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

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IV.1.b Sallen-Key Filters The Sallen-Key second order bandpass filter is described in the literature [IV.2]. The schematic is depicted in Figure 139, where K is the voltage gain of the voltage amplifier. Figure 139. Sallen-Key bandpass filter schematic The transfer function of this structure is given by: jCωKR ⎛ 1 1 ⎞ R1 ⎜ + ⎟ ⎝ R1 R3 ⎠ ( jω ) = . 2 (IV.1) 1 ⎛ 2 1− K 1 ⎞ ( jCω) 1+ jCω ⎜ + + ⎟ + 1 ⎛ 1 1 ⎞ ⎝ R2 R3 R1 ⎠ 1 ⎛ 1 1 ⎞ ⎜ + ⎟ ⎜ + ⎟ R2 ⎝ R1 R3 ⎠ R3 ⎝ R1 R2 ⎠ Thus, the resonant frequency is defined by H SK f 0 = 1 2πC and the quality factor of this bandpass filter is: Q 3 1 ⎛ 1 1 ⎞ ⎜ + ⎟ R3 ⎝ R1 R2 ⎠ 1 R ⎛ 1 ⎜ ⎝ R 1 ⎞ + R ⎟ ⎠ 1 − K 1 + R R 2 + R Filter gain at the resonant frequency is given by: 1 - 120 - 2 2 (IV.2) 3 1 2 = . (IV.3) K Gain = . ⎛1 − K 1 2 ⎞ R1 ⎜ + + ⎟ ⎝ R3 R1 R2 ⎠ (IV.4)
Thus, an equation linking Q and Gain can be deduced: R1 1 ⎛ 1 1 ⎞ Q = . Gain K R ⎜ + 3 R1 R ⎟ . (IV.5) ⎝ 2 ⎠ From the transfer function formula, a stability issue comes out. Indeed, the denominator should only have roots with negative real parts, so the jCω term of this second order polynomial has to be negative as well. This leads to the condition: ⎛ 1 2 ⎞ K < ⎜ + ⎟ ⎟R3 + 1. (IV.6) ⎝ R1 R2 ⎠ If the voltage gain K of the amplifier does not fulfill this condition, the filter is unstable. IV.1.c Rauch Filters IV.1.c.i Negative feedback Rauch filter In the literature, the “Rauch” filter is always described in a negative feedback configuration [IV.2], as depicted in Figure 140, where K is the voltage gain of the voltage amplifier. H R− Figure 140. Negative feedback Rauch bandpass filter schematic The transfer function of the filter can be computed, which gives: jCωKR3 − ⎛ 1 1 ⎞ R1 ( 1+ K ) ⎜ + ⎟ ⎝ R1 R2 ⎠ ( jω ) = 2 (IV.7) 1 ⎛ 1+ K 1 1 ⎞ ( jCω) 1+ jCω ⎜ ⎜2 + + ⎟ + 1+ K ⎛ 1 1 ⎞ ⎝ R3 R1 R2 ⎠ 1 ⎛ 1 1 ⎞ ⎜ + ⎟ ⎜ + ⎟ R3 ⎝ R1 R2 ⎠ R3 ⎝ R1 R2 ⎠ - 121 -
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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
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
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: IV. Rauch Filtering IV.1 Sallen-Key
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
Page 141 and 142: Figure 153. OA voltage gain versus
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
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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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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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