Electronic – Differential filters: high pass, low pass, band pass

If you use this circuit on a regular basis I guess it would be worth to calculate its transfer function once and for all, so you can just easily evaluate it given the concrete component values. Doing the math you get (assuming an ideal OP)

$$H(\omega)=\frac{j\omega R_1C_1}{1+j\omega R_1C_1}\left(1+\frac{j\omega R_4C_2}{1+j\omega R_2C_2}\right)\tag{1}$$

A plot of (1) in dB with the specified component values looks like this (|H|/db vs f in Hz):

from which you can see that the -3dB point is at about \$250\,\text{Hz}\$.

If you further assume that

$$R_1C_1=R_2C_2=\tau$$

and if you denote the gain at large frequencies by

$$g=1+\frac{R_4}{R_2}$$

then with a bit more math you get this exact expression for the 3dB cut-off frequency in radians

$$\omega_c=\frac{1}{\tau}\sqrt{1-\frac{1}{g^2}+\sqrt{\left(1-\frac{1}{g^2}\right)^2+1}}\tag{2}$$

which with the given component values gives

$$\omega_c=2\pi\cdot 247.28$$

For a large gain \$g\gg 1\$, formula (2) is closely approximated by

$$\omega_c=\frac{1}{\tau}\sqrt{1+\sqrt{2}}\approx\frac{1.55}{\tau}\tag{3}$$

There is a big difference here. The top picture is a cable driver, cable and differential receiver. The bottom picture is a circuit that is used to differentially drive a local ADC.

The first scenario doesn't need to use capacitors to couple data to the twisted pair but, because it does, you could argue that the DC levels on the "send" end might not always match the required DC levels on the "receive end. In addition it can be firmly concluded that this type of data transmission is synchronous and different to RS232, RS485 or RS422 - those types of transmission are asynchronous AND dc connectivity MUST BE maintained because of the long periods of time that the line is idle.

The 2nd case (the ADC driver) is a very common circuit and is used as (or to supplement) an anti-alias filter.