Radio Frequency Integrated Circuit Design - Webs

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Voltage-Controlled Oscillators V tank = i fundRp = kI AVERp 283 (8.74) Thus, equations to predict oscillation amplitude have now been derived. By comparing (8.73) and (8.74) to (8.68), it can be seen that a given amount of dc current will lead to more current at the fundamental frequency in the case of the resistive tail as opposed to the current tail. 8.17 Phase Noise A major challenge in most oscillator designs is to meet the phase noise requirements of the system. An ideal oscillator has a frequency response that is a simple impulse at the frequency of oscillation. However, real oscillators exhibit ‘‘skirts’’ caused by instantaneous jitter in the phase of the waveform. Noise that causes variations in the phase of the signal (distinct from noise that causes fluctuations in the amplitude of the signal) is referred to as phase noise. The waveform of a real oscillator can be written as V osc = A cos [� o t + � n (t)] (8.75) where � n (t) is the phase noise of the oscillator. Here amplitude noise is ignored because it is usually of little importance in most system specifications. Because of amplitude limiting in integrated oscillators, typically AM noise is lower than FM noise. There are several major sources of phase noise in an oscillator, and they will be discussed next. 8.17.1 Linear or Additive Phase Noise and Leeson’s Formula In order to derive a formula for phase noise in an oscillator, we will start with the feedback model of an oscillator as shown in Figure 8.33 [7]. From control theory, it is known that Nout(s) Nin(s) = H1(s) 1 − H(s) (8.76) where H(s) = H 1(s)H2(s). H(s) can be written as a truncated Taylor series: Figure 8.33 Feedback model of an oscillator used for phase-noise modeling.
284 Radio Frequency Integrated Circuit Design H( j�) ≈ H( j�o ) + �� dH d� (8.77) Since the conditions of stable oscillation must be satisfied, H( j�o ) = 1. We let H1( j� o ) = H 1, where H 1 is a constant determined by circuit parameters. Now (8.76) can be rewritten using (8.77) as rule Nout(s) Nin(s) = H 1 −�� dH d� Noise power is of interest here, so | Nout(s) Nin(s) | 2 = |H1| 2 (��) 2 | dH d� | 2 (8.78) (8.79) This equation can now be rewritten using H(�) = |H | e j� and the product dH d |H | = d� d� e j� + |H | je j� d� d� noting that the two terms on the right are orthogonal: | dH d� | 2 d |H | = | d� | 2 + |H | 2 | d� d� | 2 (8.80) (8.81) At resonance, the phase changes much faster than magnitude, and |H | ≈ 1 near resonance. Thus, the second term on the right is dominant, and this equation reduces to | dH d� | 2 = | d� d� | 2 Now substituting (8.82) back into (8.79), | Nout(s) Nin(s) | 2 = |H 1| 2 (��) 2 | d� d� | 2 (8.82) (8.83)
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Radio Frequency Integrated Circuit
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Radio Frequency Integrated Circuit
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Contents Foreword xv Acknowledgment
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Contents 3.8 Base Shot Noise Discus
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Contents 5.25 Packaging 135 5.25.1
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Contents 7.12 General Design Commen
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Contents 9.5 Some Simple Image Reje
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Foreword I enjoyed reading this boo
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Foreword estimates of parasitic cap
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xx Radio Frequency Integrated Circu
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2 Radio Frequency Integrated Circui
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2 Issues in RFIC Design, Noise, Lin
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Issues in RFIC Design, Noise, Linea
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The input noise is Issues in RFIC D
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2.5 Filtering Issues Issues in RFIC
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3 A Brief Review of Technology 3.1
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A Brief Review of Technology IC = I
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3.4 Small-Signal Model A Brief Revi
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3.6 High-Frequency Effects A Brief
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A Brief Review of Technology If thi
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A Brief Review of Technology Soluti
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A Brief Review of Technology 3.8 Ba
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A Brief Review of Technology • Pi
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A Brief Review of Technology 3.16,
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A Brief Review of Technology The tr
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4 Impedance Matching 4.1 Introducti
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Impedance Matching Z 2 = Z in + j
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Figure 4.5 A Smith chart. Impedance
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4.3 Impedance Matching Impedance Ma
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Impedance Matching Figure 4.9 Which
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Impedance Matching Figure 4.11 Lowp
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Impedance Matching section, convers
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Impedance Matching Much as in the p
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Impedance Matching Note that dots i
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Impedance Matching Thus, in the fir
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Impedance Matching The exact resist
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Impedance Matching 4.10 Quality Fac
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Impedance Matching Example 4.7 Matc
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Impedance Matching line to change w
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Impedance Matching S22 = b 2 a2 | a
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Impedance Matching without the need
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96 Radio Frequency Integrated Circu
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98 Radio Frequency Integrated Circu
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100 Radio Frequency Integrated Circ
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Page 326 and 327: Voltage-Controlled Oscillators back
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10 Power Amplifiers 10.1 Introducti
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Power Amplifiers where G is the pow
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Power Amplifiers Figure 10.4 Optima
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Power Amplifiers Figure 10.8 Power
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Power Amplifiers Figure 10.9 Curren
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Power Amplifiers The efficiency is
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Power Amplifiers sinusoid), this pe
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Power Amplifiers Note that this agr
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Power Amplifiers stabilization. The
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Power Amplifiers Solution The first
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Power Amplifiers Figure 10.22 Class
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Figure 10.24 Class E waveforms. Pow
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Power Amplifiers B = 0.1836 0.81Q R
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Power Amplifiers Figure 10.25 Initi
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Power Amplifiers added to the funda
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Power Amplifiers 10.8.1 Variation o
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Example 10.4 Class F Power Amplifie
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Figure 10.36 Class H amplifier. Pow
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Power Amplifiers ered quite good. O
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Power Amplifiers Figure 10.39 Time-
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Figure 10.42 High-Q matching circui
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Figure 10.44 Multiple transistors.
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Power Amplifiers Figure 10.48 Combi
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Power Amplifiers have very narrow b
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Power Amplifiers Figure 10.53 Feedf
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Power Amplifiers in class A (input
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About the Authors John Rogers recei
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Index 1-dB compression point, 30-32
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Index Damped resonator, 247-48 Emit
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Index Local oscillator, 5 Mixing co
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Index Quadrature phase shift keying
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