Radio Frequency Integrated Circuit Design - Webs

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LNA Design where VA is the Early voltage of the transistors. An ac current into the collector can be written as a function of ac current ic . ro_ac(i c ) = V A IC + ic 181 (6.88) Assuming for this analysis that there is no significant impedance in the circuit other than the transistor output resistance, the ac collector-emitter voltage can be written as Now from the relationship vce = i c r o_ac = i cV A IC + ic = V A ic IC 1 + i c IC (6.89) x 1 + x = x − x 2 + x 3 − x 4 + x 5 ... (6.90) (6.89) can be written out as a power series: vce = VA� ic IC� − VA� ic IC� 2 + VA� ic IC� 3 = ro_dc ic − ro_dc The intermodulation current can now be easily determined. k 1 i IP3 = 2 = 2 1 √3k 3 √ 3 r o_dc I 2 C ro_dc Thus, the output intermodulation voltage is just v OP3 = 2IC ro (6.93) √3 = 2I C √ 3 IC i 2 c + ro_dc I 2 i C 3 c (6.91) (6.92) This is a fairly intuitive result. As the dc current is increased, the ac current is a smaller percentage of the total, and therefore the circuit behaves more linearly. Thus, designers have two choices if the current source is not linear enough. They can either increase the current or increase the output impedance.
182 Radio Frequency Integrated Circuit Design Also, it should be noted that this relationship only holds true if the transistor does not start to saturate. If it does, the nonlinearity will get much worse. 6.4.3 High-Frequency Nonlinearity in the Bipolar Transistor Many frequency-dependent devices can reduce the linearity of a circuit. One of the most troublesome is the base-collector junction capacitance C� . This capacitance is voltage dependent, which results in a nonlinearity. This nonlinearity is especially important in circuits with low supply voltages because the capacitance is largest at low reverse bias. This capacitor’s effect is particularly harmful for both frequency response and nonlinearity in the case of a standard common-emitter amplifier. In this configuration, C� is multiplied by the gain of the amplifier (the Miller effect) and appears across the source. The value of C� as a function of bias voltage is given by C� (V ) = C�o �1 − V � o� (1/n) (6.94) where C�o is the capacitance of the junction under zero bias, � o is the builtin potential of the junction, and n is usually between 2 and 5. Since this capacitor’s behavior is highly process dependent and hard to model, there is little benefit in deriving detailed equations for it. Rather, the designer must rely on simulation and detailed models to predict its behavior accurately. 6.4.4 Linearity in Common-Collector Configuration The common-collector amplifier is often called the emitter-follower because the emitter voltage ‘‘follows’’ the base voltage. However, the amplifier cannot do this over all conditions. If the current is constant, vBE is constant and the transfer function will be perfectly linear. However, as vo changes, and iout = vo /R out will change as shown in Figure 6.31. Thus, iE will change and so will vBE, and there will be some nonlinearity. If R out is large so 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 signal. It is important to keep the peak output current less than the bias current. This means that |v o,peak| R out < IB (6.95)
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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 back
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I C_AVE = 1 Voltage-Controlled Osci
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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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