By Ayman Fayed
This publication is dedicated to the topic of adaptive recommendations for shrewdpermanent analog and combined sign layout wherein absolutely practical first-pass silicon is attainable. To our wisdom, this is often the 1st publication dedicated to this topic. The ideas defined should still result in quantum development in layout productiveness of complicated analog and combined sign platforms whereas considerably slicing the spiraling charges of product improvement in rising nanometer applied sciences.
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Extra info for Adaptive Techniques for Mixed Signal System on Chip (The International Series in Engineering and Computer Science)
Tunable Elements 43 I1 2 ª§ § · Vid · Vid · V2º § ¨ K « ¨VCM E1 ¨VCM VT ¸ VC C » ¸ ¸ ¸ 2 ¹ 2 ¹ 2 » © «¬¨© © ¹ ¼ (3-11) I2 2 ª§ § · Vid · Vid · V2º § ¨ K « ¨VCM E1 ¨VCM VT ¸ VC C » ¸ ¸ ¸ 2 ¹ 2 ¹ 2 » © «¬¨© © ¹ ¼ (3-12) I CM ª V2º 2 VT VC C » K « VCM E1 VCM 2 ¼ ¬ I O I CM I 2 ª§ V V ·V § K «¨¨ id E1 ¨ 2VCM id ¸ id 2 ¹ 2 © ¬© 2 · º ¸¸ VC » ¹ ¼ (3-14) I O I1 I CM ª§ V V ·V § K «¨¨ id E1 ¨ 2VCM id ¸ id 2 2 ¹ 2 © ¬© · º ¸¸ VC » ¹ ¼ (3-15) (3-13) Gm w I O wVid E ª1 º K « 2 E1VCM 1 Vid » VC 4 ¬2 ¼ (3-16) Gm w I O wVid E ª1 º K « 2 E1VCM 1 Vid » VC 2 4 ¬ ¼ (3-17) Equations 3-10 through 3-17 could now be used to provide a more accurate assessment of performance limitations in the circuit.
3-27 and 3-28 to Eqs. 3-19 and 3-20, Eqs. 3-27 and 3-28 show that for higher values of VC when Eq. 3-8 is not satisfied and some of the transistors operate in the saturation-mode, the transconductances, although dependent on Vid, still can be controlled by VC in a linear fashion. This is very beneficial especially at low supply voltages since it extends the range of control VC have over the transconductance. Equations 3-27 and 3-28 also show that both Gm+ and Gm- are equal, hence maintaining the truly fully differential nature of the circuit even when transistors enter into the saturation-mode of operation.
In those filters, classical active RC filters are converted to all-MOS implementations with the aid of linearization techniques of MOSFET transistors7. Figure 2-8 shows an example of such an integrator using the four-quadrant structure shown in Fig. 2-7a. In this case, the integrator time-constant can be electronically tunable using VC1 and VC2. In fact, using Eq. 2-33, the differential output voltage can be written as: K VC1 VC 2 ³ Vi Vi dt C -f t VO VO Figure 2-8. A tunable integrator.