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

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D.3 Linearity Enhancement of an Emitter-Follower D.3.a Initial Linearity Let’s consider the emitter follower illustrated in Figure 207. Figure 207. Emitter Follower Schematic Assuming that collector and emitter currents are equal, the current flowing through the load RL can be approximated to ie. Hence [D.2]: v out i e = (D.27) RL Then, considering a biasing current I, the output can be computed by: ⎛ I + ie ⎞ Vout + vout = Vin + vin −U T ln ⎜ ⎟ (D.28) ⎝ I s ⎠ Computing, this leads to: ⎛ vout ⎞ ⎜ I + ⎟ ⎜ RL V + = + − ⎟ out vout Vin vin U T ln ⎜ I ⎟ (D.29) s ⎜ ⎟ ⎝ ⎠ Thus V out + v out = V in + v Now, DC biasing leads to in −U T ⎛ vout ⎞ ⎛ I s ⎞ ln ⎜ ⎜1+ ⎟ + U T ln⎜ ⎟ (D.30) ⎝ RL I ⎠ ⎝ I ⎠ - 216 -
⎛ I s ⎞ Vout = Vin + U T ln ⎜ ⎟ , (D.31) ⎝ I ⎠ which simplifies equation (D.30). vout Since the term is close to 0, it is possible to develop Equation (D.31) with a RL I Taylor series, which gives: Hence 2 3 3 ⎡ v ⎛ ⎞⎤ out 1 ⎛ vout ⎞ 1 ⎛ vout ⎞ ⎢ ⎜⎛ vout ⎞ v + ⎟ ⎟ + ⎜ ⎟ ⎥ in = vout + U T − ⎜ o ⎢ ⎜ ⎜ ⎟ (D.32) R 2 ⎟ L I ⎥ ⎣ ⎝ RL I ⎠ 3 ⎝ RL I ⎠ ⎝⎝ RL I ⎠ ⎠⎦ ⎛ U ⎞ 1 U 1 U v in ≈ ⎜ + ⎟v − v + (D.33) ⎝ T T 2 T 3 1 out 2 out v 3 out RL I ⎟ ⎠ 2 ( R ) 3 L I ( RL I ) This expression is of the form v in = avout 2 3 + bvout + cv out (D.34) and we are looking for a solution of the type v out 2 3 = Avin + Bvin + Cvin (D.35) to compute the IIP3 of the emitter-follower stage. and in This leads to: ( ) ( ) ( ) 3 2 3 2 3 2 2 3 Av + Bv + Cv + b Av + Bv + Cv + c Av + Bv Cv v = a + (D.36) in in in in in Limiting to third order terms, we obtain: 3 2 2 v = aAv + aB + bA v + aC + cA v (D.37) in in ( ) ( ) 3 Identifying the two sides of this equation gives a system: aA = 1 Hence aC + cA 3 = 1 1 RL I A = = = a U T U T + RL I 1+ R I L in 0 4 - 217 - in in in in in (D.38) (D.39) (D.40) ( ) ( ) 4 c U T ⎛ RL I ⎞ U T RL I C = − = − 4 3 a 3 R I ⎜ = − U T RL I ⎟ . (D.41) ⎝ + ⎠ 3 U + R I This leads to: v out L T RL I 2 U T RL I 3 ≈ vin + Bvin − v 4 in (D.42) U + R I 3 T L ( U + R I ) T L L
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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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Figure 153. OA voltage gain versus
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Filtering in the mirror, by means o
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However, this feedback makes the fi
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Figure 160. OA Gain and phase versu
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IV.3.c Implemented Filter and Test
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Figure 165 depicts the layout of th
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Figure 169. PVT variations of the f
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IV.4 Rauch Filter Performances: Mea
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Figure 178. IIP3 versus input power
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IV.4.c Performances Sum-up The filt
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Table 30. Frequency Limitations of
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IV.7 References [IV.1] Y. Tsividis
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V. A Perspective for Future Develop
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V.2 4-path Filter Simulations V.2.a
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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
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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 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
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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: D.2 MOS Degenerated Common-Source C
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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