Diseño de Filtros Activos Parte 2

Understanding Salen Key Filter Architecture

Introduction to Salen Key Filters

• The video discusses the architecture of Salen Key filters, which can be used for various types of filters including low-pass, high-pass, band-pass, and notch filters.

• It introduces the Battlebor and Chebyshev filter designs, highlighting their advantages and disadvantages.

Structure of a Low-Pass Salen Key Filter

• The typical structure includes a non-inverting operational amplifier with resistors RA and RB determining the filter's gain. The gain formula is given as K = 1 + RB/RA .

• The filtering network consists of two resistors (R1 and R2) and two capacitors (C1 and C2), forming a second-order filter. A positive feedback relationship can lead to instability if not managed properly.

Frequency Cutoff Calculation

• The cutoff frequency depends on R1, R2, C1, and C2 values; it is derived from these components' product.

• Real component tolerances affect performance; however, this structure serves as an introduction to more complex designs.

Quality Factor Considerations

• The quality factor Q is influenced by both the gain K and component values. High gains can lead to instability in the filter.

• Other architectures like Rous will be discussed later; they use fewer components but require careful adjustment due to tolerance issues.

Simplifying Design Parameters

• State-variable filters offer better parameter adjustments but have their own pros and cons.

• A common simplification involves setting R1 = R2 = R and C1 = C for easier calculations while maintaining operational integrity.

Gain Limitations

• For this simplified design, the cutoff frequency becomes f_c = 1/RC .

• It's crucial that the gain does not exceed three; otherwise, Q may become excessively large or negative leading to instability.

Conclusion on Second Order Filters

• Understanding these conditions allows for straightforward design of second-order low-pass Salen Key filters.

• Variants exist such as using voltage followers instead of non-inverting amplifiers for different configurations.

This structured overview captures key insights from the transcript regarding Salen Key filter architecture while providing timestamps for easy reference back to specific parts of the video.

Proportionality in Circuit Design

Understanding Proportionality and Component Tolerance

• The proportionality constant in circuit design is not strict and can vary based on component tolerances, leading to minor discrepancies in parameters.

• Capacitors may have different values (m times C_initial and n times), but the gain remains one, complicating practical designs while offering alternatives for specific applications.

Filter Design Variations

• Variable frequency cut-off filters can be created using variable capacitors or resistors, maintaining a consistent architecture across designs.

• High-pass filters can be derived from low-pass filters by swapping resistors with capacitors, showcasing flexibility in filter design.

Advanced Filter Structures

Introduction to Salen Ki Structures

• The Salen Ki structure serves as a foundation for various filter types, including polynomial approximations like Butterworth and Chebyshev.

Characteristics of Different Filters

• The Butterworth approximation ensures a maximally flat gain within the passband but has a gradual roll-off at the cut-off frequency.

• In contrast, Chebyshev filters exhibit an abrupt transition between passband and stopband but introduce ripples in the passband gain.

Designing Higher Order Filters

Utilizing Polynomial Approximations

• The Butterworth polynomial approximation allows for designing higher-order active filters by cascading lower-order filters effectively.

• For instance, a fourth-order filter can be achieved by connecting two second-order filters in series.

Normalization of Cut-Off Frequency

• When normalizing the cut-off frequency to one, it simplifies design calculations while ensuring that quality factors remain consistent across different orders of filters.

Quality Factor Considerations

• A first-order filter has a denominator polynomial of S + 1; for second-order designs aiming for flatness, the quality factor must equal approximately 1.414.

• For third-order cascaded designs involving first and second order components, maintaining stability requires careful selection of quality factors to achieve desired characteristics.

Understanding Higher Order Filters

Introduction to Filter Orders

• The speaker discusses the design of fourth-order low-pass and high-pass filters, emphasizing that Butterworth (BB) filters provide a maximally flat response in the passband.

• It is noted that higher order filters can be mathematically calculated, allowing for the determination of coefficients and quality factors without difficulty.

Techniques for Achieving Higher Order Filters

• To create higher order filters, one can cascade two filters of the same type; for example, combining two second-order low-pass filters results in a fourth-order filter.

• For bandpass filters, a combination of low-pass and high-pass filters is necessary. The resulting frequency response is derived from the product of their transfer functions.

Frequency Cutoff Considerations

• The choice between using a low-pass or high-pass filter first depends on the noise characteristics present in the system; if there’s significant high-frequency noise, start with a low-pass filter.

• If both combined filters are second-order, their product will yield a fourth-order denominator in the overall transfer function.

Notch Filters Explained

• A notch filter (or band-stop filter), which eliminates specific frequencies, is created by summing a second-order low-pass and a second-order high-pass filter through an adder amplifier.

• For achieving a fourth-order notch filter, both constituent filters must also be of fourth order. The central frequency (Fesufedero) and symmetry depend on cutoff frequencies from both original filters.

Conclusion on Filter Design Quality

• The quality of the notch filter improves when both high and low pass components have equal gain; this ensures perfect symmetry and enhances overall performance.