International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
Volume-4, Issue-11, Nov.-2016
MODIFIED COSTA’S LOOP FOR SYNCHRONOUS DETECTION OF
AMPLITUDE MODULATED WAVE
1
1, 2, 3
JAI UTKARSH, 2AMAN KUMAR LALL, 3G. K. MISHRA
Department of Electronics and Communication Engineering, Birla Institute of Technology, Mesra, Ranchi, Jharkhand
835215
E-mail: [email protected], [email protected], [email protected]
Abstract- A modified Costas loop based synchronous detection method has been presented in this paper. The designis
developed using MATLAB tool. The ‘squarer’ and ‘square root’ is used to develop the proposed design. The design is tested
for sinusoidal wave. The result at different stages of the receiver is also analyzed.
Keywords- Costas Loop, AM Demodulation, Coherent Detection
‘squarer’and ‘square root’are used for coherent
detection of amplitude modulated message signal.
I. INTRODUCTION
Modulation is defined as the process by which some
characteristic of a carrier wave is varied in
accordance with an information-bearing signal. The
type of modulation in which the amplitude of the
carrier signal varies with that of the message signal or
the baseband signal is called amplitude modulation.
Amplitude modulation is used for analog signals [1].
At the receiver end, the message or the baseband
information is extracted from the incoming
modulated waveform [2]. In continuous carrier
modulation based communications system, the carrier
signal of the transmitter and demodulating signal of
receiver would be perfectly matched in frequency and
phase thereby permitting perfect
coherent
demodulation of the modulated baseband signal.
However, transmitters and receivers rarely share the
same carrier oscillator. And hence there are often
frequency and phase offsets and instabilities.
All these frequency and phase variations must be
estimated to perfectly reproduce or identify the
demodulating signal at the receiver end using carrier
recovery circuit and permit coherent demodulation.
The most common method for achieving this is
Costas loop or better known as Costas receiver. The
Costas loop offers an inherent ability to self-correct
the phase and frequency offsets of the recovered
carrier [3].
But the main disadvantage of using Costas receiver is
involvement of a loop settling time in the PLL or
VCO. Settling time is the time interval required for
the PLL to move from one frequency to another and
settle on the new frequency with minimum
error.Settling time and Jitter are considered in equal
propositions for deciding the performance of a PLL
[4-6]. Also, the involvement of such devices make the
circuit immensely complex[7].
II. COSTAS LOOP FOR AM DETECTION
In analog communication system, an analog message
signal is modulated by a high frequency carrier
signal. Coherent detection of an amplitude modulated
wave at the receiver end requires that the locally
generated carrier in the receiver be synchronous in
both frequency and phase with the carrier generating
oscillator in the transmitter. This is a rather
demanding requirement.One method of satisfying this
requirement is to use the Costas receiver or Costas
loop.
Fig.1. Conventional Costas Receiver [2]
The detector in the upper path referred to as the inphase coherent detector or I-channel, and the detector
in the lower path referred to as the quadrature-phase
coherent detector or Q-channel are coupledtogether to
form a negative feedback system designed to
maintain thelocal oscillator in synchronism with the
carrier wave.
In this paper, a modified Costas loop has been
proposed to replace the noise causing and complex
elements like Phase Discriminator and Voltage
Controlled Oscillator. Instead, simpler elements like
III. PROPOSED COSTAS LOOP
The proposed Costas loop replaces the phase
discriminator and voltage controlled oscillator with a
Modified Costa’s Loop For Synchronous Detection of Amplitude Modulated Wave
32
International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
Volume-4, Issue-11, Nov.-2016
(A (1 + m(t)) − − − − − − − − − − − − − −(9)
simple squarer and a ‘square root’ device. The
modified Costas loop has been shown below.
This can be applied to a ‘square root’ device to get
A 1 + m(t) − − − − − − − − − − − − − −
− (10)
which is just a clamped version of the message signal
m(t).
However, a low pass filter is required at the end of
the ‘square root’ device to provide a smooth
demodulated signal.
IV. RESULTS AND DISCUSSION
Fig.2. Proposed Costas Receiver
The output(time vs amplitude) for a given monotonic
sinusoidal signal has been plotted and compared with
that of an original costa’s receiver output for analysis
purpose. MATLAB software has been used for
obtaining the specified results. The amount of
frequency and phase discrepancy has been generated
using the randomize functions.
This device uses the simple trigonometric result
(sin x) + (cos x)
= 1 − − − − − − − − − − − (1)
We take an amplitude modulated wave :
s(t) = A 1 + Km(t) cos(ω t) − − − − − − − (2)
Here the symbols have its usual meaning.
The required demodulating signal from the detector is
A cos(ω t) − − − − − − − − − − − − − −
− −(3)
Where A is the amplitude of the carrier. But, if due
to the practical problems, the demodulating system is
not capable enough to generate the signal of
particular frequency, ω , instead it generates
A cos (ω + ω )t + x − − − − − − − − − −
− (4)
Fig.3.Demodulated Signal using Proposed Costas Loop
where‘x’ is phase error and ‘ω ’ is the frequency
error of the local oscillator with respect to carrier
frequency.
From Fig.2. , the output of the Butterworth Low pass
filter for I channel and Q channel will be:
A 1 + km(t) cos(x)) − − − − − − − − − −
− (5)
andA 1 + km(t) sin(x)) − − − − − − − −(6)
We apply the outputs of low pass filter to squarer to
get
(A 1 + m(t) cos(x)) − − − − − − − − − −(7)
Fig.4.Demodulated Signal using Conventional Costas Loop
and(A 1 + m(t) sin(x)) − − − − − − − −(8)
Then, we add the squarer outputs to get
Fig.3 and Fig. 4 showsthe output from proposed and
conventional Costas loop respectively. Both the
Modified Costa’s Loop For Synchronous Detection of Amplitude Modulated Wave
33
International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
Volume-4, Issue-11, Nov.-2016
waveforms are similar in nature. having same
frequency and phase as that of the message signal but
with different amounts of clamping.
Fig. 5-11.shows the behavior of proposed
demodulator at various intermediate steps. Refer to
the above given equationsfor the intermediate blocks
and outputs.
A random baseband signal, denoted as m, (Fig 5) is
taken as an input to the AM modulator.
Fig.7. Output of LPF in channel-I
Fig.5.Message Signal
The modulated signal is shown in Fig. 6(equation(2)).
Fig.8. Output of LPF in Q channel
The sum of output of the squarer is shown in the Fig.
9(equation-(9))
Fig.6. Modulated Signal
Fig.9. Sum of Squarer Outputs
The Butterworth output for the I Channel (equation(5)) and Q channel (equation-(6)) are Fig. 7 and Fig.
8 respectively.
This output is applied to the ‘square root’ device to
obtain Fig. 10It is a clamped version of the input
baseband signal (equation-(10)).
Modified Costa’s Loop For Synchronous Detection of Amplitude Modulated Wave
34
International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
Volume-4, Issue-11, Nov.-2016
CONCLUSION
In this paper a modified Costas carrier recovery loop
method has been presented to remove frequency and
phase ambiguity. The conventional Costas loop have
a longer settling time and moreover a very complex
circuit. This is eliminated with the help of proposed
Costas loop method. The proposed Costas loop
implementation is simple and flexible. The results
show frequency and phase ambiguity removal using
proposed Costas loop design which results in better
performance. However, the suggested Costas loop
does not give satisfactory results in case of signals
having negative amplitude.
REFERENCES
Fig.10.Output of Square Root Device
[1]. H.
Roder,
“Amplitude,
Phase,
and
Frequency Modulation”,Proceedings of the Institute of Radio
Engineers,Year: 1931, Volume: 19, Issue: 12,Pages: 2145 –
2176
[2]. Simon Haykin, Michael Moher “Introduction to Analog and
Digital Communications”, 2nd Edition, John Wiley and Sons.
[3]. Mr. Jainendra Kumar, Mr. Rajesh Mehra , “Costas Loop
Implementation for Synchronous Detection of Carrier in
Radio Receiver”, International Journal of Advances in
Electronics Engineering, Vol:1 Issue:1 ISSN 2278 - 215X
[4]. B. Kamath, R. Meyer, P. Gray, “Relationship Between
Frequency Response and Settling Time of Operational
Amplifiers”, IEEE J. Solid-state Circuits, No. 6, pp. 347-352,
Dec. 74.
[5]. Marques; Y.
Geerts; M.
Steyaert; W.
Sansen,
“Settling time analysis of third order systems,Electronics,
Circuits and Systems”, 1998 IEEE International Conference
onYear: 1998, Volume: 2 ;Pages: 505 - 508 vol.2
[6]. PallaviPaliwal, PriyankLaad, MohanraoSattineni, Shalabh
Gupta,
“Tradeoffs between settling timeand
jitterin phase locked loops”, 2013 IEEE 56th International
Midwest Symposium on Circuits and Systems (MWSCAS);
Year: 2013; Pages: 746 - 749
[7]. Sugihartono, “Acquisition Performance of Modified Costas
Loop QPSK Digital Demodulator in the Absence of Noise,”
Proceedings ofthe International Conference on Electrical
Engineering andInformatics Institute Teknologi Bandung,
Indonesia, 2007, pp.1004-1006.
However, again this output is passed through a low
pass filter to provide a smooth output. The
smoothened outputis shown in Fig. 11.
Fig.11.Demodulated Signal using Proposed Costas Receiver
Fig.11shows that the demodulated signal has similar
characteristics as that of the message signal(Fig. 5.).
Hence, it can be rightly said that the transmission is
distortionless.

Modified Costa’s Loop For Synchronous Detection of Amplitude Modulated Wave
35