View source for Activity: MOS Transition Frequency

Activity: '''MOS Transition Frequency'''
* '''Instructions''': This activity is structured as a tutorial with an activity at the end. Should you have any questions, clarifications, or issues, please contact your instructor as soon as possible. 
* At the end of this activity, the student should be able to:
# Plot the frequency response of NMOS and PMOS transistors.

== Activity 1: NMOS Transition Frequency ==
[[File:MOS ss highfreq.png|thumb|400px|Figure 1: The MOS transistor small signal model.]]
At high frequencies, the MOS gate-to-source capacitance, <math>C_{GS}</math> and the gate-to-drain capacitance, <math>C_{GD}</math> limits the MOSFET  current gain, and thus, needs to be included in the two-port model, as shown in Fig. 1. The short-circuit current gain can be expressed as:

::<math>A_i=\frac{i_{\mathrm{out}}}{i_{\mathrm{in}}}=\frac{g_m}{j\omega\left(C_{GS}+C_{GD}\right)}</math>

We then define the transition frequency, <math>f_T</math> as the frequency when magnitude of the short-circuit current gain is equal to 1, or:

::<math>\left|A_i\right|=\left|\frac{i_{\mathrm{out}}}{i_{\mathrm{in}}}\right|=\frac{g_m}{\omega_T\left(C_{GS}+C_{GD}\right)}=\frac{g_m}{2\pi f_T\left(C_{GS}+C_{GD}\right)}=1</math>

Thus, we get:

::<math>f_T=\frac{g_m}{2\pi \left(C_{GS}+C_{GD}\right)}</math>

We can determine the transition frequency by running an AC analysis to get the frequency response of the NMOS transistor. Thus, transition frequency is the frequency when the short-circuit current gain drops to 1, or equivalently 0 dB.

::<math>\left|A_i\left(j2\pi f_T\right)\right|=\left|\frac{i_{\mathrm{out}}}{i_{\mathrm{in}}}\left(j2\pi f_T\right)\right|=1</math>

You can modify this [https://github.com/louisalarcon/ee220/blob/da280a82e7628836521ddfff038a2c899d291b1e/cidr/ee-220-activity-5.sch sample schematic] and [https://github.com/louisalarcon/ee220/blob/da280a82e7628836521ddfff038a2c899d291b1e/cidr/activity-5-mos-ft.py Python script] to generate the plot of the NMOS transition frequency as a function of <math>V_{GS}</math>, and shown in Fig. 2.

{|
| [[File:Nmos-1v8-lvt-ft.png|thumb|400px|Figure 2: The NMOS Transition Frequency.]]
|-
|}

What happens to the transition frequency when you independently:
* Change the length to <math>L=0.30\mathrm{\mu m}</math> and <math>L=0.45\mathrm{\mu m}</math>
* Change number of fingers to <math>nf=10</math>
Plot the resulting <math>f_T</math>. Is this what you expected? Why?

== Activity 2: PMOS Transition Frequency ==
Repeat Activity 1 for the 1.8V LVT PMOS transistor. For the same size, how does the <math>f_T</math> of the PMOS compare to that of the NMOS? Comment on the relative values as well as on the effect of process variations.

== Report Guide ==
Write up a report (maximum of 5 pages including figures) answering the questions above. Include annotated graphs showing the different regions of operation for both the NMOS and PMOS transistors. 

== Submission ==
This activity is for both graduate and undergraduate students. For UP students, the submission bin link will be posted in Piazza.