoherent demodulation
- 7.3 Multi-stage multiplicative demodulation
Historical
In the early days of broadcasting, there were good reasons to choose as AM modulation:
- The main reason was that you could build primitive recipients with obscure and poorly understood tools such as crystal detectors based on the principle of the envelope curve and required only a few components.
- There were no device or procedure by which one could generate a frequency modulated signal in the medium-wave band or demodulate.
It was accepted that in AM unnecessarily large amount of energy must be invested in the broadcast of the " carrier " while stuck only a maximum of 18 % of the transmission power in the information-bearing sidebands. Therefore, methods have been developed in the U.S. to reduce quieter modulation at the carrier power to save energy. As over the years the number of transmitters and - due to the increased sensitivity of the now invented superheterodyne receiver - The range has increased, it became apparent that some properties of AM were very disadvantageous:
- The bandwidth is twice as large as the maximum modulation frequency. To the medium-wave band to be able to assign many stations as possible frequencies, a channel spacing was introduced from 9 kHz and therefore taken a poor modulation quality in purchasing.
- With respect to the pitch slightly offset jammer to AM broadcasts, even from a distance can disrupt effective because annoying whistling interference occurs. This works away on shortwave over thousands of kilometers.
- An envelope detector is actually a synchronous demodulator, which does not generate the required local oscillator frequency and very low power, but this gets delivered from distant transmitters in phase. When it comes to selective carrier loss from a long distance, the demodulator provides an unusable signal.
- Thunderstorms and sparks from passing cars can interfere with AM reception, more than any other type of modulation.
From a state of the art AM is obsolete, because the quality requirements have increased and can be built much simpler, cheaper and more power -efficient devices with modern FM devices. For compatibility reasons, AM will probably not be replaced in the medium-wave band.
Spectral representation
The picture shows the effects of ( low-frequency ) modulation signal whose trace is shown on the left, to the transmitted frequency spectrum.
By the modulation signal produced symmetrical to the carrier frequency (English: carrier) two additional frequencies, the distance indicating the current modulation frequency. Any change is immediately reflected in the position of this companion frequencies with respect to the carrier frequency. If the modulation frequency varies for example between 300 Hz and 4000 Hz, a frequency band of the overall width of 8000 Hz is generated. Occupied the upper frequency range is known as USB (English: Upper Side Band ); The lower occupied frequency range is called LSB (English: Lower Side Band ).
Changing the amplitude ( " volume " ) of the modulation signal, will not affect the amplitude of the carrier, but only the amplitude of the satellite frequencies. In order to reduce this waste of energy at low modulation methods have been developed, and then temporarily reduce the strength of the carrier ( Dynamic amplitude modulation).
Applying the amplitude modulation
AM is used for:
- Broadcasting on the frequency bands long wave, medium wave, short wave
- Television, depending on the television standard used, see television signal
- CB radio
- Amateur radio (mostly in modified form as single-sideband )
- Air Navigation (ADF and VOR)
- Aeronautical radio ( civil - VHF 118-137 MHz, military - UHF)
- Chopper amplifier.
Mathematical Description
Subsequently, both the actual frequency f and the angular frequency ω are denoted by frequency. This is possible since the two are related by a constant factor. Nevertheless, one must note that both are still two different sizes. If numerical values , which is expressed in terms of the units: [f ] = Hz and [ ω ] = 1 / s
Obtaining a modulated signal to the useful signal if
A DC component added and then both with a high-frequency carrier wave multiplied with
With the help of the conversion formula
One obtains:
From the formula you can read the resulting frequency spectrum. The modulated signal containing the carrier
At the carrier frequency and amplitude, as well as two vibration frequencies with the side and with each of the amplitude. This is the simplest type of modulation of AM therefore also called double-sideband modulation ( DSB DSB or English ) with carrier. Here, the information is contained in the sidebands, while the carrier itself represents only unnecessary weight in the transfer. When changing the amplitude of the modulating oscillation, also the amplitude of the side frequencies change. When changing the frequency of the modulating signal, also the frequencies of the sidebands change.
In Figure 1 one can also see the two so-called envelope below next to the modulated signal. These are illustrative only, because their course is equal to the modulating information signal. In figure 2 one can see the three spectra (left ) of the modulated useful signal, the unmodulated carrier and the modulated signal. As can be seen, the amplitudes of the information-carrying sidebands are substantially smaller than that of the support (see, in this case, the amplitude modulation with a suppressed carrier, wherein the carrier signal is completely suppressed in the ideal case, that is ).
Alternatively, the calculation of the modulated signal in the time domain, this may be done using the Fourier transform in the frequency domain. To the inverse Fourier transform back into the time domain results.
Modulation depth
The degree of modulation is specified how strong the modulating information signal affects the amplitude of the modulated (carrier) signal.
With results for
It must be greater than 0 and less than or equal to 1 in order to demodulate incoherent can. At zero no modulation takes place, it will only transmit the unmodulated carrier. In an over-modulation takes place, the resulting signal can be demodulated only coherently without distortion. Therefore, often the amplitude of the modulating signal is limited in advance, in order to avoid an excessively large signal level.
Modulation trapezoid
The trapezoidal modulation the amplitude of the modulated signal (y - axis) against the amplitude of the modulating signal (x -axis) is applied.
With sinusoidal signals, thereby creating a trapezoid.
Depending on how large m, it can be like a normal trapezoid (0
If the phase is not constant or not a pure sine signal is present, is distortion of the modulation trapezoid, or it may bulge into a cylinder.
Vector representation
In the vector representation of the modulation components are plotted as a pointer and then assembled ( as in the case of forces ) to the resulting pointer. On the rigid support Ut are the two hands of the sideband frequencies USF1 and USF2, which rotate with the modulation frequency in opposite direction. As you can see in the pictures, the x components of the vector of the side frequencies are always opposite, and therefore cancel each other out in the addition. It is only the sum of the y - components, which are added to the carrier amplitude and is subtracted. Thus, the resulting momentary amplitude of the modulated signal is always in the same direction ( in phase) to the carrier amplitude. Which is characteristic of the double-sideband modulation. In amplitude modulation with suppressed carrier Ut missing. In addition, single-sideband either USF1 or USF2 lacking.
In the vector representation can be seen that the amplitude of high frequency sum signal (consisting of the carrier frequency and sidebands ) changes in the rhythm of the modulation amplitude of the carrier Ut but remains constant. This can be either a spectrum analyzer to prove or through a narrow-band bandpass filter (bandwidth <50 Hz), which can not be pass through the modulation.
Bandwidth
The example was very simple to be able to fundamentally understand the modulation. Practically doing a low frequency, so for example a single tone of constant strength to the carrier is modulated. In reality, much more consecutive frequency -modulated onto the carrier. This amount of frequencies from 0 to is called frequency band or baseband. The areas that arise after the modulation in addition to the carrier, called sidebands. There is an upper (OSB, in English, USB, upper side band ) and a lower (USB, LSB in English, Lower Side Band) sideband; together they form the bandwidth B.
When broadcasting a standardized frequency band of 4.5 kHz width is transferred ( from 0 Hz to 4.5 kHz) in the AM range for speech and music, which leads to a = 9 kHz bandwidth B. In the image signal of the television baseband extends to about 5.5 MHz.
Performance Considerations
The actual power output is in the side bands, wherein, in two side bands, the same information is contained, thus means that one sideband is completely superfluous, as is the carrier. This results in an efficiency.
With
R is any resistance, to which the power is obtained. Depending on how well m is selected between 0 % ( m = 0) and 17 % (m = 1).
Practical realization of the modulation
The useful signal is generally a mixture of frequencies (eg, language) that comes as a microphone from a NF- source. The carrier frequency itself is generated by an oscillator circuit.
The actual modulation is done in a mixer, for example a Gilbert cell, in which the desired signal is multiplied by the carrier wave. The output of the mixer according to the band -pass filtering the amplitude modulated signal is output which is finally passes through an RF amplifier to the antenna and transmitted as an electromagnetic wave to the receiver.
Special types of amplitude modulation
In order to save transmission power and / or bandwidth of the following modulation types have been developed:
- Amplitude modulation with suppressed carrier ( DSBSC, double sideband suppressed carrier)
- Single-sideband modulation ( SSB, single side band )
- Vestigial sideband modulation
- Dynamic amplitude modulation
The increased effort in the demodulation restricts the usability an often.
Digital methods allow low susceptibility to faults or greater use of the spectrum:
- Quadrature amplitude modulation (QAM)
- Pulse amplitude modulation (PAM).
Demodulation
Coherent demodulation
The receiver has a local carrier which is in phase with the carrier of the received signal. Both are thus synchronous to each other and thus coherent. The generation of this local support is technically very complicated, which is why the method is applied only at extremely weak or highly disturbed signals. For the mathematical description of the demodulation is quite simple. First, the received signal consisting of the two side and the carrier frequencies, multiplied by the local carrier:
Using the addition theorems
One obtains:
Then the unwanted high frequency components () are filtered with a low pass and the DC component with a high pass, which only the desired user signal with half the amplitude remains:
Incoherent demodulation
This simplest form of demodulation does not require the costly generation of a local carrier and therefore allowed a hundred years ago, the distribution of broadcast transmitters. The process can be used only with sufficiently strong signals and normally requires a preceding amplifier. Here, the searched frequency band is filtered with a bandpass filter, then rectified and smoothed by a diode at the end with a low pass. The DC component present is optionally removed with a high pass.
Due to the simplicity of this method, the received signal can be easily disturbed by distortions. Practical implementations of this method represent the envelope detector and the detector receiver dar.
See also:
- Grid rectification
- Anode rectification
- Cathode rectification
Multi-stage multiplicative demodulation
Performed - First, with a tunable to the carrier frequency fT lightly damped resonant circuit has a narrow bandwidth gain ( bandpass ) of the desired frequency range ( fi fi fT max to max fT ). Then, depending on the available technology, the modulation performed at lower frequencies in n stages. Thus, for each stage, a modulator followed by a low pass filter. The modulator itself is like at the transmitter, a multiplier. In this example, for simplicity, there is only one ( n = 1) modulator. The time required for the modulator carrier frequency in the receiver RTD should as much as possible of the transmitter carrier frequency fT match, otherwise a beat produced. The readjustment of RTD effected today by a PLL ( phase locked loop).
Result of the channel: m1 = 220 kHz and fm2 = -240 kHz; fT = 230 kHz ( Phase sign shown)
In the receiver, assuming fT = RTD:
Resulting in the above data, the frequencies obtained: -10 kHz; 450 kHz; -10 KHz; -470 kHz
All frequencies above 10 kHz can now be simply a low-pass filter out.
In reality, it is hardly possible to take the carrier frequency of the transmitter sufficiently accurate. To get an idea of the required accuracy, here is an example: A beat of 50 Hz corresponds to a frequency deviation of 0.02 %, based on 230 kHz. To enable as many problems of analog technology ( needs to be adjusted, electronic components age ) to go out of the way and minimize space requirements, is increasingly placed on digital signal processing. In principle, is digitized by a high-speed analog -to-digital converter directly the received signal into sine and cosine component. The rest is done by calculation from the signal processor.
Abbreviations
- A1 - Amplitude
- A2 - sounding telegraphy
- A3 - amplitude modulated transmission of analog signals (eg speech and music )
Amplitude modulation in the electromagnetic compatibility
In the field of electromagnetic compatibility amplitude modulated signals are used as noise immunity at times. Here, two different references to the corresponding unmodulated signal can be used. If one of the reference level of the modulated signal to its peak value fixed, we speak of downward modulation. If you put the other hand, the reference level at the zero crossing of the modulated low-frequency useful signal fixed, we speak of upward modulation. As a useful signal is a sine wave at 1 kHz, used alternatively in rare cases with 400 Hz or 1 Hz. The modulation depth of the interference signal is 80 % as a rule, so that the peak value of an upward modulated interference signal is 1.8 times the reference level.
For tests in accordance with the basic standards EN 61000-4-3 and EN 61000-4-6 ( immunity to radiated or conducted electromagnetic fields) upward modulated interfering signals are used. For tests according to ISO 11451 or ISO 11452 (Road vehicles - Electrical disturbances by narrowband radiated electromagnetic energy, road vehicles or components ) down -modulated noise. Above 800 MHz of the two ISO standards, however, are usually used in the field of pulse-modulated interfering signals, whereby the same peak value of the noise signal is achieved by down-modulating the AM in both types of modulation.