AM-AMPLITUDE MODULATION AND SSB-SINGLE SIDE BAND

A circuit consisting of two sine wave generators, G1 and G2, and two linear impedances, Z1 and Z2, shown in Figure 1. If the generators have the same frequency, the waveform at the ends of Z1 and Z2 are sinusoidal and have the same frequency as that of the generators, as shown in Figure 2. No new frequency will be created. The amplitude and phase in the resistors is determined by the relative values and types of impedances.

Figure 1.

If the two sinusoidal signal generators havE different frequencies, then the sum of instantaneous values will appear as a composite wave in resistors, as shown in Figure 3. To determine the waveform across each impedance, add the instantaneous voltages (caused by each generator). The type of impedance will determine the form of the composite waveform. Because the composite waveform is the sum of THE two sinusoidal signals, the composite waveform will contain only the two original frequencies.

Figure 2.

The conclusion is that linear impedances can change the complex waveforms, but not create new frequencies.

Figure 4 shows a circuit containing two sinusoidal signal generators (G1 and G2), a line impedance Z1, and a non-linear impedance Z2 in series. When a sinusoidal voltage applied to a circuit containing linear and non-linear impedance data, the voltages that developed in impedance have the form of complex waveforms.

Figure 3.

When two sinusoidal signals are applied to a circuit such as that shown in Figure 4, the non-linear impedance Z2 creates new frequencies. The composite waveform created by the non-linear resistor comprising from the following frequencies.

(1) The two fundamental frequencies of sinusoidal signals applied to the input of the circuit.

(2) The harmonics of the two fundamental frequencies.

(3) The sum of the fundamental frequencies.

(4) The difference between the two fundamental frequencies

(5) A DC voltage

The frequencies of sum and difference appear because the phase angle of the two fundamental frequencies are constantly changing. If the generator G1 produces a voltage of 10Hz and generator G2 produces a voltage at 11Hz, the waveforms that produced because of the non-linear impedance, will have the following frequencies.

(1) A sinusoidal signal at 10Hz

(2) A sinusoidal signal at 11Hz

(3) Harmonics of the 10 Hz and 11 Hz, (the higher the harmonic, the lower the amplitude of the harmonic). The harmonics of the signal of 10 Hz will have the following frequencies, 20, 30, 40Hz, etc, and the harmonics of the signal of 11 Hz will have the following frequencies, 22, 33, 44 Hz, etc. Note that some of the harmonics can not be produced.

(4) The sum of the 10 Hz and 11 Hz, i.e. 21 Hz.

(5) The difference between 10 Hz and 11 Hz, i.e. 1 Hz.

The most important point to understand is that when two or more signals are applied to a circuit containing a nonlinear element, then the output of the circuit we have sine signals that were not at the input. The application of two or more frequencies in a non-linear impedance element, leads to the production of new frequencies. This process also called heterodyned.

Figure 4. Generators sinusoidal waves with different frequencies, with linear and non-linear complex, resistors.

HETERODYNED CIRCUIT

Figure 5 shows a basic heterodyned circuit. The diode D1 serves as the non-linear component in the circuit. The generators G1 and G2 are signal sources of different frequencies. Notice that in Figure 5 the two generators connected in series. Any of the frequencies generated by the non-linear element can be selected using a tuning circuit in series with the diode. The primary of transformer T1, together with the capacitor forming a resonant circuit, which allows the passage of frequencies desired, and cleaves (effectively leading to ground) those frequencies which are not needed in subsequent steps.

Figure 5.

WIDTH CONFIGURATION

In amplitude modulation (Amplitude Modulation, AM) the width (range) of the carrier wave varies according to the width of the shaped signal. So, a modulated carrier wave amplitude has its frequency stable (unchanged) but the magnitude changes according to the instantaneous value of the amplitude of the modulated signal (e.g. audio signal). Figure 6 shows the carrier wave and the modulated wave. (Ie the result of modulation). The amplitude of the modulated wave varies between a maximum value, which is greater than the width of the non-modulated carrier wave, and a minimum value, which is less than the width of the non-modulated carrier wave.

Figure 6. Resulting amplitude modulation, sinusoidal signal of a single frequency.

As seen from the figure 6, the modulated wave is an envelope that follows the width of the wave formed. Notice that the negative and positive half of the modulated carrier wave have the same form, and for that they carry the same information. The amplitude modulated of a wave isbused in radio to transmit speech and music, for the transmission of still pictures, on TV, etc.

SIDEBANDS

The process of the amplitude modulation does not change only the amplitude of the carrier wave, but also produces some additional frequencies. The new frequencies used in amplitude modulation is the sum and difference of the frequencies of the carrier wave and the modulated wave.

We will see that when a sinusoidal carrier wave is formed across each frequency modulated signal (the modulated signal usually consists of many frequencies, eg. If a speech signal consists of a frequency range between 250Hz and 3000Hz) creates two frequencies in the modulated signal. A frequency below the carrier frequency and one above the carrier frequency. Namely, if the shaped signal is a sine wave of a single frequency (fm), then the modulated wave consists of 3 components, (3 frequencies). The frequency of the carrier wave fc, a component with a higher frequency than the carrier, called upper side frequency, and is equal to the sum of the frequency of the carrier wave is formed and a lower frequency than the wearer, called lower side frequency, and is equal [with the various frequencies u tc carrier and modulated wave, ie (fc-fm).

For example: If a carrier wave of 100 Khz is modulated of a sine wave 5KHz, then the process of amplitude modulation, produce three frequencies, fc = 100KHz, fc + fm = 105KHz and fc-fm = 95KHz. Usually it is easier to visualize a modulated wave with the aid of a frequency spectrum. In a range of frequency ranges, each frequency is represented by a vertical line on the frequency axis. The length of each line is proportional to the width of the frequency that represents the line. The spectrum in Figure 7 shows the frequencies generated by the modulation of a carrier wave of 100 KHz with a sine wave of 5KHz.

From the above example it can be seen that the transmitter must be able to radiate frequencies from fc-fm to fc+fm. Namely, the bandwidth required to transmit a modulated carrier wave is equal to the difference between the upper side frequency band and the lower side frequency.
In cases of the sine shaping frequency and with fc > fm, the bandwidth required is given by:

BW = (fc + fm) - (fc-fm) = 2fm

So, the band width is twice the frequency of the modulated signal. The necessary bandwidth in the previous example is:

BW = (fc + fm) - (fc-fm) = 2fm = 2fm = 10Khz. (where BW is the bandwidth)

If the shaped signal concist of two sine waves, and the highest frequency is f2 and the lowest frequency is f1, then in addition to the carrier frequency, the frequency f2 will create an upper side frequency, equal to the sum of the frequencies of the carrier and the f2, ie (fc + f2), and a lower side frequency, equals to the number of frequencies of the carrier without the f2, ie (fc-f2). The frequency f1 will create an upper side frequency, equal to the sum of the carrier frequency and f1, ie (fc + f1), and a lower side frequency, equal to the number of frequencies of the carrier without f1, ie (fc-f1 ). Notice that for each frequency modulated signal amplitude modulation process produces two components, a top side and a bottom side.

Figure 7.

A composite modulated signal as the signal of speech or music composed of many sinusoidal components (many sine waves), and for each frequency modulation process will produce an upper side and lower side frequency. If the highest frequency in the formed mark is fmax and the lowest frequency is fmin, then the frequency fmax will generate an upper side frequency (fc + fmax) and a lower side frequency (fc-fmax), the frequency fmin will generate a top side frequency (fc + fmin) and a lower side frequency (fc-fmin). Therefore, in this case, the formatting process will produce many more side frequencies (fc + f1) to (fc + f2), and many lower side frequencies (fc-f2) to (fc-f1). The band of frequencies below the frequency of the carrier wave, i.e. (fc - f2) to (fc - f1) called lower side band and the frequency band above the frequency of the carrier wave (io + i1) to (fc + f2) is called the upper sideband.

Figure 8.

That is, when the wave is formed consisting of many frequencies, such as a voice wave, then instead of only two side bands, have a plurality of components contained in the upper sideband and lower sideband. Usually the sidebands generated by a composite signal formed by depicted as shown in Figure 8.

BANDWIDTH OF AN AMPLITUDE MODULATED WAVE

An ideal carrier wave have one frequency and occupies a very small part of the spectrum. When the carrier wave is modulated by amplitude apear sidebands above and below the frequency of the carrier wave. The frequency range occupied by the modulated signal is much greater than that occupied by the carrier wave when it is formed. The frequency range occupied by the modulated signal called bandwidth. The bandwidth of a modulated wave depends on the frequencies included into the modulated signal. For example, when a carrier wave of 100KHz modulated by an acoustic wave of 5KHz, then are generated side bands at 95 and 105 KHz. This modulated signal requires a range of 10KHz in the frequency range. If the same carrier wave of 100KHz modulated by an acoustic signal of 10KHz, the sideband frequencies will occur at 90 and 110KHz and the modulated signal have a bandwidth of 20KHz. Notice that as the modulated signal increases in frequency, the bandwidth required for the modulated wave becomes larger.

The bandwidth of a modulated wave in width, is equal to 2f, where f is the highest frequency of the modulated signal applied at the time. Therefore, if a carrier wave of 400KHz is formed with 3 frequencies (3, 5 and 8KHz) simultaneously, then lateral frequencies will occur at 392, 395, 397, 403, 405, and 408KHz. This modulated signal extends from 392 to 408KHz and having a bandwidth of 16KHz. That is two times greater than the highest modulated frequency of 8KHz. From the above discussion we see that the bandwidth of a transmitter should be two times the highest frequency is formed.

For this reason the tuned amplifiers in the transmitters and receivers must be able to pass the entire bandwidth, and not only the frequency of the carrier wave, because the carrier wave does not contain any information of the signal that we wish to transmit or receive. The musical instruments produce complex sound waves that contain a large number of frequencies.

Figure 9. Frequency diagram for 3 adjacent channels.

The frequencies produced by a piano, for example, ranging from about 30 to 4,200Hz with harmonics extending beyond 10 KHz. Modulated frequencies up to 15KHz should be included in the signal to be transformed to receive music with a high degree of fidelity. This requires a bandwidth of at least 30KHz to prevent the attenuation of the harmonic frequencies. If the signal we want to send out (voice) contains only frequencies, and accuracy is of secondary importance, the required bandwidth is much smaller.

A good transmission of voice can be performed in the communication system that maintains the audio frequencies up to a few thousand hertz. The frequency range to be used for transmitting speech is less than that required to transmit music. When two stations are located near each other, the carrier waves must be separated by a minimum distance of the radio frequency spectrum. Otherwise, some of the frequencies of the sidebands of a station will be in the region emitting the lateral bands of the other station. That would be interference. The specified AM radio band starts from 535 KHz and reaches 1.605 KHz. Radio frequencies start out at 540KHz and rising at 10KHz until it reaches the upper limit of the broadcast. If all the carrier frequencies used by radio stations, the maximum bandwidth that can each station, is 10KHz. This leaves 5KHz on each side of the carrier to the side bands. Figure 9 shows a frequency diagram for 3 adjacent channels. Each channel has a range of 10KHz. In total we have 107 channels or channels (carrier frequencies) across the band. Because the interference between adjacent channels would be nearly impossible to avoid, usually we avoid giving adjacent carrier frequencies to stations in the same area. In this way there are one or more empty channels between two stations broadcasting in the same region, and thus allow a station to use modulated frequencies higher than 5 KHz long as it does not create hassles in other nearby stations.

Each sideband contains all the information we want to transmit. Notice that the lower sideband contains the same information contained in the upper sideband. Therefore, to send out the information is not necessary to send out both side zones, but only one sideband. But, when using the amplitude modulation must send out both two side bands as well as the carrier wave. In order to obtain the information contained in the amplitude modulated wave, it is necessary for all the tuned circuits of the transmitter and receiver to go outside of the carrier wave and two sidebands.

MODULATION DEPTH

Figure 10. Configuration interface for a fully configured wave (100% modulation). When M = 1, the maximum voltage of the formed wave should be equal to the maximum.

The degree of modulation (also called rate or modulation depth) is very important in amplitude modulation, because it determines the strength of the transmitted signal. The degree of modulation (M) expressed as the ratio of peak voltage (Em) of the formed wave (eg acoustic wave) by the peak voltage of the carrier wave (Ec), and is given by:

Where: M is the degree of modulation, Em the maximum peak voltage of signal formed, and Ec is the peak voltage of the carrier wave.

Note that instead of the peak voltage, we can use the voltage from peak to peak, or the rms value of the voltage.

For example, if a carrier wave has a maximum range of 200 volts and is formed by a sine wave of 3KHz with a maximum range of 100volts, the rate configuration is:

Usuallythe rate modulation is multiplied by 100 and expressed as a percentage. The percentage modulation ratio (% M) is given by:

The percentage modulation ratio (% T) for the above example is:

From the above formula, we see that the rate modulation is 1 (or 100%), then the cross-educates voltage is equal to the voltage of the carrier wave. From Figure 10 we see that the maximum configuration without a change in the form of the envelope is 1 (or 100%). Figure 11 shows the waveform of a modulated wave modulation factor 0.5 (or 50%). Notice that while the carrier wave varies according to the acoustic signal, the range of variation is now smaller than in the case of 100% modulation.

Figure 11.

The greater the change in the amplitude of the carrier wave, the more powerful the signal that carries the information. For this reason it is desirable that the configuration factor to be near to 1 (100% modulation).

The detector in the receiver responds only to changes of the carrier wave and not to the maximum width of the carrier. Therefore, when the carrier wave is formed only in a small degree, as shown in the figure, the audio signal will not be strong and can maybe be less than the noise. Therefore, the larger the depth of modulation (or the rate of modulation) the stronger will be the audio signal.

DEGREE OF MODULATION

When the modulated wave is displayed in an oscilloscope, and the degree of modulation is less or equal to 1 (less or equal to 100%), then we can use the following formula to calculate the degree of modulation:

Because THE Eo may be difficult to determin at the oscilloscope, the above formula can be written as:

Grades with the configuration-which a carrier wave can be configured are the 100% Modulation and the Overmodulation.

100% MODULATION AND OVERMODULATION

As we have reported, 100% modulation occurs when the amplitude modulation signal is equal to the width of the carrier wave (Vm = Vc). Namely M = 1. In a 100% modulation, the range voltage of a sideband is 0.5 of the voltage range of carrier. Note that when M = 1, the maximum amplitude of the modulated wave is twice the non modulated wave amplitude and the minimum is zero.

Figure 12. Overmodulation. In this case the voltage wave form is increased beyond the value required to produce 100% modulation.

If the width of the shaped signal is greater than the amplitude of the carrier wave, then we have the overmodulation. This means Vm > Vc and modulation factor is greater than one. Figure 12 shows the waveform of an overmodulation. When the maximum negative value of modulated wave is greater than that of the carrier, then the modulated carrier wave drops to zero and remains to zero during the whole time during this situation.

When the modulated carrier wave drops to zero, due to overloading, deformation or distortion is generated. So we have lost a part of the signal(Waveform) that carries information (speech signal, music, etc.). The loss of a part of signal that carries the information causes a significant distortion in the sound that we get from the loudspeaker. The degree of deflection depends on the degree of overmodulation. If you have a sine wave signal frequency, and you have overmodulation, then the modulated wave will not take the form of modulated wave (the wave carrying the information) is not longer a sine wave. such as the modulated wave, and as therefore will produce undesirable harmonic which are known as splatter (dispersion).

These unwanted frequencies will appear in the lateral zones, and will create Interference with other nearby stations. For the transmission of speech or music, overmodulation must avoided because it caused distortion in the surrounding, and distorted speech or music to the receiver. For these reasons avoid formation 100% in these transmissions, because the smallest increase in the voltage wave that is formed will immediately cause the overmodulation and Therefore deformation. Usually for voice transmissions or music they use a modulation of about 60 or 70%. Besides the above problems, the overmodulation causes also very high voltages and currents at various points inside the transmitter. Therefore, adequate protection against overload should be used, like switches (circuit breakers) and fuses. When the modulator is appropriate adjusted, the strongest transmission parts will produce 100% modulation, and more softly parts of the signal will produce lesser degrees of modulation. Note that the unmodulated carrier wave represents configuration 0%.

figure 13.

POWER IN MODULATED AMPLITUDES

The power in a modulated wave by amplitude IS divided between the carrier wave and the sidebands. The strength of the carrier is constant (except overmodulation) and thus the power of the sidebands is equal to the difference of power of the carrier wave and the total power of the modulated wave. i.e:

Where Psb is the power in both sidebands, the total power Pt, and the power Pc of the carrier wave.
The power in the sidebands can be calculated once we know the strength of the carrier wave and the degree of modulation. That is:

Where Rsb is the power in both sidebands.

For example, if the degree of modulation is 70% and the power of the carrier wave is 500 Watts, then we have:

Since the total power of the sidebands is twice the force of a side band, the power that is transferred from one side band is given by the relation:

Where Psf is the power in one sideband.
So with these values, we obtain:

If the power of the carrier wave and the degree of modulation are known, then the total power can be calculated using the following formula:

By using the same values we get:

BLOCK DIAGRAM OF A SIMPLE AM TRANSMITTER

Figure 13.

A block diagram of a simple AM transmitter shown in Figure 13. An AM transmitter consists of two main parts according to the frequency in which it operates, the Board radiofrequency (RF) and audio frequency section (AF). The RF section is used to generate the carrier wave. The oscillator, amplifier (buffer), and the power amplifier used as a transmitter CW. The carrier wave is sinusoidal, have constant amplitude and frequency and is being produced in the oscillator part.

The strength of the carrier wave that produced by the main oscillator is not high enough to drive the final power amplifier and must reinforced in one or more steps before obtaining the power required at the antenna. Except for the last step, the amplifiers lying between the oscillator and the antenna are called intermediate power amplifiers. The final amplifying step associated with the antenna, is called final power amplifier (linear amplifier).

The second part of the transmitter is the audio section frequencies (AF). The microphone converts an acoustic signal (voice signal) into an electrical signal (converts acoustic energy into electrical energy). The amplifier amplifies the low frequency audio signal, and the modulator further enhances the acoustic signal in the appropriate range required to form fully the carrier wave. The output signal of the modulator is applied to the power amplifier. The carrier wave (RF) modulated wave and the power amplifier are combined to produce the lateral modulated carrier wave that we want to send out to the antenna.

BLOCK DIAGRAM OF BASIC AM RECEIVER

Figure 14.

One of the main processes of a receiver (Figure 14) is to enhance the modulated frequency transmitted by the transmitter and receive by the antenna of the receiver. An AM receiver processes the AM signals received by the antenna, and gives a signal output which is a reproduction of the signal initially formed in the carrier wave transmitter. The signal can then be applied to a playback device, such as a loudspeaker. Actual AM receivers vary widely in complexity. Some are very simple others containing a large number of complex circuits.