Modulation

When audio signals are transmitted over thousands of kilometres through radio transmission, the audio frequencies that lie within the frequency range of 15 Hertz to 20 KiloHertz has very small signal power and thus cannot be transmitted via the antenna for communication purposes. The radiation of electrical energy is only possible at frequencies above 20 KiloHertz. The main advantage of high-frequency signals is that they can be transmitted over very long distances by dissipating very small power.

Thus, the audio signals must be sent along with the high-frequency signals for communication. This can be done by superimposing electrical audio signals on a high-frequency wave called the carrier wave. The carrier wave is generated from radio-frequency oscillators and is undamped in nature. Thus, when the audio-frequency signal is superimposed on a carrier wave, the resulting wave gets all the characteristics of the audio signal. The method of superimposing an audio signal over the carrier wave is called modulation.

After modulation is done, the resulting wave can be given to the antenna and the signal can be transmitted over a long distance.

的principle of Transmission and Reception

的speech or music that is to be broadcasted consists of a series of compressions and rarefactions. A microphone acts as a transducer to convert these parameters into its corresponding varying current measures. With the difference in the measure of sound, the corresponding change in the frequency of the electrical current is also produced, and they lie in the audio-frequency range and therefore, it is known as an audio-frequency signal. Since the signal strength of this low-frequency signal is less, it has to be given to an audio-frequency amplifier to strengthen the signal to a desired level.

这些低频信号不能直接从天线上辐射出来。因此，必须使用射频载波波调制音频频率信号。可以使用任何振荡器生产载波。射频波具有恒定的幅度，并以光速沿空间传播。这就是为什么您可以看到并听到实时广播的原因很少。

的resulting modulated wave is radiated out of the transmitter antenna and travels through space until it reaches the receiver antenna. The receiving aerial consists of a receiver that separates both the carrier signal and audio-frequency signal. The process of the receiver by which the audio frequency is separated from the carrier signal is called demodulation. The demodulated audio signal is sent to the loudspeakers for the user to hear. If there was no demodulation, the high-frequency currents would have reached the loudspeaker and would have caused signal errors. Radiofrequency current also cannot be heard by humans. This shows why modulation and demodulation are important in a communication system.

What is Modulation?

的best way to define modulation is:

的process of impressing low-frequency information to be transmitted on to a high-frequency wave, called the carrier wave, by changing the characteristics of either its amplitude, frequency or phase angle is called modulation.

Another definition for modulation is:

的process of altering the characteristics of the amplitude, frequency, or phase angle of the high-frequency signal in accordance with the instantaneous value of the modulating wave is called modulation.

载波的功能

的main function of the carrier wave is to carry the audio or video signal from the transmitter to the receiver. The wave that is resulted due to superimposition of audio signal and carrier wave is called the modulated wave.

Need for Modulation

下面列出了低频信号在长距离长距离传输的原因：下面列出：

1. 短的操作范围,当一波有一个很大的frequency, the energy associated with it will also be large. Thus low-frequency signals have less power that does not enable them to travel over long distances.
2. 辐射效率差 - 低频信号的辐射效率变得非常差。
3. Mutual Interference – If all audio frequencies are sent continuously from different sources, they would all get mixed up and cause erroneous interference air. If modulation is done, each signal will occupy different frequency levels and can be transmitted simultaneously without any error.
4. 巨大的天线需求 - 对于有效的信号传输，发送和接收天线应至少为1/4^thof the wavelength of the signal. Thus, for small frequencies, the antenna will have kilometres of length. But if the signal has the range of MegaHertz frequency, then the antenna size would be less. The carrier wave cannot be used alone for transmission purposes. Since its amplitude, frequency, and phase angle are constant with respect to some preference.

Types of Modulation

的正弦载波可以情商uation

v_c= V_cSin(w_ct + θ) = V_cSin(2f_ct + θ)

V_c– Maximum Value

f_{C -}Frequency

θ – Phase Relation

Since the three variables are the amplitude, frequency, and phase angle, the modulation can be done by varying any one of them. Thus there are three modulation types namely:

• Amplitude Modulation (AM)
• Frequency Modulation (FM)
  
• Phase Modulation (PM)

Click on the links given above to know more.

In India, radio broadcasting is done through amplitude modulation. Television broadcasting is done with amplitude modulation for video signals and frequency modulation for audio signals.

Amplitude Modulation (AM)

Definition

的method of varying amplitude of a high-frequency carrier wave in accordance with the information to be transmitted, keeping the frequency and phase of the carrier wave unchanged is called Amplitude Modulation. The information is considered as the modulating signal and it is superimposed on the carrier wave by applying both of them to the modulator. The detailed diagram showing the amplitude modulation process is given below.

As shown above, the carrier wave has positive and negative half cycles. Both these cycles are varied according to the information to be sent. The carrier then consists of sine waves whose amplitudes follow the amplitude variations of the modulating wave. The carrier is kept in an envelope formed by the modulating wave. From the figure, you can also see that the amplitude variation of the high-frequency carrier is at the signal frequency and the frequency of the carrier wave is the same as the frequency of the resulting wave.

Analysis of Amplitude Modulation Carrier Wave

让v_c= V_c罪_ct

v_m= V_m罪_mt

v_c– the Instantaneous value of the carrier

V_c– Peak value of the carrier

W_c- 载体的角速度

v_m– the Instantaneous value of the modulating signal

V_m– Maximum value of the modulating signal

w_m- 调制信号的角速度

f_m- 调节信号频率

It must be noted that the phase angle remains constant in this process. Thus it can be ignored. The amplitude of the carrier wave varies at f_m.

的amplitude modulated wave is given by the equation

A = V_c+ v_m= V_c+ v_m罪_mt = v_c[1+ (V_m/V_c罪_mt)]

= V_c(1 + mSin w_mt)

m -调制指数。的ratio of V_m/V_c.

振幅调制波的瞬时值由方程式给出

v = A Sin w_ct = vc (1 + m Sin w_mt) Sin wct

= V_c罪_ct + mVc (Sin w_mt sin w_ct)

v = V_c罪ct + [mV_c/2 COS（WC-WM）T - MVC/2 COS（WC + WM）T]

的above equation represents the sum of three sine waves. One with an amplitude of Vc and a frequency of w_c/2, the second one with an amplitude of mV_c/2and frequency of (w_c- w_m）/2and the third one with an amplitude of mV_c/2和一个频率（w_c+ w_m）/2.

In practice the angular velocity of the carrier is known to be greater than the angular velocity of the modulating signal (w_c>> w_m). Thus, the second and third cosine equations are more close to the carrier frequency. The equation is represented graphically as shown below.

Frequency Spectrum of AM Wave

Lower side frequency – (w_c- w_m）/2

Upper side frequency – (w_c+w_m）/2

的frequency components present in the AM wave are represented by vertical lines approximately located along the frequency axis. The height of each vertical line is drawn in proportion to its amplitude. Since the angular velocity of the carrier is greater than the angular velocity of the modulating signal, the amplitude of sideband frequencies can never exceed half of the carrier amplitude.

因此，原始频率不会有任何变化，而是侧带频率（w_c- w_m）/2和（w_c+w_m）/2will be changed. The former is called the upper sideband (USB) frequency and the later is known as lower sideband (LSB) frequency.

由于信号频率w_m/2is present in the sidebands, it is clear that the carrier voltage component does not transmit any information.

Two side banded frequencies will be produced when a carrier is amplitude modulated by a single frequency. That is, an AM wave has a bandwidth from (w_c- w_m）/2to (w_c+w_m）/2, that is, 2w_m/2or twice the signal frequency is produced. When a modulating signal has more than one frequency, two sideband frequencies are produced by every frequency. Similarly for two frequencies of the modulating signal 2 LSB’s and 2 USB’s frequencies will be produced.

的sidebands of frequencies present above the carrier frequency will be the same as the ones presented below. The sideband frequencies present above the carrier frequency is known to be the upper sideband and all those below the carrier frequency belong to the lower sideband. The USB frequencies represent the some of the individual modulating frequencies and the LSB frequencies represent the difference between the modulating frequency and the carrier frequency. The total bandwidth is represented in terms of the higher modulating frequency and is equal to twice this frequency.

Modulation Index (m)

的ratio between the amplitude change of carrier wave to the amplitude of the normal carrier wave is called Modulation index. It is represented by the letter ‘m’.

它也可以定义为载波波的幅度通过调制信号而变化的范围。

m = V_m/V_c

Percentage modulation, %m = m*100 = V_m/V_c* 100

的percentage modulation lies between 0 and 80%.

Another way of expressing the modulation index is in terms of the maximum and minimum values of the amplitude of the modulated carrier wave. This is shown in the figure below.

From the figure we know that

2 v_in= V_max- v_min

V_in=（v_max- v_min）/2

V_c= V_max- v_in

= V_max– (V_max-v_min）/2

=(V_max+ v_min）/2

Substituting the values of Vm and Vc in the equation m = Vm/Vc , we get

M = V_max- v_min/V_max+ v_min

As told earlier, the value of ‘m’ lies between 0 and 0.8. The value of m determines the strength and the quality of the transmitted signal. In an AM wave, the signal is contained in the variations of the carrier amplitude. The audio signal transmitted will be weak if the carrier wave is only modulated to a very small degree. But if the value of m exceeds unity, the transmitter output produces erroneous distortion.

Power Relations in an AM wave

A modulated wave has more power than had by the carrier wave before modulating. The total power components in amplitude modulation can be written as:

P_全部的= P_载体+ p_LSB+ p_USB

Considering additional resistance like antenna resistance R.

P_载体= [(V_c/√2)/ R]²= V²_C/2R

Each side band has a value of m/2 V_cand r.m.s value of mV_c/2√2。因此，LSB和USB的电源可以写为

P_LSB= P_USB= (mV_c/2√2)²/R = m²/4*V²C/2R = m₂/4 P_载体

P_全部的= V²_C/2R + [m²/4*V²C/2R] + [m²/4*V²C/2R] = V²_C/2R (1 + m²/2) = P_载体(1 + m²/2)

In some applications, the carrier is simultaneously modulated by several sinusoidal modulating signals. In such a case, the total modulation index is given as

Mt = √(m1²+ m2²+ m3²+ m4²+ …..)

If Ic and It are the r.m.s values of unmodulated current and total modulated current and R is the resistance through which these current flow, then

P_全部的/ P_载体=（it.r/ic.r）²=（IT/IC）²

P_全部的/ P_载体= (1 + m²/2)

IT/IC = 1 + M²/2

Limitations of Amplitude Modulation

1. Low Efficiency- Since the useful power that lies in the small bands is quite small, so the efficiency of AM system is low.
2. Limited Operating Range – The range of operation is small due to low efficiency. Thus, transmission of signals is difficult.
3. Noise in Reception – As the radio receiver finds it difficult to distinguish between the amplitude variations that represent noise and those with the signals, heavy noise is prone to occur in its reception.
4. Poor Audio Quality – To obtain high fidelity reception, all audio frequencies till 15 KiloHertz must be reproduced and this necessitates the bandwidth of 10 KiloHertz to minimise the interference from the adjacent broadcasting stations. Therefore in AM broadcasting stations, audio quality is known to be poor.