MOSFET as a switch: Foundations — Hardware deep dive

Symbol 0 — What "voltage" and "current" even mean here

Before any transistor, we need two ideas the whole topic leans on.

Why the topic needs both: a switch is judged by two things — does current flow (ON) or not (OFF), and how much voltage does it waste while flowing. Everything else on the parent page is built from these two words.

Figure s01 — Two water tanks joined by a pipe: the height difference of the water levels is the voltage $V$ (the push), and the flow rate through the pipe is the current $I$ (what the push causes).

Symbol 1 — The four terminals: G, D, S, and the body B

A MOSFET is really a four-wire device, though the fourth wire is usually hidden.

Why the topic needs it: the parent note's very first claim — "voltage on the gate opens a channel between drain and source" — is meaningless until you know which wire is which. And the body is not optional trivia — it sets two behaviours the parent quietly relies on (next callout).

Figure s02 — Cross-section of the four terminals: Source (left) and Drain (right) sit in a silicon slab (the Body, tied to Source), with the Gate plate on top separated by an insulating oxide. An arrow shows the gate voltage pressing down through the glass while no current enters it. The built-in source-to-drain body diode is marked at the bottom.

Symbol 2 — The channel, the oxide, and "N-channel enhancement"

Why the topic needs it: the parent note is specifically about the N-channel enhancement device — "the most common switch." Its ON/OFF logic (positive gate ⇒ ON) only makes sense once you know the carriers are electrons pulled up by a positive plate.

Figure s03 — Two side-by-side beds. LEFT (OFF): $V_{GS} < V_{T H}$ , the bed is empty, no channel. RIGHT (ON): $V_{GS} > V_{T H}$ , the positive gate pulls electrons (upward arrows) into the bed to form a conducting channel from source to drain.

Symbol 3 — $V_{GS}$ , $V_{T H}$ , the overdrive, and cut-off

Symbol 4 — $I_{D}$ and $V_{D S}$ : what flows and what's dropped

Symbol 5 — Ohm's law and $R_{D S (o n)}$

The parent treats a closed MOSFET as a resistor. You need the resistor idea first.

Why the topic needs all three: Steps 3–4 of the parent derivation literally are Ohm's law ( $R = V / I$ ) plus the power law ( $P = I^{2} R$ ) applied to the channel. No new physics — just these two laws pointed at the transistor.

Symbol 6 — The two operating regions: triode vs saturation

A MOSFET behaves differently depending on how big $V_{D S}$ is compared to the overdrive $V_{O V} = V_{GS} - V_{T H}$ . Two named zones matter here, and the boundary is exactly $V_{D S} = V_{O V}$ .

Figure s04 — Drain current $I_{D}$ versus $V_{D S}$ for a fixed $V_{GS}$ . Left of the dashed boundary $V_{D S} = V_{O V}$ is the shaded TRIODE region (resistor-like, where the switch operates near the origin). Right of it is SATURATION, where $I_{D}$ is nearly flat but slopes gently upward due to channel-length modulation.

Symbol 7 — $k$ , and why $μ_{n}$ , $C_{o x}$ , $W / L$ bundle into one number

The parent's $k$ collects four factory-and-geometry facts into one "gain" constant. Here is where it comes from so it isn't a magic letter.

Intuition Why the three factors multiply together

Channel current is just charge on the move: $I_{D} = (charge available to move) \times (how fast it moves) / (how far it travels)$ . Track each piece:

The gate pulls charge onto the channel through the oxide. Charge per area delivered per volt of overdrive is the oxide capacitance $C_{o x}$ ; over a gate of width $W$ and length $L$ the total mobile charge scales with $C_{o x} W L (V_{GS} - V_{T H})$ .
How fast that charge drifts under the drain field is set by the mobility $μ_{n}$ .
The charge only has to travel the channel length $L$ , so dividing by $L$ (drift time) brings in one more $1/ L$ .

Multiply the pieces and the $L$ 's combine: the current is proportional to $μ_{n} C_{o x} \frac{W}{L} (V_{GS} - V_{T H}) V_{D S}$ . Everything except the voltages is fixed by fabrication, so we lump it into one symbol.

Definition

$k = μ_{n} C_{o x} \frac{W}{L}$ — the transconductance parameter A single "gain" number telling how much channel current you get per volt of overdrive, so the triode current is $I_{D} = k [(V_{GS} - V_{T H}) V_{D S} - \frac{V _{D S}^{2}}{2}]$ and the saturation current is $I_{D} = \frac{k}{2} (V_{GS} - V_{T H})^{2}$ .

$μ_{n}$ (mobility) — how easily electrons slide through the silicon. Picture: how slippery the riverbed is.
$C_{o x}$ (oxide capacitance per area) — how strongly the gate plate can pull electrons up per unit area. Picture: how close and effective your finger-through-glass press is.
$W / L$ (width over length) — the channel's shape: wide ( $W$ ) and short ( $L$ ) means more, easier flow. Picture: a broad short canal versus a thin long ditch.

Bigger $k$ ⇒ more current for the same push ⇒ a lower $R_{D S (o n)}$ ⇒ a better switch.

Why the topic needs it: $k$ sits in the denominator of $R_{D S (o n)} = 1/ [k (V_{GS} - V_{T H})]$ . Knowing what its three factors are — and that they multiply because current is charge-times-speed-over-length — is what lets you read "bigger $W / L$ = better switch" as a physical statement, not a magic formula.

How these foundations feed the topic

Equipment checklist

Cover each answer and test yourself before opening the parent note.

What does the subscript in

V_{GS}

tell you?

It equals

V_{G} - V_{S}

— first letter is the plus/measured node, second is the reference

How many terminals does a MOSFET really have, and where does the fourth one go in a switch?

Four — G, D, S and the body B; the body is factory-tied to the source in a discrete switch

What are the body effect and the body diode?

Body effect =

V_{T H}

shifts up if body and source differ; body diode = built-in source-to-drain diode that conducts when the drain is pulled below the source

Which terminal is the control knob, and does current flow into it?

The Gate; almost no steady current flows in because the oxide insulates it

In an N-channel enhancement MOSFET, what carriers form the channel and which gate polarity builds it?

Electrons; a positive gate voltage attracts them to form the channel

What is

V_{T H}

in one sentence?

The minimum

V_{GS}

at which the conducting channel first appears

Is a cut-off MOSFET perfectly zero current?

No — a tiny subthreshold leakage flows that fades exponentially as

V_{GS}

drops below

V_{T H}

; driving the gate to

0 V

makes it negligible

What happens for

V_{GS} = 0

V_{GS} < 0

on an enhancement device?

Both are below

V_{T H}

→ cut-off → OFF (negative just holds it OFF harder; mind the oxide voltage rating)

What is the overdrive and why care?

V_{GS} - V_{T H}

; bigger overdrive means a denser channel and a lower

R_{D S (o n)}

State Ohm's law and rearrange it for resistance.

V = I R

, so

R = V / I

How much heat does a resistor

R

carrying current

I

make?

P = I^{2} R

watts

Where is the triode/saturation boundary, and which side is the switch?

Boundary at

V_{D S} = V_{GS} - V_{T H}

; below it is triode (the switch's home), above it is saturation

Why isn't saturation current perfectly constant?

Channel-length modulation — rising

V_{D S}

shortens the effective channel, so

I_{D}

slopes gently up as

(1 + λ V_{D S})

What three physical factors hide inside

k = μ_{n} C_{o x} W / L

, and why do they multiply?

Mobility, oxide capacitance per area, and width-over-length; current = charge (from

C_{o x} W L

) × speed (from

μ_{n}

) ÷ travel length (

L

), so they combine into

μ_{n} C_{o x} W / L

Connections

2.4.14 MOSFET as a switch (Hinglish)
Enhancement vs Depletion MOSFET
Threshold voltage VTH
Triode vs Saturation regions
R_DS(on) and switching losses
Low-side vs High-side switching