Modulation is the process of modifying the characteristic of one signal in accordance with some characteristic of another signal.

In most cases, the information signal, be it voice, video, binary data, or some other information, is normally used to modify a higher-frequency signal known as the carrier.

The information signal is usually called the modulating signal, and the higher-frequency signal which is being modulated is called the carrier or modulated wave.

The carrier is usually a sine wave, while the information signal can be of any shape, permitting both analog and digital signals to be transmitted. In most cases, the carrier frequency is considerably higher than the highest information frequency to be transmitted.

4.2 Amplitude Modulation (AM)

Amplitude modulation is the process of changing the amplitude of a relatively high frequency carrier signal in proportion with the instantaneous value of the modulating signal (information).

The carrier frequency remains constant during the modulation process but that its amplitude varies in accordance with the modulating signal. An increase in the modulating signal amplitude causes the amplitude of the carrier to increase. Both the positive and negative peaks of the carrier wave vary with the modulating signal. An increase or decrease in the amplitude of the modulating signal causes a corresponding increase or decrease in both the positive and negative peaks of the carrier amplitude.

If you interconnect the positive and negative peaks of the carrier waveform with an imaginary line, then you re-create the exact shape of the modulating information signal. This imaginary line on the carrier waveform is known as the envelope, and it is the same as the modulating signal.

Amplitude modulation that results in two sidebands and a carrier is often called double sideband amplitude modulation (DSB-AM).

In its basic form, amplitude modulation produces a signal with power concentrated at the carrier frequency and in two adjacent sidebands. Each sideband is equal in bandwidth to that of the modulating signal and is a mirror image of the other.

Amplitude modulation is inefficient in terms of power usage and much of it is wasted. At least two-thirds of the power is concentrated in the carrier signal, which carries no useful information; the remaining power is split between two identical sidebands, though only one of these is needed since they contain identical information.

4.2.1 Mathematical Representation of AM

Suppose we wish to modulate a simple sine wave on a carrier wave. The equation for the carrier wave of frequency fc, taking its phase to be a reference phase of zero, is

The equation for the simple sine wave of frequency fm (the signal we wish to broadcast) is

Amplitude modulation is performed simply by adding vm(t) to Vc. The amplitude-modulated signal is then

The formula for vam(t) above may be written

The broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from fc, known as sidebands. For the sinusoidal signals used here, these are at fc + fm and fc − fm. As long as the broadcast (carrier wave) frequencies are sufficiently spaced out so that these side bands do not overlap, stations will not interfere with one another.

4.2.2 Modulation Index of AM

A measure of the degree of modulation is m, the modulation index. This is usually expressed as a percentage called the percent modulation.

Modulation index is simply the ratio of the modulating signal voltage to the carrier voltage.

The modulation index should be a number between 0 and 1.

If the amplitude of the modulating voltage is higher than the carrier voltage, m will be greater than 1. This will cause severe distortion of the modulated waveform. Here, a sine wave information signal modulates a sine wave carrier, but the modulating voltage is much greater than the carrier voltage. This condition is called overmodulation. For overmodulation, the waveform is flattened near the zero line. The received signal will produce an output waveform in the shape of the envelope, which in this case is a sine wave whose negative peaks have been clipped off.

By keeping the amplitude of the modulating signal less than the carrier amplitude, no distortion will occur.

The ideal condition for AM is where Vm = Vc or m = 1, since this will produce the greatest output at the receiver with no distortion.

In the time domain, the degree of modulation for sinusoidal modulation is calculated as follows,

Since the modulation is symmetrical,

And

From this, it is easy to show that:

4.2.3 Amplitude Modulation Power Calculation

To communicate by radio, the AM signal is amplified by a power amplifier and fed to the antenna with a characteristic impedance, R.

The total transmitted power divides itself between the carrier and the upper and lower sidebands. This is expressed by the following equation:

The power in the sidebands depends upon the value of the modulation index. The greater the percentage of modulation, the higher the sideband power. Of course, maximum power appears in the sidebands when the carrier is 100 percent modulated. The power in each side band Ps is given by the expression:

One way to calculate the total AM power is to use the formula:

A common way to determine modulated power is to measure antenna current. Current in an antenna can be measured because accurate radio-frequency current meters are available.

If the carrier is modulated, the antenna current will be higher because of the additional power in the sidebands. The antenna current IT is:

The total AM power then is:

If the modulated and the unmodulated carrier antenna currents are known, the percentage modulation can be computed by using this formula:

Modulation by Several Sine Waves

In practice, modulation of a carrier by several sine waves simultaneously could happen.

Let V1, V2, V3, etc., be the simultaneous modulation voltages. Then the total modulating voltage Vt is:

The total modulation index would be:

If several sine waves simultaneously modulate the carrier, the carrier power will be unaffected, but the total sideband power will now be the sum of the individual sideband powers.

AM Transmitter Efficiency

AM transmitter efficiency,η:

If m=1, the AM transmitter efficiency is at the maximum.

Example 1

A 400 W carrier is modulated to a depth of 75 percent. Calculate the total power in the modulated wave.

Example 2

A broadcast radio transmitter radiates 10 kW when the modulation percentage is 60. How much of this is carrier power?

Example 3

The antenna current of an AM transmitter is 8 A when only the carrier is sent, but it increases to 8.93 A when the carrier is modulated by a single sine wave.

Find the percentage modulation.

Determine the antenna current when the percent of modulation changes to 0.8.

Example 4

A certain transmitter radiates 9 kW with the carrier unmodulated, and 10.125 kW when the carrier is sinusoidally modulated. Calculate the modulation index, percent of modulation. If another sine wave, corresponding to 40 percent modulation, is transmitted simultaneously, determine the total radiated power.

Example 5

The antenna current of an AM broadcast transmitter, modulated to a depth of 40 percent by an audio sine wave, is 11 A. It increases to 12 A as a result of simultaneous modulation by another audio sine wave. What is the modulation index due to this second wave?

4.2.4 Standard AM Transmitter

An AM transmitter can be divided into two major sections according to the frequencies at which they operate, radio-frequency (RF) and audio-frequency (AF) units.

The RF unit is the section of the transmitter used to generate the RF carrier wave.

The carrier originates in the master oscillator stage is generated as a constant-amplitude, constant-frequency sine wave. The carrier is not of sufficient amplitude and must be amplified in one or more stages before it attains the high power required by the antenna. With the exception of the last stage, the amplifiers between the oscillator and the antenna are called INTERMEDIATE POWER AMPLIFIERS (IPA). The final stage, which connects to the antenna, is called the FINAL POWER AMPLIFIER (FPA).

The second section of the transmitter contains the audio circuitry. This section of the transmitter takes the small signal from the microphone and increases its amplitude to the amount necessary to fully modulate the carrier. The last audio stage is the MODULATOR. It applies its signal to the carrier in the final power amplifier. In this way, intelligence is included in the radiated rf waveform.

4.2.5 Advantages and Disadvantages of Standard AM

The major advantage of the standard AM system is that it uses straightforward and inexpensive transmitting and receiving equipment.

However, it has several disadvantages. The three most important are as follows:

Power is wasted in the transmitted signal.

The transmitted signal requires twice the bandwidth of the transmitted intelligence.

Very precise amplitude and phase relationships between the sidebands and carrier are required.

4.2.10 Types of Radio Receivers

Various types of radio receivers have been proposed, but only two types have survived the test of time; the tuned radio frequency (TRF) receiver and the superheterodyne (superhet) receiver. Today only the superheterodyne is in general use, although the TRF may be found in some fixed-frequency applications.

4.2.10.1 The TRF Receiver

The figure shows a TRF or Tuned Radio Frequency receiver. The TRF receiver offers simplicity and high sensitivity.

The TRF receiver started with an antenna, usually a long wire strung outdoors.

Then came two or more RF tuned circuits, separated by RF amplifiers. These were called RF because they all amplified the actual radio frequency (RF) signal.

Eventually came a detector, which was simply a rectifier diode and capacitor.

This was followed by an AF amplifier, because it now amplified the audio frequency signal. The audio signal then went to a speaker.

One difficulty of the TRF was that, each time you wanted to change stations, you had to retune all the tuned circuits.

A second problem had to do with the actual physical construction of the radio. If two tuned circuits were too close to each other, the two inductors would act as a transformer. Some of the amplified signal from one of the later stages would get back into an earlier stage, only to be amplified again and again. The more the tuned circuits there were, the worse the problem became.

4.2.10.2 The Superheterodyne Receiver

The amplification in the superheterodyne circuit is provided in three separate sections: the RF section (extends from the antenna to the mixer), the IF section (goes from the mixer to the detector), and the AF section (extends from the detector to the speaker).

4.2.10.2 The Superheterodyne Receiver

In an AM superheterodyne radio receiver, the AM signal that operates in the 535 – 1605 kHz range is received by the antenna and coupled into a tunable-circuit RF section, which must be capable of tuning over the entire broadcast band.

The frequency-conversion section, more commonly called the mixer stage, where mixing (heterodyning) of the received RF signal and the LO signal occurs. Note that the RF, mixer and LO stages are ganged (interconnected) for simultaneous tuning.

The mixer circuit is tunable over the entire broadcast band, and it is tuned to the same frequency as the RF stage for any setting on the selector dial.

The LO is also a variable-frequency stage, the frequency of which is always fixed amount higher than the RF frequency of the other two ganged stages.

The output of the mixer stage is the difference frequency is a constant value because of the relation between RF and LO tuning.

For AM, the standard difference frequency is 455 kHz. It is still a radio frequency, but to distinguish it from the received RF signal, and because it lies between the original RF carrier and AF modulating frequencies, it is termed the intermediate frequency (IF). In the process, the modulating signal contained in the original carrier signal is converted from a higher region in the RF spectrum to a lower IF region.

The IF section is designed for optimum results at the single, fixed frequency of 455 kHz. For this reason, there is no tracking problem. It can contain any number of amplifier circuits. The IF section primarily determines the sensitivity and selectivity characteristics of the superheterodyne receiver.

The amplified IF signal is coupled to the detector where the original modulating information is recovered. The detected audio signal is coupled to suitable voltage and power amplifiers, and finally to the loudspeaker load.

4.2.11 SSB Transmitter

The figure below is the block diagram of a single-sideband transmitter.

4.2.11 SSB Transmitter

The audio amplifier increases the amplitude of the incoming signal to a level adequate to operate the SSB generator. Usually the audio amplifier is just a voltage amplifier.

The SSB generator (modulator) combines its audio input and its carrier input to produce the two sidebands. The two sidebands are then fed to a filter that selects the desired sideband and suppresses the other one. By eliminating the carrier and one of the sidebands, intelligence is transmitted at a savings in power and frequency bandwidth.

In most cases SSB generators operate at very low frequencies when compared with the normally transmitted frequencies. For that reason, we must convert (or translate) the filter output to the desired frequency. This is the purpose of the mixer stage. A second output is obtained from the frequency generator and fed to a frequency multiplier to obtain a higher carrier frequency for the mixer stage. The output from the mixer is fed to a linear power amplifier to build up the level of the signal for transmission.

In ssb the carrier is suppressed (or eliminated) at the transmitter, and the sideband frequencies produced by the carrier are reduced to a minimum. You will probably find this reduction (or elimination) is the most difficult aspect in the understanding of ssb. In a single-sideband suppressed carrier, no carrier is present in the transmitted signal. It is eliminated after modulation is accomplished and is reinserted at the receiver during the demodulation process.

4.3 Frequency Modulation (FM) Principles

Frequency modulation is the process of changing the frequency of the carrier signal as the amplitude of the modulating (information) signal varies. In FM, the carrier amplitude remains constant. Frequency modulation produces pairs of sidebands spaced from the carrier in multiples of the modulating frequency.

As the modulating signal amplitude varies, the carrier frequency varies above and below its normal center frequency with no modulation. The amount of change in carrier frequency produced by the modulating signal is known as the frequency deviation. Maximum frequency deviation occurs at the maximum amplitude of the modulating signal.

4.3.1 Phase Modulation (PM)

Phase modulation produces frequency modulation. Since the amount of phase shift is varying, the effect is changing as the carrier frequency is changed. Since FM is produced by phase modulation, the latter is often referred to as indirect FM. (FM is only produced as long as the phase shift is being varied.)

4.3.3 FM Sidebands and the Modulation Index

In FM and PM, sum and difference sideband frequencies are produced. In addition, a theoretically infinite number of pairs of upper and lower sidebands are generated. As a result, the spectrum of an FM/PM signal is usually wider than an equivalent AM signal.

From the spectrum of a typical FM signal, the sidebands are spaced from the carrier fc and are spaced from one another by a frequency equal to the modulating frequency fm.

As the amplitude of the modulating signal varies, the frequency deviation will change. The number of sidebands produced, their amplitude, and their spacing depend upon the frequency deviation and modulating frequency.

Although the FM process produces an infinite number of upper and lower sidebands, only those with the largest amplitudes are significant in carrying the information. Typically any sideband whose amplitude is less than 1 percent of the unmodulated carrier is considered insignificant. As a result, this markedly narrows the bandwidth of an FM signal.

4.3.3 FM Sidebands and the Modulation Index

4.3.3 FM Sidebands and the Modulation Index

The ratio of the frequency deviation to the modulating frequency is known as the modulation index mf.

Whenever the maximum allowable frequency deviation and the maximum modulating frequency are used in computing the modulation index, mf is known as the deviation index.

Knowing the modulation index, you can compute the number and amplitudes of the significant sidebands. This is done through a complex mathematical process known as the Bessel functions.

As you can see, the spectrum of an FM signal varies considerably in bandwidth depending upon the modulation index. The higher the modulation index, the wider the bandwidth of the FM signal.

The unmodulated carrier has a relative amplitude of 1.0. With modulation, the carrier amplitude decreases while the amplitudes of the various sidebands increase. With some values of modulation index, the carrier can disappear completely.

A Graph of the Bessel Coefficients

Bessel Functions Table

4.3.3 FM Sidebands and the Modulation Index

The total bandwidth of an FM signal can be determined by knowing the modulation index and the Bessel functions. The bandwidth can then be determined with the sample formula:

Narrowband FM (NBFM) is defined as the condition where mf is small enough to make all terms after the first two in the series expansion of the FM equation negligible. Narrowband Approximation: mf = fd/fm < 0.2.

An alternative way to calculate the bandwidth of an FM signal is to use Carson’s rule. This rule takes into consideration only the power in the most significant sidebands whose amplitudes are greater than 2 percent of the carrier. Carson’s rule is given by the expression:

4.3.3 FM Sidebands and the Modulation Index

In FM and PM, increasing the amplitude or the frequency of the modulating signal will not cause overmodulation or distortion.

Increasing the modulating signal amplitude simply increases the frequency deviation. This, in turn, increases the modulation index which simply produces more significant sidebands and a wider bandwidth.

For practice reasons of spectrum conservation and receiver performance, there is usually some limit put on the upper frequency deviation and the upper modulating frequency.

The maximum deviation permitted can be used in a ratio with the actual carrier deviation to produce a percentage of modulation for FM. The FM percentage of modulation is:

When maximum deviations are specified, it is important that the percentage of modulation be held to less than 100 percent. The reason for this is that FM stations operate in assigned frequency channels. These are adjacent to other channels containing other stations. If the deviation is allowed to exceed the maximum, a greater number of pairs of sidebands will be produced and the signal bandwidth may be excessive. This can cause undesirable adjacent channel interference.

4.3.3 Advantages and Disadvantages of FM

4.3.4 FM Transmitter

The figure below is a block diagram of an fm transmitter showing waveforms found at various test points. In high-power applications you often find one or more intermediate amplifiers added between the second doubler and the final power amplifier.

4.3.4 FM Transmitter

The following shows the block diagram of a frequency-modulated transmitter. The modulating signal applied to a varicap causes the reactance to vary. The varicap is connected across the tank circuit of the oscillator. With no modulation, the oscillator generates a steady center frequency. With modulation applied, the varicap causes the frequency of the oscillator to vary around the center frequency in accordance with the modulating signal. The oscillator output is then fed to a frequency multiplier to increase the frequency and then to a power amplifier to increase the amplitude to the desired level for transmission.

4.3.5 FM Receiver

The figure below is a block diagram showing waveforms of a typical fm superheterodyne receiver.

4.3.5 FM Receiver

The amplitude of the incoming signal is increased in the RF stages.

The mixer combines the incoming RF with the local oscillator signal to produce the intermediate frequency, which is then amplified by one or more IF amplifier stages.

The FM receiver has a wide-band IF amplifier. The bandwidth for any type of modulation must be wide enough to receive and pass all the side-frequency components of the modulated signal without distortion. The IF amplifier in an FM receiver must have a broader bandpass than an AM receiver.

There are two fundamental sections of the FM receiver that are electrically different from the AM receiver. These are the discriminator (detector) and the limiter.

In FM receivers, a DISCRIMINATOR is a circuit designed to respond to frequency shift variations. A discriminator is preceded by a LIMITER circuit, which limits all signals to the same amplitude level to minimize noise interference. The audio frequency component is then extracted by the discriminator, amplified in the AF amplifier, and used to drive the speaker.

4.3.6 Phase-Locked Loop Demodulator

The development of ICs has made the phase-locked loop (PLL) increasingly popular as an FM demodulator. The PLL offers many advantages over the other types of demodulator.

It requires no costly inductors or transformers, eliminating the need for intricate and time-consuming coil adjustments.

It provides excellent performance at low cost with a minimum of external components.

A basic PLL consists of a phase detector, a dc amplifier, an LP filter, and a voltage-controlled oscillator (VCO).

The VCO operates at the input frequency. The phase detector compares the input and VCO frequencies. The phase detector then develops an error voltage proportional to the amount and direction of the frequency difference. The dc amplifier increases the error voltage to a level needed to drive the VCO. The error signal is then coupled to the LP filter.

The filter sets many of the dynamic characteristics of the PLL. It determines the frequency range over which the loop will capture and hold its phase lock, and it determines the speed with which the loop will respond to variations of the input frequency.

The error voltage from the filter is used to control the VCO. For example, if the input frequency swings above fs (source frequency), an error voltage generated by the phase detector is amplified, fed to the filter, and applied to the VCO. The error voltage will cause the VCO frequency to increase in an exact lock with the input frequency. When the input signal is frequency modulated, the VCO tracks the FM deviation exactly, and the resulting error voltage is an exact reproduction of the intelligence signal.