Analog Integrated Circuits (Jieh Tsorng Wu)

However to avoid unnecessary noise aliasing u should

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Unformatted text preview: detection scheme V1 = Vr · 1 ωr RC V2 = Vr · R2 R1 + R2 The feedback adjusts VF so that V1 = V2, thus R1 1 R·C = · 1+ ωr R2 • The above tuning system is a magnitude locked loop (MLL). • Usually use ωr RC 1 to place ωr in the filter stopband. • Phase-response detection scheme can also be used. • The reference circuit can be any filter. Gm-C Filters 22-51 Analog ICs; Jieh-Tsorng Wu Frequency Tuning Using Phase-Locked Loop Gm-C Main Filter G Variable-Frequency Oscillator m G m G C fo m C C VF f Gm-C Filters ref Phase-Freq Detector 22-52 Low-Pass Filter Analog ICs; Jieh-Tsorng Wu Frequency Tuning Using Phase-Locked Loop The phase-locked loop (PLL) forces fref 1 Gm · = fo = 2π C ⇒ Gm = 2πfref C • For best matching between the reference VFO and the main filter, it is best to choose fref at the upper passband edge. However, the reference signal may leak into the main filter’s output. • If fref moves away from the upper passband edge, the matching will be poorer, but an improved immunity to the reference signal results. • If the VFO is sensitive to supply variation, any power-supply noise can inject jitter into VF . Gm-C Filters 22-53 Analog ICs; Jieh-Tsorng Wu Q-Factor Tuning Using MLL Vi Slave Filter Bandpass Biquad Vo Hbq (s) = Peak Det ωps ω s2 + Qp s + ω2 p p V ref VQ Vref = A sin ωr t Peak Det Qd • At s = j ωr = j ωp, the MLL forces Hbq (j ωp) = Qp = Qd . • For high Q biquad, mismatch between ωr and ωp results in large Q-tuning error. • Distortion in Vref can also cause error. Gm-C Filters 22-54 Analog ICs; Jieh-Tsorng Wu Q-Factor Tuning Using LMS Vi Slave Filter Vo Hbq (s) = Bandpass Biquad V ref ωps ω s2 + Qp s + ω2 p p Vref = A sin ωr t 1 Qd VQ d VQ (t ) = µ · Vref(t ) − Vbq (t ) · Vbq (t ) dt The modified continuous-time least-mean-squares (LMS) algorithm will force 2 Vref (t ) − Vbq (t ) · Vbq (t ) = Vref(t ) · Vbq (t ) − Vbq (t ) = 0 Gm-C Filters 22-55 Analog ICs; Jieh-Tsorng Wu Q-Factor Tuning Using LMS If ωr = ωp, Vbq (t ) = ⇒ LMS Qp Qd · A sin ωr t = B · sin ωr t A·B B·B = 2 2 ⇒ B= A=B Qp Qd ·A ⇒ Qp = Qd If ωr = ωp, Vbq (t ) = LMS ⇒ Qp Qd cos φ · A sin (ωr t + φ) = B · sin (ωr t + φ) A · B · cos φ B · B = 2 2 ⇒ B= A cos φ = B Qp Qd ⇒ cos φ · A Q p = Qd • Insensitive to mismatch between ωr and ωp. Gm-C Filters 22-56 Analog ICs; Jieh-Tsorng Wu Q-Factor Tuning Using LMS • Require no peak detector. • The scheme is also insensitive to Vref waveform shape. • Square wave can be used for Vref(t ). • Reference: J.-M. Stevenson, et al., An Accurate Quality Factor Tuning Scheme for IF and High-Q Continuous-Time Filters, JSSC 12/1998, pp. 1970–1978. Gm-C Filters 22-57 Analog ICs; Jieh-Tsorng Wu Switched-Capacitor Filters Jieh-Tsorng Wu ES A October 23, 2002 1896 National Chiao-Tung University Department of Electronics Engineering Switched-Capacitor Equivalent Resistor fs V1 V2 φ1 φ2 Ts C V1 V2 φ1 C φ2 Req V1 V2 Ieq Ieq = ∆Q ∆t C · V1 − C · V2 = = C · (V1 − V2) · fs Ts Geq SC Filters Ts = 1 fs Ieq 1 = = = C · fs Req V1 − V2 23-2 Analog ICs; Jieh-Tsorng Wu Switched-Capacitor Integrators C2 C2 R1 Vi Vi Vo fs Vo C1 Vo C1 1 1 Geq1 1 =− =− · = − · fs · s C2 s Vi sR1 C2 C2 • Consist of analog switches, capacitors and opamps. • Discrete-time (or sampled-data) analog filters. • Time constant is determined by capacitance ratio and switching frequency. SC Filters 23-3 Analog ICs; Jieh-Tsorng Wu SC Integrator Analysis Ts C2 Q Vi 1 Q 2 1 φ1 2 φ2 Vo n-1 C1 n n-1/2 n+1 n+1/2 a φ1 CLK Vi C1 C2 Va z 1 φ1 Vo φ2 a φ2 −1 C1 z =− × C2 1 − z −1 Vi (z ) Vo(z ) SC Filters 23-4 Analog ICs; Jieh-Tsorng Wu SC Integrator Analysis At cycle n, i.e., t = nTs , we have Q1(n) = C1Vi (n) and Q2(n) = C2Vo(n) At cycle n + 1/2, i.e., t = (n + 1/2)Ts , Q1(n + 1/2) = 0 Q2(n + 1/2) = Q2(n) − Q1(n) = C2Vo(n) − C1Vi (n) At cycle n + 1, i.e., t = (n + 1)Ts , Q1(n + 1) = C1Vi (n + 1) Q2(n + 1) = C2 Vo(n + 1) = Q2(n + 1/2) = C2Vo(n) − C1Vi (n) Thus, the time-domain difference equation is C2Vo(n + 1) = C2Vo(n) − C1Vi (n) In the z-domain zC2Vo(z ) = C2Vo(z ) − C1Vi (z ) SC Filters ⇒ C1 C1 1 z −1 =− × =− × C2 z − 1 C2 1 − z −1 Vi (z ) Vo(z ) 23-5 Analog ICs; Jieh-Tsorng Wu SC Differential Integrators C2 C2 Q R1 Vo Vi1 Vi1 Vi2 R1 Q C2 Vi2 RC Integrator SC Integrator SC Filters 1 1 2 1 2 Vo C1 2 → 1 Vo(s) = − (V − Vi 2) sR1 C2 i 1 → C1 z −1 Vo(z ) = − × × [Vi 1(z ) − Vi 2(z )] C2 1 − z −1 23-6 Analog ICs; Jieh-Tsorng Wu Effects of Parasitic Capacitances Cp3 Vi1 1 Va 2 Cp4 C2 Vo A C1 Cp1 Cp2 Vi2 1 2 Cp1 C1 z −1 Vo(z ) = − [Vi 1 (z ) − Vi 2(z )] − V (z ) × C2 C2 i 1 1 − z −1 SC Filters 23-7 Analog ICs; Jieh-Tsorng Wu Effects of Parasitic Capacitances • Among the parasitic capacitors, only Cp1 contribute charge to C2 if A = ∞. • Consider a finite value of A, then Vo = −A · Va, and C1[Vi 1 (n) − Vi 2(n)] + C2[Va(n) − Vo(n)] + Cp1Vi 1 + Cp3Va(n) = C1 + Cp1 + Cp3 Va(n + 1) + C2[V...
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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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