CMOS Inverter LTSpice simulation on Phase and Gain plot

[promach]

Dear all Sonsivri seniors.

I am doing a LTspice simulation on CMOS inverter Phase and Gain.

The LTspice amplifier symbol inside the test circuit is a CMOS inverter.

Please find below the gain and phase graph.



The line with red arrow pointing to it indicates the phase and the other line indicates the gain in dB

I have tried to google and look into books and find out the theory behind the graph but I could not get the answer.

Please advise.

[sarbandi70]

Hi;
you can click on Vout on your graph and a graph cursor will be appear.
you can change the position of cursor and watch any value of the graph.

best regards;

[PICker]

Have a look to the last plot on this link:
http://www.ee.surrey.ac.uk/Projects/CAL/linear-systems/m303-frequency.htm

[promach]

I understand gain margin and phase margin.

What I need to understand is how the gain and phase are calculated for this CMOS inverter.
I mean calculation and equation to verify the simulation.

I am sorry if I seem to be too theoretical, but I am only trying to learn more.

[PICker]

I've found some links but I do not know if they can help you.
http://www.edaboard.com/thread199980.html
http://www.prenhall.com/howe3/microelectronics/pdf_folder/lectures/tth/lecture11.fm5.pdf
http://www.ti.com/lit/an/szza043/szza043.pdf
http://www.egr.msu.edu/classes/ece410/mason/files/Ch7.pdf
http://www-inst.eecs.berkeley.edu/~ee105/fa98/lectures_fall_98/093098_lecture16.pdf
http://www.aicdesign.org/SCNOTES/2006notes/Chap05(7_5_06).pdf

Usually the analog simulators use ODE (ordinary differential equation) systems for simulating changes in continous parameters by defining small time intervals and re-calculatng the entire ODE system for each time interval (using the parameters generated in the previous interval):
http://www.eng.auburn.edu/~wilambm/pap/2011/02_ijee2410ns.pdf

[sarbandi70]

for verify the simulation of this circuit you need to read chapter of 6 of Behzad Razavi-Design of Analog CMOS Integrated Circuits-McGraw-Hill Science_Engineering_Math (2000).
this is very good book for you.