Electronic – Summing amplifier with bypass

It looks like both filter sections are designed with the -3dB point at the same frequency, or very close together, so this filter is doing what it should.

In the crossover region, both sections contribute to the output, so it is higher than either alone. The slight peax at the crossover frequency would be 3dB if both signals were in phase(so they added coherently), so presumably they aren't. EDIT : apparently the small separation between -3dB points, rather than phase, accounts for this peak being less than 3dB.

For a classic design without that bulge, read up on the Linkwitz-Riley crossover, commonly used in loudspeakers where you want HPF and LPF outputs to sum to unity.

I don't know what you were expecting but if you wanted a notch you'd have to separate the -3dB frequencies, then the depth of notch will depend how far apart they are, and it won't be a deep notch.

If you wanted a deep notch, one approach is the Twin-T filter which can be made as narrow as you want.

Or start by specifying the frequency, notch width (at -3dB), and notch depth you want, and research filter design techniques to meet that specification.

Supposedly the operation of this circuit is v0= 3v1 + 1.5v2, but I don't know what that means.

This means that you should be able to calculate the output voltage from the two input voltages using algebra, according to the given formula.

If you work out the circuit, you will find a formula that gives \$v_o\$ in terms of \$v_1\$, \$v_2\$, \$R_1\$, \$R_2\$, \$R_{f1}\$, and \$R_{f2}\$. Your job is to find values of the resistors that makes the constants in the formula come out to 3 and 1.5.