MOSFET

Id=K(Vgs-Vto)^2  (537)

K = (W/L) (KP/2), K (mA/V^2) and KP are constants, KP n-channel enchancement devices typical value is 50uA/V^2, W = width of the polysilicon, L=length of the polysilicon(535)

Av =Vo/Vi=-gm(R_L’), Voltage Gain of common source amplifier (Av), Vo = Output Voltage, Vi=Input Voltage, gm= transconductance (543)

gm = 2K(Vgsq- Vto) = Id/Vgs, transconductance (537)

Vdd=Rd x Id(t) + Vds(t), Load Line Analysis of simple NMOS Amplifier, if Rd = 1k ohm, Id in mA, then Vdd = Id(t) + Vds (t)( 531)

(609) Ideal Operational Amplifiers

1. Infinite input impedance

2. Infinite gain for the differential input signal

3. Zero gain for the common-mode input signal

4. Zero output impedance

5. Infinite bandwidth

RC RL Circuit Complete Response

X(t) = X(infinite) +[ X(0+) - X(infinite)] e^-t/tou

X is Voltage or Current, tou for Capacitor = RC, t is time

Capacitor

V(t) = V0*e^(-t/RC), RC circuit natural response

I(t) = C*(dV/dt), current across capacitor

V(t) = L*(dI/dt), voltage across inductor

<@ = cos @ + isin@ = e^(j@) , < is the sign for angle, here used for the sign for phasor. @ to Telta sign. (196)(802)

j = -1/j , where j =sqrt(-1). (201)

Time Domain <-> LaPlace Domain

sin(wt) = w/(s^2 + w^2)

cos(wt) = s/(s^2 + w^2)

Step function = 1/s

Dicac's delta(t) = 1

e^(sot) = 1/(s-so)

Partial Fraction:

Case (a-i are all constants)

I. (dx + e) / (ax^2 + bx + c) = A/(fx + g) + B/(hx + i)

II. (cx^2 + dx + e) / (ax + b)^3 = A/(ax + b) + B/(ax + b)^2 + C/(ax + b)^3

III. (x^2 + 4x - 23)/ ((x + 3)(x^2 + 4)) = A/(x + 3) + (Bx + C)/(x^2 + 4)

IV. (-3x^3 - x)/(x^2 + 1)^2 = (Ax + B)/(x^2 + 1) + (Cx + D)/(x^2 + 1)^2

V. x^m(....) / x^n(...) use long division when m>=n