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Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters Switched Capacitors

Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

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Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters Switched Capacitors. Filter Transmission, Types and Specification. Linear Filters. - PowerPoint PPT Presentation

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Page 1: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Chapter 11

Filters and Tuned Amplifiers

Passive LC Filters

Inductorless Filters

Active-RC Filters

Switched Capacitors

Page 2: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Filter Transmission, Types and Specification

Linear Filters

Transfer Function

T s( )Vo s( )

Vi s( )

The Filter Transmisson found by evaluating T(s) for physical frequencies

s j T j T j ej ( )

Gain Function

G 20 log T j dB

Attenuation Function

A 20 log T j dB

Page 3: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Specification of the transmission characteristics of a low-pass filter. The magnitude response of a filter that just meets specifications is also shown.

Filter Specification

Frequency-Selection functionPassingStoppingPass-BandLow-PassHigh-PassBand-PassBand-StopBand-Reject

Summary – Low-pass specs-the passband edge, wp-the maximum allowed variation in passband, Amax-the stopband edge, ws-the minimum required stopband attenuation, AminPassband ripple

Ripple bandwidth

Page 4: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Transmission specifications for a bandpass filter. The magnitude response of a filter that just meets specifications is also shown. Note that this particular filter has a monotonically decreasing transmission in the passband on both sides of the peak frequency.

Filter Specification

Page 5: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Exercises 11.1 and 11.2

Page 6: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Pole-zero pattern for the low-pass filter whose transmission is shown.

This filter is of the fifth order (N = 5.)

The Filter Transfer Function

transfer function zeros or transmission zeros

T s( )aM s z1 s z2 s z3 s zM

s p1 s p2 s p3 s pN

transfer function poles or the natural poles

Page 7: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Pole-zero pattern for the bandpass filter whose transmission is shown. This filter is of the sixth order (N = 6.)

The Filter Transfer Function

Page 8: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

The magnitude response of a Butterworth filter.

Butterworth Filters

Page 9: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Magnitude response for Butterworth filters of various order with = 1. Note that as the order increases, the response approaches the ideal brickwall type transmission.

Butterworth Filters

Page 10: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Graphical construction for determining the poles of a Butterworth filter of order N. All the poles lie in the left half of the s-plane on a circle of radius 0 = p(1/)1/N, where is the

passband deviation parameter :

(a) the general case, (b) N = 2, (c) N = 3, (d) N = 4.

Butterworth Filters

Page 11: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Sketches of the transmission characteristics of a representative even- and odd-order Chebyshev filters.

Chebyshev Filters

Page 12: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

First-Order Filter Functions

Page 13: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

First-Order Filter Functions

Page 14: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Fig. 11.14 First-order all-pass filter.

First-Order Filter Functions

Page 15: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Second-Order Filter Functions

Page 16: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Second-Order Filter Functions

Page 17: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Second-Order Filter Functions

Page 18: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Realization of various second-order filter functions using the LCR resonator of Fig. 11.17(b): (a) general structure, (b) LP, (c) HP, (d) BP, (e) notch at 0, (f) general notch, (g) LPN (n 0), (h) LPN as s , (i) HPN (n < 0).

The Second-order LCR Resonator

Page 19: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

The Antoniou inductance-simulation circuit. (b) Analysis of the circuit assuming ideal op amps. The order of the analysis steps is indicated by the circled numbers.

The Second-Order Active Filter – Inductor Replacement

Page 20: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

The Antoniou inductance-simulation circuit.

Analysis of the circuit assuming ideal op amps. The order of the analysis steps is indicated by the circled numbers.

The Second-Order Active Filter – Inductor Replacement

Page 21: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Realizations for the various second-order filter functions using the op amp-RC resonator of Fig. 11.21 (b). (a) LP; (b) HP; (c) BP, (d) notch at 0;

The Second-Order Active Filter – Inductor Replacement

Page 22: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

(e) LPN, n 0; (f) HPN, n 0; (g) all-pass. The circuits are based on the LCR circuits in Fig.

11.18. Design equations are given in Table 11.1.

The Second-Order Active Filter – Inductor Replacement

Page 23: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

The Second-Order Active Filter – Two-Integrator-Loop

Vhp

Vi

K s2

s2

so

Q

o2

Two integrations of signal

with time constant

o

sVhp

Vhp1

Q

o

sVhp

o

2

s2

Vhp

K Vi1

o

Vhp K Vi1

Q

o

s Vhp

o2

s2

Vhp Summing Point

Page 24: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

The Second-Order Active Filter – Two-Integrator-Loop

Circuit Implementation

Page 25: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

The Second-Order Active Filter – Two-Integrator-Loop

Circuit Design and Performance

T

a 12 40 b 12 20 j 1

w0 2103 K 3

wa

100700a Qb

0.10.2b

Ta b

K jwa

2

jwa

2 jwa

w0

Qb

w02

Page 26: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

The Second-Order Active Filter – Two-Integrator-Loop

Exercise 11.21

Page 27: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Derivation of an alternative two-integrator-loop biquad in which all op amps are used in a single-ended fashion. The resulting circuit in (b) is known as the Tow-Thomas biquad.

The Second-Order Active Filter – Two-Integrator-Loop

Page 28: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Fig. 11.26 The Tow-Thomas biquad with feedforward. The transfer function of Eq. (11.68) is realized by feeding the input signal through appropriate components to the inputs of the three op amps. This circuit can realize all special second-order functions. The design equations are given in Table 11.2.

Page 29: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Fig. 11.37 A two-integrator-loop active-RC biquad and its switched-capacitor counterpart.

Page 30: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Fig. 11.47 Obtaining a second-order narrow-band bandpass filter by transforming a first-order low-pass filter. (a) Pole of the first-order filter in the p-plane. (b) Applying the transformation s = p + j0 and adding a complex conjugate pole results in the poles of the second-order bandpass filter.

(c) Magnitude response of the firs-order low-pass filter. (d) Magnitude response of the second-order bandpass filter.

Page 31: Chapter 11 Filters and Tuned Amplifiers Passive LC Filters Inductorless Filters Active-RC Filters

Fig. 11.48 Obtaining the poles and the frequency response of a fourth-order stagger-tuned narrow-band bandpass amplifier by transforming a second-order low-pass maximally flat response.