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

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Figure 55. Rejections of a constant Q (Q=10) and constant BW (BW=20MHz) second order bandpass filter II.1.d Double Notch Topologies Another possible topology has been studied, consisting in two cascaded notch filters creating a selective bandwidth as illustrated in Figure 58. Once again, the transfer function of a single notch filter can be obtained from the low-pass transfer function by means of the following transformation: s. BWω s → , 2 2 (II.22) s + ω0 where BWω is the filter stopband bandwidth. This leads to the following transfer function of a double notch, considering their quality factor: H DNF ( s) 2 2 2 2 s + ω1 s + ω2 = . . 2 sω1 2 2 sω2 2 ω1 + + s ω2 + + s Q Q 1 - 46 - 2 (II.23) The low-pass to notch transformation [II.3] corresponds to the transformation of the passive elements of the circuit given in Figure 56:
Figure 56. Low-pass to Notch Transformation Hence, a possible implementation of such a filter is given in Figure 57. Figure 58 shows that, although it can reject close adjacent channels, this solution requires a low pass filtering of harmonic frequencies as well as a high pass filter for the rejection of low frequency interferers. Vin - 47 - Vout Figure 57. Double Notch Filter schematic
Page 1: UNIVERSITE DE LIMOGES ECOLE DOCTORA
Page 5 and 6: Acknowledgments En préambule à ce
Page 7 and 8: Summary ACKNOWLEDGMENTS ...........
Page 9 and 10: V. A PERSPECTIVE FOR FUTURE DEVELOP
Page 11 and 12: French Introduction Les signaux TV
Page 13 and 14: I. Introduction to TV tuners and to
Page 15 and 16: I.1.b.ii Digital modulations In dig
Page 17 and 18: makes the covering of a large terri
Page 19 and 20: I.1.c.iii Terrestrial spectrum Firs
Page 21 and 22: I.1.e Broadband Reception Systems F
Page 23 and 24: I.2.b TV Tuner High Performance Spe
Page 25 and 26: I.2.b.ii High linearity Although co
Page 27 and 28: I.3 RF Filter Specifications I.3.a
Page 29 and 30: 27. This leads to the downconversio
Page 31 and 32: These adjacent channel rejection re
Page 33 and 34: Above 870MHz, there are no more ter
Page 35 and 36: Newest silicon tuners generations,
Page 37 and 38: I.6 References [I.1] B. Razavi, RF
Page 39 and 40: II. Challenges of RF Selectivity Fo
Page 41 and 42: Figure 39. H3 and N+5 rejections of
Page 43 and 44: Figure 43. Second order Low-pass Fi
Page 45 and 46: Figure 46 illustrates the transfer
Page 47 and 48: H HPF s ( s) = s 1 + ω This corres
Page 49: Topologies comparison for a same Q-
Page 53 and 54: II.2 Passive LC Second Order Bandpa
Page 55 and 56: A possible solution is to split the
Page 57 and 58: II.2.c Second Order Bandpass Filter
Page 59 and 60: Figure 69. Band Switching Figure 70
Page 61 and 62: Another paper [II.7] provides a FOM
Page 63 and 64: A parallel self resonating circuit
Page 65 and 66: This gives the following values for
Page 67 and 68: Vb - 63 - M1 M2 Zin Figure 76. Anot
Page 69 and 70: when given, reported noise figures
Page 71 and 72: In all publications dedicated to Gm
Page 73 and 74: II.4.c Second Order Bandpass Filter
Page 75 and 76: Figure 87. Biquad Schematic The Gm-
Page 77 and 78: Vin Rm - 73 - C Vout Figure 89. Der
Page 79 and 80: Figure 93 depicts the RF performanc
Page 81 and 82: A second advantage of advanced BiCM
Page 83 and 84: II.7 Conclusion As a conclusion, th
Page 85 and 86: [II.13] C. Andriesei, L. Goras, and
Page 87 and 88: III.I Theoretical Study III. Gm-C F
Page 89 and 90: g V m3 in III.1.b Linearity Conside
Page 91 and 92: Assuming an ideal input transconduc
Page 93 and 94: Figure 102. Linearity of the filter
Page 95 and 96: Furthermore, a Gm-C circuit is not
Page 97 and 98: In terms of noise, the Flicker nois
Page 99 and 100: 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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The frequency tunability is ensured
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V.3 State-of-the-Art V.3.a 4-path F
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V.4 Conclusion In this chapter, it
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IEEE International, 2009, pp. 222-2
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RF selectivity challenges In this t
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The positive feedback Rauch filter
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It is worth highlighting that FOM1
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étudiée. Il s’avère que la lin
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It is worth noticing that S0 only d
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A.3 Signal-to-Noise Ratio These dif
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A.5 Friis’ Formula In case of mul
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A.7 References [A.1] Friis, H.T., N
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To estimate the influence of the di
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Now, let’s have a look to the cub
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Figure 200. Third order intercept p
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B.2 RF Filter Linearity Measurement
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B.2.c IIP2 measurement To measure t
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- 199 -
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C.1 Gyrator-C filtering year Ref. f
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C.2 Gm-C Filtering year Ref. f0 (MH
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year C.3 Rm-C filtering Ref. f0 (MH
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C.5 References C.5.a Gyrator-C filt
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[C.23] J. De Lima and C. Dualibe,
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- 211 -
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this gives: I I I md d1 d 2 = I I =
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D.2 MOS Degenerated Common-Source C
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⎛ I s ⎞ Vout = Vin + U T ln ⎜
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Computing, this leads to: V out + v
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- 221 -
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- 223 -
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FIGURE 54. H3 AND N+5 REJECTIONS AC
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FIGURE 168. PVT VARIATIONS OF THE F
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