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

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II.3 Towards a Fair Figure-of-Merit II.3.a Required Parameters to Handle a Fair Comparison To be able to compare the performances of the various structures of RF filters (passive LC, Gyrator-C, Gm-C, n-path filters or else) that may be found in the literature, a common reference figure is needed. This figure, called figure-of-merit (FOM), should take into account all parameters related to the specifications discussed in introduction, which are: - RF dynamic range: linearity and noise; - Frequency tuning range; - Selectivity: quality factor, harmonics and adjacent channels rejections; - Maximum working frequency. Some other aspects might as well be taken into account, such as the process variations, the gain at the central frequency or even the area occupied by the circuit. II.3.b Study of the Figures-of-Merit Found in the Literature Let’s have a look at some FOMs found in the literature. In [II.5], K. Kwon et al, a FOM for linear and low-noise low-pass filters is presented. Their FOM is the following: OIP3. f max . TR. N FOM = (II.29) ( F −1) Pdc where F is the noise factor, Pdc/N is the power consumption per pole and TR is the frequency tuning range. The quality factor of the filter, for a band-pass, is an important parameter to consider and is not taken into account in this FOM. Although too high power consumption would be an issue, it is not a primary specification since TV is not a portable application. Input parameters would also be preferred because of their independence of the filter gain. Another FOM is introduced in [II.6]. After having described a passive band-pass filter, F. Dülger et al. have introduced the following figure-of-merit, which is taken in dB: N. SFDR. f 0. Q FOM dB = (II.30) Pdc where Pdc/N is still the power consumption by pole, SFDR is the Spurious Free Dynamic Range. However, this FOM does not take into account the frequency tunability. There is reference neither to linearity nor to noise in this figure, which makes this FOM not suitable for the previously described purposes. - 56 -
Another paper [II.7] provides a FOM but here again no mention is made about linearity or noise: This FOM is plotted versus ⎛ f 0 N ⎞ FOM = log ⎜ ⎟ (II.31) ⎝ Pdc ⎠ f f max min . II.3.c Proposed Figure-of-Merit To be sure to use a suitable figure-of-merit, a new FOM is introduced, taking into account all the parameters that have been mentioned previously. f max where TR = is the tuning range. f min IIP3− NF . FOM 10 moy max 10 = Q . f . TR (II.32) This FOM can also be normalized to the power consumption. - 57 -
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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 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: Figure 69. Band Switching Figure 70
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
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
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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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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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