14.3 Electronics: p-n Junction, Rectifiers, Transistors, Op-Amps & Logic Gates

Electronics: p-n Junction, Rectifiers, Transistors, Op-Amps & Logic Gates

Electronics builds directly on the n-type and p-type semiconductors introduced in Section 14.2. Most questions test either a definition (biasing, majority carriers, gate outputs) or a short calculation (transistor currents, amplifier gain), so clarity on the basic rules is enough to score well.

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1. The p-n Junction

When p-type and n-type material are joined, electrons diffuse from the n-side into the p-side and holes diffuse the other way. They recombine near the boundary, leaving a thin depletion region of fixed ions (negative on the p-side, positive on the n-side) with no free carriers. The resulting electric field creates a potential barrier:

• about $0.7\text{ V}$ for silicon
• about $0.3\text{ V}$ for germanium

Biasing

The diode's I–V curve is therefore highly non-linear: almost no current below about 0.7 V (Si) in forward bias, then a steep rise. A very large reverse voltage causes breakdown.

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2. Rectification

A rectifier converts AC into DC.

• Half-wave rectifier: one diode in series with the load conducts only during the half-cycles that forward-bias it; the other half-cycles are cut off. Output is pulsating DC at the supply frequency.
• Full-wave bridge rectifier: four diodes arranged in a bridge. In each half-cycle, two diodes conduct and route the current through the load in the same direction. The output pulses at twice the supply frequency (100 Hz from 50 Hz mains).
• Smoothing: a capacitor connected across the load charges near each peak and discharges slowly between peaks, reducing the ripple.

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3. Special-Purpose Diodes

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4. The Transistor

A bipolar junction transistor (BJT) is a thin, lightly doped base sandwiched between an emitter (heavily doped) and a collector (moderately doped, largest). It may be npn or pnp; in the circuit symbol the arrow on the emitter points in the direction of conventional current.

Currents

$I_E = I_B + I_C, \qquad \beta = \frac{I_C}{I_B}$

Because the base is thin and lightly doped, most carriers from the emitter cross into the collector, so $I_B$ is only a small fraction of $I_E$ and $\beta$ is typically 50 to a few hundred.

Example: with $I_B = 20\,\mu\text{A}$ and $\beta = 150$, $I_C = 3.0\text{ mA}$ and $I_E = 3.02\text{ mA}$.

Transistor as an Amplifier

For amplification, the base–emitter junction is forward biased and the collector–base junction is reverse biased. In the common-emitter amplifier, a small change in base current produces a large change in collector current; the voltage across the collector load resistor $R_C$ changes correspondingly. The output voltage is inverted ($180^\circ$ out of phase) relative to the input.

Transistor as a Switch

• Cut-off (OFF): base current is zero, collector current is (almost) zero, and the transistor behaves like an open switch.
• Saturation (ON): a large base current drives the collector current to its maximum, and the voltage across the transistor is very small, like a closed switch.

Switching circuits are used in automatic lighting (with a light-dependent resistor) and in digital electronics.

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5. The Operational Amplifier (Op-Amp)

An op-amp is an integrated-circuit amplifier with an inverting input ($-$), a non-inverting input ($+$) and one output. Its open-loop gain $A_{OL}$ is very high (around $10^5$ or more), its input resistance is very high and its output resistance is low. Without feedback, the output is

$V_o = A_{OL}(V_+ - V_-)$

and it saturates near the supply voltage for any appreciable difference between the inputs.

Example: an inverting amplifier with $R_1 = 10\text{ k}\Omega$ and $R_f = 100\text{ k}\Omega$ has $G = -10$, so a 0.2 V input gives $-2.0\text{ V}$. A non-inverting amplifier with the same resistors has $G = 11$.

A comparator with a thermistor or light-dependent resistor in a voltage divider forms a night switch or temperature alarm: the output changes state when the sensor voltage crosses a reference.

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6. Logic Gates

Digital circuits use two voltage levels, written 1 (high) and 0 (low).

The NOT gate (inverter) has one input and outputs its complement: $\bar{A}$.

Universal gates: NAND alone (or NOR alone) can build every other gate. Joining both inputs of a NAND gate makes a NOT gate; a NAND followed by a NOT gives AND.

De Morgan's theorems for logic, $\overline{A + B} = \bar{A}\cdot\bar{B}$ and $\overline{A \cdot B} = \bar{A} + \bar{B}$, mirror the set-theory laws in Section 2.1. Logic gates are used in alarms (for example, sounding if a door is open AND the system is armed), in arithmetic circuits and in computer memory.