C H A P T E R 16
Filters and Tuned Amplifiers
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Figure 16.2 Ideal transmission characteristics of the four major filter types: (a) low-pass (LP), (b) high-pass (HP),
(c) bandpass (BP), and (d) bandstop (BS).
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Figure 16.3 Specification of the transmission characteristics of a low-pass filter. The magnitude response of a filter that just meets
specifications is also shown.
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Figure 16.4 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.
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Figure 16.5 Pole–zero pattern for the lowpass filter whose transmission is sketched in Fig. 16.3. This is a fifth-order filter (N = 5).
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Figure 16.6 Pole–zero pattern for the bandpass filter whose transmission function is shown in Fig. 16.4. This is a sixth-order filter
(N = 6).
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Figure 16.7 (a) Transmission characteristics of a fifth-order low-pass filter having all transmission zeros at infinity. (b) Pole–zero pattern for
the filter in (a)
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Figure 16.8 The magnitude response of a Butterworth filter.
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Figure 16.11 Poles of the ninth-order Butterworth filter of Example 16.1.
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Figure 16.12 Sketches of the transmission characteristics of representative (a) even-order and (b) odd-order Chebyshev filters.
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Figure 16.13 First-order filters.
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Figure 16.14 First-order all-pass filter.
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Figure 16.16 Second-order filtering functions.
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Figure 16.16 (continued)
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Figure 16.16 (continued)
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Figure 16.17 (a) The second-order parallel LCR resonator.
(b, c) Two ways of exciting the resonator of (a) without changing its natural structure :
resonator poles are those poles of Vo/I and Vo/Vi.
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Figure 16.19 Realization of the second-order all-pass transfer function using a voltage divider and an LCR resonator.
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Figure 16.20 (a) 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.
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Figure 16.21 (a) An LCR resonator. (b) An op amp–RC resonator obtained by replacing the inductor L in the LCR resonator of (a) with a
simulated inductance realized by the Antoniou circuit of Fig. 16.20(a). (c) Implementation of the buffer amplifier K.
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Figure 16.23 Derivation of a block diagram realization of the two-integrator-loop biquad.
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Figure 16.24 (a) The KHN biquad circuit, obtained as a direct implementation of the block diagram of Fig. 16.23(c). The three basic
filtering functions, HP, BP, and LP, are simultaneously realized. (b) To obtain notch and all-pass functions, the three outputs are
summed with appropriate weights using this op-amp summer.
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Figure 16.25 (a) Derivation of an alternative two-integrator-loop biquad in which all op amps are used in a single-ended fashion. (b) The resulting
circuit, known as the Tow–Thomas biquad.
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Figure 16.26 The Tow–Thomas biquad with feed forward. The transfer function of Eq. (16.68) 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 16.2.
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Figure 16.27 (a) Feedback loop obtained by placing a two-port RC network n in the feedback path of an op amp. (b) Definition of the
open-circuit transfer function t(s) of the RC network.
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Figure 16.28 Two RC networks (called bridged-T networks) that can have complex transmission zeros. The transfer functions given are
from b to a, with a open-circuited.
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Figure 16.29 An active-filter feedback loop generated using the bridged-T network of Fig. 16.28(a).
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Figure 16.30 (a) The feedback loop of Fig. 16.29 with the input signal injected through part of resistance R4. This circuit realizes the bandpass
function. (b) Analysis of the circuit in (a) to determine its voltage transfer function T(s) with the order of the analysis steps indicated by the
circled numbers.
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Figure 16.31 Interchanging input and ground results in the complement of the transfer function.
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Figure 16.32 Application of the complementary transformation to the feedback loop in (a) results in the equivalent loop (same poles)
shown in (b).
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Figure 16.33 (a) Feedback loop obtained by applying the complementary transformation to the loop in Fig. 16.29. (b) Injecting the input
signal through C1 realizes the high-pass function. This is one of the Sallenand-Key family of circuits.
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Figure 16.34 (a) Feedback loop obtained by placing the bridged-T network of Fig. 16.28(b) in the negative feedback path of an op amp.
(b) Equivalent feedback loop generated by applying the complementary transformation to the loop in (a). (c) A low-pass filter obtained by
injecting Vi through R1 into the loop in (b).
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Figure 16.36 A pair of complementary stray-insensitive, switched-capacitor integrators. (a) Noninverting switched-capacitor integrator.
(b) Inverting switched-capacitor integrator.
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Figure 16.37 (a) A two-integrator-loop, active-RC biquad (b) its switched-capacitor counterpart.
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Figure 16.38 Frequency response of a tuned amplifier.
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Figure 16.39 The basic principle of tuned amplifiers is illustrated using a MOSFET with a tuned-circuit load. Bias details are not shown.
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Figure 16.40 Inductor equivalent circuits.
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Figure 16.41 A tapped inductor is used as an impedance transformer to allow using a higher inductance, L’, and a smaller capacitance, C’.
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Figure 16.42 (a) The output of a tuned amplifier is coupled to the input of another amplifier via a tapped coil. (b) An equivalent circuit.
Note that the use of a tapped coil increases the effective input impedance of the second amplifier stage.
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Figure 16.43 A BJT amplifier with tuned circuits at the input and the output.
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Figure 16.44 Two tuned-amplifier configurations that do not suffer from the Miller effect: (a) cascode and (b) common-collector,
common-base cascade. (Note that bias details of the cascode circuit are not shown.)
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Figure 16.45 Frequency response of a synchronously tuned amplifier.
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Figure 16.46 Stagger-tuning the individual resonant circuits can result in an overall response with a passband flatter than that obtained with
synchronous tuning (Fig. 16.45).
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Figure 16.46 Stagger-tuning the individual resonant circuits can result in an overall response with a passband flatter than that obtained with
synchronous tuning (Fig. 16.45).
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Figure 16.48 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.
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Figure P16.11
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Figure P16.27
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