Analogue Modulation (FM)

COMM 1208 Unit 4 FM

1. Frequency Modulation...... 2 1.1 Frequency Deviation...... 2 1.2 Modulator Sensitivity...... 2 1.3 Modulation Index ...... 3 1.4 Power in an FM Signal and Noise Immunity...... 4 1.5 Rule to calculate BW of an FM signal...... 4 2. Radio Receivers...... 5 2.1 Introduction...... 5 2.2 TRF Receiver...... 5 2.3 Characteristics of a Receiver...... 6 3. Superheterodyning...... 6 3.1 Heterodyning...... 6 3.2 The Superheterodyne Receiver...... 6 3.3 Further Explanation on the Superheterodyne Receiver...... 7 3.4 Choice of Local Oscillator Frequency...... 8 3.5 Image Channel Interference...... 10 3.6 Further Explanation on Image Channel Interference...... 10 4. FM Stereo...... 11 4.1 Stereo Transmitter...... 11 4.2 Stereo Receiver...... 12 5. Relative merits of AM against FM...... 13 6. Frequency Bands...... 14

of 13 COMM 1208 Unit 4 FM

1. Frequency Modulation This also uses a sinusoidal carrier. The frequency of the carrier is made to change in accordance with the characteristics of the modulating (audio) signal. The nominal value of the carrier frequency is the frequency it has when the instantaneous value of the modulating signal is 0V. When the instantaneous voltage of the modulating signal is high the carrier frequency increases; when the instantaneous voltage of the modulating signal is low the carrier frequency decreases. The size of the change in the carrier frequency at any instant is proportional to the value of the modulating signal at that instant

1.1 Frequency Deviation The frequency deviation of the carrier from its nominal frequency at any instant is directly proportional to the level of the modulating signal at that instant. There is no inherent limit to the maximum amount of frequency deviation. (Remember with AM there is a limit to the amount of amplitude deviation, which occurs when the modulation index m = 1.) However a transmitting station will have a frequency band which it has been allocated and it must ensure that the frequency deviation never goes outside of this band. The maximum allowed frequency deviation is also called the rated system deviation = fd. A symbol for frequency deviation is F. Remember that at different times the frequency deviation can be positive or negative. The frequency swing is defined as the difference between the maximum and the minimum frequencies output = 2 * F.

1.2 Modulator Sensitivity This is a measure of how great an output frequency deviation is produced by a given amplitude of input signal. Its value will be fixed for any given modulator. If an incoming voltage of V causes a frequency deviation of F then the sensitivity is Sensitivity = Hz per Volt.

Example: An audio signal has an amplitude of 3.5 V and frequency modulates a carrier of 100 MHz. It causes the frequency to swing from 99.975 MHz to 100.025 MHz. What is the sensitivity of the modulator? Answer: The positive peak of the modulating signal (3.5V) causes the carrier frequency to go from 100.00 to 100.025 MHz. This is a deviation of 0.025 MHz or 25 kHz. The sensitivity is 25,000/3.5 = 7,140 Hz/V or 7.14 kHz/V.

Example: A frequency modulated system has a sensitivity of 4 kHz/V and a rated system deviation of 30 kHz. What is the maximum allowed modulating signal voltage? Answer: Use the equation: Sensitivity = Hz per Volt. This gives V = F / Sensitivity Using the maximum value of F = 30 kHz and Sensitivity = 4 kHz/V gives the maximum value of V as 30 kHz / 4 kHz/V = 7.5 V.

Example: An FM system has a rated system deviation of 75 kHz, produced by an input signal of 10 V. What is the sensitivity of the modulator and the frequency deviation produced by a 2 V signal. Answer: Sensitivity = 75 kHz / 10 V = 7.5 kHz/V Deviation = 7.5 kHz/V * 2 V = 15 kHz

1.3 Modulation Index  This is NOT the same as the modulation index for AM. It is a pure number defined as  = = The modulation index for FM can have any value, i.e. it can be less than or greater than 1. The modulation index can be expressed in a number of ways e.g.  = = =

Example: A 100 MHz carrier is frequency modulated by a 10 V peak to peak signal of 10 kHz. The instantaneous carrier frequency varies between 99.95 and 100.05 MHz. Calculate: the modulator sensitivity, the modulation index. Answer; Frequency deviation = 100.05 - 100 MHz = 50 kHz. This is caused by a 10 V signal. Therefore sensitivity is 50/10 kHz/V = 5 kHz/V The modulation index is 50 kHz / 10 kHz = 5.

Example: What will be the new value for the frequency and modulation index if the modulating signal is changed to one of 6 V peak to peak and frequency 8 kHz. Answer: The sensitivity has already been found to be 5 kHz/V. The new frequency deviation is therefore 5 kHz/V * 6 V = 30 kHz. The modulation index is Frequency deviation/Modulating frequency = 30 kHz / 8 kHz = 3.75

1.4 Power in an FM Signal and Noise Immunity The amplitude of an FM signal does not vary. Therefore the power in an FM signal is constant and is always equal to the power of the unmodulated carrier. The power does not depend in any way on the modulation. (Unlike AM). Every transmitted signal picks up noise between the transmitter and the receiver. Usually this noise adds to the amplitude of the signal. In the case of an AM signal the function of the radio receiver is to recover the envelope of the signal as this should be an exact copy of the original audio input. If noise changes the amplitude of the signal then the shape of the envelope has changed and the radio receiver will recover the noise - it will reproduce this as part of the audio signal. The noise will appear in the audio output. AM is susceptible to noise. In the case of FM the radio receiver does not depend on the amplitude of the envelope to recover the audio signal. If noise has changed the amplitude then the receiver will be able to ignore this. The noise will not be passed on to the audio output. FM is much less susceptible to noise than AM, it permits a much more accurate reproduction of the original audio signal.

V 2 2 R

1.5 Rule to calculate BW of an FM signal A quick way to estimate the bandwidth (BW) of the FM signal is: BW = 2 (frequency of modulating signal + frequency deviation)

= 2 ( fm + F)

= 2 ( 1 + F/fm) * fm

= 2 ( 1 +  ) * fm The expressions in bold are used in practise. This is known as Carson’s Rule.

Example: A radio station wishes to use an audio signal containing frequencies up to 15 kHz (for Hi-Fi reproduction of music) to frequency modulate a carrier. The rated system deviation is 75 kHz. What will be the bandwidth of the modulated signal? Answer: Using equation 1 the bandwidth will be BW = 2( 15 kHz + 75 kHz) = 180 kHz. Equations 2 and 3 will give the same result. (Try them)

The spacing between FM transmitters in the VHF band is normally 200 kHz

If  is much less than 1.0 then the bandwidth will be 2 * fm. This is the same as for AM If  is much greater than 1.0 then the bandwidth will be 2 * f. It should be noted that the bandwidth is always greater than the frequency swing. Any FM transmitter has to be designed to cater for the maximum level and frequency of modulating signal which are likely to occur so that the output bandwidth required is Output Bandwidth = 2 * (Maximum modulating frequency + Maximum allowed frequency deviation)

Example: Speech is incorporated into a TV channel as an FM signal. If the maximum allowed frequency deviation is 25 kHz and the maximum modulating frequency is 15 kHz, what is the modulation index and the bandwidth of the output FM signal Answer: Modulation index = frequency deviation/modulating frequency = 25 kHz/15 kHz = 1.67 Bandwidth is 2 (modulating frequency + frequency deviation) = 2 (25 kHz + 15 kHz) = 80 kHz

2. Radio Receivers

2.1 Introduction A receiver picks up an electromagnetic radio wave, converts it to an electrical current or voltage and recovers the wanted signal (which contains all the signals broadcast plus noise). It has an antenna (or aerial) to convert the electromagnetic waves into electrical current, coupled to the receiver through an antenna circuit - simply a wire or a more complex system. It is necessary to be able to select the desired frequency (or station). This is done by the tuner which can be a BPF with a variable centre frequency. The signals picked up by the antenna are weak and must be amplified for the information to be easily removed from the modulated wave. This RF Audio Tuner Detector Loudspeaker amplification can be done before the tuner, after the Amplifier Amplifier tuner or both. In the diagram the amplification is done after the tuner by the RF amplifier. The information can now be detected (i.e. demodulated). The resulting signal which should be a scaled replica of the original audio signal, is amplified by an audio amplifier and then fed to a loudspeaker. The above simple description of a TRF receiver holds for AM, SSB and FM. The tuned radio receiver and the superheterodyne receiver are two practical receivers. The superheterodyne receiver is the most commonly used because of its many advantages over the TRF receiver. But the TRF receiver will be discussed as it is simpler and because the reason for the overwhelming popularity of the superheterodyne receiver is clear after the shortcomings of the TRF receiver are shown.

2.2 TRF Receiver The simplest type of TRF receiver is shown here. The resonant frequency of the tuned circuit can be changed by Antenna adjusting capacitor C so the desired station can be selected. The diode to D, capacitor C and headphones are a simple diode detector (the Headphones headphones have an internal resistance R through which the capacitor D can discharge between peaks of the input AM wave form). The AF C output power can be increased if an AF amplifier is added Further increase in the output power delivered by the receiver can be achieved if a second and third stage of AF gain are used but the output signal to noise ratio would be rather poor.

The above receiver lacks both selectivity and sensitivity. Also harmonics produced within the

Ganged detector stage could radiate from the aerial. One method of overcoming these problems and also RF in RF out increasing the AF power output is to employ radio- to Demodulator frequency (RF) amplification between the antenna and the detector circuits.

2.3 Characteristics of a Receiver The five basic characteristics that determine the quality of a receiver are 1. SELECTIVITY The ability to reject adjacent unwanted signals. The spacing between the carrier frequencies allocated to different transmitters is limited by the available frequency spectrum. e.g. 9 kHz for broadcast in the medium waveband. The selectivity of a receiver is its ability to reject signals at carrier frequencies adjacent to the wanted carrier frequency. In the superheterodyne receiver see later) the selectivity is mainly determined by the gain versus frequency characteristics of the IF amplifier. The adjacent channel ratio is the ratio, in decibels of the input voltages at the wanted and adjacent channel signal frequencies necessary to produce the same output power. 2. SENSITIVITY The ability to receive very small signals and produce an output of satisfactory signal to noise ratio. Usually expressed as the minimum input signal (generally in micro

volts), modulated at 400 Hz required to produce 50 mW output power with a signal to noise ratio of 15 dB It is necessary to include a signal to noise in the measurement of sensitivity because it would otherwise be possible for the output power to consist mainly of noise.

3. SIGNAL TO NOISE RATIO The ratio of signal power to noise power: S/N = 10 log (Ps/ Pn). The signal is the desired signal and the noise is all other electrical signals, manmade or natural (noise is covered later). It is most desirable to have a high signal to noise ratio. 4. STABILITY The ability to remain tuned to a station once it has been set 5. FIDELITY The ability to preserve the exact shape of the information envelope of the carrier while the signal progresses through the receiver circuits

Example A receiver is tuned to a certain frequency at which an input voltage if 10 V produces an output power of 50 mW. If the signal voltage required at the adjacent channel to produce the same output power is 1 mV, find the adjacent channel ratio. Solution The adjacent channel ratio = 20 log[ 1 * 10-3 / 10 * 10-6) = 40 dB.

3. Superheterodyning

3.1 Heterodyning From Wikipedia, the free encyclopaedia. In telecommunications, physics, and radio astronomy, heterodyning is the generation of new frequencies by mixing two or more signals in a nonlinear device such as a vacuum tube, transistor, diode mixer, Josephson junction, or bolometer. The mixing of each two frequencies results in the creation of two new frequencies, one at the sum of the two frequencies mixed, and the other at their difference. A low frequency produced in this manner is sometimes referred to as a beat frequency. A beat frequency, or "beating," can be heard when multiple engines of an aircraft are running at close but not identical speeds, or two musical instruments are playing slightly out of tune. For example, a frequency of 3,000 hertz and another of 3,100 hertz would beat together, producing an audible beat frequency of 100 hertz. A heterodyne radio or infrared receiver is one which uses such a frequency shifting process.

3.2 The Superheterodyne Receiver The superheterodyne receiver ( superhet for short) is more practical than the TRF receiver because it provides better selectivity, sensitivity and stability. The basic principle if the superhet is illustrated in the block diagram below:

RF IF Audio Tuner Mixer Detector Loudspeaker Amplifier Amplifier Amplifier

Local AGC Oscillator A transmitted radio frequency signal is picked up by the receiving aerial and is selected by an RF stage. The RF stage, mixer and local oscillator have manually ganged tuned circuits for selecting a desired station. One of the functions of the RF stage is to couple the input signal to the mixer. The output of a self excited oscillator is also applied to the mixer. When selecting a station the frequency of the local oscillator tracks the frequency of the input signal in such a manner that there exists a constant frequency difference between the two signals. This frequency difference is known as the intermediate frequency (IF).

The frequencies which appear in the o/p of the mixer include the sum and difference frequencies. The sum frequencies are rejected and the difference or intermediate frequency is selected and amplified by a fixed tuned IF amplifier. The IF amplifier may consist of one or more amplifier stages. The process of mixing

of 13 COMM 1208 Unit 4 FM moves the signal from the RF carrier to a lower frequency IF carrier. The IF carrier still retains the modulation which was initially imposed on the RF carrier at the transmitter. The output of the IF transmitter is fed to a detector. The AF signal which results from detection is amplified by audio frequency amplifiers whose output activates the speaker. The superhet system is used in virtually all AM and FM receivers and also in TV and radar.

3.3 Further Explanation on the Superheterodyne Receiver From Wikipedia, the free encyclopaedia. In receivers using the superheterodyne principle, a signal at variable frequency is converted to a fixed lower frequency, , before detection. is called the intermediate frequency, or "IF". In typical AM (Medium Wave) home receivers, that frequency is 455 kHz; for FM VHF receivers, it is usually 10.7 MHz. Heterodyne receivers "mix" all of the incoming signals with an internally generated waveform called the local oscillator. The user tunes the radio by adjusting the set's oscillator frequency, In the mixer stage of a receiver, the local oscillator signal multiplies with the incoming signals, which shifts them all down in frequency. The one that shifts to is passed on by tuned circuits, amplified, and then demodulated to recover the original audio signal. The oscillator also shifts a "copy" of each incoming signal up in frequency by amount Those very high frequency "images" are all rejected by the tuned circuits (Filters) in the IF stage. Most receivers now use this method. The superheterodyne receiver principle overcomes certain limitations of previous receiver designs. Tuned radio frequency (TRF) receivers suffered from poor selectivity, since even filters with a high Q factor have a wide bandwidth at radio frequencies.

The diagram below shows the basic elements of a single conversion superhet receiver. In practice not every design will have all these elements, nor does this convey the complexity of other designs, but the essential elements of a local oscillator and a mixer followed by a filter and IF amplifier are common to all superhet circuits. Cost-optimized designs may use one active device for both local oscillator and mixer—this is sometimes called a "converter" stage.

The advantage to this method is that most of the radio's signal path has to be sensitive to only a narrow range of frequencies. Only the front end (the part before the frequency converter stage) needs to be sensitive to a wide frequency range. For example, the front end might need to be sensitive to 1–30 MHz, while the rest of the radio might need to be sensitive only to 455 kHz, a typical IF frequency. Only one or two tuned stages need to be adjusted to track over the tuning range of the receiver; all the intermediate-frequency stages operate at a fixed frequency which need not be adjusted. Sometimes, to overcome obstacles such as image response, more than one IF is used. In such a case, the front end might be sensitive to 1–30 MHz, the first half of the radio to 5 MHz, and the last half to 50 kHz. Two frequency converters would be used, and the radio would be a "Double Conversion Super Heterodyne"—a common example is a television receiver where the audio information is

of 13 COMM 1208 Unit 4 FM obtained from a second stage of intermediate frequency conversion. Occasionally special-purpose receivers will use an intermediate frequency much higher than the signal, in order to obtain very high image rejection. Super Heterodyne receivers have superior characteristics to simpler receiver types in frequency stability and selectivity. It is much easier to stabilize an oscillator than a filter, especially with modern frequency synthesiser technology, and IF filters can give much narrower passbands at the same Q factor than an equivalent RF filter. A fixed IF also allows the use of a crystal filter in very critical designs such as radiotelephone receivers which have exceptionally high selectivity.

3.4 Choice of Local Oscillator Frequency The IF is the difference between the wanted signal frequency and the local oscillator (LO) frequency. The LO frequency can be set either above, or below the wanted signal frequency. In practice however it is set higher than the signal frequency. The reason for this can be seen from the following example.

Example: Consider a receiver operating over the frequency range; 500 kHz to - 1500 kHz. If the LO is 465 kHz below the signal frequency then the oscillator frequency must vary from 35 kHz to 1035 kHz. This is a frequency ratio of 1035/35.1 or 29.6 to 1 and would require the use of a variable capacitor having a ratio of maximum capacitance to minimum capacitance of (29.6)2 to 1, or 874 to 1 . Such a large capacitance ratio could not be obtained with a single variable capacitor and would not be easy or cheap to achieve. If the LO is 465 kHz higher than the wanted signal then the local oscillator must vary from 965 kHz to 1965 kHz, a frequency ratio of 1965/965 to 1 or 2.04 to 1. This would require a capacitance ratio of (2.04)2 or 4.14 to 1. Such a capacitance ratio is easily obtained. It is therefore usual to make the LO frequency higher than the wanted signal frequency,

i.e. fLO = fs + fIF.

NOTE The sum frequency component of the mixer output (RF + LO) is not chosen for the IF because RF + LO is not constant - both increase at the same time.

3.5 Image Channel Interference There is always another frequency (apart from the signal) that will produce the intermediate frequency, no matter what frequency a superhet receiver is tuned to. This other frequency is called the image frequency.

The image signal has a frequency fim such that the difference between it and the local oscillator is equal to the intermediate frequency i.e. fIF = fim - fLO = fim - (fs + fIF) = fim - fs - fIF Therefore fim = fs + 2 fIF

The image signal is thus separated from the wanted signal by twice the intermediate frequency. The image signal must be prevented from reaching the mixer or it will produce an interference signal which, since it is at the intermediate frequency, cannot be eliminated by the selectivity of the IF amplifier. The RF stage must include a resonant circuit with sufficient selectivity to reject the image signal when tuned to the wanted signal frequency. Tuning is necessary because the wanted signal frequency and hence the image signal frequency, will vary. It is not difficult to obtain a resonant circuit with good enough selectivity to accept the wanted signal and reject the image signal when their separation is an acceptable fraction of the wanted signal frequency. The image rejection is less efficient as the signal frequency is increased because the fractional frequency separation becomes smaller. Any vestige of the image signal reaching the mixer will produce crosstalk at the output of the receiver. If a signal at a few kilohertz away from the image signal reaches the mixer, then the two IF signals will beat together to produce a whistle at the output of the receiver. The image response ratio is the ratio, in decibels, of the voltages at the wanted signal and image signal frequencies necessary at the receiver input terminals to produce the same audio output.

3.6 Further Explanation on Image Channel Interference From Wikipedia, the free encyclopaedia. (Called High-side and low-side injection)

The amount that a signal is down-shifted by the local oscillator depends on whether its frequency ( ) is higher or lower than That is because its new frequency is in either case. Therefore, there are potentially two signals that could both shift to the same one at and another at . One or the other of those signals has to be filtered out prior to the mixer to avoid aliasing. When the upper one is filtered out, it is called high-side injection, because is above the frequency of the received signal. The other case is called low-side injection. High-side injection also reverses the order of a signal's frequency components. Whether or not that actually changes the signal depends on whether it has spectral symmetry or not. The reversal can be undone later in the receiver, if necessary.

4. FM Stereo FM stereo broadcasts have been made since 1961. The essence of stereo is that there are two channels - one channel carrying the sound which would be heard by the left ear and the other to carry the sound to the right ear. One direct method of transmitting stereo is to have two transmitters and two receivers - one for each channel. This method is not used because  it uses too much equipment - 2 complete sets of equipment,  it requires two transmission bands in the limited bands available to commercial users,  the listener must tune into two receivers simultaneously - with only one receiver he loses half of the signal,  if there is any difference in the transmission or processing paths for the two signals, the signals will lose synchronism and lifelike stereo will not be received. A method is required so that  the two channels are transmitted by one transmitter and received by a single receiver  if the receiver can only receive one channel it should lose any of the information - the stereo signal must be compatible with monaural,  the left and right signals must not get out of synchronism.

RF oscillator L+R L L+R 30Hz -15kHz audio input pre adder delay rest FM (left) emphasis of modulator L transmitter

R audio input pre adder balanced (right) emphasis inverter adder L-R modulator 23-53kHz R -R L-R 19kHz pilot carrie r 38 kHz divide oscillator by 2 4.1 Stereo Transmitter A block diagram of a typical system which is used is shown in the diagram. The L+R channel contains the sum of the information in both audio channels i.e. all of the audio information. It passes straight through unchanged (a small delay is introduced to compensate for the time delay in the L-R signal as it passes through the inverter) and is used directly to modulate the RF carrier in the FM modulator. If a radio receiver is not capable of reproducing stereo it will merely need to demodulate this component to reproduce both channels of the audio signal as a single audio signal and output all the audio information in a single loudspeaker. The L-R contains the difference between the information in the two channels. This signal is moved into an inaudible frequency band in the range 23 kHz to 53 kHz, using the balanced modulator and a 38 kHz carrier. This channel is used by the receiver to reproduce the stereo signal. The frequency spectrum is as shown. Note that the 38 Pilot Suppressed sub-carrier kHz carrier is not transmitted. This is because there is sub-carrier a gap of only 60 Hz ( = 2 *30) between the top of the L + R lower sideband and the bottom of the upper sideband Audio L - R L - R so making extraction difficult at the receiver end. Lower Upper sideband sideband Instead a sub- carrier of 19 kHz ( = 38/2) is 0.03 15 19 23 38 53 freq (kHz) transmitted. This is in the centre of an unused band of frequencies from 15 kHz to 23 kHz and is easily extracted in the receiver.

4.2 Stereo Receiver

audio In the receiver the two receiver amplifier channels are L+R and L-R. These

Left are added and subtracted as in this 2L lowpass L + R Speaker de - diagram to produce the R and L delay adder filter emphasis audio channels which are passed on to each speaker. L - R L + R 23-53 kHz The 19 kHz sub-carrier pilot is from FM AM lowpass bandpass inverter adder receiver demodulator filter picked out of the received signal filter L - R -L + R and used to generate the 38 kHz 38 kHz 2R carrier to input into the AM 19 kHz demodulator - in this demodulator bandpass x2 de - filter emphasis a simple diode envelope detector Right Speaker can suffice.

audio amplifier

5. Relative merits of AM against FM

5.1.1 Why use AM?  Full wave envelope detection is easy and cheap. This is important when there are millions of receivers as in the case of domestic users.

 The bandwidth is narrow (2 * fm ). This is important for MW transmission because  the available bandwidth is small and  the same band can not be used over a very large geographical area  The bandwidth (and the output power of the transmitter) can be reduced by SSB methods (but complexity and cost of the receiver is increased). For portable transmitters and receivers power and size considerations are important but cost not so important as there will only be a small number of units.  Over the horizon reception is possible in the case of medium wave.

5.1.2 Why not use AM?  If the modulation index is greater than 1.0 the envelope does not follow the waveform of the modulation (intelligence) signal but is a distorted version of it.  If there is noise on the received signal it cannot be removed. Sound quality is not good on AM and it is mainly used now for speech rather than music.

5.1.3 Why use FM?  Noise on the received signal can be removed by limiting the level of the signal  A large modulation index is possible. This allows the peak levels of music or speech to be followed- important when trying to recover all frequencies and levels in music for hi-fi.

5.1.4 Why not use FM?

 Wide bandwidth is required ( = 2 fm ( +1) ). This is more than is available in medium wave and means that VHF is required to make the bandwidth available.  The transmitter and receiving equipment is relatively complex and expensive.

Use of VHF means that reception is possible only in line of sight of transmitter. Therefore the same frequencies can be re-used in relatively close locations, making it useful for local broadcast radio, services such as taxi etc. But for a national service a lot of transmitters are required. Each station is assigned 200 kHz 1/2 and there is often space for new stations. (Line of sight range = (2 * r * h + h * h) where h is the height of the transmitting aerial and r is the radius of the Earth = 6400 km.) If MW is used a single transmitter can serve an entire country. But there is the chance that there will be reception across a continent. The same frequencies cannot be re-used on the same continent. This means that the band is very limited. Each station is assigned 9 kHz and there is no space for more stations.

6. Frequency Bands Long Wave (Low Frequency) (LW) 30 kHz to 300 kHz Medium Wave (Medium Frequency) 300 kHz to 3 MHz Short Wave (High Frequency) (SW) 3 MHz to 30 MHz Very High Frequency (VHF) 30 MHz to 300 MHz Ultra High Frequency (UHF) 300 MHz to 3 GHz