7.5 Stability

Chapter 7.5 Stability

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

  • 214 LNA DesignIf Rout is large enough that iout is always much less than IB, the linearity will be good, as the operating point will not change significantly over a cycle of the sig-nal. It is important to keep the peak output current less than the bias current. This means that: ,peakout||oBvIR< (7.106)If this is the case, then there will be no clipping of the waveform.The linearity can be improved by increasing IB, or Rout. This will continue to improve performance as long as the power supply voltage is large enough to al-low this swing. Thus, for large Rout, the power supply limits the voltage swing and therefore the linearity. In this case, the current is not a limiting factor.7.5  StabilityA number of different but equivalent measures of stability can be derived from S-parameters [5]. For RFIC design, the stability factor K and the auxiliary stability factor B1 are typically determined directly using a simulator rather than calculating them from the S-parameters. Unconditional stability is guaranteed by the following two conditions: >>110KB (7.107)For the sake of completeness, these are based on S-parameters as follows [5]: --+ D=222112212 211 ||||| |2 ||SSKS S (7.108)and = +-- D222111221 ||||| |BSS (7.109)where 11 2212 21S SS SD =- (7.110)Instability at any frequency, not just at the operating frequency, can result in unwanted oscillations that render the circuit inoperable and hence must be avoided. Thus, frequencies are swept and K and B1 are determined over the full frequency range for which the transistor has gain. For any frequency for which K is less than 1 or B1 is less than 0, the circuit is not unconditionally stable, meaning that a load or source impedance exists for which the circuit will be unstable. Having identified problem frequencies, a typical further step might be to plot source and load stability circles at the problem frequency to determine the impedance for which the instability occurs. If such problem impedances are safely away from the actual impedance, it may not be necessary to modify the circuit. However, in some cases the source or