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

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The quality factor QL of a non-ideal inductor can also be defined as: ω0 L QL = , (II.12) R s with Rs being the series losses of this inductor. By means of a series to parallel transformation, this circuit can be converted into a parallel resonator. Then, a parallel to L and C resistance Rp appears which is computed as follows: This leads to the following circuit: R = ( Q 1) R (II.13) p 2 L + Figure 49. RLC parallel circuit Let’s compute the quality factor of this circuit: s R p Q0 = . (II.14) ω0 L Replacing with previous equations, we get: Now, Q 1 Q ≈ 0 2 ( QL + 1) Rs = . (II.15) ω L 0 = QL + QL with L >> 1 QL 0 - 42 - Q (II.16) If it is considered that the Q-factor of the inductor is above 10, then the latter equation can be obtained. It demonstrates how crucial it is to use high-Q inductors since the quality factor of the filter is directly the one of the inductor. II.1.c.iii Difference Between BPF and a Combination of HPF and LPF The combination of a first low-pass filter with a first order high-pass filter also creates a second order bandpass filtering. A high-pass transfer function may be obtained from a low- pass one by means of the following transformation [II.3]: ωHPF s → s . (II.17) Considering ω1 as cut-off frequency, this leads to:
H HPF s ( s) = s 1 + ω This corresponds to inverting capacitors and inductors in the circuit (see Figure 50), and to modify their value according to the transformation. Figure 50. Low-pass to High-pass Transformation 1 - 43 - (II.18) Combining low-pass (with ω2 as cut-off frequency) and high-pass topologies, it leads to the following bandpass filter transfer function: s H BPF ( s) = H LPF ( s). H HPF ( s) = . 2 ⎛ 1 1 ⎞ s (II.19) 1+ s ⎜ + + ω1 ω ⎟ ⎝ 2 ⎠ ω1ω2 Assuming ω1ω2 Q = and ω 0 = ω1ω2 , (II.20) ω1 + ω2 this gives: 1 H BPF ( s) = . ⎛ s ω0 ⎞ (II.21) 1+ jQ ⎜ − ⎟ ⎝ ω0 s ⎠ 1 Thus, Q is maximum when ω1=ω2 and this gives max 2 = Q . The combination of a low-pass and a high-pass filter gives a bandpass filter, but this filter has a selectivity limited to 1 . Figure 67, shown further, underlines that such selectivity is not enough to reach the RF 2 selectivity specifications. II.1.c.iv Assessment of the Topology The main advantage of the bandpass filter topology is its ability to reach a smaller bandwidth than a combination of a low-pass and a high-pass filters. Based on only two reactive components for a second order filter, the selectivity can be adjusted to whatever -3dB
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: Figure 46 illustrates the transfer
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 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
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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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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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