Filtros ideais

D f t l• Defasamento nuloentre entrada e saída

Figure 12 2 Ideal transmission characteristics of the four major filter types: (a) low pass (LP) (b) high pass (HP) (c) bandpass (BP) and (d)

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Figure 12.2 Ideal transmission characteristics of the four major filter types: (a) low-pass (LP), (b) high-pass (HP), (c) bandpass (BP), and (d)bandstop (BS).

Projeto de filtrosProjeto de filtros• Gabarito para o projeto do

filtro:– borda da faixa de passagem– borda da faixa de passagem

p;– máxima variação do ganho

na faixa de passagem A ;na faixa de passagem Amax;– borda da faixa de bloqueio

s;ã í i f i– atenuação mínima na faixa

de passagem Amin;• Determinação da função de

transferência a partir do gabarito:– métodos empíricos,

Figure 12.3 Specification of the transmission characteristics of a low-pass filter. The magnitude response of a filter that just meets specifications

métodos empíricos, iterativos ou baseados em otimização.

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g p p g p j pis also shown.

• F.T. de 5a ordem;– zeros na faixa de bloqueio;q– zeros no infinito (1)– pólos complexos

j d f i dconjugados na faixa de passagem (parte real negativa);

• Influência dos pólos e zeros no defasamento entre a entrada e a saídaentrada e a saída.

Figure 12.5 Pole–zero pattern for the low-pass filter whose transmission is sketched in Fig. 12.3. This is a fifth-order filter (N = 5).

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g p p g ( )

Figure 12.4 Transmission specifications for a bandpass filter. The magnitude response of a filter that just meets specifications is also shown. Note

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g p p g p j pthat this particular filter has a monotonically decreasing transmission in the passband on both sides of the peak frequency.

Figure 12.6 Pole–zero pattern for the band-pass filter whose transmission function is shown in Fig. 12.4. This is a sixth-order filter (N = 6).

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g p p g ( )

Figure 12.7 (a) Transmission characteristics of a fifth-order low-pass filter having all transmission zeros at infinity. (b) Pole–zero pattern for the

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g p g y pfilter in (a).

Topologias de filtros IIR (infinite impulse response)

• Butterworth:– resposta maximamente plana;– polos em um círculo centrado na origem.polos em um círculo centrado na origem.

• Chebyshev tipos I e II– ondulação na faixa de passagem (tipo I) ou na faixa de bloqueio.ç p g ( p ) q

• Elíptico;• Bessel.• Os coeficientes dos filtros são tabelados e podem ser obtidos

utilizando, por exemplo, o MATLABMATLAB já f ã d tóti b i f ê i– o MATLAB já faz a conversão do protótipo passa baixas com frequência

de corte normalizada para o filtro desejado.

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h f i d (f t d i t )

Filtros ativos utilizando amplificadores operacionais

• ganho na faixa de passagem (fontes de energia externas);• projeto de circuito que simula indutância;• adaptação das impedâncias de entrada e de saída utilizando• adaptação das impedâncias de entrada e de saída utilizando

realimentação;• resposta em frequência do amp. op. afeta o desempenho do filtro.p q p p p

• http://focus.ti.com/docs/toolsw/folders/print/filterpro.html• http://designtools.analog.com/dt/filter/filterW.html• http://www.circuitsage.com/filter.html

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Propostas de exercíciosPropostas de exercícios

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Figure 12.13 First-order filters.

Figure 12.14 First-order all-pass filter.

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g p

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Figure 12.16 Second-order filtering functions.

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Figure 12.16 (Continued)

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Figure 12.16 (Continued)

Figure 12.20 (a) The Antoniou inductance-simulation circuit. (b) Analysis of the circuit assuming ideal op amps. The order of the analysis steps

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g y g p p y pis indicated by the circled numbers.

Figure 12.21 (a) An LCR resonator. (b) An op amp–RC resonator obtained by replacing the inductor L in the LCR resonator of (a) with a

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g p p y p g ( )simulated inductance realized by the Antoniou circuit of Fig. 12.20(a). (c) Implementation of the buffer amplifier K.

TopologiaTopologia SallenSallen--KeyKey

passa altaspassa baixas

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Topologia Sallen-Key

http://www.ilb2b.it/node/25245

• Filtros de ordem maior que 2: composição em cascata dos estágios de primeira e segunda ordemde primeira e segunda ordem.

• Proposta de exercício: – Projetar filtro passa baixas tendo não mais do que 1 dB de ripple entre dc e j p q pp

1kHz e uma atenuação mínima de 40 dB em 2kHz. Para solução, vide Millman e Grabel, Microelectronics.

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TopologiaTopologia SallenSallen--KeyKey

• Simplificação 1: ajustar os componentes como razões

• Simplificação 2: ajustar os componentes como razões e ganho i á iunitário;

• Simplificação 3: utilizar resistores e capacitores de igual valor.

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TopologiaTopologia biquadbiquad comcom dois dois integradoresintegradores

Figure 12.23 Derivation of a block diagram realization of the two-integrator-loop biquad.

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g g g p q

Figure 12.24 (a) The KHN biquad circuit, obtained as a direct implementation of the block diagram of Fig. 12.23(c). The three basic filtering

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g q p g g ( ) gfunctions, 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.

Figure 12.25 (a) Derivation of an alternative two-integrator-loop biquad in which all op amps are used in a single-ended fashion. (b) The

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g g p q p p gresulting circuit, known as the Tow–Thomas biquad.

Filtro biquad com um amplificador

• Projeto:– Projetar a rede de realimentação RC para alocar os polos do filtro (complexos e

conjugados);– Escolhar o ponto de aplicação do sinal de entrada para definir os zeros de

Figure 12.27 (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-

p p ç ptransmissão (em um nó anteriormente aterrado).

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g p y p g p p p p pcircuit transfer function t(s) of the RC network.

• Para ganho A elevado, os polos de malha fechada são iguais aos zeros de malha g , p gaberta (vide lugar das raízes).

Figure 12.28 Two RC networks (called bridged-T networks) that can have complex transmission zeros. The transfer functions given are from b to

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g ( g ) p ga, with a open-circuited.

Figure 12.30 (a) The feedback loop of Fig. 12.29 with the input signal injected through part of resistance R4. This circuit realizes the bandpass

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g p g p g j g p 4 pfunction. (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.

Figure 12.49 Circuits for Example 12.5. (a) Fifth-order Chebyshev filter circuit implemented as a cascade of two second-order simulated LCR

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g p y presonator circuits and a single first-order op amp–RC circuit.

Figure 12.50 Magnitude response of the fifth-order lowpass filter circuit shown in Fig. 12.49: (a) an expanded view of the passband region; (b) a view

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g g p p g p p gof both the passband and stopband regions.

Figure 12.51 One-pole equivalent circuit macromodel of an op amp operated within its linear region.

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g p q p p p g

Figure 12.52 Circuit for Example 11.6. Second-order bandpass filter implemented with a Tow–Thomas biquad circuit having f0 = 10 kHz, Q = 20, and

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g p p p q g f0 Qunity center-frequency gain.

Figure 12.53 Comparing the magnitude response of the Tow–Thomas biquad circuit (shown in Fig. 12.52) constructed with 741-type op amps, with

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g p g g p q ( g ) yp p pthe ideal magnitude response. These results illustrate the effect of the finite dc gain and bandwidth of the 741 op amp on the frequency response of the Tow–Thomas biquad circuit.

Figure 12.54 (a) Magnitude response of the Tow–Thomas biquad circuit with different values of compensation capacitance. For comparison, the ideal

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g g p q p p presponse is also shown.

Figure 12.54 (Continued) (b) Comparing the magnitude response of the Tow–Thomas biquad circuit using a 64-pF compensation capacitor and the

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g ( ) p g g p q g p p pideal response.