High-performance CSAs are often found to be multi-stage. In between input and output, there could be additional gain stages for signal enhancement. If such a device is bidirectional, it generally comes with an output stage that is based on difference amplifier which accomplishes differential to single-ended conversion. This section builds upon what has previously been explored from single-stage difference amplifiers, and extrapolates that information to multi-stage CSAs.

Since the output stage is a difference amplifier, the output error Equation 12 still applies. Similar to the single-stage case, the external reference voltage is known, as well as the source impedance. However, for multi-stage, the input to the output difference amplifier is an internal node. Internal operating condition is generally not published in product data sheets. Both the common-mode and differential input voltages must be found to utilize the error equation.

Figure 5-4 shows a two-stage voltage feedback CSA. The differential input is easy to calculate if the gain of each stage is known. This particular example is made up of two stages with gain of G₁ and G₂, respectively. The overall gain equals to the product of all gains:

The differential input to the output stage equals to the differential output of the input stage:

The common-mode input is a value determined by design and is unique to the individual device. It is bound between ground and power supply for voltage compliance. Practical choices often put the common-mode voltage near mid supply. It should be noted that the common-mode operating point is independent of the input common-mode voltage of the device, which is the reason behind very high CMRR specifications of such devices.

Rewriting the output error equation, with V_cm2 being the common-mode voltage: