2022-10-04 10:55 Status: # Small-signal Models A MOS biased with a large signal VGS, VDS and a current ID:  For small signal, we want to transfer these highly non-linear responses to a linear model. Find the tangent of the curve in the operating point!  $i_D=g_mv_{GS}+g_{ds}v_{DS}$ Where $g_{DS}=1/r_{DS}$  ## More Complete Model Include the bulk/body voltage: Recall it looks like another gate - find a bulk referred transconductance - another VCCS in the small-signal model (SSM).  The definitions of bulk and gate transconductance are *completely symmetrical* in this source referred model. ## Pi Model   ## Alternative - T Model  These are identical from a terminal point of view.  ## Use of Small Signal Models Usually the SSM is used for amplifiers (in the saturation region) but they can be used in any operating point. ### Saturation #### Transconductance  $g_m\approxeq\frac{2I_D}{V_{GS}-V_{TH}}$ or $g_m\approxeq\sqrt{2I_D\mu C_{OX}\frac{W}{L}}$ are the most common design equations. ### Output Conductance  $r_{ds}=\frac{1}{g_{ds}}=\frac{L}{k_\lambda I_D}$ $r_{ds}$ is inversely prop to drain current and prop to length of the transistor (good from a gain point of view). ## Intrinsic Gain Largest gain you can get from a transistor: $A = g_mr_{ds} = \frac{1}{k_\lambda}\sqrt{\frac{{2\mu C_{OX}WL}}{I_D}}$ Large gain requires large transistor area and small drain current. Squareroot means it is hard to get very large gain (slow growing). ## Transition Frequency $f_T=\frac{g_m}{2\pi C_{gate}}= \frac{\mu C_{OX}\frac{W}{L}(V_{GS}-V_{TH})}{2\pi C_{OX}WL} = \frac{\mu(V_{GS}-V_{TH})}{2\pi L^2}$ Frequency doesn't depend on channel width. High frequency requires high effective voltage and very small channel length. ## PMOS Small Signal Model **Identical to NMOS small signal model**! All that changes is the parameters in the model. [^1] --- # References [^1]: [vr-4602-wk03-sc05-smallsignal](../../Spaces/University/ELEC4602%20–%20Microelectronics%20Design%20and%20Technology/Lectures/W2/vr-4602-wk03-sc05-smallsignal.mp4)