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

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g V m3 in + g′ ′ V 3 m3 in Replacing: 3 g 1g 2r ⎛ 0 3 g 1r0 g 1r ⎞ m m m m 0 3 3 3 1 jr0C bω ( αVin βV ) ⎜ ′ ⎛ ⎞ + = + in + gm 2 + g′ ′ ⎟ m2 ( αVin + βVin ) + ( αVin + βVin ) 1 jr0C aω ⎜ 1 jr0C aω ⎜ 1 jr0C aω ⎟ + + ⎟ r0 ⎝ ⎝ + ⎠ ⎠ (III.15) Thus, this leads to: α m3 = , gm1g m2r0 1 + jr0C bω + 1 + jr C ω r which corresponds to the gain of the filter transfer function. 0 a g - 86 - 0 (III.16) The second equation gives: 3 g 1g 2r ⎛ 0 g 1r0 g 1r ⎞ m m m m 0 3 1 jr0C bω gm3 β ⎜ ′ ⎛ ⎞ + ′′ = + gm 2 + g ′′ ⎟ m2 α + β 1 jr0C aω ⎜ 1 jr0C aω ⎜ 1 jr0C aω ⎟ (III.17) + + ⎟ r0 ⎝ ⎝ + ⎠ ⎠ Hence, β g ′′ This finally gives: ⎛ − ⎜ g g ′′ m1 0 m1 0 3 m3 m2 m2 ⎜ 1 + jr0C aω ⎜1 jr0C aω ⎟ ⎟ ⎝ ⎝ + ⎠ = ⎠ (III.18) gm1g m2r0 1 + jr0C bω + 1 + jr C ω r 0 r a ⎛ + g′ ′ ⎜ 0 g r 3 ⎞ ⎞ ⎟ ⎟α 3 3 ⎛ g 1 2 0 1 ⎞ ⎛ ⎞ 0 ⎜ ′′ ⎛ ⎞ m gm r + jr Cbω gm1r0 gm1r0 3 g ′′ ′ ⎟ m3 ⎜ + 2 2 3 1 ⎟ − gm + gm ⎜ 0 0 1 ⎜ 0 1 ⎟ gm ⎝ + jr C ⎠ + ⎟ aω r jr C ⎝ aω ⎝ + jr0C aω ⎠ β = ⎠ 4 , (III.19) ⎛ g 1g 2r0 1 + jr ⎞ m m 0Cbω ⎜ + 1 ⎟ ⎝ + jr0C aω r0 ⎠ which corresponds to the third order non-linear term. Determining by design the achievable IIP3 of all transconductors leads to the various gmi3, thanks to the formula: 4 IIP3 g ′′ mi = . gmi . 10 . (III.20) 3 β and α can thus be computed and this gives the achievable IIP3 of the filter.
Assuming an ideal input transconductor Gm3, it is possible to plot an abacus of the linearity of the filter versus the linearity of Gm2, for various Gm1 linearity levels. Gm1 and Gm2 have been set to a common same value for the plot. Figure 99. Filter Linearity versus Gm linearity Figure 100. Filter Linearity versus Q-factor Figure 99 and Figure 100 show that linearity is intrinsically strongly degraded by the gyrator. For instance, if both transconductors have 20dBm OIP3, filter linearity will reach 10dBm IIP3 for a filter Q-factor of 5. And the higher the Q-factor, the stronger this degradation. - 87 -
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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
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 and 50: Topologies comparison for a same Q-
Page 51 and 52: Figure 56. Low-pass to Notch Transf
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: g V m3 in III.1.b Linearity Conside
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
Page 101 and 102: Idiff (A) levels reached with this
Page 103 and 104: III.2.e Unbalanced Differential Pai
Page 105 and 106: Hence, the combination of the expon
Page 107 and 108: Technique Current Increase Source D
Page 109 and 110: Using this structure and considerin
Page 111 and 112: The dimensioning of the transistors
Page 113 and 114: III.3.c Gm-cells with MGTR III.3.c.
Page 115 and 116: Furthermore, the high sensitivity t
Page 117 and 118: Figure 136. Filter in-band IIP3 ver
Page 119 and 120: III.4 Comparison of the filters III
Page 121 and 122: III.5 Conclusion Once the Gm-C seco
Page 123 and 124: IV. Rauch Filtering IV.1 Sallen-Key
Page 125 and 126: Thus, an equation linking Q and Gai
Page 127 and 128: IV.1.c.ii Proposed positive feedbac
Page 129 and 130: For both Rauch and Sallen-Key filte
Page 131 and 132: The high sensitivity to passive com
Page 133 and 134: 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
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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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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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FIGURE 54. H3 AND N+5 REJECTIONS AC
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FIGURE 168. PVT VARIATIONS OF THE F
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