Analog Integrated Circuits (Jieh Tsorng Wu)

Discrete time or sampled data analog lters time

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Unformatted text preview: The use of feed-in capacitors can simplify design, but requires inputs of low source impedance. Gm-C Filters 22-33 Analog ICs; Jieh-Tsorng Wu Gm-C Second-Oder Filters Using Miller Integrators 1 Vi α0 1/Q 1 sτ 1 sτ Vo α1 + α2s 2C A 2C B G m1 Vo G m2 2C A 2C B 2C X Vi G m4 G m5 Vi G m3 2C X Gm-C Filters 22-34 Analog ICs; Jieh-Tsorng Wu Gm-C Second-Oder Filters Using Miller Integrators The transfer function is Vo Vi = α2s + α1s + αo s2 + ωp Q + ω2 p CX CB s2 2 = +s s2 + s G m5 CB G m3 CB + + G m2 G m4 CA CB G m1 G m2 CA CB Thus CX = α2CB and Gm1 = ωpCA Gm-C Filters Gm2 = ωpCB Gm3 = ωpCB Q 22-35 Gm4 α0CA = ωp Gm5 = α1CB Analog ICs; Jieh-Tsorng Wu Ladder Filter Using Simulated Gyrators C2 Vo R Vi S L2 C1 Single-Ended Implementation R C3 L C2 Vo Vi G mi G mS G m2 G m1 G m1 G m2 G mL C C1 C3 Fully Differential Implementation Vi G mi G mS G m2 C2 G m1 C1 G m1 C G m2 G mL Vo C3 C2 Gm-C Filters 22-36 Analog ICs; Jieh-Tsorng Wu Ladder Filter Using Simulated Gyrators • Inductors are replaced with Gm-C gyrators. • Floating capacitors are required. • Finite go of the transconductors results in lossy inductors and capacitor, i.e., Q degradation; while phase shift causes Q enhancement. • The Q-control automatic tuning circuits may be required. Gm-C Filters 22-37 Analog ICs; Jieh-Tsorng Wu Ladder Filter Using Signal-Flow Graph I V R in V 0 V 2 1 I V C5 V 2 1/(sL2) V 5 C3 V -1/(sC 1) V L4 C1 0 4 3 L2 S 1/R S V I -1/(sC 3) -1/(sC 5) R 6 V 4 1/(sL4) I out L 6 1/R L V in V V V 1 V 0 V 3 V 2 out 5 V 4 6 G mL G mS C1 V in Gm-C Filters V 1 C2 C3 V 3 22-38 C4 C5 V 5 V out Analog ICs; Jieh-Tsorng Wu Ladder Filter Using Signal-Flow Graph • Floating capacitors are not necessary. • Finite go of the transconductors results in lossy inductors and capacitor, i.e., Q degradation; while phase shift causes Q enhancement. • Signal-level scaling is possible. Gm-C Filters 22-39 Analog ICs; Jieh-Tsorng Wu Gm-C Simulation of Ladder Branches (I) Shunt Branch Series Branch I1 L4 V1 I3 V2 V3 R0 L1 C2 L3 C3 C4 I2 R0 C1 L2 V1 V1 G mi1 V3 G mi2 C2 G m0 C1 C3 Gm-C Filters 22-40 C4 Analog ICs; Jieh-Tsorng Wu Gm-C Simulation of Ladder Branches (II) V1 V1 G mi1 V3 G mi2 G m0 C2 C1 C3 C4 Gm-C Filters 22-41 Analog ICs; Jieh-Tsorng Wu Gm-C Simulation of Ladder Branches The branch characteristics are I2 = (V1 − V3 ) · Y (s) = (V1 − V3) · 1 1 R0 + sL1 + sC + 2 V2 = (I1 − I3) · Z (s) = (I1 − I3) · 1 1 sC3 + sL 4 1 1 G0 + sC1 + sL + 2 1 1 sL3 + sC 4 The Gm-C circuit’s transfer function is V2 = (Gmi 1 · V1 − Gmi 2 · V3) · 1 1 Gm0 + sC1 + sC + 2 1 1 sC3 + sC 4 • Method 2 usually uses more transconductors than method 1, but may have advantages in terms of sensitivity to and compensation for parasitic effects. • For better matching, use identical transconductors whenever possible. Gm-C Filters 22-42 Analog ICs; Jieh-Tsorng Wu Gm-C Resonators V I V i G o C1 i L R V m1 C1 G G G m2 o m4 m3 C2 Gm-C Filters 22-43 Analog ICs; Jieh-Tsorng Wu Gm-C Resonators • The inductor L is simulated by Gm2, Gm3, and C2. The resistor R is simulated by Gm4. • The resonant frequency and the quality factor are ωo = 1 = LC1 Gm2Gm3 C1C2 Q = ωoRC1 = C1 × C2 Gm2Gm3 2 Gm4 The voltage gain at the resonant frequency is Avo vo Gm1 = = Gm1R = vi Gm4 • Reference: Silva-Martinez, et al., JSSC 12/92, pp. 1843–1853. Gm-C Filters 22-44 Analog ICs; Jieh-Tsorng Wu Gm-C Quadrature Oscillators I G L C GL Vo GD m1 G V Vo m2 C1 C2 G m3 G m4 • The combination of Gm1, Gm2 and C1 simulates an inductor. • The oscillation frequency is ωo = Gm1Gm2/(C1 C2). • The oscillation condition is Gm4 = Gm3. In many cases, Gm3 and Gm4 are not required. • The nonlinear resistor is used to control the output amplitude. • Reference: Rodriguez-Vazquez, Transactions on Circuits and Systems, 2/90, pp. 198–211. Gm-C Filters 22-45 Analog ICs; Jieh-Tsorng Wu On-Chip Tuning Strategies S in S out Filter to be Tuned (Slave) U cntrl Indirect Tuning Reference Circuit (Master) S ref Control Circuit S in LPF S out Filter A to be Tuned U cntrl Direct Tuning Filter B to be Tuned S ref Control Circuit Gm-C Filters 22-46 LPF Analog ICs; Jieh-Tsorng Wu Separate Frequency and Q Control S in S out Filter to be Tuned UF UQ Ref Ckt 1 LPF Ref Ckt 2 Control Ckt Control Ckt Freq Tuning Loop Gm-C Filters S rf S rQ 22-47 LPF Q Tuning Loop Analog ICs; Jieh-Tsorng Wu Gm Tuning Rext C1 VR Gm VR Gm VC VR VC R ext C1 • VC is automatically adjusted so that Gm = 1 Rext • C1 is an integrating capacitor used to maintain loop stability. Gm-C Filters 22-48 Analog ICs; Jieh-Tsorng Wu Frequency Tuning Using Switched Capacitors 1 Cm 2 1 2 Gm = VR R1 Gm VF 1 = fs Cm Req ⇒ CI Gm = fs Cm C1 N IB IB CI Gm 1 Cm 2 1 1 · = IB Gm Req ⇒ Gm = Nfs Cm R1 VF 2 Gm-C Filters NIB · 1 C1 22-49 Analog ICs; Jieh-Tsorng Wu Frequency Tuning Using Response Detection Ca Cb Ra Rb MOST-C Filter Tuning System C Peak Detector R V1 VF Peak Detector R1 Vr sin(ωr t + θ ) Gm-C Filters V2 R2 22-50 Analog ICs; Jieh-Tsorng Wu Frequency Tuning Using Response Detection For this amplitude-response...
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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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