1. A general method for TF It’s systematic Uses Mason’s formula
Will use the two stage op amp to illustrate
Will modify to obtain exact TF for lead compensated op amp

2. First step Identify all interesting node
At each node (other than input), denote current going into the node and voltage of the node
Find total admittance from each node to ground
Find inter-node admittance

3. vs vb cc VDD VDD VDD M9 M12 M11 vo Iref M1 M2 vin vin+= voQ CL vf=vin

4. Second step Find current into each node Find voltage at each node
gm effects
Inter-node admittance
Find voltage at each node
Current into the node / admittance to ground
Arrange into a directed graph from input to output

5. vs vb cc VDD VDD VDD M9 M12 M11 vo Iref M1 M2 vin vin+= voQ CL vf=vin

10. Mason’s Gain Formula A forward path: a path from input to output
Use Mk: total gain along the k-th path
A loop is a closed path in which you can start at any point, follow the arrows, and come back to the starting point
Use Li: total gains along the i-th loop
Loop i and loop j are non-touching if they do not share any nodes or branches

11. The determinant of the total graph Δ:
Δk: The determinant of the residue graph excluding the k-th forward path
Mason’s Gain formula:

12. vs vb cc VDD VDD VDD M9 M12 M11 vo Iref M1 M2 vin vin+= voQ CL vf=vinRc R M5 M6
M10 M7 M8
vin2

13. With Miller compensation, the inter-node admittance:
With lead compensation, the inter-node admittance:
To get new TF, only need to divide sCc by (1+sRcCc)