9.12:
Passive Filters
Consider an audio speaker system with filter circuits. These circuits selectively pass desired frequencies while attenuating others, limiting signals to a specific frequency band.
Filters are categorized as passive when exclusively using passive components like resistors, inductors, and capacitors.
A low-pass audio filter channels low-frequency components to the woofer or subwoofer, while a high-pass filter directs high-frequency components to the tweeter.
The transfer function, expressed as the output-to-input voltage ratio, is estimated for low and high frequencies to achieve the desired frequency response for the filter circuits.
Well-designed filters transmit frequencies up to the cutoff frequency without attenuation for low-pass filters, and above the cutoff frequency for high-pass filters.
A band-pass filter directs mid-range frequencies to the dedicated driver. While, a band-stop filter targets overlapping frequencies to prevent interference.
Similarly, the transfer function can be approximated for low and high frequencies to optimize the frequency response of band-pass and band-stop filters.
Band-pass filters transmit frequencies around a center frequency, whereas band-stop filters block these frequencies.
9.12:
Passive Filters
Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency is defined by:
They are commonly employed to route audio signals to woofers or subwoofers, ensuring that only bass frequencies reach these devices. The typical transfer function H(s) for an RC low-pass filter is given by:
In this equation, Vo is the output voltage, Vi is the input voltage, ω is the angular frequency, R is the resistance, and C is the capacitance.
High-Pass Filters
In contrast, high-pass filters allow frequencies above ωc to pass while blocking those below. These filters are vital in directing high-frequency components to tweeters in audio systems. An RC high-pass filter has the following transfer function:
Band-Pass Filters
Band-pass filters are engineered to pass a band of frequencies, making them ideal for channels dedicated to mid-range audio frequencies.
Band-stop Filters
These are also known as notch filters; band-stop filters reject a specific band of frequencies to avoid interference, which is particularly useful in complex electronic systems where multiple signals overlap.
The design of passive filters is a delicate balance of selecting the right component values to achieve the desired cutoff frequencies and attenuation levels.