There are many types of phase-locked loops: digital (e.g. In this example our input signal will be simply a complex sinusoid without noise or modulated information. As its name implies, a phase-locked loop (PLL) is designed to lock the phase of an oscillator to the phase of a reference signal, providing a mechanism for synchronization on different platforms. For many modulation schemes the receiver's oscillator needs to be locked in phase to that of the transmitter however, in practice there is a small bit of residual carrier offset between the two. Wireless communications systems modulate the data signal with a high-frequency carrier before transmitting over the air. V0 = delta_phi - v1*a1 - v2*a2 // compute new lower register V1 = v0 // shift lower register to center register V2 = v1 // shift center register to upper register push result through loop filter, updating phase estimate I, crealf(x), cimagf(x), crealf(y), cimagf(y), delta_phi) Y = cosf(phi_hat) + _Complex_I*sinf(phi_hat) compute PLL output from phase estimate
Gnuplot loop update#
compute input sinusoid and update phase
Printf("# a = \n", 1., a1, a2) įloat phi = phase_offset // input signal's initial phaseįloat phi_hat = 0.0f // PLL's initial phase print filter coefficients (as comments) generate loop filter parameters (active PI design) Unsigned int n = 400 // number of samples : simulate a phase-locked loopįloat phase_offset = 0.00f // carrier phase offsetįloat frequency_offset = 0.30f // carrier frequency offsetįloat zeta = 0.707f // pll damping factor
Gnuplot loop code#
A walk-through of the source code follows. The problem statement and a brief theoretical description of phase-locked loops is given in the next section. Once compiled, the program will run a simulation of the phase-locked loop, generating a data file which can be plotted using either Gnuplot or Octave.
Gnuplot loop full#
The source code is provided up front in a single file with a full description of its operation.
Gnuplot loop download#
You can download the multiplot template here: band_multiplot.p. #= # Standard initialization to create the plot # some tags are for latin-american speakers #= set termopt enhanced # Permite pone ^super/_" at 4, 18 set output "doss_multiplot.png" #= # Plot instructions #= data1000.dat each having the same number of columns. Suppose I have files like data1.dat, data2.dat.
In gnuplot we can to iteratively retrieve data from multiple files and plot them on the same graph. Plot, in this case we are plotting the next directions of the Brillouin cell.
Use the general gnuplot template and modify the data you want to First column represents the path traveled by an electron in the reciprocal space, and the second is the energy of the electron in Hartree. Now to plot the band structure create a new directory and copy the supercell.dat file to this directory. You can skip the previus step and download the files here: band_ To make a band structure calculation, first we have to localize the high symmetry points in the Brillouin Zone of the solid, to study the behaviour of this states. The distribution of this energy bands discriminates materials between, insulators, conductors or semiconductors. There are two types of bands: the allowed energy bands (valence band & conduction band) and the forbbiden ones (gap). It calculates the allowed energy states for the electrons within the system. The band theory describes the electronic properties of periodic systems.
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