2022-10-01 11:02
Status:
# MOSFET Current Equations
Drain current flows into the drain terminal.
ID can be derived from the operating range of the transistor.
Cutoff: $I_D = 0$
Triode:
$I_D=\mu C_{OX} \frac{W}{L}((V_{GS}-V_{TH})V_{DS}-\frac{1}{2} V_{DS}^2)$
Where $\mu C_{OX}$ is the current factor (can be called K, K' but these are ambiguous - use $\mu C_{OX}$ for clarity)
$V_{TH}$ is the threshold voltage.
Given $V_{GS}>V_{TH}$, $V_{DS}<V_{GS}-V_{TH}$
Saturation:
(Current independent of drain-source voltage)
$I_D=\frac{1}{2}\mu C_{OX} \frac{W}{L}(V_{GS}-V_{TH})^2$
for $V_{GS}>V_{TH}$, $V_{DS}>V_{GS}-V_{TH}$
Graph:
Saturation for MOSFET vs. active for BJT
## Further Detail
Best idea is to use the simplest equation that explains the phenomena you're looking for else it's too difficult to do analysis.
### Issues with simple model for current
Output impedance in saturation becomes infinite (1/slope)
This implies an amplifier with infinite gain can be created.
Need to include [channel length modulation](channel%20length%20modulation.md).
This becomes a factor:
Introduces a slope: also include in the triode (not really necessary)
$\lambda = \frac{k_\lambda}{L}$
## Process Constant Summary
Can be found in the design kit.
- $\mu C_{OX}$ is the current factor
- $V_{TH}$ is the threshold voltage
- $k_\lambda$ is the [[channel length modulation](channel%20length%20modulation.md)](channel%20length%20modulation.md) constant
## Bulk Source Voltage
$V_{TH} = V_{THO} + \gamma(\sqrt{|2\Phi_F-V_{BS}|}-\sqrt{|2\Phi_F|})$
Process constants:
Ignore whenever you can if possible.
If you increase the bulk source voltage, the threshold voltage decreases and the current increases. The bulk is called the 'back-gate'' because it has a similar effect to the gate (increase bulk V, increase the current!)
## PMOS
We can also define these voltages as reversed so the equations to make it the same!
### PMOS Equations
ON:
$V_{GS} < 0$
$V_{DS}<0$
$V_{BS}\geq0$ (else forward bias the diode)
$I_D<0$
$\mu C_{OX}<0$
$V_{TH}<0$
and so on...
### NMOS Equations
Flip the PMOS signs:
$V_{GS} > 0$
$V_{DS}>0$
$V_{BS}\leq0$
$I_D>0$
$\mu C_{OX}>0$
$V_{TH}>0$
...
[^1]
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# References
[^1]: [vr-4602-wk03-sc03-currentequations](../../Spaces/University/ELEC4602%20–%20Microelectronics%20Design%20and%20Technology/Lectures/W2/vr-4602-wk03-sc03-currentequations.mp4)