Analog Integrated Circuits (Jieh Tsorng Wu)

# For qp 1 3 has a peaking nmax 4qpp at n for 2nd order

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Unformatted text preview: x gm 1 1 = + + Ix s2C1C2 sC1 sC2 C1C2 C2 = C1 + C2 Analog ICs; Jieh-Tsorng Wu Single-Transistor Negative-Resistance Oscillators L L L L C1 C1 C2 C2 C1 C2 C2 C1 VDD L VDD VDD L L VB C2 VB C1 C1 C2 C1 OSCs C2 19-23 Analog ICs; Jieh-Tsorng Wu Piezoelectric Crystals +jX Circuit Model R C 0 L Co OSCs ωs ω −jX Z (j ω) = 1 ωs = √ LC ωa ωa = [R + (j ωC)−1 + j ωL](j ωCo )−1 R + (j ωC)−1 + j ωL + (j ωCo)−1 1 L(C Co ) ωa = ωs 19-24 C 1+ Co ωs L 1 = Q= ωs RC R Analog ICs; Jieh-Tsorng Wu Piezoelectric Crystals • Example: R = 16.3 Ω, C = 0.009 pF, L = 7.036 nH, Co = 2.3 pF; thus fo = 20 MHz, Q = 54245. • The serial RLC can be transformed into a parallel circuit Rp = R 1 + 2 Qs At ω = ωa, with Qs Xp = Xs 1+ 1 1 Xs = ωL − ωC where 2 Qs Xs Qs = R 1, we have 1 Xp = ωaCo 2 2 Xp Xs 1 ≈ = Rp ≈ R R R (ωa Co)2 • Circuits containing crystals are designed so that the frequency range of interest is between ωs and ωa. OSCs 19-25 Analog ICs; Jieh-Tsorng Wu Crystal Oscillators Colpitts Oscillator L VB Pierce Oscillator VDD L C2 C1 C2 C1 VDD VDD VB C2 C2 C1 OSCs 19-26 C1 Analog ICs; Jieh-Tsorng Wu Relaxation Oscillators (Multivibrators) Tab State A State B Ta Tb fo = 1 Ta + Tb + Tab + Tba fo,max 1 ≈ Tab + Tba Tba • The two states are created by positive feedback. • Ta and Tb are usually determined by the charging and discharging of timing capacitors, while Tab and Tba are the transient response of the circuit. • Comparing with the frequency-tuned oscillators, the relaxation oscillators have wider tuning range, predictable waveforms, but poorer spectral purity. OSCs 19-27 Analog ICs; Jieh-Tsorng Wu Constant-Current Charge/Discharge Oscillators Schmitt Trigger VDD VA VA Vo I1 D S Vo VB Q R D C VB T1 D x I2 C · (VA − VB ) T1 = I1 fo = OSCs T2 C · (VA − VB ) T2 = I2 − I1 I1 I1 1 1− = T1 + T2 C · (VA − VB ) I2 19-28 Analog ICs; Jieh-Tsorng Wu The Banu Oscillator VDD VD D Vx C C Vx Vy Vy Vth Va Va Vb IB Vb • Oscillation frequency is fo = 1/(2T ) where T = C · (VDD − Vth )/IB . • Reference: Banu, M., “MOS Oscillators with Multi-Decade Tuning Range and GHz Maximum Speed,” JSSC, 12/1998, pp. 1386–1393. OSCs 19-29 Analog ICs; Jieh-Tsorng Wu A CMOS Relaxation Oscillator VDD VDD V1 V2 V1 V3 V DD Vx R C V DD 0 t Vo V DD T1 V2 V x V DD Vi V3 −t/(RC) V1 (t ) = 0 + (Vx + VDD − 0)e −t/(RC) V1(t ) = VDD + (Vx − VDD − VDD )e OSCs 19-30 T2 ⇒ ⇒ Vx + VDD T1 = RC ln Vx 2VDD − Vx T2 = RC ln VDD − Vx Analog ICs; Jieh-Tsorng Wu A Emitter-Coupled Multivibrator Q1 Off Q2 On VCC Vc1 D1 R2 R1 Vc1 Q3 Q4 Q1 D2 Vc2 C I1 V CC V CC T1 V BE(on) V CC I2 V BE(on) V CC 2V BE(on) Ve2 V CC 2V BE(on) T2 Ve2 Vx V CC Ve1 Q2 Ve1 Vc2 Q1 On Q2 Off Vi V BE(on) Vx 0 V BE(on) OSCs 19-31 Analog ICs; Jieh-Tsorng Wu A Emitter-Coupled Multivibrator • Q1, Q2, Q3, and Q4 are never saturated. • D1 and D2 act as voltage clamps. Thus the maximum voltage across R1 and R2 are VBE (on) . • The relaxation times are T1 = C · 2VBE (on) T2 = I1 C · 2VBE (on) I2 • If I1 = I2 = I , the frequency of oscillation is I 1 1 =· fo = T1 + T2 4 C · VBE (on) OSCs 19-32 Analog ICs; Jieh-Tsorng Wu Fundamentals of Analog Filters Jieh-Tsorng Wu ES A July 16, 2002 1896 National Chiao-Tung University Department of Electronics Engineering Filters Continuous Analog Filter Xi (t) H(s) Sampled Data Filter Xi (t) Xo (t) H(z) Digital Filter Xi (t) A/D H(z) Anti−Aliasing Filter Filters Xo (t) Xo (t) D/A Reconstruction Filter 20-2 Analog ICs; Jieh-Tsorng Wu Filters Continuous-Time Analog Filters • Diﬀerential equations. • Laplace transforms. s = j ω Discrete-Time (Sampled-Data) Analog Filters • Diﬀerence equations. • Z-transform; z−1 is unit delay operator. z = ej ωTs ; Ts is sampling period. Discrete-Time (Sampled-Data) Digital Filters • Discrete-time systems. • A/D introduces quantization noise. Filters 20-3 Analog ICs; Jieh-Tsorng Wu Low-Pass Filter Speciﬁcations |H (j ω)| (dB) PB Ripple A SB Attenuation SB PB TB ω ωc Filters ωs 20-4 Analog ICs; Jieh-Tsorng Wu High-Pass Filter Speciﬁcations |H (j ω)| (dB) PB Ripple A SB Attenuation SB PB TB ω ωs Filters ωc 20-5 Analog ICs; Jieh-Tsorng Wu Band-Pass Filter Speciﬁcations |H (j ω)| (dB) A SB L SB H PB ωsL Filters ω ωcH ωcL ωsH 20-6 Analog ICs; Jieh-Tsorng Wu Band-Reject Filter Speciﬁcations |H (j ω)| (dB) A SB PB L PB H ωcH ωcL ωsL Filters ω ωsH 20-7 Analog ICs; Jieh-Tsorng Wu Second-Order Filter (Biquadratic Function) jω 2 H (s ) = = σ a2 s + a1 s + a0 s2 + b1s + b0 a2(s − z1)(s − z2) (s − p1)(s − p2) 2 =K · ωp = Pole Frequency = |p1 | = |p2| ωp Qp = Pole Quality Factor = 2Re(p1) Filters 20-8 2 s + (ωz /Qz )s + ωz s2 + (ωp/Qp)s + ω2 p ωz = Zero Frequency = |z1| = |z2| Qz = Zero Quality Factor = ωz 2Re(z1) Analog ICs; Jieh-Tsorng Wu Second-Order Filter (Biquadratic Function) ∗ ∗ • For complex poles and zeros, z2 = z1 and p2 = p1. 2 2 • H (0) = K ωz /ωp and H (∞) = K . • |H (j ω)| is maximum, at ω ≈ ωp. • The sharpness of the maximum is determined by Qp. • |H (j ω)| is minimum, at ω ≈ ωz . • The depth of the minimum is determined by Qz . Filters 20-9 Analog ICs; Jieh-Tsorng Wu Second-Order Low-Pass (LP) Filter |H (j ω)| jω M K σ ωM ω 2 H (s) = ωM = ωp · K ωp s2 + (ωp/Qp)s + ω2 p 1 − 1/(2Q2) M= KQ 1 − 1/(4Q2) Filters 20-10 Analog ICs; Jieh-Tsorng Wu Second-Order High-Pass (HP) Filter |H (j ω)|...
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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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