FM Receivers FM receivers, like AM receivers, utilize the superheterodyne principle, but they operate at uch higher frequencies (88-108 MHz). A liiter is often used to ensure the received signal is constant in aplitude before it enters the discriinator or detector.
Block Diagra of FM Receiver
FM Deodulators The FM deodulators ust convert frequency variations of the input signal into aplitude variations at the output. The Foster-Seeley discriinator and its variant, the ratio detector are coonly found in older receivers. They are based on the principle of slope detection using resonant circuits.
Slope Detector La Ca produce an output voltage proportional to the input frequency. Center frequency is place at the center of the ost linear portion of the voltage versus-frequency curve When IF deviates above or below fc, output voltage increases or decreases Tuned circuit converts frequency variation to voltage variation
S-curve Characteristics of FM Detectors v o E d f IF d f i
Balanced Slope Detector Two single-ended slope detectors connected in parallel and fed 180 o out of phase Phase inversion accoplished by centertapping secondary winding Top tuned circuit is tuned to a frequency above the IF center frequency by approx. 1.33 X f (1.33 X 75 k = 100kHz ) Siilarly, the lower to 100 khz bellow the IF
At the IF center frequency, the output voltage fro the two tuned circuits are equal in aplitude but opposite in polarity, v out = 0 V When IF deviate above resonance, top tuned circuit produces a higher output voltage than the lower circuit and voltage goes positive When IF deviate below resonance, lower tuned circuit produces higher output than upper, and output goes negative
Foster-Seely Discriinator Siilar to balanced slope detector Output voltage versus frequency deviation is ore linear Only one tuned circuit: easier to tune Slope-detector and Foster-Seely discriinator respond to aplitude variation as well as frequency deviation: ust be preceded by a separate liiter circuit
Ratio Detector Advantages over slope detector & Foster-Seely: It is insensitive to aplitude variation in input signal
Phased Locked Loop (PLL) PLL initially locks to the IF frequency After locking, voltage controlled oscillator (VCO) would track frequency changes in the input signal by aintaining a phase error The PLL input is a deviated FM and the VCO natural frequency is equal to the IF center frequency The correction voltage produced at the output of the phase coparator is proportional to the frequency deviation that is equal to the deodulated inforation signal
PLL FM Detector PLL detectors are coonly found in odern FM receivers. FM IF Signal Aplitude Liiter Phase Detector f LPF Deodulated output VCO
Aplitude Liiter Most frequency discriinators use envelope detection to extract the intelligence fro the FM wave for Envelope detection will deodulate incident aplitude variations as well as frequency variation Transission noise and interference add to the signal to produce unwanted aplitude variations
In the receiver, unwanted AM and rando noise are deodulated along with the signal: unwanted distortion is produced A liiter circuit is used to produce a constant aplitude output for all input signal above a specified threshold level
FM Stereo Broadcasting: Baseband Spectra To aintain copatibility with ono syste, FM stereo uses a for of FDM or frequency-division ultiplexing to cobine the left and right channel inforation: L+R (ono) 19 khz Pilot Carrier L-R L-R SCA (optional).05 15 23 38 53 60 67 74 khz
FM Stereo Broadcasting To enable the L and R channels to be reproduced at the receiver, the L-R and L+R signals are required. These are sent as a DSBSC AM signal with a suppressed subcarrier at 38 khz. The purpose of the 19 khz pilot is for proper detection of the DSBSC AM signal. The optional Subsidiary Carrier Authorization (SCA) signal is norally used for services such as background usic for stores and offices.
Chapter 7: Angle Modulation Transission What is Angle odulation What is the difference between frequency and phase odulation What is direct and indirect odulation Deviation sensitivity, phase deviation, odulation index Bandwidth of angle-odulated wave Bandwidth requireents Phasor representation of angle-odulated wave Frequency up-conversion FM transitters Angle odulation versus AM
Angle odulation angleod c cos inst v t V t inst (t) = instantaneous phase (radians) Question: What is the instantaneous frequency?
Angle odulation angleod c cos inst v t V t inst inst t t t d 0 inst inst dt t t dt v angleod (t) V c inst inst = angle odulated wave (Volt) = peak carrier aplitude (Volt) = instantaneous angular frequency (rad/sec) = instantaneous phase (radians)
Phase odulation The instantaneous phase of a haronic carrier signal is varied in such a way that the instantaneous phase deviation i.e. the difference between the instantaneous phase and that of the carrier signal is linearly related to the size of the odulating signal at a given instant of tie. vpm inst inst t? t? t?
Phase odulation The instantaneous phase of a haronic carrier signal is varied in such a way that the instantaneous phase deviation i.e. the difference between the instantaneous phase and that of the carrier signal is linearly related to the size of the odulating signal at a given instant of tie. vpm t Vc cos ct K pv t c t inst c p t t K v t c p d t d t K v t dv t K dt dt dt inst inst c p K p is the phase deviation sensitivity (rad/volt)
Frequency odulation The frequency of a haronic carrier signal is varied in such a way that the instantaneous frequency deviation i.e. the difference between the instantaneous frequency and the carrier frequency is linearly related to the size of the odulating signal at a given instant of tie. inst inst vfm t? t? t?
Frequency odulation The frequency of a haronic carrier signal is varied in such a way that the instantaneous frequency deviation i.e. the difference between the instantaneous frequency and the carrier frequency is linearly related to the size of the odulating signal at a given instant of tie. t K v t inst c f t t t dt t K v t dt inst inst c f 0 0 t vfm t Vc cosct K f v tdt c 0 rad / s K f is the frequency deviation sensitivity Volt t
PM: inst t ct K pv t vpm t Vc cosct K pv t d inst t d ct K pv t dv t t K inst c p FM: t K v t dt dt dt inst c f t t t dt t K v t dt inst inst c f 0 0 t vfm t Vc cosct K f v tdt 0 t K p is the deviation sensitivity K f is the deviation sensitivity TASK: Make block diagras of PM and FM odulators
PM: inst t ct K pv t vpm t Vc cosct K pv t d inst t d ct K pv t dv t t K inst c p K p is the deviation sensitivity dt dt dt Modulating signal source Phase odulator PM wave Direct V c cos 2 f t c Modulating signal source Differentiator Frequency odulator PM wave Indirect V c cos 2 f t c
FM: t K v t inst c f t t t dt t K v t dt inst inst c f 0 0 t vfm t Vc cosct K f v tdt 0 t K f is the deviation sensitivity Modulating signal source Frequency odulator FM wave Direct V c cos 2 f t c Modulating signal source Integrator Phase odulator FM wave Indirect V c cos 2 f t c
Frequency odulation of single frequency signal PM: cos v t V t cos cos v t V t K V t PM c c p FM: v t V cos t t vfm t Vc cosct K fv cost dt 0 KV f Vc cosct sin t
PM and FM of sine-wave signal Carrier Modulating signal??
PM and FM of sine-wave signal Carrier Modulating signal FM PM
Phase Deviation and Modulation Index cos cos v t V t t angle c c is the peak phase deviation or odulation index PM: cos cos v t V t K V t PM c c p K V p (radians) FM: KV vfm t Vc ct t KV f (unitless) f cos sin
FM: PM: KV f Frequency Deviation KV vfm t Vc ct t f cos sin t K V cos t inst c f KV f (peak) frequency deviation cos cos v t V t K V t PM c c p t K V sin t inst c p dependent of the frequency inst t f KV p K V d inst dt FM PM t KV p (peak) frequency deviation KV p K pv independent of the frequency
PM and FM of sine-wave signal KV PM K pv f FM KV f KV f KV p KV f
Bessel function of the first kind cos cos v t V t t angle c c cos cos Jn cos n n n 2 Jn is the Bessel function of the first kind is the odulation index KV f K V n vangle t Vc Jn cos ct nt n 2 J0 cosct vangle t Vc J1cos c t J1cos c t 2 2 J2cos c 2 t J2cos c 2 t... p FM PM
Relation AM and angle od cos cos 2 f f c s2 v 2 2 2 o a t Ec fct c t fc f t J0 cosct vangle t Vc J1cos c t J1cos c t 2 2 J2cos c 2 t J2cos c 2 t...
Bessel function of the first kind
Bandwidth requireents of Angle-od waves 1 Low-index odulation (narrowband FM) < 1 ( f >>> f ) B f (Hz) 2 2 High-index odulation (wideband FM) > 10 (f >>> f ) B2f 2 f KV f f f 3 Actual bandwidth (look at Bessel table page 266) B 2nf where n is the nuber of significant sidebands 4 Carson s rule (approx 98 % of power) B f f 2
Exaple FM odulator f = 10 khz f = 10 khz V c = 10 V f c = 500 khz Draw the spectru? What is the bandwidth using Bessel table? What is the bandwidth using Carson s rule?
f = 10 khz f = 10 khz V c = 10 V f c = 500 khz =1 Exaple Fig 7-7
Phasor representation of Angle-od wave < 1 (narrowband FM) Fig 7-9
Phasor representation of Angle-od wave >> 1 (Wideband FM) Fig 7-10
P c Average Power of Angle-od wave Instantaneous power in unodulated carrier is 2 Vc 2R (W) P c = carrier power (Watts) V c = peak unodulated carrier voltage (volts) R = load resistance (ohs) Instantaneous power in angle-od carrier is 2 2 2 vangle od t Vc _ un 2 Vc _ un 1 1 t c c P cos t t cos 2 t 2 t R R R 2 2 So the average power of the angle-od carrier is equal to the unodulated carrier 2 2 2 2 2 Vc _ un V 2V1 2V2 2 c Vn Pt... 2R 2R 2R 2R 2R
Frequency and Phase odulators Direct FM Modulator Fig 7-16
Linear integrated-circuit direct FM odulator High-frequency deviations and high odulation indices. Fig 7-20
Frequency up-conversion heterodyne ethod With FM and PM odulators, the carrier at the output is generally soewhat lower than the desired frequency of transission Fig 7-24 a
Frequency up-conversion ultiplication Fig 7-24
Indirect FM Transitter f 15 khz fc 200 khz Fig 7-27 J0 cosct vangle t Vc J1cos c t J1cos c t 2 2 J2cos c 2 t J2cos c 2 t...
Indirect FM Transitter < 1 f fc 15 khz 200 khz V V ax arctan V V c c Fig 7-28 Proble!!!!!!
Indirect FM Transitter f f < 1 f fc 15 khz 200 khz ax? f? Fig 7-28 ax = 1.67 iliradiance Ai f = 75 khz and f t = 90 MHz
Arstrong Indirect FM Transitter Where are the frequency conversions? Fig 7-27
Angle od versus AM Advantages of Angle odulation Noise iunity Noise perforance and signal-to-noise iproveent Capture effect Power utilization and efficiency Disadvantages of Angle odulation Bandwidth Circuit coplexity and costs
End Lecture 7
Suary and Outlook g Next lecture: Chapter 8 Angle odulation reception