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

More documents

Recommendations

Info

II.4.b Gm-C filtering Gm-C and OTA-C filtering are both based on a similar principle which consists in synthesizing a transfer function by means of integrators built with Gm-cells or OTAs. As said, Gyrator-C filters consist in emulating an inductive behaviour. II.4.b.i From Integrators to Transfer Function Synthesis In the literature, it has been shown [II.15 and II.16] that all continuous time filters can be decomposed into an association of integrators. Thus, combining a few Gm-cell and capacitors, several different filters can be obtained. For instance, a possible way is to transform the circuit in an equivalent LC ladder and to replace inductors by gyrators. A way to create an integrator is to associate a capacitor to the transconductance. Indeed, the computation of the transfer function has an integrator form: Vout g m = . (III.62) V jCω in Assuming the transconductor non-infinite output resistance r0, this leads to a lossy integrator as depicted on Figure 81, having the following transfer function. V Figure 81. Lossy Integrator Vout m in g r0 = (III.63) 1 + jr Cω 0 Hence, the basic cell of these integrators, and so of Gm-C filters, is the Gm-cell. It is a transconductance amplifier which is able to convert an input voltage into an output current with a given gain gm, called transconductance. The literature deals with both OTAs and Gmcells when describing integrators. However, an OTA, which stands for Operational Transconductance Amplifier, is regarded as an operational amplifier whose output impedance is very low. As mentioned in [II.15], OTAs transconductance value is almost irrelevant as long as its voltage gain is high. On the contrary, a Gm-cell is a more general term, referring to a voltage-controlled current-source having a well determined transconductance value. That is why the term “OTA-C” filters will be avoided in the following. - 66 -
In all publications dedicated to Gm-C or OTA-C filters, the basic idea is first to design a transconductor. For our application, we have to associate a few of these transconductors in a way that the transfer function of the circuit corresponds to the desired type of filter. A large number of the second order bandpass topologies are given in [II.17] in a complete study by R.L. Geiger and E. Sánchez-Sinencio. II.4.b.ii Gm-C Filters in the Literature One way to synthesize a given transfer function is to find its LC equivalent circuit and then to replace inductors by gyrators and resistors by 1/Gm cells. In this case, Gyrator-C and Gm-C filters are equivalent. This is especially the case for simple transfer function. For more complex transfer function, this synthesis method may not be optimal in terms of number of components. Figure 82 depicts an LC elliptic third order low-pass filter circuit above its equivalent in a Gm-C structure [II.2]. It may be seen that the inductor has been replaced by a differential double gyrator made of four Gm cells. Figure 82. Elliptic 3rd order low-pass filters Reference [II.7], written by R.G. Carvajal et al is one example of a Gm-C tunable filter which is based on a very linear Gm-cell architecture, shown on Figure 83. The structure is quite complex with both common-mode feed-forward and feed-back to ensure a high linearity. Once this transconductor is designed, several are associated as depicted in Figure 84 to synthesize a second-order bandpass filter. Though this structure can be used over a very wide frequency range, from 300kHz to 32MHz, the complexity of the transconductor limits the use at higher frequencies. It exhibits a good linearity (8 dBm IIP3) but no information about noise is given. Figure 84 shows that the transconductance of the Gm-cells is tunable, by means of Vtuning. Hence, the frequency tunability of the filter is achieved by gm tuning. - 67 -
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 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: when given, reported noise figures
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 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
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
Page 177 and 178:
RF selectivity challenges In this t
Page 179 and 180:
The positive feedback Rauch filter
Page 181 and 182:
It is worth highlighting that FOM1
Page 183 and 184:
étudiée. Il s’avère que la lin
Page 185 and 186:
It is worth noticing that S0 only d
Page 187 and 188:
A.3 Signal-to-Noise Ratio These dif
Page 189 and 190:
A.5 Friis’ Formula In case of mul
Page 191 and 192:
A.7 References [A.1] Friis, H.T., N
Page 193 and 194:
To estimate the influence of the di
Page 195 and 196:
Now, let’s have a look to the cub
Page 197 and 198:
Figure 200. Third order intercept p
Page 199 and 200:
B.2 RF Filter Linearity Measurement
Page 201 and 202:
B.2.c IIP2 measurement To measure t
Page 203 and 204:
- 199 -
Page 205 and 206:
C.1 Gyrator-C filtering year Ref. f
Page 207 and 208:
C.2 Gm-C Filtering year Ref. f0 (MH
Page 209 and 210:
year C.3 Rm-C filtering Ref. f0 (MH
Page 211 and 212:
C.5 References C.5.a Gyrator-C filt
Page 213 and 214:
[C.23] J. De Lima and C. Dualibe,
Page 215 and 216:
- 211 -
Page 217 and 218:
this gives: I I I md d1 d 2 = I I =
Page 219 and 220:
D.2 MOS Degenerated Common-Source C
Page 221 and 222:
⎛ I s ⎞ Vout = Vin + U T ln ⎜
Page 223 and 224:
Computing, this leads to: V out + v
Page 225 and 226:
- 221 -
Page 227 and 228:
- 223 -
Page 229 and 230:
FIGURE 54. H3 AND N+5 REJECTIONS AC
Page 231 and 232:
FIGURE 168. PVT VARIATIONS OF THE F
Page 233 and 234:
- 229 -
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?