Definition of the offset voltage for a single-ended op-amp

Let's consider an op-amp:

The book I'm reading says that, ideally, if the voltage difference between the two inputs is zero (thus vin1=vin2) then the output voltage should be zero. However, because of mismatches in the circuit implementation at the transistor level, even if the input differential input is zero, the output will be different from zero. Thus a voltage, called the offset voltage, must be applied between the two inputs in order to really set the output voltage to zero.

Another book I'm reading considers the following fully differential circuit:

Ideally, if v1=v2, then the output differential voltage vo is zero. In reality however vo is not zero because of mismatches; the book calculates then the value of the offset in order to have the differential output voltage equal to zero. In every case, the author of the book is consistent with the definition of offset voltage: he wants to set the output differential voltage to zero, accordingly to the definition

Question: if I have a single-ended output voltage, how do we define the offset voltage? Let's consider the following two-stages op-amp:

If I rigorously apply the definition of the offset voltage, I should find that voltage which, applied between the two inputs, sets the voltage of the output node to zero. But this would be meaningless: I must indeed have necessarily a dc voltage different from zero at the output node, otherwise the circuit for sure will not work!

• You should think of the offset voltage as being what is required for the circuit to be in balance - depending upon the particular implementation it might not be zero at the output. In the last example with a single-supply, mid-rail would usually be the value that is used as the output being "zero". In general it doesn't matter because for most DC analysis the gain of the opamp is considered to be extremely high so the voltage change required at the input to change the output over the full range is considered negligible. Commented Sep 9, 2019 at 0:22
• Most data sheets will provide the test circuit and definitio Commented Sep 9, 2019 at 0:31