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Phase detector

The goal of the PLL is to maintain a demodulating sine and cosine that match the incoming carrier. Suppose ω c is the believed digital carrier frequency. We can then represent the actual received carrier frequency as theexpected carrier frequency with some offset, ω c ˜ ω c θ ˜ n . The NCO generates the demodulating sine and cosine with the expected digital frequency ω c and offsets this frequency with the output of the loop filter. The NCO frequency can then be modeled as ω c ^ ω c θ ^ n . Using the appropriate trigonometric identities A B 1 2 A B A B and A B 1 2 B A A B . , the in-phase and quadrature signals can be expressed as

z 0 n 1 2 θ ˜ n θ ^ n 2 ω c θ ˜ n θ ^ n
z Q n 1 2 θ ˜ n θ ^ n 2 ω c θ ˜ n θ ^ n
After applying a low-pass filter to remove the double frequency terms, we have
y 1 n 1 2 θ ˜ n θ ^ n
y Q n 1 2 θ ˜ n θ ^ n
Note that the quadrature signal, z Q n , is zero when the received carrier and internallygenerated waves are exactly matched in frequency and phase. When the phases are only slightly mismatched we can use therelation
θ small θ θ
and let the current value of the quadrature channel approximate the phase difference: z Q n θ ˜ n θ ^ n . With the exception of the sign error, this difference is essentially how much we need to offset our NCOfrequency If θ ˜ n θ ^ n 0 then θ ^ n is too large and we want to decrease our NCO phase. . To make sure that the sign of the phase estimate is right, in this example the phase detector issimply negative one times the value of the quadrature signal. In a more advanced receiver, information from boththe in-phase and quadrature branches is used to generate an estimate of the phase error. What should the relationship between the I and Q branches be fora digital QPSK signal?

Loop filter

The estimated phase mismatch estimate is fed to the NCO via a loop filter, often a simple low-pass filter. For thisexercise you can use a one-tap IIR filter,

y n β x n α y n 1
To ensure unity gain at DC, we select β 1 α

It is suggested that you start by choosing α 0.6 and K 0.15 for the loop gain. Once you have a working system, investigate the effects of modifying these values.

Matlab simulation

Simulate the PLL system shown in [link] using MATLAB. As with the DLL simulation, you will have to simulate the PLL on a sample-by-sample basis.

Use [link] to implement your NCO in MATLAB. However, to ensure that the phase term does not grow toinfinity, you should use addition modulo 2 in the phase update relation. This can be done by setting θ n θ n 2 whenever θ n 2 .

[link] illustrates how the proposed PLL will behave when given a modulated BPSK waveform. In this case thetransmitted carrier frequency was set to ω c ˜ 2 1024 to simulate a frequency offset.

Output of PLL sub-system for BPSK modulated carrier.

Note that an amplitude transition in the BPSK waveform is equivalent to a phase shift of the carrier by 2 . Immediately after this phase change occurs, the PLL begins to adjust the phase to force the quadraturecomponent to zero (and the in-phase component to 1 2 ). Why would this phase detector not work in a real BPSK environment? How could it be changed to work?

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
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Crow Reply
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RAW Reply
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I think
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Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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scanning tunneling microscope
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what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Stoney Reply
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Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
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Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
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Smarajit Reply
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