Combining High and Low Pass Filters

[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?

 

[berkeman]

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?

 

[waley]

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)^-?