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

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The quality factor of such a circuit is given by the formula: Q 1 R ⎛ 1 ⎜ ⎝ R 1 ⎞ + R ⎟ ⎠ 1+ K 1 2 + R R 1 + R ( 1+ K ) 3 1 2 = . (IV.8) 3 1 Major drawback of this structure is that it requires a very high gain K to reach useable Q-factors. This limits the use of this topology at RF frequencies. Figure 141 highlights, for a certain combination of passive components (R1=50Ω, R2=10Ω and R3=500Ω), that gain K should be higher than 100, meaning a 40dB voltage gain, to obtain a quality factor of 2.5 or more. Such a high gain-bandwidth product (GBW) amplifier becomes very difficult to design. Due to a very poor selectivity versus gain trade-off, this structure has not been studied further. Figure 141. Q-factor of the negative feedback Rauch filter versus gain K - 122 - 2
IV.1.c.ii Proposed positive feedback Rauch filter The positive feedback Rauch filter is proposed, whose schematic is depicted in Figure 142, where K is the voltage gain of the voltage amplifier. It shows different trade-offs in terms of selectivity versus K and passive components values than its negative feedback counterpart. H R+ Figure 142. Positive feedback Rauch bandpass filter schematic Hence, the filter transfer function HR(jω) can be computed as: jCω K R ⎛ 1 1 ⎞ R1 ( 1− K ) ⎜ + ⎟ ⎝ R1 R2 ⎠ ( jω ) = (IV.9) 2 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 ⎠ Such a filter resonates at a central frequency determined by the passive components of the circuit f 0 = 1 2πC - 123 - 3 1 ⎛ 1 1 ⎞ ⎜ + ⎟ . (IV.10) R3 ⎝ R1 R2 ⎠ The resonant frequency is similar to the Sallen-Key topology. However, in the present case, the quality factor is: Q ( 1− K ) 3 1 2 = . (IV.11) 1 2 1 R ⎛ 1 ⎜ ⎝ R 1 ⎞ + R ⎟ ⎠ − K R 1 + R 1 + R The filter gain at the central frequency is given by: 3 1 2
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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
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 and 124: IV. Rauch Filtering IV.1 Sallen-Key
Page 125: Thus, an equation linking Q and Gai
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
Page 175 and 176: 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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