III. Gm-C Filtering - Epublications - Université de Limoges

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A.2 The Various Origins of Noise A.2.a Origins of Noise There are three main origins of noise in electronic systems [A.3]. Thermal noise comes from the thermal Brownian motion of electrons, or any other charged particles, in an electrical component like a resistor for instance. This kind of noise is proportional to the absolute temperature. Indeed, since there would be no motion at the absolute zero temperature, this would mean the absence of noise. Thermal noise power are given by the following formulas: 2 vn = 4kTRB (A.4) 2 1 in = 4kT B (A.5) R where, k is the Boltzmann constant, T the absolute temperature given in Kelvin, B the effective noise bandwidth and R the resistance of the material in Ω. Shot noise originates from the corpuscular nature of the energy transport. The finite number of charged particles, electrons for example, creates a quantized random current flow which can be described by a Poisson distribution. It can be demonstrated that it gives the following shot noise power: i = 2qI B (A.6) 2 n d Flicker noise is a low-frequency phenomenon, also called “1/f noise”. It is due to conductivity variations of the material where the current flows, like the presence of contaminants and of defects in the crystal structure of the semiconductor material. The equivalent noise power is given by: α 2 I in = K B (A.7) β f K being a constant, α and β being coefficients. A.2.b Available Input and Output Noise Powers Input noise NI is defined as the thermal noise generated in the resistance of the signal source. The available noise power from a resistor is then: 2 v n N I = = kTB (A.8) 4R The available output noise can also be defined and will be referred as NO in the following. - 182 -
A.3 Signal-to-Noise Ratio These different types of noise together create a background noise power. This unwanted noise can degrade or mask a desired signal. To characterize this degradation, the Signal to Noise Ratio, called SNR in the following, is defined [A.4]. Taken at the input, the SNRin is defined as the ratio between the available signal power SI at the input and the available input noise NI: SI SNRin = (A.9) N I Taken at the output, SNRout is defined as the ratio of the available output power SO by the available output noise NO, which includes amplified input noise. SO SNRout = N (A.10) O Hence, signal quality is characterized by the final output SNR. A low SNRout corresponds to a signal strongly corrupted by noise. - 183 -
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UNIVERSITE DE LIMOGES ECOLE DOCTORA
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Acknowledgments En préambule à ce
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Summary ACKNOWLEDGMENTS ...........
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V. A PERSPECTIVE FOR FUTURE DEVELOP
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French Introduction Les signaux TV
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I. Introduction to TV tuners and to
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I.1.b.ii Digital modulations In dig
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makes the covering of a large terri
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I.1.c.iii Terrestrial spectrum Firs
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I.1.e Broadband Reception Systems F
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I.2.b TV Tuner High Performance Spe
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I.2.b.ii High linearity Although co
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I.3 RF Filter Specifications I.3.a
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27. This leads to the downconversio
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These adjacent channel rejection re
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Above 870MHz, there are no more ter
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Newest silicon tuners generations,
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I.6 References [I.1] B. Razavi, RF
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II. Challenges of RF Selectivity Fo
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Figure 39. H3 and N+5 rejections of
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Figure 43. Second order Low-pass Fi
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Figure 46 illustrates the transfer
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H HPF s ( s) = s 1 + ω This corres
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Topologies comparison for a same Q-
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Figure 56. Low-pass to Notch Transf
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II.2 Passive LC Second Order Bandpa
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A possible solution is to split the
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II.2.c Second Order Bandpass Filter
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Figure 69. Band Switching Figure 70
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Another paper [II.7] provides a FOM
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A parallel self resonating circuit
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This gives the following values for
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Vb - 63 - M1 M2 Zin Figure 76. Anot
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when given, reported noise figures
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In all publications dedicated to Gm
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II.4.c Second Order Bandpass Filter
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Figure 87. Biquad Schematic The Gm-
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Vin Rm - 73 - C Vout Figure 89. Der
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Figure 93 depicts the RF performanc
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A second advantage of advanced BiCM
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II.7 Conclusion As a conclusion, th
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[II.13] C. Andriesei, L. Goras, and
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III.I Theoretical Study III. Gm-C F
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g V m3 in III.1.b Linearity Conside
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Assuming an ideal input transconduc
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Figure 102. Linearity of the filter
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Furthermore, a Gm-C circuit is not
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In terms of noise, the Flicker nois
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Table 7 summarizes the specificatio
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Idiff (A) levels reached with this
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III.2.e Unbalanced Differential Pai
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Hence, the combination of the expon
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Technique Current Increase Source D
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Using this structure and considerin
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The dimensioning of the transistors
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III.3.c Gm-cells with MGTR III.3.c.
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Furthermore, the high sensitivity t
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Figure 136. Filter in-band IIP3 ver
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III.4 Comparison of the filters III
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III.5 Conclusion Once the Gm-C seco
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IV. Rauch Filtering IV.1 Sallen-Key
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Thus, an equation linking Q and Gai
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IV.1.c.ii Proposed positive feedbac
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For both Rauch and Sallen-Key filte
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The high sensitivity to passive com
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Furthermore, it should also be take
Page 135 and 136: IV.2.b Innovative Implementation of
Page 137 and 138: esulting gain K, constituted of the
Page 139 and 140: Table 25. Sum-up of the OA specific
Page 141 and 142: Figure 153. OA voltage gain versus
Page 143 and 144: Filtering in the mirror, by means o
Page 145 and 146: However, this feedback makes the fi
Page 147 and 148: Figure 160. OA Gain and phase versu
Page 149 and 150: IV.3.c Implemented Filter and Test
Page 151 and 152: Figure 165 depicts the layout of th
Page 153 and 154: Figure 169. PVT variations of the f
Page 155 and 156: IV.4 Rauch Filter Performances: Mea
Page 157 and 158: Figure 178. IIP3 versus input power
Page 159 and 160: IV.4.c Performances Sum-up The filt
Page 161 and 162: Table 30. Frequency Limitations of
Page 163 and 164: IV.7 References [IV.1] Y. Tsividis
Page 165 and 166: V. A Perspective for Future Develop
Page 167 and 168: V.2 4-path Filter Simulations V.2.a
Page 169 and 170: The frequency tunability is ensured
Page 171 and 172: V.3 State-of-the-Art V.3.a 4-path F
Page 173 and 174: V.4 Conclusion In this chapter, it
Page 175 and 176: IEEE International, 2009, pp. 222-2
Page 177 and 178: RF selectivity challenges In this t
Page 179 and 180: The positive feedback Rauch filter
Page 181 and 182: It is worth highlighting that FOM1
Page 183 and 184: étudiée. Il s’avère que la lin
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Page 189 and 190: A.5 Friis’ Formula In case of mul
Page 191 and 192: A.7 References [A.1] Friis, H.T., N
Page 193 and 194: To estimate the influence of the di
Page 195 and 196: Now, let’s have a look to the cub
Page 197 and 198: Figure 200. Third order intercept p
Page 199 and 200: B.2 RF Filter Linearity Measurement
Page 201 and 202: B.2.c IIP2 measurement To measure t
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Page 205 and 206: C.1 Gyrator-C filtering year Ref. f
Page 207 and 208: C.2 Gm-C Filtering year Ref. f0 (MH
Page 209 and 210: year C.3 Rm-C filtering Ref. f0 (MH
Page 211 and 212: C.5 References C.5.a Gyrator-C filt
Page 213 and 214: [C.23] J. De Lima and C. Dualibe,
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Page 217 and 218: this gives: I I I md d1 d 2 = I I =
Page 219 and 220: D.2 MOS Degenerated Common-Source C
Page 221 and 222: ⎛ I s ⎞ Vout = Vin + U T ln ⎜
Page 223 and 224: Computing, this leads to: V out + v
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Page 229 and 230: FIGURE 54. H3 AND N+5 REJECTIONS AC
Page 231 and 232: FIGURE 168. PVT VARIATIONS OF THE F
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