This work deals with the problems of the design of two stage operational amplifier with automatic offset compensation for precise measurement. Full design operational amplifier is aimed at appropriate realization in technology CMOS07 with usage Cadence design environment. The goal of the design is minimum offset value as well as the adherence to the parameters of the operational amplifier which are introduced in submission of the thesis.

Precise measurements of both absolute frequencies and small frequency differences of atomic energy levels have played an important role in the development of physics. For example, high precision measurements of absolute frequencies of the 2S½ → 2P ½ transition (D1 line) of alkali atoms form an important link in the measurement of the fine structure constant, α. Similarly, precise interferometric measurements of the local gravitational acceleration (g) rely on the knowledge of the absolute frequencies of the 2S½ → 2P 3/2 transition (D2line) in alkali atoms. Difference frequency measurements of hyperfine structure and isotope shifts of atomic energy levels provide valuable information about the structure of the nucleus, which in turn helps in fine tuning the atomic wave functions used in theoretical calculations. The work reported in this thesis starts with the development and refinement of high precision measurement of absolute frequencies using a ring-cavity resonator. The measurement technique is relatively simple and cost-effective, but the accuracy is comparable to that achieved with the frequency comb technique (10¯11) when the accuracy is limited by the natural linewidth of the transition being measured. The technique combines the advantages of using tunable diode lasers to access atomic transitions with the fact that the absolute frequency of the D2 line in87Rb is known with an accuracy of 6 kHz. A frequency-stabilized diode laser locked to this line is used as a frequency reference, along with a ring-cavity resonator whose length is locked to the reference laser. For a given cavity length, an unknown laser locked to an atomic transition has a small frequency offset from the nearest cavity resonance. We use an acousto-optic modulator (AOM) to compensate for this frequency offset. The measured offset is combined with the cavity mode number to obtain a precise value for the frequency of The unknown laser. We have used this technique for absolute frequency measurements Of the D lines in133Cs and 6,7Li, and the 398.8nm line in Yb. We have also developed a technique to measure the ‘difference frequency’ of atomic energy levels using a single diode laser and an AOM. In this technique, the laser is first locked to a given hyperfine transition. The laser frequency is then shifted using the AOM to another hyperfine transition and the AOM frequency is locked to this difference. Thus the AOM frequency directly gives a measurement of the hyperfine interval. Applying this AOM technique we have measured the hyperfine interval of the D1 lines of all alkali atoms with high precision. We have further developed a technique of coheren-tcontrol spectroscopy (CCS) using co-propagating control and probe beam that is useful for highresolution spectroscopy. In this technique, the probe beam is locked to a transition and its absorption signal is monitored while the control beam is scanned through neighbouring transition. As the control comes into resonance with another transition, the probe absorption is reduced and the signal shows a Doppler free dip. This technique allows us to resolve transitions that are otherwise swamped by crossover resonances in conventional saturated absorption spectroscopy (SAS). We have applied this technique to measure hyperfine intervals in the D2 line of several alkali atoms. Thus, we were able to do high-precision measurements of both absolute and difference frequency of atomic transitions. The precision of the absolute frequency measurement is finally limited by the accuracy of 6 kHz with which the reference frequency is known. The nearby two photon transition in Rb, i.e. the 5S1/2→5D3/2 transition at 778 nm, is known with an accuracy of 1 kHz. In future, we hope to improve the accuracy of our technique using this transition as the reference. This thesis is organized as follows: In Chapter1,we give a brief introduction to our work.. We review the importance of frequency measurements and precision spectroscopy, followed by a comparison of the frequency comb and our ring cavity technique. In Chapter2, we describe measurements of the absolute frequency of the D lines of 133Cs using the ring cavity. We give a detailed discussion of the technique, the Possible sources of errors, and ways to check for the errors. The measurement of the absolute frequency of the D lines of Cs allows a direct comparison to frequency comb measurements, and thus acts as a good check on our technique. In Chapter 3, we describe the absolute frequency and isotope shift measurements in the 398.8 nm line in Yb. We probed this line by frequency doubling the output of a tunable Ti:Sapphire laser. We obtained< 60 kHz precision in our measurements and were able to resolve several discrepancies in previous measurements on this line. In Chapter 4, we describe the measurement of hyperfine structure in the D1 lines of alkali atoms. We used conventional saturated-absorption spectroscopy in a vapor cell to probe different hyperfine transitions and then used our AOM technique to measure the hyperfine interval with high precision. In Chapter 5 we discuss our measurements of hyperfine structure in the D2 lines of several alkali atoms. In the case of 23Na and 39K, the closely-spaced hyperfine transitions are not completely resolved in conventional saturatedabsorption spectroscopy due to the presence of cross over resonances. We have used coherent control spectroscopy to obtain crossover-free spectra and then measured the hyperfine intervals using an AOM. This technique was also used for high resolution spectroscopy in the D2 line of 133Cs. Finally, we describe our measurements of hyperfine structure in the D2 line of Rb using normal saturated absorption spectroscopy. Chapter 6, describes the relative and absolute frequency measurements in the D lines of6,7 Li at 670nm. High-precision measurements in lithium are of special interest because theoretical calculations of atomic properties in this simple three electron system are fairly advanced. Lithium spectroscopy poses an experimental challenge and we describe our efforts in doing highresolution spectroscopy on this system. Chapter 7 describes the hyperfine spectroscopy on the1P 1 state of 173Yb. Measurement of hyperfine structure in 173Yb has a problem because two of the hyperfine transitions overlap with the transition in 172Yb. In our earlier work (described in chapter 4), we had solved this problem by using multipeak fitting to the partially resolved spectrum. Here, we directly resolve the hyperfine transitions by using transverse laser cooling to selectively deflect the 173Yb isotope. In Chapter 8 , we give a broad conclusion to the work reported in this thesis and suggest future avenues of research to continue the work commenced here.

La première mesure du spectre en phi*_eta du boson Z à 7 TeV a été réalisée dans cette thèse. Cette variable permet de sonder la dynamique de production des Z de façon fine. L’échantillon complet des données enregistrées par ATLAS en 2011 a été utilisé ce qui correspond à 4.7/fb de luminosité intégrée. Les résultats de cette mesure sont publiés dans la Ref. [18] fondé sur la note interne Ref. [69]. La section efficace différentielle de Z->ee en fonction phi*_eta a été mesurée et comparée aux calculs perturbatifs à ordre fixé, avec/sans resommation pour la région des petits phi*_eta. Le code RESBOS fournit la meilleure description des données, cependant il est incapable de reproduire, à mieux de 4%, la forme détaillée de la section efficace mesurée. La section efficace différentielle a également été comparée aux prédictions de différents générateurs Monte Carlo interfacés avec un algorithme de parton shower. Les meilleures descriptions du spectre en phi*_eta mesuré sont données par les générateurs SHERPA et POWHEG+PYTHIA8. La mesure précise de la section efficace différentielle en phi*_eta fournit des informations précieuses pour l’ajustement des codes Monte Carlo. La précision expérimentale typique de cette mesure (~0.5%) est dix fois meilleure que la précision des calculs théoriques et elle est donc aussi précieuse pour contraindre la théorie. La mesure du spectre en ptZ a également été faite pour quantifier l’incertitude systématique de cette mesure en utilisant la grande statistique de l’échantillon de données. Cela permet de comparer deux mesures qui traitent de l’impulsion transverse du boson Z. Dans la plupart du domaine en phi*_eta l’incertitude systématique de la mesure de ptZ est deux fois plus grande que celle de la mesure de phi*_eta. Cette comparaison confirme l’intérêt de la variable phi*_eta. Les résultats présentés dans cette thèse ont beaucoup d’implications pour les études futures. Ajustant les générateurs Monte Carlo en utilisant les résultats de la mesure précise du spectre en phi*_eta minimisera l’incertitude sur leurs paramètres. Une mesure de la section efficace doublement différentielle en ptZ et phi*_eta est intéressante pour mieux comprendre la corrélation entre ces deux variables. La mesure précise du spectre en ptZ utilisant la variable phi*_eta peut être appliquée au spectre en ptW et on sait que des mesures plus fines du ptW sont importante pour une détermination précise de la masse du boson W. De plus, une compréhension précise du spectre en ptZ est importante pour comprendre les propriétés cinématiques de la production du boson de Higgs. / The first measurement of the phi*_eta spectrum of Z bosons at 7 TeV of pp collisions has been studied in this thesis, which is an alternative way to probe the transverse momentum of Z bosons. The full data sample recorded by the ATLAS detector during 2011 run of the LHC was used, which corresponds with 4.7/fb integrated luminosity. The results of this measurement were reported in Ref. [18] supported by the internal note in Ref. [69]. The differential cross section of Z->ee as a function of phi*_eta has been measured and compared to fixed order perturbative QCD calculations with/without a resummation for the low phi*_eta region. Calculations using RESBOS provide the best descriptions of the data. However, they are unable to reproduce the detailed shape of the measured cross section to better than 4%. The differential cross section was also compared to predictions from different Monte Carlo generators interfaced to a parton shower algorithm. The best descriptions of the measured phi*_eta spectrum are provided by SHERPA and POWHEG+PYTHIA8 Monte Carlo event generators. The precise measurement of the differential cross section as a function of phi*_eta provides valuable information for the tuning of MC generators. The typical experimental precision of this measurement (~0.5%) is ten times better than the typical theoretical precision and therefore is valuable to constrain the theoretical predictions further. The ptZ measurement has been also studied to quantify the systematic uncertainty of this measurement using the high statistic data sample. This allows to compare two measurements which both address the physics issues of the Z transverse momentum. In most of the phi*_eta range, the systematic uncertainty of the ptZ measurement is two times larger than the one of the phi*_eta measurement. This comparison confirms the interest for the phi*_eta variable. The measurements presented in this thesis has many implications for future studies. Tuning MC generators using the result of the precise measurement of the phi*_eta spectrum will minimize the uncertainty on the tuned parameters. A double differential cross section measurement as a function of ptZ and phi*_eta is interesting to understand the correlation between ptZ and phi*_eta variables. The precise measurement of the ptZ spectrum using the new variable phi*_eta can be applied to ptZ. More precise measurement of ptZ are important to obtain precise measurements of the W mass. In addition, a precise understanding of the ptZ spectrum is important to understand kinematic properties of Higgs boson production.