Lecture 7 Kah Das

8/13/2019 Lecture 7 Kah Das

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LECTURE 7:

DEMODULATION OF AN ANGLE-MODULATED

WAVE

A/Prof Zhuquan Zang and Dr. Narottam Das

Dept of Electrical and Computer Engineering

Curtin University

Perth, Western Australia


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CE304-DC603 LECTURE NOTES [email protected]

LECTURE 7:DEMODULATION OF AN ANGLE-MODULATED

WAVE

An angle-modulated wave is constant envelope, but due to transmission imperfections,

such as multipath fading, band limitation, the signalr(t) arriving at the receiver suffers

from amplitude variation as represented by

r(t) =e(t) cos[ct+c(t)]

To help minimising distortion in demodulation, the amplitude variation in the received

signal is suppressed by passing r(t) through an amplitude hardlimiter. The resulting

output is given by

sgn(r(t)] =

E for cos() 0

E for cos()< 0

where = ct+c(t).

Since

sgn[r(t)] =4E

cos()

cos(3)

3

+cos(5)

5

...this indicates that the hard-limited signalSgn[r(t)] contains the desired constant enve-

lope signal component given by

r(t) =4E

cos[ct+c(t)].

Demodulation of an FM wave

To recover the original message signal from an FM wave, changes in instantaneous

frequency of the FMwave must be converted to the corresponding amplitude changes

Lecture Note 7, Semester 2, 2012 2


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of the original message. This can be carried out using a frequency-selective network

with a transfer function such that

H() =A+B

where AandBare constants.

A device which exhibits the above transfer functionH()is the frequency discriminator.

There are several practical networks, which can approximate the above ideal character-

istic |H()|, e.g., tuned circuit and differentiator.For example, an ideal differentiator with the transfer function,j , followed by an enve-

lope detector can serve as a frequency discriminator.

Bandpass filter BP1 to exclude the out-of-band noise Bandpass filter

BP2 to extract the desired signal component from the limited signal v1(t).

Signals at the various stages ofFMdemodulation using a frequency discriminator:



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vr(t) =e(t) cos[ct+c(t)]v1(t) =sgn[vr(t)] =

4E{cos[ct+c(t)]

cos[3(ct+c(t))]3

+....}

v2(t) = 4E

cos[ct+c(t)]

v3(t) = d[v2(t)]

dt = 4E

c+

d[c(t)]dt

sin[ct+c(t)]

.

Note that the information bearing signal appears in the envelope ofv3(t). This message

signal can be recovered by applyingv3(t) to an envelope detector followed by a lowpass

filter.

In practice, the ideal differentiator is often approximated by a scheme similar to the

following:

The delay may be realised using a short length of a transmission line or a frequency

selective network.

A simple tuned circuit followed by an envelope detector can also act as a frequency

discriminator:

This is based on the transfer characteristic of the tuned circuit above (or below) the

resonant frequency being approximately linear.

Main disadvantage:



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This scheme has a very small linear operating range and is only suitable for an FM

signal with a small peak frequency deviation.

Note: This method is also called slope detector.

The linear operating range of the transfer characteristic of the slope detector can be

increased by using two tuned circuits:

The top tuned circuit is tuned to a frequency above the carrier frequency c,while the

bottom tuned circuit is tuned below c. The two signals, e1 and e2, at the outputs of

the envelope detectors are equal in magnitude but in antiphase.



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The output demodulated signal e0 =e1 e2, and e0 = 0 when the carrier is unmodu-

lated.

Differential detection

Another practical method of FM detection is differential detection. This method is

popular and there are several single-chip integrated circuits available for implementing

thisFMdetector.

Let the input FM signal be represented by cos[(c+ )t], and its delayed replica be

cos[(c+ )(t )].

The output of the product demodulator is

vo(t) = cos[(c+ )t] cos[(c+ )(t )]

= 12{cos[(c+ )] + cos[2(c+ )t (c+ )]}

.

The high frequency component of v

o(t) is removed by a lowpass filter, so that the

output becomes

vo(t) = 12cos[(c+ )]

= 12 {cos(c) cos() sin(c) sin()}

.



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When c= 2

or = Tc4

where Tc= 1fc

is the period of the carrier, then the demodulated output becomes

vo(t) = 1

2sin( ) =

1

2

This is the desired output if


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The difference frequency terme(t) is extracted by the lowpass loop filter LPF, so that

its output is

e(t) =AB

2 sin[

(t) c(t)].

This error signal e(t) is applied to the VCO in such a sense as to drive its frequency

towards lock. When locked, the phase difference [(t) c(t)] becomes very small,

so that

e(t) sin[(t) c(t)] =(t) c(t).

Under this condition,

(t) c(t)

= (q c)t+ e()t.

ForFM, (t) c(t) =kf t

m()d.

Differentiate (t) with respect to t, then

d[(t)]

dt =

d[c(t)]

dt =kfm(t) = (q c) + e(t),

ore(t) = kfm(t)

qc

=k fm(t) C.

This indicates that the control signale(t) of the VCOcorresponds to the demodulated

output. In practice, e(t) is subjected to further amplification and lowpass filtering.

Note:

The same PLL arrangement can also be used to demodulate a PM signal.

In this case, c(t) =kpm(t), so that

e(t) = 1

d[c(t)]

dt =

1

d[

c(t)]

dt =

kp

d[m(t)]

dt =k

p

d[m(t)]

dt .

To obtain the message signal m(t), e(t) needs to be integrated.

Phase locked loop (PLL) is a very popular demodulator in modernFMreceivers for the

following reasons:

1. Its performance is superior to other frequency discriminators at low carrier-to-

noise ratio, i.e., in a high noise environment.

Note: At high carrier-to-noise ratio, PLL has the same performance as the other

frequency discriminators.



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2. The components needed to implement aPLLcan be readily integrated on a single

chip.

3. A well designed PLL FMdemodulator requires little or no alignment. For proper

operation, it is only necessary to set the free-running or quiescent frequency of

the VCOto within the capture range of the PLL.

Note: Reasons (2) and (3) suggest lower cost in manufacturing.


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