1 Frequeny Modulation (FM) Tutorial Lawrene Der, Ph.D. Silion Laboratories In. Introdution Edwin H. Arstrong, known as one of the founding fathers of radio tehnology, invented the superheterodyne radio reeiver in 1918 and frequeny odulation (FM) in 1933 . These two onepts, along with his regenerative iruit tehnique developed in 1912, fored the basis of radio frequeny eletronis as we know it today. In the United States, FM radio stations broadast between radio frequenies of 88 MHz to 108 MHz with a hannel bandwidth of 200 khz. FM radio was first deployed in onaural in 1940; and in 1960, FM stereo was introdued. This artile presents a basi tutorial on FM with desriptions of ultiple (MPX) signaling and noise iproveent tehniques suh as stereo-ono blending and soft ute. FM Basis Frequeny odulation is a for of analog angle odulation in whih the baseband inforationarrying signal, typially alled the essage or inforation signal (, varies the frequeny of a arrier wave. Audio signals transitted by FM radio ouniations are the ost oon. However, FM radio an also transit digital data with the low bandwidth digital inforation known as Radio Data Syste (RDS) in Europe and Radio Broadast Data Syste (RBDS) in the U.S. The siplest approah to generating FM signals is to apply the essage signal diretly to a voltage-ontrolled osillator (VCO) as shown in Figure 1. Figure 1. FM Generation with a VCO A voltage essage signal, (, is applied to the ontrol voltage of the VCO, and the output signal, FM (, is a onstant aplitude sinusoidal arrier wave whose frequeny is ideally a linear funtion of its ontrol voltage. When there is no essage or the essage signal is zero, the arrier wave is at its enter frequeny, f. When a essage signal eists, the instantaneous frequeny of the output signal varies above and below the enter frequeny and is epressed by f ( = f K ( i + where K VCO is the voltage-to-frequeny gain of the VCO epressed in units of Hz/V, and the quantity, K VCO* (, is the instantaneous frequeny deviation. The instantaneous phase of the output signal is equal to 2π ultiplied by the integral of the instantaneous frequeny as shown below θ ( = 2πf t + 2πK i VCO t VCO 0 (dt where the initial ondition of the phase is assued to be zero for sipliity. Hene, the FM output signal, FM (, is given by the following equation
2 t FM ( = A os 2πf t + 2πK VCO (dt 0 A few observations an be ade fro the FM output signal. First, the aplitude of an FM signal is onstant regardless of the essage signal, giving it a onstant envelope property with an 2 output power equal to A 2 into a 1 Ω resistor. Seond, the frequeny-odulated output, FM (, has a nonlinear dependene to the essage signal, (, aking it diffiult to analyze the properties of an FM signal. To estiate the bandwidth of an FM signal, a single tone essage signal is used as shown below ( = A os(2πf where A is the aplitude of the essage signal and f is the frequeny of the essage signal. Substituting this essage signal into the above forulas, we find KVCO A ( = A os 2 f t + sin(2 f FM π π f f = A os 2 + sin(2 f π f t π f ( = A os 2π f t + β sin(2πf FM ( ) The quantity f = K VCO A represents the peak frequeny deviation of the FM signal fro the enter frequeny and is diretly proportional to the aplitude of the essage signal and the gain of the VCO. This quantity, f, is alled the aiu instantaneous frequeny deviation. The ratio of the frequeny deviation, f, to the essage signal frequeny, f, is alled the odulation inde, β. For a single tone essage signal, the nuber of signifiant sidebands in the output spetru is a funtion of the odulation inde. This an be seen by first writing the FM output signal in ters of n th order Bessel funtions of the first kind [2, 3]. ( 2 ( f nf ) FM t = A ( ) J n ( β )os π + n= By taking the Fourier transfor, we see a disrete FM output spetru with agnitude oeffiients as a funtion of β as shown in the equation below. A ( f ) J (β ) + FM = 2 n= n [ δ ( f f nf ) + δ ( f + f nf )] The nuber of sidebands of an FM signal and its assoiated agnitude oeffiient an be found with the help of Bessel funtion tables suh as the one shown in Table 1.
3 β J0 J1 J2 J3 J4 J5 J6 J7 J Table 1. Bessel Funtions of the First Kind Rounded to Two Deial Plaes. 2 If A 2 =1, β=1, f = 1 khz, and f = 100 khz, then the result is the FM voltage spetru shown in Figure 2 Figure 2. FM Voltage Spetru for 2 A =1, β=1, f = 1 khz, and f = 100 khz. 2 A key point of odulation inde, β, is that it deterines the bandwidth of the signal by deterining the nuber of effetive sidebands of an FM signal. For instane, if β=0.25, only one sideband is needed; while if β=5, eight sidebands are required. Another iportant point about the odulation inde: it an hange a lot even for a fied frequeny deviation beause the essage signal frequeny an vary. In general, as the odulation inde inreases, the nuber of sidebands inreases and the bandwidth goes up. However, the inrease in odulation inde due to dereasing essage frequeny (reall β = f f ) ay not neessarily inrease the FM bandwidth. The bandwidth is equal to the nuber of disrete spetral tones ultiplied by the frequeny spaing set by the essage signal frequeny f. For ore opliated essage signals, the bandwidth of an FM signal an also be approiated with Carson s rule, BW FM 2 ( β + 1) f [2, 3]. The epirial relation states that the nuber of signifiant spetral tones in an FM spetru is 2 ( β + 1), not inluding the arrier. For eaple , in North Aeria, the aiu frequeny deviation, f, is 75 khz for oerial FM broadasting. If the aiu essage frequeny is equal to 15 khz for audio, then β = 75 khz 15kHz = 5, and the FM bandwidth is BW FM = 2 (5 + 1)15kHz = 180kHz. This is lose to the allotted 200 khz hannel bandwidth. If the Bessel funtions are used to approiate the bandwidth, the bandwidth of (2 8 +1)15 khz = 255 khz is ahieved. In pratie, the last few side tones ay ontribute negligible power, thus reduing the bandwidth to about 200 khz (assuing the tones
4 that are below -10 db are negligible). Again, it is iportant to reeber that these equations are derived fro a single tone essage signal, whih is uh different fro real-world essage signals that ontain any different frequenies at the sae tie. In this ase, the aiu frequeny of the real essage signal an be used as an approiation for f. To reover the essage signal fro the FM signal, frequeny deodulation ust be perfored. The ost basi frequeny deodulator onsists of a frequeny disriinator, whih is a differentiator followed by an envelope detetor, as shown in Figure 3. d dt Envelope Detetor Figure 3. Ideal Frequeny Disriinator The differentiator onverts the FM signal to an AM signal as shown in the following equation t d FM ( = A (2π f + 2πK VCO( )sin(2πf t + 2πK VCO ( d dt and the envelope detetor an be used to reover ( . Differentiation is one of the key steps used in FM deodulation. However, an unfortunate by-produt of differentiation is that it aplifies high-frequeny noise and degrades the overall signal-to-noise ratio (SNR) of the reovered essage signal. To opensate, FM broadasters insert a pre-ephasis filter prior to FM transission to aplify the high-frequeny ontent of the essage signal. All FM reeivers inorporate a reiproal de-ephasis filter after the FM reeiver to attenuate high-frequeny noise and interferene and restore a flat essage signal frequeny response. Figure 4 shows the blok diagras of an FM transitter with a pre-ephasis filter, H pe (f), and an FM reeiver with a de-ephasis filter, H de (f). 0 ( ' ( FM ( FM ( '( ( Figure 4. Pre-Ephasis and De-Ephasis in FM Syste The pre-ephasis filter has a high-pass harateristi transfer funtion given by H pe ( f ) = 1+ j2πfτ and the de-ephasis filter has a low-pass harateristi transfer funtion given by H de ( f ) = 1+ 1 j2πfτ
5 where the tie onstant, τ, is the pre-ephasis/de-ephasis tie onstant. The two tie onstants used in various regions of the world are 75 µs (in regions inluding the US) and 50 µs (in regions inluding Europe). The SNR of an FM syste for ono signals without pre-ephasis and de-ephasis is ( ) CNR SNR FM = 3β 2 β + 1 BT SNRFM 3 CNR 2W where B T is the FM transission bandwidth (= BW FM ), W is the essage signal bandwidth ( f ) 2 and CNR is the arrier-to-noise ratio equal to A 2BT No where N o 2 is the two-sided power spetral density of white noise . The above SNR equation illustrates the trade-off that eists between essage signal quality (SNR) and FM transission bandwidth. With an FM transission bandwidth of 200 khz and a essage signal bandwidth of 15 khz (β 5.67), it is reasonable to epet the SNR at the output of an FM reeiver to have an FM gain of 27 db above the CNR. However, the above SNR equations are only valid for large CNRs. As the CNR at the input of the FM disriinator is dereased, it will eventually generate ipulse noise, resulting in liks and rakling. The onset of ipulse noise tells us that the FM reeiver has just entered a noise threshold region known as the threshold effet. The FM threshold is defined as the iniu CNR yielding FM iproveents that do not signifiantly deviate fro the theoretial equation given for FM SNR . As noted previously, the use of pre-ephasis and de-ephasis filters is one approah to iproving the SNR of an FM syste by attenuating high frequeny noise. The atual iproveent fator, I, in output SNR of an FM reeiver using pre-ephasis and de-ephasis filters is where f W f I = W 1 3 tan W f f = 1 2πτ is the 3-dB orner frequeny of the pre-ephasis and de-ephasis filters . With a 3-dB orner frequeny of 2.1 khz and a essage signal bandwidth of 15 khz, an iproveent fator of 13 db an be ahieved fro the pre-ephasis and de-ephasis filters. This iproveent fator also assues a large CNR at the input of the FM disriinator. Thus, the total SNR iproveent for a ono signal above threshold fro FM gain and pre-ephasis and de-ephasis filtering is 27 db + 13 db = 40 db, assuing an FM transission bandwidth of 200 khz, a essage signal bandwidth of 15 khz, and a 3-dB pre-ephasis and de-ephasis orner frequeny of 2.1 khz ( τ = 75 s ). Care ust be taken when interpreting this result µ beause the equation suggests that it is possible ahieve an FM SNR of 40 db with a arrier-tonoise ratio of 0 db. Generally, this will not be the ase beause standard FM deodulators typially ehibit a threshold at 12 db CNR  invalidating the above results. Moreover, the SNR iproveent for stereo signals is only 17 db above CNR [db] for CNRs above threshold . The equations below suarize the audio SNR iproveents for FM 3 3
6 when the CNR is above threshold . SNR MONO = 40 + CNR [db] SNR STEREO = 17 + CNR [db] Stereo FM Multiple Signal Prior to 1961, onaural broadasting of audio signals was the standard for AM, FM and TV. FM broadasts at that tie also inluded Subsidiary Couniations Authorization (SCA) servies that were ultipleed with the ain onophoni hannel to provide bakground usi and other servies to offies and stores. In 1961, the FCC approved the transission of stereophoni sound, whih etends the idea of ultipleing signals to generate stereo audio. One of the key requireents of the stereo ultiple signal was to be bakwards opatible with the large eisting base of FM onophoni reeivers. To aoplish this goal, the 0 to 15 khz baseband part of the ultiple (MPX) signal had to ontain the left (L) and right (R) hannel inforation (L+R) for onophoni reeption. Stereophoni sound is ahieved by aplitude odulating the (L-R) inforation onto a suppressed 38 khz subarrier in the 23 to 53 khz region of the baseband spetru. A 19 khz pilot tone is added to the ultiple signal to enable FM stereo reeivers to detet and deode the stereo left and right hannels. The oposite baseband signal forat eets the bakwards opatibility needed for FM ono reeivers while siultaneously providing enough inforation for FM stereo reeivers to deode the left and right stereo hannel outputs. Today s MPX signal inludes a 57 khz subarrier that arries RDS and RBDS signals . Figure 5 shows a spetru of a odern-day MPX baseband signal. Power Mono Audio Left + Right Stereo Pilot Stereo Audio Left - Right RDS/ RBDS Frequeny (khz) Figure 5. MPX Baseband Spetru The atheatial analysis presented in the previous setion assues that the essage signal, (, is a single-tone sinusoidal signal. In reality, the essage signal used in today s FM broadasts is the MPX signal with a baseband spetru siilar to the one shown in Figure 5. The FCC has set odulation liits of 100% odulation (an instantaneous frequeny deviation of 75 khz orresponds to a 100 perent odulation) for stereophoni transission and up to 110
7 perent odulation for SCA ultiple subarriers under ertain onditions . Figure 6 shows an eaple odulation level breakdown for the various signals in a typial MPX essage signal. Figure 6. MPX spetru showing odulation level The total odulation level for the MPX signal shown in Figure 6, assuing no orrelation, is the aritheti su of eah of the subhannel levels giving perent odulation or a peak frequeny deviation of khz. Fro the last setion, the frequeny deviation is related to the aplitude of the essage signal by the onstant, K VCO, sine f = K VCO A. Thus, for a fied K VCO, the aplitude of all the subhannel signals within the MPX essage signal ust be saled to give the appropriate total frequeny deviation. Figure 7. MPX Enoder
8 Figure 7 shows a oneptual blok diagra of an MPX enoder used to generate the MPX signal. L( and R( denote the tie doain wavefors fro the left and right hannels and RDS( denotes the tie doain wavefor of the RDS/RBDS signal. The MPX essage signal an be epressed as ( = C0[ L( + R( ] + C1 os(2π *19kHz * + C0[ L( R( ]os(2π *38kHz * + C2RDS( os(2π *57kHz * where C 0, C 1, and C 2 are gains used to sale the aplitudes of the ( L ( ± R( ) signals, the 19 khz pilot tone, and the RDS subarrier, respetively, to generate the appropriate odulation level. Figure 8. MPX Deoder Figure 8 shows a oneptual blok diagra of an MPX deoder used to reover the left, right and RDS signals fro the MPX essage signal, (. The essage signal is applied to three bandpass filters with enter frequenies at 19, 38 and 57 khz and to a low-pass filter with a 3-dB utoff frequeny of 15 khz. The 19 khz bandpass filter is a high-q filter used to etrat the 19 khz pilot tone fro the MPX essage signal. The reovered pilot tone is frequeny-doubled and tripled to produe the required loal osillator (LO) signals needed to deodulate the (L-R) and RDS signals, respetively. By adding and subtrating the (L+R) and (L-R) signals, a saled version of the left and right hannels is reovered for stereophoni sound. RDS is brought bak down by iing with a 57 khz LO, and the data an be reovered by sending this signal to a athed filter. The above analysis reveals the diffiulty in aintaining good stereo separation. First, if a onaural signal is applied to the input of the deoder, the pilot tone, (L-R), and RDS signals are equal to zero beause they do not eist for onaural signals. The left and right outputs of the
9 deoder would be the sae and equal to the (L+R) signal thereby reovering the ono signal. Seond, any gain or phase isath in the generation of the MPX essage signal and/or reovery of the left and right hannels leads to finite stereo separation, so the left hannel has soe right hannel inforation, and the right hannel has soe left hannel inforation (also known as hannel separation or ross talk). For eaple, if the 15 khz low-pass filters of the deoder in Figure 8 have a gain isath of 1 perent, the stereo separation would be about -46 db. This eaple illustrates that the left and right signal paths ust ath in both aplitude and phase to aintain good stereo separation, whih an be diffiult if the enoder and deoder iruits are ipleented with analog iruits. Noise Iproveent Tehniques Reent ipleentations of FM tuners, suh as Silion Laboratories Si4700 FM tuner and Si4701 FM tuner with RDS/RBDS, have inorporated noise iproveent tehniques suh as stereo-ono blending and soft ute to iprove the audio quality of FM radios. Mono SNR Stereo SNR Stereo Seperation Figure 9. FM Charateristi Curve Figure 9 shows a plot of a generi FM harateristi urve. The X ais represents the RF signal level and the Y ais represents the left audio output noralized to its aiu output level, i.e., 0 db represents the aiu output level for the left audio output signal. The left audio, right audio, stereo noise and ono noise levels are plotted on this graph; all signals are plotted relative to the left audio output. In this eaple, an RF input level of RF3 and higher brings the FM tuner in full stereo ode, resulting in a stereo separation of 30 db and a stereo SNR of 55 db. If the FM tuner is fored in ono ode in this region, the ono SNR would be 60 db. The larger ono SNR oes fro a saller onaural bandwidth of 15 khz as opared to a stereo MPX signal requiring a bandwidth of 53 khz. In the region between RF2 to RF3, stereo-ono blending ours as shown by the erging of the left and right audio signals. As the left and right audio signals erge, the stereo noise also erges to the ono noise and thus effetively inreases the SNR of the audio signal. If blending was not ipleented, the stereo noise would trak the dashed dark-blue line, and the audio SNR and RF sensitivity level would be lower than an FM tuner with stereo-ono blending. In this eaple, RF0 ould represent the sensitivity level of an FM tuner with stereo-ono blending, and RF1 ould represent the sensitivity level of an FM tuner without stereo-ono blending.
10 Sensitivity is defined as the iniu RF input level to ahieve a ertain aount of audio SNR. In this fititious eaple, sensitivity is defined as the RF level neessary to ahieve an audio SNR of 1 db. In addition, when the RF input level to the FM tuner dereases, the noise level inreases at a uh faster rate than the rate of derease in the audio output level. In this eaple, the audio output only drops by about 6 db fro its aiu output level, but the noise level an inrease all the way up to the audio output level when the RF level drops below sensitivity (RF0). When this ours, the noise and audio signals are at the sae level, and this level an be relatively loud sine it is only 6 db below the aiu audio output level. One approah to iniizing the audible noise level in this weak RF region is to attenuate both the audio and the noise signals together in a tehnique known as soft ute. Figure 10 shows an FM harateristi urve with soft ute. In this eaple, when soft ute is enabled, the audio noise and signals are attenuated by 14 db to a level that is 20 db below the aiu audio output level to iniize audible noise and iprove the overall user eperiene. Figure 10. FM Charateristi Curve with Soft Mute Si4700/01 FM Tuners The Si4700 and Si4701 FM tuners are the industry s first radio tuner ICs to leverage a digital low-if arhiteture and a 100 perent CMOS proess tehnology, resulting in a opletely integrated solution that requires only one eternal supply bypass apaitor and less than 20 2 of board spae. Figure 11 shows a blok diagra of the Si4700 and Si4701 FM tuners. The digital low-if arhiteture allows for the eliination of eternal oponents and fatory adjustents due to analog proess variations. This ied-signal arhiteture allows digital signal proessing (DSP) to perfor hannel seletion, FM deodulation and stereo audio proessing to ahieve superior perforane opared to traditional analog arhitetures.
11 CONTROL INTERFACE CONTROLLER AMPLIFIER Figure 11. Blok Diagra of the Si4700/01 Digital-Low IF FM Tuner The Si4700 and Si4701 FM tuners inlude prograable, stereo-ono noise thresholds and soft ute paraeters to allow aiu fleibility for noise iproveents. DSP is utilized to provide optiu sound quality for varying signal reeption onditions. This rih feature set and high levels of integration and perforane are diretly attributable to the digital low-if radio arhiteture and the digital ipleentation of the FM deodulation, MPX deoding and noise iproveent funtions. Besides siplifying and reduing design-in tie, the high integration of the digital low-if arhiteture inreases quality and iproves anufaturability by having only one eternal bypass apaitor. FM radio is one of the ost prevalent fors of edia ouniation in the world today. As listeners all over the world ontinue to buy and use FM radios, designers for portable devies suh as MP3 players and obile phones are inreasingly inluding FM radio apability in their produts. Understanding the basis of FM radio will assist designers in reating high perforane produts, be they traditional standalone radios or net-generation, ulti-use devies. Referenes  E. H. Arstrong Web Site,  S. Haykin, Couniation Systes, 3 rd Edition, Wiley, 1994  R. E. Zieer, W. H. Tranter, Priniples of Couniations, Systes, Modulation, and Noise, Fourth Edition, Wiley, 1995  B. Razavi, RF Miroeletronis, Prentie Hall, 1998  J. Kean, FM Stereo and SCA Systes, National Assoiation of Broadasters Engineering Handbook, 9 th Edition, NAB, 1999, pgs  S. A. Wright, Radio Broadast Data Syste (RBDS), National Assoiation of Broadasters Engineering Handbook, 9 th Edition, NAB, 1999, pgs