2.3 Linearity and Distortion in RF Circuits

Chapter 2.3 Linearity and Distortion in RF Circuits

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

  • 1 Issues in RFIC Design: Noise, Linearity, and Signalswhere f2rms is the rms phase-noise power density in units of [rad2/Hz]. Note that single-sideband phase noise is by far the most common type reported and often it is not specified as SSB, but rather simply reported as phase noise. However, alterna-tively, double sideband phase noise is given by: LOLO2DSBrmscarrierLO()()() 10log10log[]()NoiseNoisePNPωωωωωϕωéù+ D +- DD ==êúëû (2.38)From either the single-sideband or double-sideband phase noise, the rms jitter can be obtained as: DSBSSB( )( )1010rms180180 2( )1010[deg/ Hz]PNfPNffϕππDDD == (2.39)It is also quite common to quote integrated phase noise. The rms integrated phase noise of a synthesizer is given by: 212rmsrmsIntPN( )fff dfϕDD=ò (2.40)The limits of integration are usually the offsets corresponding to the lower and upper frequencies of the bandwidth of the information being transmitted. In addition, it should be noted that dividing or multiplying a signal in the time domain also multiplies or divides the phase noise. Thus, if a signal frequency is multiplied by N, then the phase noise is related by: 222rmsLOrmsLO2LOrmsLO2rms2()()()NNNNϕωωϕωωωϕωωϕω+ D =×+ D+ Dæö+ D=ç÷èø (2.41)Note this assumes that the circuit that did the frequency translation is noiseless. Also, note that the phase noise is scaled by N2 rather than N to get units of V2 rather than noise voltage. 2.3  Linearity and Distortion in RF CircuitsIn an ideal system, the output is linearly related to the input. However, in any real device the transfer function is usually a lot more complicated. This can be due to ac-tive or passive devices in the circuit, or the signal swing being limited by the power supply rails. Unavoidably, the gain curve for any component is never a perfectly straight line, as illustrated in Figure 2.6.The resulting waveforms can appear as shown in Figure 2.7. For amplifier satu-ration, typically the top and bottom portions of the waveform are clipped equally,