I designed this as it would pass frequencies between 400-600 Hz. But it passes every single frequency anyway. What is the problem?
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The problem is you are designing your poles in the wrong place, if you want a pass band, your going to have to space them further apart, or add gain. It looks like you have a passband, but you will see attenuation on all frequencies. When you simulated your using a 10V signal but that is probably because a 1V signal showed much more attenuation so it was increased.
The cutoff frequency is for the -3dB point, not the frequencies where attenuation starts.
I split the two filters out to illustrate, The lowpass is blue and highpass green. (sorry LT spice wouldn't give me bigger lines) Both filters by themselves never reach more than -2.2dB together they never reach 4.4dB. Even at 1kHz there is attenuation.
I would suggest going back to the drawing board and spacing the filter poles farther apart, make sure you know what your pass band looks like. It may be necessary to increase the roll off with more poles (-40dB with two poles or -60dB with three) to achieve the desired results (and impedance buffers may be necessary).
Or you may just want to add some gain with an op amp at the end of the filter to bring the -4.4dB point up to your desired passband.
Use the .AC command in lt spice to see the frequency results of the simulated filter.
Impedance ratios are MOST important and 1st order bandpass filters are not very steep. (6dB per octave) Note the changes in LPF I made Rx10 and C/10
Although you have yet to give specs for BW , Q, gain, dB vs f, this is not optimized but shows two cascaded BPF which could be isolated in parallel with 37dB gain and a Q=10
This trace from 10Hz to 30kHz shows a range of 80dB from +37dB gain in the pass band. Minor Pole shift is easy with the input shunt R to gnd.