7.4.2 Nonlinearity in the CMOS Transistor

Chapter 7.4.2 Nonlinearity in the CMOS Transistor

Radio Frequency Integrated Circuit Design Second Edition Book
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Radio Frequency Integrated Circuit Design Second Edition Book

  • 7.4 Linearity in Amplifiers 211conditions, k3 can be set to zero for improvements in linearity [4]. In MOSFETs, it turns out to be quite challenging to take advantage of this linearity improvement, since the peak occurs for a narrow region of bias conditions and the use of degen-eration resistance or inductance reduces this linearity improvement. 7.4.2  Nonlinearity in the CMOS TransistorWith perfect square law equations, it would seem there should be no third-order intermodulation. However, there are several reasons why third-order nonlinearity occurs. The standard square law equations are always accompanied with additional constraints that the input voltage is bigger than the threshold voltages (vGS > vT) and that the drain-source voltage is larger than the on voltage (vDS > vGS – vT). With large input or output voltages, these limits will introduce clipping and hence a third-order component. The small signal output current is related to the input by the transconductance gm, where gm is the derivative of current with respect to the input voltage. The voltage required to cause clipping can be estimated as Io/gm. This voltage is roughly equal to the one-tone 1-dB compression voltage, and vIP3 can be estimated to be larger by roughly 9.6 dB, or a voltage ratio of 3.02. For square law equations as given in Chapter 4, this can be expressed as: µλµλ-+»==--+ox2IP3ox() (1)23.023.021.51()()(1)GSTDSoGSTmGSTDSC WvvvILvvvWgCvvvL (7.97)Thus, given an operating current Io, linearity can be estimated if the transcon-ductance is known or if the input voltage and threshold voltage are known.Furthermore, all real CMOS transistors do not follow the square law model; hence, there will be some third-order component even without clipping. Finally, by adding degeneration, a third-order term is introduced due to the second-order term feeding back to the input and mixing with the fundamental component.7.4.3  Nonlinearity in the Output Impedance of the Bipolar TransistorAnother important nonlinearity in the bipolar or CMOS transistor is the output impedance. An example of where this may be important is in the case of a transis-tor being used as a current source. In this circuit, the base of the transistor is biased with a constant voltage and the current into the collector is intended to remain constant for any output voltage. Of course, the transistor has a finite output im-pedance, so if there is an ac voltage on the output, there is some finite ac current that flows through the transistor, as shown by ro in Figure 7.33. Worse than this, however, is the fact that the transistor’s output impedance will change with applied voltage and therefore can introduce nonlinearity.The dc output impedance of a transistor is given by: _ DCAoCVrI= (7.98)