DC input random offset voltage for diff. amplifier with current-mirror load

[eyeweyew]

TL;DR Summary

how the expression for DC input offset voltage for diff. amplifier with current mirror load come about

I am trying to figure out how the derivation of equation 6.69 come about on page 426 in the book Analysis and Design of Analog Integrated Circuits, 5th Edition by Gray and Meyer. They defined on page 424 under section 6.3.3 the input offset voltage (V_OS) of op amps with differential inputs and single-ended outputs as the differential input voltage for which the dc output voltage is midway between the supplies. But I don’t see V_SS and V_DD in the equation so I am not sure if they are using this definition since they did mention another definition for V_OS under 6.3.3 which is the differential input voltage for which the op-amp output voltage is zero but I try to follow the similar derivation on pg. 234-236 under 3.5.6.6 and 3.5.6.7 for diff. amp with resistors pair as loads but I still don’t get how do they come about equation 6.69?Analysis and Design of Analog Integrated Circuits, 5th Edition
http://fa.ee.sut.ac.ir/Downloads/AcademicStaff/24/Courses/73/[Gray___Meyer]_Analysis_and_Design_of_Analog_Integrated_Circuits_5th_ed.pdf

 

[Baluncore]

But I don’t see VSS and VDD in the equation so I am not sure if they are using this definition ...

The supply voltages can be assumed typical, equal and opposite, and sufficient for the circuit to operate.

Supply voltage is independent, since the circuit is symmetrical. The supplies are isolated from the differential input pair, by the collector or drain voltage of the other transistors employed.

Part of the elegance of employing a current mirror as the load, is supply voltage independence, while the gain of the differential input pair is effectively squared.

 

[eyeweyew]

TL;DR Summary: how the expression for DC input offset voltage for diff. amplifier with current mirror load come about

I am trying to figure out how the derivation of equation 6.69 come about on page 426 in the book Analysis and Design of Analog Integrated Circuits, 5th Edition by Gray and Meyer. They defined on page 424 under section 6.3.3 the input offset voltage (V_OS) of op amps with differential inputs and single-ended outputs as the differential input voltage for which the dc output voltage is midway between the supplies. But I don’t see V_SS and V_DD in the equation so I am not sure if they are using this definition since they did mention another definition for V_OS under 6.3.3 which is the differential input voltage for which the op-amp output voltage is zero but I try to follow the similar derivation on pg. 234-236 under 3.5.6.6 and 3.5.6.7 for diff. amp with resistors pair as loads but I still don’t get how do they come about equation 6.69?Analysis and Design of Analog Integrated Circuits, 5th Edition
http://fa.ee.sut.ac.ir/Downloads/AcademicStaff/24/Courses/73/[Gray___Meyer]_Analysis_and_Design_of_Analog_Integrated_Circuits_5th_ed.pdf

Ok, Never mind. The derivation is actually on page 332-333 in the same book.