Final answer:
The voltage gain for a low-pass filter is a function of frequency and can be represented by the equation B(ω) = Bout/Bin = 1 / √(1 + (ωRC)^2), which shows the gain decreasing as frequency increases.
Step-by-step explanation:
The voltage gain for a low-pass filter as a function of frequency (ω) can vary based on the specific configuration of the filter components such as resistors, capacitors, and inductors. However, a standard first-order low-pass filter composed of a resistor (R) and a capacitor (C) will have a voltage gain (B) that is a function of frequency given by the following equation:
B(ω) = Bout/Bin = 1 / √(1 + (ωRC)^2)
This equation shows that the gain decreases as the frequency increases beyond the cutoff frequency, which is determined by the values of R and C. At lower frequencies, the output voltage (Bout) approaches the input voltage (Bin), and the gain is near unity. As the frequency increases, the gain drops, and the filter effectively attenuates higher frequencies.
Resonant frequency, inductive reactance, and capacitive effects are considerations that impact the behavior of the low-pass filter. For instance, at the resonant frequency, the inductive and capacitive effects balance each other out, and the gain reaches a maximum point before starting to decrease.