Radio Frequency Integrated Circuit Design - Webs

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Voltage-Controlled Oscillators Figure 8.15 Feedback analysis of a Colpitts common-base oscillator. vc is the output of the oscillator, we can define forward gain as vc /ve and feedback gain as ve ′ /v c . Forward Gain The forward gain is H1(s) = vc v e = g m Z tank 259 (8.27) where Z tank is defined in Figure 8.16 and has the following transfer function: Z tank = Z tank = Z L ||Rp || Z FB = 1 j�L 1 1 + R p + j�C 1(1 + j�r e C 2) 1 + j�re (C 1 + C 2) j�LR p [1 + j�re (C 1 + C 2)] (8.28) (R p + j�L)[1 + j�re (C 1 + C 2)] + j�LR p � j�C1(1 + j�re C 2) (8.29) Figure 8.16 Definition of Z tank and Z FB in oscillator small-signal model.
260 Radio Frequency Integrated Circuit Design Feedback Gain The feedback circuit is just a highpass filter as described in the previous section and has the following transfer function: Loop Gain Expression H2( j�) = This can be solved as follows: ve ′ vc = j�re C 1 1 + j�re (C 1 + C 2) (8.30) A = H1H2 (8.31) g m � j�r e C 1 � j�LR p = (R p + j�L)[1 + j�re (C 1 + C 2)] + j�LR p � j�C1(1 + j�re C 2) Gathering terms: A = H1H2 = −� 2 � g m re C 1LR p B (8.32) where B = (−j� 3 )re C 1C2LR p + (−� 2 )[re (C 1 + C 2)L + R p C 1L] + j�[r e R p (C 1 + C 2) + L] + R p . To determine oscillating conditions, (8.32) can be set equal to 1, and then the real and imaginary terms can be solved independently. The real part, which includes the even-order terms, is set equal to 1, and this sets the condition for gain. The result can be shown to be the same as for the closed-loop analysis, as done previously with final gain expression given by g m = �(C 1 + C 2) Q L (8.33) The imaginary part, which is defined by the odd-order terms, is also set equal to zero. This is equivalent to setting the phase equal to zero. The result, again, is equal to the previous derivation, with the result � = �o√ 1 + 8.7.4 Simplified Loop Gain Estimates 1 Q L � /� c (8.34) To gain understanding, to explain this simple result, and to provide advice on how to do the design, in this section appropriate simplifications and approxima-
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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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Voltage-Controlled Oscillators Loop
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Voltage-Controlled Oscillators freq
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Voltage-Controlled Oscillators Figu
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Voltage-Controlled Oscillators from
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Voltage-Controlled Oscillators [10]
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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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