Angle Demodulator using AM

1

Angle Demodulator using AM FM demodulators first generate an AM signal and then use an AM

demodulator to recover the message signal.

To transform the FM signal into an AM signal, Pass the FM signal through an LTI system, whose frequency response is approximately a straight line in the frequency band of the FM signal.

If the frequency response of such a system is given by

And if the input to the system is

Then the output will be the signal

The next step is to demodulate this AM signal to obtain Ac(Vo+kkfm(t)), from which the message m(t) can be recovered.

20)( cBcc ffforffkVfH

t

fcc dmktfAtu )(22cos)(

t

fcfc dmktftmkkVAtv )(22cos)()( 00

2

Angle Demodulators using AM Many circuits can be used to implement the first stage of an

FM demodulator, i.e., FM to AM conversion. One candidate is a simple differentiator with Another candidate is the rising half of the frequency characteristics

of a tuned circuit, as shown in below Such a circuit can be easily implemented, but usually the linear

region of the frequency characteristic may not be wide enough. To obtain linear characteristics over a wide range of frequencies,

usually two circuits tuned at two frequencies f1 and f2 are connected in a configuration, which is known as a balanced discriminator.

ffH 2)(

3

Angle Demodulator using AM

A balanced discriminator and the corresponding frequency response.

4

Angle Demodulator using PLL A different approach to FM-signal demodulation is to use a ph

ase-locked loop (PLL) => PLL-FM demodulator

The input to the PLL is the angle-modulated signal

(where, for FM, )

The VCO generates a sinusoid of a fixed frequency; in this case, it generates the carrier frequency fc, in the absence of an input control voltage.

)(2cos)( ttfAtu cc

t

f dmkt )(2)(

)(tu)(te

)(tyv

)(tv

5

Angle Demodulator using PLL Now, suppose that the control voltage to the VCO is the loop fil

ter's output, denoted as v(t). Then, the instantaneous frequency of the VCO is

where kv is a deviation constant Consequently, the VCO output may be expressed as

where The phase comparator is a multiplier and a filter that rejects the

signal component centered at 2fc. Hence, its output may be expressed as

where the difference (t) - v(t)e(t) constitutes the phase error.

The signal e(t) is the input to the loop filter.

)()( tvkftf vcv

)(2sin)( ttfAty vccv

t

vv dvkt0

)(2)(

)()(sin)( 21 ttAAte vcv

6

Angle Demodulators using PLL Let us assume that the PLL is in lock position, so the phase err

or is small. Then, under this condition, so we may deal with the linearized model of the P

LL, shown in below

We may express the phase error as Or equivalently, either as

Or as (Eq. 1)

)()()()()(sin ttttt evv

t

ve dvktt0

)(2)()( )()(2)( t

dt

dtvkt

dt

dve

)()()(2)(0

tdt

ddtgkt

dt

deve

Linearized PLL:

7

Angle Demodulators using PLL The Fourier transform of (Eq. 1) is

Hence

(Eq.2)

Now, suppose that we design G(f) such that

Then, from (Eq.2),

Or equivalently,

Since the control voltage of the VCO is proportional to the message signal, v(t) is the demodulated signal.

)()2()()(2)()2( ffjfGfkffj eve

)(

)(1

1)( f

fGjfk

fv

e

)(

)(1

)()()()( f

fGjfk

fGfGffV

v

e

1)(

jf

fGkv

)}(2{2

1)(

2

2)( ffj

kf

k

fjfV

vv

)()(2

1)( tm

k

kt

dt

d

ktv

v

f

v

8

FM-Radio Broadcasting Commercial FM-radio broadcasting utilizes the frequency ban

d 88-108 MHz for the transmission of voice and music signals. The carrier frequencies are separated by 200 kHz and the peak

frequency deviation is fixed at 75 kHz. Preemphasis is generally used, as described in Chapter 6, to im

prove the demodulator performance in the presence of noise in the received signal.

The receiver most commonly used in FM-radio broadcast is a superheterodyne type.

The block diagram of such a receiver is shown in below

9

FM-Radio Broadcasting

Block diagram of a superheterodyne FM-radio receiver.

10

FM-Radio Broadcasting As in AM-radio reception, common tuning between the RF am

plifier and the local oscillator allows the mixer to bring all FM-radio signals to a common IF bandwidth of 200 kHz, centered at fIF = 10.7 MHz.

Since the message signal m(t) is embedded in the frequency of the carrier, any amplitude variations in the received signal are a result of additive noise and interference.

The amplitude limiter removes any amplitude variations in the received signal at the output of the IF amplifier by bandlimiting the signal.

A bandpass filter, which is centered at fIF = 10.7 MHz with a bandwidth of 200 kHz, is included in the limiter to remove higher-order frequency components introduced by the nonlinearity inherent in the hard limiter.

11

FM-Radio Broadcasting A balanced frequency discriminator is used for frequency d

emodulation. The resulting message signal is then passed to the audio-frequ

ency amplifier, which performs the functions of deemphasis and amplification.

The output of the audio amplifier is further filtered by a lowpass filter to remove out-of-band noise, and this output is used to drive a loudspeaker.

12

FM-Stereo Broadcasting<Transmitter> Many FM-radio stations transmit music programs in stereo by

using the outputs of two microphones

FM-stereo transmitter and signal spacing.

13

FM-Stereo Broadcasting The signals from the left and right microphones, ml(t) and mr

(t), are added and subtracted . The sum signal ml(t)+mr(t) is left unchanged and occupies the f

requency band 0-15 kHz. The difference signal ml(t)-mr(t) is used to AM modulate (DSB

-SC) a 38 kHz carrier that is generated from a 19-kHz oscillator.

A pilot tone at the frequency of 19 kHz is added to the signal for the purpose of demodulating the DSB-SC AM signal.

We place the pilot tone at 19 kHz instead of 38 kHz because the pilot is more easily separated from the composite signal at the receiver.

The combined signal is used to frequency modulate a carrier.

14

FM-Stereo Broadcasting By configuring the baseband signal as an FDM signal, a mono

phonic FM receiver can recover the sum signal ml(t)+mr(t) by using a conventional FM demodulator. Hence, FM-stereo broadcasting is compatible with conventional FM. In addition, the resulting FM signal does not exceed the allocated 200-

kHz bandwidth.

<Receiver> The FM demodulator for FM stereo is basically the same as a

conventional FM demodulator down to limiter/discriminator. Thus, the received signal is converted to baseband.

Following the discriminator, the baseband message signal is separated into the two signals, ml(t)+mr(t) and ml(t)-mr(t), and passed through deemphasis filters, as shown in Figure 4.18.

15

FM-Stereo Broadcasting The difference signal is obtained from the DSB-SC signal via

a synchronous demodulator using the pilot tone. By taking the sum and difference of the two composite signal

s, we recover the two signals, ml(t) and mr(t). These audio signals are amplified by audio-band amplifiers, an

d the two outputs drive dual loudspeakers. As indicated, an FM receiver that is not configured to receive t

he FM stereo sees only the baseband signal ml(t)+mr(t) in the frequency range 0-15 kHz.

Thus, it produces a monophonic output signal that consists of the sum of the signals at the two microphones.

16

FM-Stereo Broadcasting

Figure 4.18 FM-stereo receiver.

17

Television Broadcasting Commercial TV broadcasting began as black-and-white picture

transmission in London in 1936 by the British Broadcasting Corporation (BBC).

Color TV was demonstrated a few years later, but commercial TV stations were slow to develop the transmission of color-TV signals. This was due to the high cost of color-TV receivers. With the development of the transistor, the cost of color TV decreased significantly. By the middle 1960s, color TV broadcasting was widely used by the industry.

The frequencies allocated for TV broadcasting fall in the VHF and UHF bands. Table 4.2 lists the TV channels allocated in the United States. The channel bandwidth allocated for the transmission of TV signals is 6 MHz. In contrast to radio broadcasting, standards for television-signal transmission vary

from country to country. The US standard was set by the National Television Systems Committee (NTSC).

18

Television Broadcasting