I'm studying CMOS op-amps. At the very beginning of the chapter, the author of my book says:
"obtaining low output impedance can be problematic. Nevertheless, the typical use that we make of op-amps in integrated systems does not lead to a strict request for low output impedance. Even better, in some cases the output impedance may not be a problem at all."
To prove it, he proposes the following example:
He finds the following expressions:
He then says:
"Since 1/gm is much smaller than r0, the time behaviour of the output voltage is mainly controlled by the transconductance gain and is almost independent of the output resistance. [...] When the feedback network comprises only capacitors (and switches) the output resistance is not relevant. We can use a special class of operational amplifiers where the output resistance can be very high and, possibly, used to enhance the voltage gain. This class of operational amplifiers is called OTA (operational transconductance amplifier)."
Question 1: why does the author model the op-amp with a transconductance generator gm*vi having in parallel the output resistance r0? The model of an op-amp should be the following:
Question 2: I'm able to find expressions 5.3 and 5.4: the charge on C1 (i.e. Q1=C1*vin) is shared with the series connection C-C0. But why does the charge on C1 distribute only on the series connection C-C0? Actually this charge has also two paths toward ground through which it can flow: r0 and the voltage-controlled current source.
Question 3: I'm not able to find expressions 5.5, 5.6 and 5.7. Can you give me some hints?
Question 4: the author says that it is an OTA, whose working principle is based on a very large value of the output resistor. But why does he talk about OTA if the chapter is dedicated to op-amps?