Hi Therion, I think you are doing great in your *paper* experiments. I wish the simulators had been available when I started. Keep up the digging and asking questions and you will end up understanding and will be able to avoid common mistakes when building the actual hardware.
Your most recent diagram still shows Op Amp 3 shorted out, its not there. Therefore, you don't get any gain from it at all. I also noticed you changed Res 8 from 1K to 500K. If the Op Amp 3 was not shorted that would give you a gain slightly less that 1, i.e., 500k / (500K + 1K). The gain is Rfeedback / (Rinput) where Rinput is the total series resistance in the input leg. Cap 4 is also in the series input leg but is not a resistance - it causes phase shift and affects the LPF cutoff but not midband gain. Looking from the input of Op Amp 3 toward the output of Op Amp 2 you see Res 13 + Res 8 (originally 1K + 1k to give the 2K mentioned above). They make up the Rinput, the Total resistance. The output impedance of Op Amp 2 is very low so its output impedance (resistance) compared to Res 13 and Res 8 is negligible. So that's why the Rinput is calculated as 2K previously and now is501K in the new circuit. Cap 4 affects the LPF frequency calculations. So if you change Rinput, to change gain, then you must adjust Cap 4 to restore the ratio to give you the desired frequency response.
In the formula: Fc = 1 / (2 x Pi x R x C), note I added the ( ) to clarify that 1 gets divided by all the denominator terms, consider the RC product as controlling the frequency response - everything else is a constant. Hence if either R, (the total resistance as discussed above) or C, (Cap 4) change, then Fc will also change. But you probably understood all this anyway.
I really haven't looked at calculating your Hi and Lo cutoff frequences but even if the shape of the Amplitude curve is what you want, the -133dB tells you its 133dB of attenuation, not gain. When you are looking for Gain, a Negative dB, rather than a hoped for Positive dB, means it is signal attenuation. [The negative dB can also mean a 180 degree phase shift between input and output signals. Since the sign of the dB can be interpreted two ways it can get a bit confusing but if the sign (+ or -) of the expected Gain is opposite what you are expecting, then you have attenuation.] Clear as mud??? Note that for an Op Amp, signal input on the negative, (-) terminal or inverting input will give a 180 degree inversion of the signal (at MIDBAND - the frequency range where the LPF and HPF neither give any attenuation), where as a signal input on the non-inverting, (+) input will give a positive gain, slightly different in magnitude than the negative input gain.
Just as Gain is controlled by the ratio of Rfeedback and Rinput, the phase shift at higher and lower frequencies (outside *mid band*) will change as the Capacitive reactance (Xc) of the capacitor changes with frequency.
Xc = -j1/(2 x Pi x F x C) where j represents a 90 degree phase shift and the calculations represent the numerical value of Xc. So, as far as phase shift is concerned, you get what your particular circuit gives you at different frequencies. And it changes with frequency because the *capacitive effect* of the capacitor changes with frequency. The actual phase shift which occurs depends on the ratio of R to C or C to R. Again, sorry for the mud. May I suggest you read up on RC circuits, particularly the mathematical effects which lead to the phase shift (due to the present of Capacitance or in other circuits the presence of Inductance). The math will get you into the Tangent function. If you are familiar with trig functions studying some RC circuits (attenuation and phase shift) from a mathematical perspective will clear up a lot of things for you.
As for the very low *gain* (in the mid-band) in your circuit there are two possible causes.
1. Op Amp 3 (is shorted out and therefore) does not exist, electrically. Res 8 = 500K is a very high series resistance. Op Amp 2 has a mid band gain of ONE, Rf = 10K and Rin = 10K. Op Amp 6 has a mid band gain of Res 15/ (Res 8 + Res 13 + Res14) or just under ONE.
2. The other is the frequency overlap (Midband range) of the Hi pass and Low pass sections. The pass frequencies of each must overlap where neither LPF or HPF have any appreciable attenuation - this is the MIDBAND. If the pass frequencies of the LPF and HPF don't overlap then there is no Midband region. The HP filter section should come first and the LP second and the cutoff frequencies of each adjusted so that signals in the desired bandpass are not attenuated by either filter.
Edit Note: The LPF cutoff frequency, Fc(LP), should determine the highest frequency desired and the HPF cutoff frequency, Fc(HP), should determine the lowest frequency desired.
Its fun to learn but you have many different things happening simultaneously that you have to sort out several different effects which are happening together.
Hope this helps and not confuses. If you have specific questions about my comments I'll try to further explain.
Edits to correct spelling and add a couple of sentences, hopefully to clarify.
Jess