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# Chapter 5

## on Jul 05, 2013

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• Angle modulation encompasses phase modulation (PM) and frequency modulation (FM). The phase angle of a sinusoidal carrier signal is varied according to the modulating signal.
• It can provide a better discrimination (robustness) against noise and interference than AM This improvement is achieved at the expense of increased transmission bandwidth In case of angle modulation, channel bandwidth may be exchanged for improved noise performance Such trade-off is not possible with AM
•  (t)=10  t+  t 2 f i =d  (t)/dt x (1/2  )= 5+ t (Hz)
• For phase modulation (PM), the instantaneous phase deviation  ( t ) is proportional to the modulating signal m ( t ). Thus  ( t ) = k p m ( t )+  0 where k p is a constant Let  0 =0,  ( t ) = k p m ( t ) So a PM signal is represented by x PM ( t ) = A cos [  c t + k p m ( t )]
• For FM, the instantaneous frequency deviation is proportional to the modulating signal m(t) The instantaneous angular frequency is  i (t) So an FM signal is represented by x FM (t)
• Because frequency and phase modulation are closely related, any variation in phase will necessarily result in a variation in frequency and vice versa. By looking at an-angle modulated carrier is generally impossible to tell whether it is FM or PM.
• Phase and frequency modulation are inseparable x PM ( t ) = A cos [  c t + k p m ( t )] If we integrate the modulating signal m(t ) and phase-modulate using the integrated signal, we get a FM signal. On the other hand, If we differentiate the modulating signal m ( t ) and frequency-modulate using the differentiated signal, we get a PM signal. Therefore, we can generate a PM signal using a frequency modulator or we can generate an FM signal using a PM modulator.
• Frequency modulation: (a) Modulating signal,
• (b) instantaneous frequency, and (c) FM signal.
• Bandwidth of Angle Modulated Signals
• m p = max |m(t)|
• m p ’ = max |m’(t)|
• The last significant spectral component is for n=  +1
• J n (  ) gets smaller as n decreases and  decreases.
• WBFM is used widely in space and satellite communication systems. The large bandwidth expansion reduces the required SNR and thus reduces the transmitter power requirement. WBFM is also used for high fidelity radio transmission over rather limited areas.
• The modulation index is small (  &lt; 0.2)
• When the modulation index is not small, a narrowband frequency-modulated signal is first generated using an integrator and a phase modulator as shown earlier. A frequency multiplier is then used to increase the modulation index from  to N  (that is increase the peak frequency deviation from  f to N  f ) . A frequency multiplier is a nonlinear device. Example the square law device: e 0 (t)= a e i 2 (t) If N=12 We can use 12 th order nonlinear device or two 2 nd order and one 3 rd order devices. Use of frequency multiplication normally increases the carrier frequency from f c to n f c . What if the desired carrier frequency is not multiple of f c ?
• What if the desired carrier frequency is not multiple of f c ? A mixer or double-sideband modulator is required to shift the spectrum down to the desired range for further frequency multiplication or transmission as shown.
• Example: Armstrong Indirect FM Transmitter (Fig. 5.10) The final output is required to have 91.2 MHz and  f=75kHz. Note total multiplication=64x48=3072, if no frequency conversion is used, we get  f=76.8kHz but f c = 614.4 MHz
• In the direct method of generating an FM signal, the modulating signal m(t) directly controls the carrier frequency. A common method is to vary L or C of a tuned electric oscillator. Any oscillator whose frequency is controlled by the modulating signal is called a voltage controlled oscillator (VCO). We can use varactor diode whose capacitance varies with the bias voltage. Assuming that the capacitance of the tuned circuit varies linearly with the modulating signal m ( t ), we have C = C 0 - k m ( t ) L can be varied by a current in a second coil of a core reactance..
• C = C 0 - k m ( t ) We can show that for [k m(t)] &lt;&lt; C 0 ,
• The varactor diode is a semiconductor diode that is designed to behave as a voltage controlled capacitor. When a semiconductor diode is reverse biased no current flows and it consists of two conducting regions separated by a non-conducting region. This is very similar to the construction of a capacitor. By increasing the reverse biased voltage, the width of the insulating region can be increased and hence the capacitance value decreased. If the information signal is applied to the varactor diode, the capacitance will therefore be increased and decreased in sympathy with the incoming signal.
• Solution:  f 2 =20kHz;  f 1 =20Hz, N=  f 2 /  f 1 = 1000  f 2 =20kHz;  f 1 =(100/50) 20=40 Hz, N=  f 2 /  f 1 = 500
• The information in an FM signal resides in the instantaneous frequency.  i = d  (t)/dt=  c + d  (t)/dt =  c + k f m(t) Demodulation of an FM signal requires a system that produces an output proportional d  (t)/dt. Such system is called a frequency discriminator. For FM signal, y(t)=k d  (t)/dt= k k f m(t)
• The characteristics of an ideal frequency discriminator can be better described by a linear voltage/frequency characteristic as shown in Figure.  i (t)=  c + k f m(t) The instantaneous frequency  i (t) changes linearly with m(t) The basic requirement of any FM demodulator is therefore to convert frequency changes into changes in output voltage, with the minimum amount of distortion.
• There are several possible networks with such characteristics the simplest is the ideal differentiator
• Since  c + k f m(t)>0 for all t, m(t) can be obtained by envelope detection as in AM demodulation. Note that for a differentiator, H(  )= j  The basic idea is to convert FM into AM and then use AM demodulator. In practice, channel noise and other factors may cause A to vary. If A varies, y ( t ) will vary with A . Hence, it is essential to maintain the amplitude of the input signal to the frequency discriminator using a bandpass limiter (amplitude limiter). For demodulation of PM signals, we simply integrate the output of a frequency discriminator. This yields a signal which is proportional to m ( t ).
• A bandpass limiter consists of hard limiter and BPF. It is usually used to eliminate any amplitude variations. A hard limiter is a device which limits the output signal to (say) +1 or -1 volt. Figure shows the input-output characteristic of a hard limiter. If the input is x(t)=A(t) cos  (t) = A(t) cos[  c t+  (t)] The output of the low pass filter is (4/  ) cos[  c t+  (t)] For proof see textbook page 234-235.
• An amplitude limiter circuit is able to place an upper and lower limit on the size of a signal. In Figure, the preset limits are shown by dotted lines. Any signal which exceeds these levels are simply chopped off. This makes it very easy to remove any unwanted amplitude modulation due to noise or interference.
• The FM slope detector is composed of two parts: Frequency to amplitude converter (Tuned circuit) Envelope detector The magnitude frequency response |H(f)| of the frequency to amplitude converter is shown in next slide
• The magnitude frequency response |H(f)| of the frequency to amplitude converter is shown. Note the frequency band for linear FM/AM conversion. Note that we can use the linear part in the left of f 0 or its right. The frequency f c must be in the centre of the linear part. However, the slope detection suffers from the fact that the slope of |H(f)| is linear over only a small band and, hence, causes considerable distortion in the output.
• The slope detection suffers from the fact that the slope of |H(f)| is linear over only a small band and, hence, causes considerable distortion in the output. This fault can partially be corrected by a balanced discriminator. The balanced discriminator is composed of two slope detectors, one tuned f c1 and the other f c2 such that the desired carrier frequency f c falls in between Frequency response of the tuned circuit#1 and #2 and their overall response is shown.
• Frequency response of the tuned circuit#1 and #2 and their overall response.
• In this case, FM is converted into PM then PM detector is used to recover message signal The block diagram for a quadrature demodulator is shown. It contains a phase shifter, a phase comparator and a LPF. In modern systems if a noncoherent FM discriminator is required then the quadrature demodulator is used: Low- and medium-quality FM receivers Audio FM discriminator of TV sets TRF6900A SoC RF transceiver
• Simplified circuit diagram of a quadrature Demodulator. Principle of operation 1. Phase shifter converts FM modulation into PM but preserves the FM 2. Analog multiplier serves as a phase detector (PD) and produces an output being linearly proportional to PM. PD is not sensitive to FM 3. Low-pass filter suppresses sum-frequency output
• 1. The phase shift is linearly proportional to the instantaneous frequency deviation about the carrier frequency fc = 10 : 7 MHz 2. FM modulation is converted into PM (FM is preserved) 3. Phase shift at carrier frequency is equal to -90 o
• Quadrature demodulator: Almost exclusively used circuit configuration to implement a modern frequency discriminator
• x(t)=AB/2 [sin(  i -  o )+sin(2  c t+  i +  o )] The higher component is suppressed by the loop filter The output of the Loop filter is e 0 (t)=h(t)*0.5 AB sin(  i -  o )= h(t)*0.5 AB sin(  e ) where  e =  i -  o . The PLL will keep  i (t)  o (t),  VCO (t)=  c + c e 0 (t) The instantaneous frequency of the VCO output is  VCO (t)=  c + d  o /dt Thus d  o /dt= c e 0 (t) During phase-locked  i (t)  o (t), and Thus e 0 (t)  c -1 d  i /dt= (k f /c) m(t)

## Chapter 5Presentation Transcript

• Chapter 5 ANGLE MODULATION: FREQUENCY and PHASE MODULATIONS(FM,PM)
• Outlines • Introduction • Concepts of instantaneous frequency • Bandwidth of angle modulated signals • Narrow-band and wide-band frequency modulations • Generation of FM signals • Demodulation of FM signals • superhetrodyne FM radio
• Introduction • Angle modulation: either frequency modulation (FM) or phase modulation (PM). • Basic idea: vary the carrier frequency (FM) or phase (PM) according to the message signal.
• • While AM is linear process, FM and PM are highly nonlinear. • FM/PM provide many advantages (main – noise immunity, interference, exchange of power with bandwidth ) over AM, at a cost of larger transmission bandwidth. • Demodulation may be complex, but modern ICs allow cost-effective implementation. Example: FM radio (high quality, not expensive receivers).
• Concepts of Instantaneous Frequency • A general form of an angle modulated signal is given by is the instantaneous angle is the instantaneous phase deviation. • The instantaneous angular frequency of ( ) cos ( ) cos(2 ( ))EM i c iS t A t A f t tθ π φ= = + ( ) ( ) ( ) i i i c d t d t t dt dt θ φ ω ω= = + ( )i tθ ( )i tφ ( )EMS t
• • The instantaneous frequency of • The instantaneous frequency deviation ( ) ( )1 1 ( ) 2 2 i i i c d t d t f t f dt dt θ φ π π = = + ( )1 ( ) 2 i i d t f t dt φ π ∆ = ( )EMS t
• Example • for the signal below find the instantaneous frequency and maximum frequency deviation. 2 ( ) cos(10 )x t A t tπ π= +
• • For phase modulation (PM), the instantaneous phase deviation is • kp is the phase sensitivity of the PM modulator expressed in (rad/ V) if m(t) is in Volts • The instantaneous frequency of ( ) ( )i c p dm t f t f k dt = + Phase modulation (PM) ( ) ( )i t kp m tφ = ( ) cos [2 ( )]PM c pS t A f t k m tπ= + ( )PMS t
• • For Frequency Modulation (FM), the instantaneous phase deviation is • kf is the frequency sensitivity of the FM modulator expressed in rad/ V s if m(t) in Volts. • The instantaneous frequency of ( ) cos 2 ( ) t FM c fS t A f t k m dπ α α −∞   = +    ∫ Frequency Modulation (FM) ( ) ( ) t i ft k m dφ α α −∞ = ∫ ( )FMS t ( ) ( ) 2 f i c k f t f m t π = +
• Angle modulation viewed as FM or PM
• Phase Modulator Frequency Modulator Phase Modulator∫ Frequency Modulator ( )m t ( )PMS t ( )m t ( )FMS t ( )m t ( )FMS t ( )PMS t( )m t d dt
• • A PM/FM modulator may be used to generate an FM/PM waveform • FM is much more frequently used than PM • All the properties of a PM signal may be deduced from that of an FM signal • In the remaining part of the chapter we deal mainly with FM signals.
• Example 5.1 • Sketch FM and PM waves for the modulating signal m(t) shown in Fig. 5.4a. The constants kf and kp are 2πx105 and 10π, respectively, and the carrier frequency fc is 100 MHz..
• Example
• Bandwidth of Angle Modulated Signals 1) FM signals [ ] 2 3 2 3 ( ) cos(2 ) ( )sin(2 ) ( )cos(2 ) ( )sin(2 ) ... 2! 3! FM c f c f f c c S t A f t k a t f t k k A a t f t a t f t π π π π = −   + − + +    where ( ) ( ) t a t m dα α −∞ = ∫
• • Narrow-Band Frequency Modulation (NBFM): • Narrow-Band Phase Modulation (NBPM): [ ]( ) cos(2 ) ( )sin(2 )NBFM c f cS t A f t k a t f tπ π≈ − ( ) cos(2 ) ( )sin(2 )NBPM c p cS t A f t k m t f tπ π ≈ −  BBNBFM 2= | ( ) | 1fk a t << 2NBPMB B= | ( ) | 1Pk m t <<
• Generation of NBFM m(t)
• Generation of NBPM m(t)
• • If ∆f: maximum carrier frequency deviation β: deviation ratio or modulation index • Wide- Band Frequency Modulation (WBFM) |kf a(t)|>>1 or β>100 fBWBFM ∆= 2 π2 pf mk f =∆ )1(2)(2 +=+∆= βBBfBFM B f∆ =β | ( ) | 1fk a t ? max ( )Pm m t=
• • For phase modulation: if π2 ' ppmk f =∆ | ( ) | 1Pk m t ? 2( ) 2 ( 1)PMB f B B β= ∆ + = + ' ' max ( )Pm m t= 2WBPMB f= ∆
• Single tone modulation • Let [ ])2sin(2cos)( tftfAtx mcFM πβπ += [ ]∑ ∞ −∞= += n mcnFM tfnfJAtx )(2cos)()( πβ ( ) cos2 mm t f tα π=
• • The results is valid only for sinusoidal signal • The single tone method can be used for finding the spectrum of an FM wave when m(t) is any periodic signal. 2 ( 1) 2 FM m f m B f k f f f β α π β = + ∆ = ∆ =
• Example 1 • A single tone FM signal is Determine a) the carrier frequency fc b) the modulation index β c) the peak frequency deviation d) the bandwidth of xFM(t) 6 3 FMx (t)=10 cos[ 2 (10 )t+ 8 sin(2 (10 )t)]π π
• Example 2 • A 10 MHz carrier is frequency modulated by a sinusoidal signal such that the peak frequency deviation is ∆f=50 KHz. Determine the approximate bandwidth of the FM signal if the frequency of the modulating sinusoid fm is a) 500 kHz, b) 500 Hz, c) 10 kHz.
• Example 3 • An angle modulated signal with carrier frequency 100kHz is Find a) the power of xFM(t) b) the frequency deviation ∆f c) The deviation ratio β d) the phase deviation ∆φ e) the bandwidth of xFM(t). EM cx (t)=10 cos[ 2 f t+ 5 sin(3000 t)+10 sin(2000 t) ]π π π
• Example 5.3 (Txt book) a) Estimate BFM and BPM for m(t) when kf= 2πx105 rad/sV and kp= 5πrad/V b) Repeat the problem if the amplitude of m(t) is doubled.
• Features of Angle Modulation • Channel bandwidth may be exchanged for improved noise performance. Such trade-off is not possible with AM • Angle modulation is less vulnerable than AM to small signal interference from adjacent channels and more resistant to noise. • Immunity of angle modulation to nonlinearities thus used for high power systems as microwave radio.
• • FM is used for: radio broadcasting, sound signal in TV, two-way fixed and mobile radio systems, cellular telephone systems, and satellite communications. • PM is used extensively in data communications and for indirect FM. • WBFM is used widely in space and satellite communication systems. • WBFM is also used for high fidelity radio transmission over rather limited areas.
• Generation of FM Signals • There are two ways of generating FM waves: –Indirect generation –Direct generation
• Indirect Generation of NBFM m(t)
• Indirect Generation of Wideband FM • In this method, a narrowband frequency- modulated signal is first generated and then a frequency multiplier is used to increase the modulation index. m(t) NBFM xFM(t) Frequency Multiplier
• m(t) N fc NBFM Frequency Multiplier BPF Local Oscillator (fLo) xFM(t) fc Frequency Converter
• m(t) NBFM Frequency Multiplier x64 Power Amplifier Crystal Oscillator 10.9 MHz fc1=200 kHz ∆f1= 25 Hz Frequency Multiplier x48 fc2=12.8MHz ∆f2= 1.6 kHz fc3=1.9 MHz ∆f3= 1.6 kHz fc4= 91.2MHz ∆f4= 76.8 kHz Armstrong Indirect FM TransmitterArmstrong Indirect FM Transmitter BPF
• Direct Generation • The modulating signal m(t) directly controls the carrier frequency. [ ] • A common method is to vary the inductance or capacitance of a voltage controlled oscillator. ( ) ( )i c ff t f k m t= +
• • In Hartley or Colpitt oscillator , the frequency is given by • We can show that for k m(t) << C0 LC 1 =ω       += 02 )( 1 C tmk cωω 0 1 LC c =ω
• Varactor Modulator Circuit
• • Advantage - Large frequency deviations are possible and thus less frequency multiplication is needed. • Disadvantage - The carrier frequency tends to drift and additional circuitry is required for frequency stabilization. To stabilize the carrier frequency, a phase- locked loop can be used.
• Example 5.6 • Discuss the nature of distortion inherent in the Armstrong FM generator –Amplitude distortion –Frequency distortion
• Example • A given angle modulated signal has a peak frequency deviation of 20 Hz for an input sinusoid of unit amplitude and a frequency of 50 Hz. Determine the required frequency multiplication factor, N, to produce a peak frequency deviation of 20 kHz when the input sinusoid has unit amplitude and a frequency of 100Hz, and the angle-modulation used is (a) FM; (b) PM
• Demodulation of FM Signals • Demodulation of an FM signal requires a system that produces an output proportional to the instantaneous frequency deviation of the input signal. • Such system is called a frequency discriminator. FM Demodulator [ ])(cos)( ttAtx c φω += dt td kty )( )( φ =
• • A frequency-selective network with a transfer function of the form |H(ω)|= a ω+b over the FM band would yield an output proportional to the instantaneous frequency. • There are several possible examples for frequency discriminator, the simplest is the FM demodulator by direct differentiation
• FM demodulator by direct differentiation • The basic idea is to convert FM into AM and then use AM demodulator. [ ]' ( ) 2 ( ) sin 2 ( ) t c c f c fs t A f k m t f t k m dπ π α α −∞   = − + +    ∫
• Bandpass Limiter • Input-output characteristic of a hard limiter Hard Limiter BPF
• • Any signal which exceeds the preset limits are simply chopped off
• Practical Frequency Demodulators • There are several possible networks for frequency discriminator –FM slope detector –Balanced discriminator – Quadrature Demodulator • Another superior technique for the demodulation of the FM signal is to use the Phased locked loop (PLL)
• FM Slope Detector
• FM Slope Detector
• FM Slope Detector
• Balanced Discriminator
• Balanced Discriminator (Cont.)
• Balanced Discriminator (Cont.)
• Quadrature Demodulator • FM is converted into PM • PM detector is used to recover message signal