t
t
14-12 CHUNG-YU WU
(2) Band-Pass Filter
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2.Approximation
(1)Classical approximation
a.Butterworth
b.Chebyshev
c.Elliptic
d.Bessel
(2)Modern approximation
3.Realization Two methods:
(1)Realization of the biquad (2nd order filter)and the first-order filter >cascade or couple them to form a high-order filter.
(2)Realize H(s) using LC network >replace L by some integrated-circuit
simulator or simulate the LC network using integrators. * Low-sensitivity, high-performance
14-14 CHUNG-YU WU
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(2)φe phase |
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φe |
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n −1 |
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t |
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vin
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vout |
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vout (Tn ) |
vout (Tn+1 ) |
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C1 |
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vout (Tn−1 ) |
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14-15 CHUNG-YU WU
"Ideal OP AMP"
Vout(Tn)=Vc2(Tn)=Vout(Tn-1)- C1 Vin(Tn)
C2
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Vout (Tn ) −Vout (Tn −1 ) |
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TC2 |
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R1C2 |
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V = − |
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V = − |
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V = − |
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High-precision integrator time constant |
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Z-domain Expression: |
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Vout (z)=Vout(z)Z-1 |
C1 |
Vin(z) |
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>H(z) ≡ |
Vout (z) |
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(1 − Z −1 ) |
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V (z) |
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Backward Euler Transformation: |
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S→ |
1− Z −1 |
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H(S)= |
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(C |
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Parasitic-Free structure:
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φe |
C |
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vin |
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CP4 |
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CP2 CP3 |
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φo |
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CP6 |
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CP5
14-17 CHUNG-YU WU
Z-domain expression: |
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V (z) |
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Forward Euler Transformation: S→ |
1− Z −1 |
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TZ −1 |
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H(s) ≡ + |
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C2 |
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R C S |
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(C |
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Simpler non-inverting integrator!
§14-5 Fully Differential-Type SC Integrators Using OP AMPs.
φe φo
VBIAS |
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αC |
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vin |
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vout |
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VBIAS |
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vout + |
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vin − |
αC |
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*Better noise rejection
*Better CMRR and PSRR
*Better Frequency response
*Better slew rate
**More components (switches, capacitor, OP AMPs)
**Thermal noise ↑ due to the added components and switching operations.
**Need common-mode feedback or common-mode bias circuit
14-18 CHUNG-YU WU
§14-6 SC Differentiators Using OP AMPs
R
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C1 |
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Vout |
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Inverting:
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φo |
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Vin φ |
e |
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Vout |
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V'out |
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Vout(Tn)=Vout' (Tn)= CC1 [Vin (Tn ) −Vin (Tn −1 )]
>H(z)= CC1 (1-Z-1)
Backward-Euler Transformation: S→1−TZ −1
H(S)=-S |
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R= |
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Noninverting: |
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φo |
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CC |
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14-19 CHUNG-YU WU
φo
2
C
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vout |
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φ |
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C1 |
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H(z)=+ CC1 (1− Z −1 ) |
φo
Differential-Type SC Differentiator:
φo
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vin |
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Characteristics of SC differentiators:
1.Parasitic-free structure.
2.No dc instability problem as in SC integrators.
3.No high-frequency-noise problem as in continuous-time differentiators.
4.Can be used to design filters as SC integrators.
Ref: IEEE JSSC vol.sc-24, pp.177-180, 1989.