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

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201. B.1.d Example Let’s consider a differential pair made with bipolar transistors as depicted in Figure Figure 201. Differential pair The output voltage is then given by : ⎛ Vin Vout = RI e tanh ⎜ ⎝ 2U T ⎞ ⎟ ⎠ (B.22) Developing this expression leads to: ⎛ Vin V ⎜ out = RI e ⎜ ⎝ 2U T 3 Vin ⎞ − ⎟ 3 24U ⎟ T ⎠ (B.23) Hence, Thus, one gets: Rc I e k1 2U T = (B.24) Rc I e k 3 = − 3 24U T (B.25) 4 k1 IIP3 = = 4U T (B.26) 3 k 3 - 194 -
B.2 RF Filter Linearity Measurements In the following, it is assumed that the RF filter has a unity gain. If it were not the case, intercept point values would have to be corrected by the gain of the filter. This chapter aims at presenting how linearity has been measured in the laboratory [B.2]. B.2.a In-band IIP3 measurement To measure the in-band input referred third order intercept point, two closely-spaced tones are applied within the bandwidth of the filter. As explained, these two tones create intermodulation products. IIP3 can then be related to the difference between the wanted signal level and the intermodulation products levels by the following equation: IMR3 IIP3 = + Pin _ 2tones (B.27) 2 where Pin_2tones is the power level of the two applied tones. Power IMR3 Figure 202. Measurement of the in-band ΙΙΠ3 - 195 - Frequency
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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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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 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: Figure 200. Third order intercept p
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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