Combining High and Low Pass Filters

In summary, by using a combination of low-pass and high-pass filters with appropriate component values, the desired part of a noisy signal at a specific frequency can be isolated. The cutoff frequency for the filters can be calculated using the equation w = (RC)^-1, and the attenuation at that frequency and 200 MHz away can be determined from the Bode plots of the filters. By choosing appropriate R and C values, the desired signal can be passed through while blocking out the noise.
  • #1
waley

Homework Statement


Suppose we have a noisy signal (superposition of many frequencies), but
we are only concerned with a particular part of the signal within the noise at a frequency
f(desired) = 1 GHz. In a sentence or two, explain how you could isolate the desired part
of the signal by using low-pass and high-pass filters. Assuming the noise is far from the desired signal in frequency (≥ ±200 MHz from f(desired)), suggest component values that should achieve this effect.

Homework Equations


cutoff frequency: w = (RC)^-1

The Attempt at a Solution


If I use the high-pass filter, all lower frequencies will be blocked; if I use the low-pass, all higher frequencies will be blocked. If I use a combo of both in the same circuit with the same R,C values, then wouldn't all frequencies be blocked?
 
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  • #2
waley said:

Homework Statement


Suppose we have a noisy signal (superposition of many frequencies), but
we are only concerned with a particular part of the signal within the noise at a frequency
f(desired) = 1 GHz. In a sentence or two, explain how you could isolate the desired part
of the signal by using low-pass and high-pass filters. Assuming the noise is far from the desired signal in frequency (≥ ±200 MHz from f(desired)), suggest component values that should achieve this effect.

Homework Equations


cutoff frequency: w = (RC)^-1

The Attempt at a Solution


If I use the high-pass filter, all lower frequencies will be blocked; if I use the low-pass, all higher frequencies will be blocked. If I use a combo of both in the same circuit with the same R,C values, then wouldn't all frequencies be blocked?
Are you familiar with the Bode plots of LPF and HPF circuits? What is the attenuation at that ω value you have listed for a single pole filter? What is the attenuation 200MHz away from that cutoff frequency?
 
  • #3
berkeman said:
Are you familiar with the Bode plots of LPF and HPF circuits? What is the attenuation at that ω value you have listed for a single pole filter? What is the attenuation 200MHz away from that cutoff frequency?
I'm guessing that the plots look something like: they're constant at first but at a certain frequency the curve drops to zero eventually. I'm not sure how to calculate attenuation - all I can guess is that somehow I have to have two values of R and C to fulfill 1.0x10^9 Hz = (2*pi*R*C)^-?
 

1. What is the purpose of combining high and low pass filters?

The purpose of combining high and low pass filters is to create a bandpass filter, which allows only a specific range of frequencies to pass through while attenuating all others. This is useful in various applications, such as audio signal processing and communication systems, where certain frequencies need to be isolated and amplified.

2. How do high and low pass filters work together to create a bandpass filter?

High and low pass filters work together by combining their respective frequency response curves. The high pass filter allows frequencies above a certain cutoff point to pass through, while the low pass filter allows frequencies below a certain cutoff point to pass through. By overlapping these curves, a bandpass filter is created with a specific range of frequencies that can pass through.

3. What is the difference between a high pass and low pass filter?

A high pass filter allows high frequencies to pass through while attenuating low frequencies. Conversely, a low pass filter allows low frequencies to pass through while attenuating high frequencies. This is why combining these two filters creates a bandpass filter that only allows a specific range of frequencies to pass through.

4. What are some common applications of combining high and low pass filters?

Combining high and low pass filters is commonly used in audio signal processing, such as in equalizers to adjust the frequency response of a sound system. It is also used in communication systems, such as in radio and television broadcasting, to isolate and amplify specific frequencies for better reception.

5. Are there any limitations or drawbacks to combining high and low pass filters?

One limitation of combining high and low pass filters is that the frequency response curve of the resulting bandpass filter may not be as steep as desired, which can lead to some frequencies bleeding through. Additionally, the combined filters may introduce phase shifts and distortions in the signal. It is important to carefully design and adjust the filters to minimize these effects.

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