Foundations — Transmission gates

This page assumes you have seen none of the notation in the parent note. We will earn every symbol before we use it. By the end you will read each inequality in the parent note — like the condition that turns a transistor on — as an ordinary sentence.

0. The most basic picture: voltage as height

Before any transistor, we need one idea: voltage.

Look at the figure: two tanks. The left is full (high voltage), the right is empty (low voltage). Open a pipe and water flows left→right until the heights match. That "wanting to equalise" is the whole reason current flows. We will keep re-using this height picture.

Why we need this: the entire topic is about whether a signal reaches the full ceiling or full floor, or stops short. Without naming the ceiling and floor, "weak 1" has no meaning.

1. A transistor as a switch (from zero)

In the figure the gate is drawn as a little bar sitting near but not touching the channel. Put the right voltage on the gate and the pipe (channel) between source and drain opens; wrong voltage and it stays shut.

Why we need $\bar{s}$: the two transistors in a TG turn on with opposite gate voltages, so one gets $s$ and the other gets $\bar{s}$. You'll build $\bar{s}$ physically with a CMOS inverter.

2. Two flavours of transistor: NMOS and PMOS

The figure shows both. Notice the little bubble on the PMOS gate — that bubble is the universal drawing symbol for "active LOW", i.e. "this turns on when the gate is 0".

3. The threshold voltage — the number that decides ON/OFF

This is the single most important symbol in the whole topic.

Why the topic can't live without $V_{tn}$: as an NMOS charges its output up, the source voltage climbs, so $V_{GS}=V_{\text{gate}}-V_{\text{source}}$ shrinks. The instant it shrinks down to $V_{tn}$, the pipe slams shut. That is why the NMOS output stops at $V_{DD}-V_{tn}$ instead of the full ceiling — the famous weak 1. Everything the parent derives comes straight from this one inequality.

4. Strong vs weak, and "parallel" resistance

Why we need this: an ON transmission gate is literally the NMOS pipe (resistance $R_n$) and PMOS pipe (resistance $R_p$) side by side between the same two nodes — a parallel pair. That formula is how fast the switch is.

5. How every symbol feeds the topic

Read it top-down: voltage-as-height gives you rails and $V_{GS}$; the transistor gives you source/drain; together they define the threshold; the threshold creates weak outputs; the NMOS/PMOS mirror pair plus complementary gates fix the weakness — and that fixed switch is the transmission gate.

Equipment checklist

Test yourself — reveal only after you've answered.

Connections

• 3.2.09 Transmission gates (Hinglish) — the parent topic these foundations unlock.
• Pass transistor logic — where the weak-1 / weak-0 problem first bites.
• MOSFET threshold voltage — the deep dive on $V_{tn}$ and $V_{tp}$.
• CMOS inverter — the circuit that physically makes $\bar{s}$ from $s$.
• Multiplexers and Latches and flip-flops — where TGs get used.
• RC delay in interconnects — why the resistance $R_{TG}$ matters for speed.