Phasor decomposition method Research Papers

About the Phasor Pathways in Analogical Amplitude Modulations

2023

Phasor diagrams have long been used in Physics and Engineering. In telecommunications, this is particularly useful to clarify how the modulations work. This paper addresses rotating phasor pathways derived from different standard... more

descriptionView Paper arrow_downwardDownload

Tunable Diode Laser Spectroscopy With Wavelength Modulation: A Phasor Decomposition Method for Calibration-Free Measurements of Gas Concentration and Pressure

by David Moodie

2014, IEEE/OSA Journal of Lightwave Technology

Recovery and analysis of the 1st harmonic signals in tunable diode laser spectroscopy (TDLS) with wavelength modulation (WM) are limited by the presence of a high background signal upon which the small gas signals are superimposed. This... more

descriptionView Paper arrow_downwardDownload

Tunable Diode-Laser Spectroscopy With Wavelength Modulation: A Calibration-Free Approach to the Recovery of Absolute Gas Absorption Line Shapes

by David Moodie

2014, IEEE/OSA Journal of Lightwave Technology

Recovery and analysis of the 1st harmonic signals in tunable diode laser spectroscopy (TDLS) with wavelength modulation (WM) are limited by the presence of a high background signal upon which the small gas signals are superimposed. This... more

Fig. 1. Schematic diagram of the experimental system for TDLS with WM and RAM nulling.

Fig. 2. Receiver outputs illustrating the performance of the system with regards to noise and RAM nulling. The receiver output with no applied modulation is shown in (a) with delay arm disconnected (lower black trace), delay arm connected with the PCs adjusted to maximise optical noise (grey trace) and delay arm connected with the PCs adjusted to minimise optical noise (upper black trace). The receiver output with the sinusoidal modulation applied is shown in (b) with delay arm dis- connected (lower black trace) and the delay arm connected with the system set up to optimise RAM nulling and minimise the optical noise (upper black trace). The amplitude under RAM nulling conditions is doubled due to the combination of the dc components from the gas cell and delay arms.

Fig. 3. Recorded signal from photodidode—delay line disconnected. Investigations of the new technique were carried out using the 1650.96 nm absorption line of methane at concentrations of

Fig. 4. Recorded signal from photodidode—delay line connected and system opti- mised to achieve RAM nulling.

Fig. 5. Recorded signal on x-axis of LIA for RAM-nulled PD and normal PD.

Fig. 6. Recorded signal on y-axis of LIA for RAM-nulled PD and normal PD.

Fig. 8. Recovered lineshape using PD method with RAM nulling compared tc theory—1.02%CH4:No.

Fig. 7. Recovered lineshape using PD method with RAM nulling compared to theory—10.13%CH4:No.

Fig. 10. Comparison of recorded and processed signals—0.5%CH4:N2 at m=0.5. The grey trace is the recorded 1st harmonic signal (x-axis of LIA) containing the gas concentration-dependant RAM term mixed with a projection of the WM/AM (derivative) signal onto the x-axis of the LIA. The grey dashed trace is the recorded 2nd harmonic signal on the LIA. The black trace is the gas absorption lineshape (the gas concentration-dependant RAM signal) recovered from the recorded 1st harmonic signal (grey trace) using the PD method. Fig. 9 illustrates the benefit of RAM nulling, first Fig. 9(a) shows the recorded signal at the x-axis of the LIA using RAM nulling with the signal isolated from the WM/IM signal for 0.1% methane in OFN, cleary gas absorption is present sitting on a small sloping back- ground. The sloping background could easily be removed by taking ano gas signal or through a curve fitting process, as mention early. Fig. 9(b) shows the same but without RAM nulling and it can be seen

Fig. 9. Recorded signal on x-axis of LIA with RAM component isolated from the WM/IM signal with and without RAM nulling—0.1%CH,4:Np. (a) Clearly shows gas absortio. on zero with a small sloping background. This sloping background could easily be removed by taking a no gas signal or through a curve fitting process, as mentioned early.(b Shows gas absorption being lost within the background RAM.

Fig. 11. Comparison of recorded and processed signals—0.5%CH4:N2 at m=2.2. The grey trace is the recorded 1st harmonic signal (x-axis of LIA) containing the gas concentration-dependant RAM term mixed with a projection of the WM/AM (derivative) signal onto the x-axis of the LIA. The grey dashed trace is the recorded 2nd harmonic signal on the LIA. The black trace is the gas absorption lineshape (the gas concentration-dependant RAM signal) recovered from the 1st harmonic signal (grey trace) using the PD method. With the removal of the high background RAM signal, the usual disadvantages of recovering 1st harmonic TDLS/WM signals rela- tive to higher harmonics (e.g. the 2nd harmonic) are no longer there. To illustrate this point Figs. 10 and 11 show the recovered RAM- nulled 1st harmonic signals (LIA x-axis) compared with the 2nd harmonic recovered under the same conditions for 0.5% methane in OFN (using m=0.5 and m= 2.2, respectively). Clearly the signals, both recovered by the same LIA gain settings, are of similar ampli- tude and quality as regards signal to noise ratio and resolution. Also shown in Figs. 10 and 11 are the absoulte gas lineshape functions derived from these 1st harmonic signals using the PD method. The relative vertical scale is the same in all cases to enable comparsion. Clearly the ampltiude of the concentration-dependant RAM signal

descriptionView Paper arrow_downwardDownload

About the Phasor Pathways in Analogical Amplitude Modulations

by h.m. de oliveira and

2014, International Journal of Research in Engineering and Science (IJRES)

Phasor diagrams have long been used in Physics and Engineering. In telecommunications, this is particularly useful to clarify how the modulations work. This paper addresses rotating phasor pathways derived from different standard... more

About the Phasor Pathways in Analogical Amplitude Modulations Fig.2 A3E-Modulation Parameters- m=0.5 and frequency ratio f,,/f-: a) 0.1 b) 0.3 c) 0.5 d) 0.7.

Lissajours figures are patterns generated by the junction of a pair of sinusoidal waves with axes that are perpendicular to one another. So are also these phasor diagrams, which are generate from in quadrature AM waves. In effect, in order to display such phasor diagrams in a screen of an oscilloscope, an arrangement quite similar to the Hartley phase shift method for SSB modulation [9] can be used, as illustrated in Fig.5. About the Phasor Pathways in Analogical Amplitude Modulations

Cases in which the frequency of the modulating signal f, is greater than the carrier f, generates pathways of particular concern (even if the ratio f,,/f,>lis not of usual interest in telecom). If the relationship is exact and the modulation index is unity, one has "rosettes" figures (Fig.7) with exactly the same number of lobes to this ratio (rose or rhodonea curve). These curves are some sort of different epicycloids [10-11]. When the modulation tone has a frequency that is twice the frequency of the carrier, curves of the phasor tip bear a resemblance to a Lemniscate of Bernoulli and Nephroids with the modulation depth (AM modulation index) Fig.4 A3E-Modulation Parameters- (closed eye) m=1,0 and the frequency ratio f,,/f-: a) 0.1 b) 0.3 c) 0.5 d) 0.7.

playing a role to “tighten/slacken” the “knot”. A gif animation to illustrate this effect is available at the URL http://www2.ee.ufpe.br/codec/T ransition2.gif.

Fig.7 Rhodonea-like curves. Parameters: m=1 and the frequency ratio f,,/f-: a) 2b) 3c) 5 d) 7. Simple gif animations for clarifying the role of the modulation index are available at the URL http://www2.ee.ufpe.br/codec/Transition3.gif and http://www?2.ee.ufpe.br/codec/Transition5.gif. The Un atale" af tha cirnzae are enarad atan angla of 97/M where nnaie atl rad

Fig.8 Phasor pathways for a fixed musical note (do) and further notes of the same octave.

A few examples of geometric figures built by bi-tones phasor pathways are presented in the sequel, for instance, assuming two sinusoidal tones with fiy/f=5 and fino/f,=0.1. The modulation indexes are then varied (Fig.9).

Fig.10 Phasor trajectory of two tones of frequencies fini & fing AM-modulated. The chosen (normalized frequencies) are: a) 2&0.1b)3&0.1c)5&0.1d)7&0.1. Let us now consider another bi-tone example (for instance, by assuming always m,=0.5 and m)=0.2), ut now varying the ratio between the frequencies of the two sinusoidal tones (Fig.10). ; PHASOR TRAJECTORIES IN THE BROAD-SENSE AM

Fig.11 f,,/f.=5, m=0.3 a) A3E-modulation AM a@=1, b) H3E-Modulation SSB+C @=0, c) J3E-Modulation SSB a@=0. To gain some insight into the effects of the modulation index in a single tome modulation, we consider only SSB-+C (the effects are much apparent), and gradually increase the value of m. where the parameters a< {0,1} corresponds to single and double side band, respectively, and the value of the amplitude A {0,1} accounts for suppressed carrier or not, respectively. Surprisingly, the “vertices” of many SSB-pathway are often some kind [11] of folium of Descartes, Tschirnhaus's Cubic or Conchoid of de Sluze (Fig.11-13). However, the exact relationships with known curves are not on the scope of this primary approach.

About the Phasor Pathways in Analogical Amplitude Modulations D. Lhe case of dynamic phasor Of vestigial sideband modulation In order to glimpse the phasor envelope for Vestigial Side Band modulation (C3F), we consider a simple case of a single tone, setting the modulation index m=0.3 and assuming a slow carrier (with is indeed unusual in practical telecommunication applications). This can be achieved by considering a real value for a, constrained in the range 0<a<1. We start with a low residue (compare with SSB, Fig.12a) and gradually increase the factor o towards AM, i.e. unity (AM double side band, Fig.11a). As in earlier cases. some resemblance can be found to further interesting known alaebraic curves such

Fig.13 C3F-Modulation (VSB) with f,,/f.=5, m=0.3 and different degrees of vestigial side bands: a) a=0.1, b) a=0.3, c) a=0.5.

Fig.14 (a) Phasor pathways for a single tone f,,=3f, (W=3) and modulation index m=0.2, (b) idem, now with a 10% random frequency drift (random fluctuation).

Fig.15 Phasor pathways for irrational envelope-to-carrier frequency ratio: m=0.25, fn/f-=2V2 (a) initial pathways that never close; (b) long-run pathway tends to fulfill the ring of radius from 1-m to 1+m

descriptionView Paper arrow_downwardDownload

Phasor decomposition method

Related Topics