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

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B.1 General Considerations APPENDIX B B.1.a “Single-tone” input signal Though classical electronic components such as amplifiers are considered as linear elements for small signals, they have non-linear transfer characteristics. On Figure 197 are shown the theoretical transfer characteristic of an amplifier as well as its simulated one. It consists in a linear zone between two saturated portions. Let’s consider x ( t) = X cos( ωt) = X cosφ (B.1) For X < X max , the response to a sinusoidal input remains sinusoidal since the transfer characteristic is linear. In the frequency domain, a single frequency tone in both input and output is then obtained. Figure 197. Theoretical and simulated saturated gain of an amplifier Now, if max X X > , the input signal will be subject to saturation in the amplifier. The output signal will no longer be sinusoidal since the sine edges are cut. Thus discontinuities will lead to harmonics in the frequency domain. This phenomenon is called distortion. - 188 -
To estimate the influence of the distortion on a system, let’s expand, for small signal, the non-linear response with a Taylor series: 2 3 y = k0 + k1x + k2 x + k3 x + ... (B.2) Introducing the previously defined input signal, we get: With: y = Y + Y φ + Y cos( 2φ) + Y cos( 3φ ) (B.3) 0 1 cos 2 3 Y Y 1 0 1 2 = k0 + k2 X 2 Y 2 1 2 = k2 X 2 = k1X + k3 X 4 Y 3 + ... 3 3 1 3 = k3 X 4 + ... - 189 - + ... + ... (B.4) (B.5) (B.6) (B.7) If the system were perfectly linear and without offset, only k1 would remain among all kis, since this factor corresponds to the gain of the system. For a non-linear system, the amplitude of the fundamental Y1 is changed with the addition of a cubic term. Thus Y1 can be either smaller or larger than that obtained with a linear system. It is referred as an expansive characteristic when k3>0 and to a compressive characteristic when k3 0 Figure 198. Expansion and compression point at 1dB Linear characteristic Non-linear characteristic k3 < 0 X (log)
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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
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IV.2.b Innovative Implementation of
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esulting gain K, constituted of the
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Table 25. Sum-up of the OA specific
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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 187 and 188: A.3 Signal-to-Noise Ratio These dif
Page 189 and 190: A.5 Friis’ Formula In case of mul
Page 191: A.7 References [A.1] Friis, H.T., N
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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