Chapter 10, PASSIVE FILTERS Video Solutions, Design and Analysis of Analog Filters: A Signal Processing Perspective | Numerade (2024)

Summarize the procedure for designing and realizing a passive analog filter.

An important step in realizing a passive $R L C$ analog filter is implementing the filter, that is drawing a circuit schematic diagram of the filter with all element values given. Summarize the implementation procedure as presented in this chapter.

Explain why SPICE simulation is an important step in implementation.

Briefly explain how MATLAB and SPICE each play an important part in analog filter design and implementation. How do the two relate to each other? That is, how does MATLAB provide analysis of an $R L C$ analog filter implementation?

Similar to Example 10.1, with $\omega_c=1 \mathrm{rad} / \mathrm{s}$ and $R_S=R_L=1 \Omega$, determine two passive ladder implementations for a 2nd-order lowpass Butterworth filter using the procedure of Section 10.2. Compare your results with that found in Table 10.1.
Figure 10.15 can't copy The passive 4th-order bandstop implementation of the Butterworth filter of Example 10.4 based on Figure 10.4, with $A_p=3 d B, B_p=1,000 \mathrm{~Hz}$, and $f_o=10,000 \mathrm{~Hz}$.
Figure 10.16 can't copy The magnitude frequency response, as obtained by SPICE, of the passive 4th-order bandstop implementation of the Butterworth filter of Example 10.4, as illustrated in Figure 10.15, with $A_p=3 d B, B_p=1,000 \mathrm{~Hz}$, and $f_o=10,000 \mathrm{~Hz}$.

Similar to Example 10.1, with $\omega_c=1 \mathrm{rad} / \mathrm{s}$ and $R_S=R_L=1 \Omega$, determine two passive ladder implementations for a 4th-order lowpass Butterworth filter using the procedure of Section 10.2. Compare your results with that found in Table 10.1.

Similar to Example 10.1, with $\omega_p=1 \mathrm{rad} / \mathrm{s}$, passband ripple $=A_p=$ $0.5 \mathrm{~dB}, R_S=0.5 \Omega$, and $R_L=1^p \Omega$, determine two passive ladder implementations for a 2nd-order lowpass Chebyshev Type I filter using the procedure of Section 10.2. Compare your results with that found in Table 10.4.

Similar to Example 10.1, with $\omega_p=1 \mathrm{rad} / \mathrm{s}$, passband ripple $=A_p=$ $0.5 \mathrm{~dB}, R_S=0.5 \Omega$, and $R_L=1^p \Omega$, determine two passive ladder implementations for a 3rd-order lowpass Chebyshev Type I filter using the procedure of Section 10.2. Compare your results with that found in Table 10.4.

Similar to Example 10.1, with $\omega_p=1 \mathrm{rad} / \mathrm{s}$, passband ripple $=A_p=$ $0.5 \mathrm{~dB}, R_S=0.5 \Omega$, and $R_L=1^p \Omega$, determine two passive ladder implementations for a 4th-order lowpass Chebyshev Type I filter using the procedure of Section 10.2. Compare your results with that found in Table 10.4.m all of the results of Example $\mathbf{1 0 . 2}$ including the SPICE magnitude

Beginning only with the specifications given in the first paragraph, repeat and confirm all of the results of Example 10.2 including the SPICE magnitude frequency plot. Determine and plot the magnitude frequency response for the circuit of Figure 10.11 as well. Compare the two magnitude responses. In addition, determine and plot the phase response of both circuits, the group delay response, the phase delay response, and the unit impulse response.

Repeat and confirm the results of Example 10.3. In addition, determine and plot the phase response, the group delay response, the phase delay response, and the unit impulse response.

Repeat and confirm the results of Example 10.4. In addition, determine and plot the phase response, the group delay response, the phase delay response, and the unit impulse response.

Suppose it is desired to implement a Chebyshev Type I highpass filter that meets the following specifications with minimum order: passband ripple $=0.5 \mathrm{~dB}, f_p=1,000 \mathrm{~Hz}, f_s=300 \mathrm{~Hz}, A_s=60 \mathrm{~dB}$, and $R_L=1,200 \Omega$. Determine two such passive circuit implementations. Using SPICE, determine and plot the magnitude frequency response of each circuit.

Suppose it is desired to implement a sixth-order elliptic bandpass filter that meets or exceeds the following specifications: passband ripple $=A_p=0.1$ $d B$, minimum attenuation in the stopband relative to the peak response $=A_s$ $=62 \mathrm{~dB}, B_p=1,000 \mathrm{~Hz}, B_s=8,500 \mathrm{~Hz}$, and $f_o=20,000 \mathrm{~Hz}$. Suppose it is also desired to use $5,000 \widehat{\Omega}$ resistors. Determine two such passive circuit implementations. Using SPICE, determine and plot the magnitude frequency response of each circuit.

Suppose it is desired to implement a fourth-order Butterworth bandstop filter that meets the following specifications: $A_p=3 \mathrm{~dB}, \quad B_p=1,000 \mathrm{~Hz}$, $f_o=25,000 \mathrm{~Hz}$, and $R_L=600 \Omega$. Determine two such passive circuit implementations. Using SPICE, determine and plot the magnitude frequency response of each circuit.

Suppose it is desired to design and implement a Butterworth bandpass filter that meets the following specifications with minimum order: $A_p=3 \mathrm{~dB}$, $A_s=50 \mathrm{~dB}, f_o=455 \mathrm{kHz}, B_p=10 \mathrm{kHz}$, and $B_s=30 \mathrm{kHz}$. Suppose it is also required that $1,000 \Omega$ resistors be used. Determine two such passive circuit implementations. Using SPICE, determine and plot the magnitude frequency response of each circuit.

Suppose it is desired to design and implement a time delay circuit that has a delay at very low frequencies of $10 \mu \mathrm{s}$, and a minimum time delay of $8 \mu \mathrm{s}$ at $80 \mathrm{kHz}$. Determine two such passive circuit implementations.

Suppose it is desired to design and implement a passive Bessel lowpass filter that meets the following specifications with minimum order: $f_p=3,500 \mathrm{~Hz}$, $f_s=20,000 \mathrm{~Hz}, A_p=2.5 \mathrm{~dB}$, and $A_s=60 \mathrm{~dB}$. Using MATLAB and Table 10.6, design and implement two such passive filters with $1,000 \Omega$ resistors. Using SPICE, plot the magnitude frequency response of the circuit implementation. Also plot the phase response.

Suppose it is desired to implement a sixth-order passive Bessel bandpass filter with the following specifications: $A_p=1 d B, B_p=1,000 \mathrm{~Hz}$, and $f_o=20,000 \mathrm{~Hz}$. Using Figure 10.7 as the prototype circuit schematic diagram, and using $1,000 \Omega$ resistors, determine and draw the circuit schematic diagram of the bandpass filter. Using SPICE, plot the magnitude frequency response of the bandpass filter circuit. Also plot the phase response.