Analog Integrated Circuits (Jieh Tsorng Wu)

Use only grounded capacitors gm c filters 22 28

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Unformatted text preview: 2 k g(VX 0 ) = ge(VX 0) + go(VX 0 ) ge(−VX 0) = ge(VX 0) go(−VX 0 ) = −ge(VX 0) 1 12 1 2 · VX 0 + γ (V0B + φ0)− 2 · VX 0 + · · · 2 4 3 1 3 go(VX 0 ) = − γ (V0B + φ0)− 2 · VX 0 + · · · 24 ge(VX 0 ) = Gm-C Filters 22-3 Analog ICs; Jieh-Tsorng Wu MOSTs in the Triode Region Thus ID = IL − IN IL = k (VG 0 − VT ) × VDS = G × VDS IN = k g(VD0 ) − g(VS 0 ) • Both ge and go are independent of VG . • go(VD0 ) − go(VS 0 ) is very small comparing to IL (e.g., 0.1 percent of it or less). • ge(VD0 ) − ge(VS 0 ) can be large and its effect must be eliminated to obtain a linear resistor. • If only IL is considered, the resistance between VD and VS is ID W = k (VG 0 − VT ) = µCox (VG 0 − VT ) G= VDS L Gm-C Filters 22-4 Analog ICs; Jieh-Tsorng Wu MOST-C Fully-Balanced Integrators C R I1 M1 Vi C VG Vi1 Vo Vi2 V0 M2 Vi Vi 2 = − + V0 2 Vi Vi − ge + I1 = G × + 2 2 Vi I2 = G × − 2 − ge I1 − I2 = G × Vi − 2go Gm-C Filters Vi 2 Vi − 2 Vo2 I2 VG Vi Vi 1 = + + V0 2 Vo1 Vo1 C Vo = + + V0 2 Vo2 Vo = − + V0 2 − ge (0) − go Vi + 2 − go (0) − ge (0) − go Vi − 2 − go (0) ≈ G × Vi 22-5 G = k (VG − V0 − VT ) Analog ICs; Jieh-Tsorng Wu MOST-C Fully-Balanced Integrators Therefore Vo(s) Vi (s) = I1(s) − I2(s) Vi (s) ·− 1 sC =− G sC • Even-order nonlinearities are eliminated. • The common-mode voltage along the differential signal path must be maintained at V0. • Linearities around 50 dB have been achieved. Gm-C Filters 22-6 Analog ICs; Jieh-Tsorng Wu Double MOST-C Differential Integrators VGA M1 C VGB I1 M3 Vi1 Vo1 Vi2 Vo2 M4 VGB I2 C M2 Vi Vi 1 = + + V0 2 Vi Vi 2 = − + V0 2 Vo Vo1 = + + V0 2 Vo Vo2 = − + V0 2 GA = k1,2 (VGA − V0 − VT ) GB = k3,4 (VGB − V0 − VT ) VGA Vi I1 = GA × + 2 Vi −g+ 2 Vi − g (0) + GB × − 2 Vi −g− 2 − g (0) Vi I2 = GA × − 2 Vi −g− 2 Vi − g (0) + GB × + 2 Vi −g+ 2 − g (0) Gm-C Filters 22-7 Analog ICs; Jieh-Tsorng Wu Double MOST-C Differential Integrators We have I1 − I2 = (GA − GB ) × Vi Vo(s) Vi (s) = I1(s) − I2(s) Vi (s) 1 ·− sC GA − GB =− sC • Both even-order and odd-order nonlinearities are eliminated. • Differential signals are not required to be fully balanced. • Around 10 dB linearity improvement over the two-transistor MOST-C integrators. • Linearity performance is limited by the deviation of the above device model and mismatches among the MOSTs. • Reference: Ismail, JSSC 2/88, pp. 183–194. Gm-C Filters 22-8 Analog ICs; Jieh-Tsorng Wu R-MOST-C Differential Integrators V CA R2 M1 V R1 V CB C M3 V i1 V V i2 R1 M4 V CB o1 o2 C M2 V CA Gm-C Filters 22-9 R2 Analog ICs; Jieh-Tsorng Wu R-MOST-C Differential Integrators Vo R2/R1 =− R Vi sC R2 1 + R RM 1 R 1 2 M2 +1 • The dc gain is not adjustable. • The integrator’s time constant can be varied by changing RM 1 and RM 2 • At low-frequencies, the linear resistors, R1 and R2 , dominate the transfer function, thus reducing distortion. A linearity of 90 d B has been achieved. • In the criss-cross version, M3 and M4 reduce the effective dc gain and bandwidth of the integrator, enhance the unity-gain frequency sensitivity to component mismatches, and increase noises. • Reference: U-K Moon, et al., JSSC 12/93, pp. 1254–1264. Gm-C Filters 22-10 Analog ICs; Jieh-Tsorng Wu A MOST-C Tow-Thomas Biquad VG MR VG MRQ VG VG C MR/K Vi C MR Vb MR/K C Vl MR VG VG C MRQ VG MR VG Gm-C Filters 22-11 Analog ICs; Jieh-Tsorng Wu Transconductors Ideal Model Nonideal Model Io Io Io Vi Gm Vi Vi go Ci Io Vi Vi Gm Io Vi Ci Io go Io Io = Gm × Vi Gm-C Filters 22-12 Analog ICs; Jieh-Tsorng Wu Transconductor Basic Circuits Voltage Amplifier Controlled Resistance Vi1 Lossless Integrator G m1 Vi G m3 G m1 Zi Vo G m2 Vi Vi1 G m3 G m1 G m1 Gm-C Filters G m1 Vo C Vo 2C Vi Vi2 1 Zi = Gm1 Vo C Vi2 Zi G m1 Vo G m1 G m2 2C 1 Vo = · (Gm1 Vi 1 − Gm2Vi 2) Gm3 22-13 Vo(s) Gm =− sC Vi (s) Analog ICs; Jieh-Tsorng Wu Gm-C Lossy Integrator Vi G m1 G m2 G m1 Vo C Vi Vo C G m2 C Vi G m1 C G m2 Vo Vi Vo G m1 = G m2 G m1 Vo(s) Gm1 =− sC + Gm2 Vi (s) • Since no feedback for the integrators, they can be wide-band. • A transconductor’s output current should be linearly related to the input over the entire input voltage range. Gm-C Filters 22-14 Analog ICs; Jieh-Tsorng Wu Fully-Differential Gm-C Integrators 2C Cp Vi Vo Gm Vi Vo Gm C Cp C Vo(s) Vi (s) =− Vi Cp Gm Vo 2C Cp Gm s(C + Cp/2) • Can use only grounded capacitors. • The Cp can affect the integration time constant. • Partially nonlinear Cp can also cause linearity problems. Gm-C Filters 22-15 Analog ICs; Jieh-Tsorng Wu Gm-C Opamp Integrators (Miller Integrators) VDD VDD 2C 2C 2C Io Vi Cp Vo Gm VB Vo Cp Io VB Io 2C Io VSS VSS Vo(s) Gm =− sC Vi (s) • The effects of parasitic capacitances are reduced. • The Gm’s output stage can be simplified, since no large voltage swing is required. • The lower impedances at the Gm’s output nodes make those nodes less sensitive to capacitive coupling of noise. Gm-C Filters 22-16 Analog ICs; Jieh-Tsorng Wu Gyrators I1 I2 Grounded Inductor V1 V1 V2 V1 C G m2 Model I1 V1 I2 V2 L1 G m1 Floating Inductor V1 L2 V2 C Gm1 V2 Gm2 V1 L1 = G...
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This note was uploaded on 03/26/2013 for the course EE 260 taught by Professor Choma during the Winter '09 term at USC.

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