# Chaotic behaviour of deterministic systems (lectures of by G. Iooss

By G. Iooss

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Extra resources for Chaotic behaviour of deterministic systems (lectures of Orszag & Patera only)

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44 25. In the circuit of Fig. 5 mA for IX = 1:3 mA. Determine the required IS . 26. For what value of IX in Fig. 44, does R1 carry a current equal to IX =2? Assume IS = 3  10,16 A. 27. We have received the circuit shown in Fig. 45 and wish to determine R1 and IS . 45 ments indicate that IX = 1 mA ! VX = 1:2 V and IX = 2 mA ! VX = 1:8 V. Calculate R1 and IS . 28. The circuit illustrated in Fig. 46 employs two identical diodes with IS = 5  10,16 A. 46 Calculate the voltage across R1 for IX = 2 mA.

The breakdown resulting from a high voltage (and hence a high electric field) can occur in any material. A common example is lightning, in which case the electric field in the air reaches such a high level as to ionize the oxygen molecules, thus lowering the resistance of the air and creating a tremendous current. 1 Zener Breakdown The depletion region in a pn junction contains atoms that have lost an electron or a hole and, therefore, provide no loosely-connected carriers. However, a high electric field in this region may impart enough energy to the remaining covalent electrons to tear them from their bonds [Fig.

Res ,1 . 89) BR Wiley/Razavi/Fundamentals of Microelectronics Sec. cls v. 2006] June 30, 2007 at 13:42 45 (1) PN Junction 45 Using this value along with L = 11:9 nH in Eq. 90) An oscillator whose frequency can be varied by an external voltage (VR in this case) is called a “voltage-controlled oscillator” and used extensively in cellphones, microprocessors, personal computers, etc. 2 GHz. 2 GHz. In summary, a reverse-biased pn junction carries a negligible current but exhibits a voltagedependent capacitance.