3.3 KiB
3.3 KiB
title, description, date, math
| title | description | date | math |
|---|---|---|---|
| Oppsumering av TFE4152 | Stort sett formler i faget TFE4152, høsten 2020. | 2020-12-16 | true |
Konstander
| Symbol | Verdi | Kommentar |
|---|---|---|
q |
1.602\cdot 10^{-19}\text{C} |
|
k |
1.38\cdot 10^{-23}\text{J}\cdot\text{K}^{-1} |
|
n_i |
1.1\cdot 10^{16}\text{bærere}/\text{m}^3 |
Ved T=300\text{ K} |
\epsilon_0 |
8.854\cdot 10^{-12}\text{F}/\text{m} |
|
K_{ox (oksid)} |
\cong 3.9 |
|
K_{Si (silikon)} |
\cong 11.8 |
|
| {: .table } |
Revers-forspent diode
C_j = \frac{C_{j0}}{\sqrt{1+\frac{V_R}{\Phi_0}}}
Q = 2 C_{j0} \Phi_0 \sqrt{1 + \frac{V_R}{\Phi_0}}
C_{j0} = \sqrt{\frac{q K_{Si} \epsilon_0}{2 \Phi_0} \frac{N_D N_A}{N_D + N_A}}
C_{j0} = \sqrt{\frac{q K_{Si} \epsilon_0 N_D}{2 \Phi_0}}, \text{ hvis } N_A \gg N_D
\Phi_0 = \frac{k_B T}{q}\ln\left(\frac{N_A N_D}{n_i}\right)
Normalt forspent diode
I_D = I_S \exp{\frac{V_D}{V_T}}
I_D = A_D q n_i^2 \left(\frac{D_n}{L_n N_A}+\frac{D_p}{L_p N_D}\right)
V_T = \frac{k T}{q} \approx 26\text{mV, ved } T=300\text{ K}
Småsignal for forspent diode
r_d = \frac{V_T}{I_D}
C_T = C_d + C_j
C_d = \tau_T \frac{I_D}{V_T}
C_j \approx 2 C_{j0}
\tau_T = \frac{L_n^2}{D_n}
Transisor i triodeområdet
Dette gjelder for V_{GS} > V_{tn}, V_{DS} \leq V_\text{eff}.
I_D = \mu C_{ox} \left(\frac{W}{L}\right) \left[(V_{GS} - V_{tn})V_{DS} - \frac{V_{DS}^2}{2}\right]
V_\text{eff} = V_{GS} - V_{tn}
V_{tn} = V_{\text{tn-}0} + \gamma\left(\sqrt{V_{SB} + 2\Phi_F} - \sqrt{2\Phi_F}\right)
\Phi_F = \frac{k T}{q}\ln\left(\frac{N_A}{n_i}\right)
\gamma = \frac{\sqrt{2 q K_{Si} \epsilon_0 N_A}}{C_{ox}}
C_{ox} = \frac{K_{ox} \epsilon_0}{t_{ox}}
Småsignal av transistor i triodeområdet
r_{ds} = \frac{1}{\mu_n C_{ox} \left(\frac{W}{L}\right)V_\text{eff}}
C_{gd} = C_{gs} \frac{1}{2}W L C_{ox} + WL_{ov}C_{ox}
C_{sb} = C_{db} = \frac{C_{j0} \left(A_s + \frac{WL}{2}\right)}{\sqrt{1 + \frac{V_{sb}}{\Phi_0}}}
Transistor i aktivt område
Dette gjelder bare for V_{GS} > V_{tn}, V_{DS} \geq V_\text{eff}.
I_D = \mu C_{ox} \left(\frac{W}{L}\right) (V_{GS} - V_{tn})^2 \underbrace{\left[1 + \lambda(V_{DS} - V_\text{eff})\right]}_\text{body-effect}
\lambda \propto \frac{1}{L\sqrt{V_{DS} - V_\text{eff} + \Phi_0}}
V_{tn} = V_{tn\text{-}0} - \gamma\left(\sqrt{V_{SB} + 2\Phi_F} - \sqrt{2\Phi_F}\right)
V_\text{eff} = V_{GS} - V_{tn} = \sqrt{\frac{2 I_D}{\mu_n C_{ox} \frac{W}{L}}} = V_{DS, \text{sat.}}
Småsignal for transistor i aktivt område
$$\begin{aligned} g_m &= \mu_n C_{ox} \frac{W}{L} V_\text{eff} \ &= \sqrt{2 \mu_n C_{ox} \frac{W}{L} I_D} \ &= \frac{2 I_D}{V_\text{eff}} \end{aligned}
\begin{aligned} g_s &= \frac{\gamma g_m}{2 \sqrt{V_{SB} + |2\Phi_F|}}\ &\approx 0.2 g_m \end{aligned}
$$ r_{ds} = \frac{1}{\lambda I_{D\text{, sat.}}} \approx \frac{1}{\lambda I_D} $$
$$\lambda = \frac{k_{r_{ds}}}{2 L \sqrt{V_{DS} - V_\text{eff} + \Phi_0}} $$
$$ k_{r_{ds}} \sqrt{\frac{2 K_{Si} \epsilon_0}{q N_A}} $$
$$ C_{gs} = \frac{2}{3} W L C_{ox} + WL_{ov} C_{ox} $$
$$ C_{gd} = WL_{ov} C_{ox} $$