220-A3.3

Activity: MOS Frequency Response

• 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:

1. Plot the frequency response of NMOS and PMOS transistors.

MOS Transition Frequency

Figure 1: The MOS transistor small signal model.

At high frequencies, the MOS gate-to-source capacitance, $C_{GS}$ and the gate-to-drain capacitance, $C_{GD}$ limits the MOSFET current gain at high frequencies, 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:

$A_{i}={\frac {i_{\mathrm {out} }}{i_{\mathrm {in} }}}={\frac {g_{m}}{j\omega \left(C_{GS}+C_{GD}\right)}}$

(1)

We then define the transition frequency, $f_{T}$ as the frequency when magnitude of the short-circuit current gain is equal to 1, or:

$\left|A_{i}\right|=\left|{\frac {i_{\mathrm {out} }}{i_{\mathrm {in} }}}\right|={\frac {g_{m}}{\omega _{T}\left(C_{GS}+C_{GD}\right)}}={\frac {g_{m}}{2\pi f_{T}\left(C_{GS}+C_{GD}\right)}}=1$

(2)

Thus, we get:

$f_{T}={\frac {g_{m}}{2\pi \left(C_{GS}+C_{GD}\right)}}$

(3)

Assuming $C_{GD}\ll C_{GS}$, we can plot the transition frequency of an NMOS transistor as a function of $V_{GS}$ as shown in Fig. 2, using this SPICE file and Python script.

Figure 2: The NMOS Transition Frequency.

Figure 3: The Short-Circuit NMOS Current Gain.

We can also verify the transition frequency by running an AC analysis. For example, using and , we can plot the short-circuit current gain, as shown in Fig. 3. Thus, the transition frequency is the frequency when the short-circuit current gain drops to 1, or equivalently 0 dB.