Comprehensive theory, key formulas, diagrams, and memory aids for Electronics.
A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. The most important semiconductor is silicon, which has four valence electrons forming a covalent lattice.
In a p-type semiconductor, the silicon is doped with elements like boron (3 valence electrons), creating "holes" — positive charge carriers — as majority carriers.
In an n-type semiconductor, silicon is doped with phosphorus (5 valence electrons), providing extra electrons as majority carriers.
A p-n junction diode is formed by joining p-type and n-type silicon. At the junction, electrons and holes recombine, creating a depletion region — a zone depleted of free charge carriers, which acts as a potential barrier.
A diode's I-V characteristic is exponential forward, essentially flat reverse — a non-ohmic component.
A transistor is a three-terminal semiconductor device used for amplification and switching. Two common types:
Three regions: Collector (C), Base (B), Emitter (E).
In common-emitter configuration: - A small base current ($I_B$) controls a large collector current ($I_C$). - DC current gain: $\beta = h_{FE} = \frac{I_C}{I_B}$, typically 50–500. - Collector current: $I_C = \beta I_B$ - Emitter current: $I_E = I_B + I_C$
As a switch: When $I_B = 0$, transistor is cut off (OFF). When $I_B$ is large enough to saturate the transistor, it acts like a closed switch (ON). Used in logic circuits, relay drivers, LED controllers.
As an amplifier: Operating in the linear (active) region — $V_{CE}$ is between saturation and cutoff. Small AC input signal at base → amplified AC output at collector. The voltage gain $= -\beta R_C / R_{in}$ (negative sign indicates 180° phase inversion in common-emitter configuration).
An operational amplifier is an integrated circuit with two inputs and one output, designed for high-gain amplification. The ideal op-amp has: - Infinite open-loop voltage gain ($A_{OL} \rightarrow \infty$) - Infinite input impedance (draws no current from the signal source) - Zero output impedance - Infinite bandwidth
Real op-amps (e.g., 741) have open-loop gain ~100,000, which is so large that even tiny differential inputs saturate the output. Therefore, op-amps are almost always used with negative feedback.
Input connected to inverting input (−) via $R_{in}$, with feedback resistor $R_f$ from output back to (−): $$V_{out} = -\frac{R_f}{R_{in}} V_{in}$$ Voltage gain $= -R_f / R_{in}$. Negative sign: output is 180° out of phase with input.
Input connected to non-inverting input (+): $$V_{out} = \left(1 + \frac{R_f}{R_1}\right) V_{in}$$ Voltage gain $= 1 + R_f/R_1$. Output is in phase with input.
graph LR
A[Input Vin] --> B[Inverting Op-Amp]
C[Rf from output to -ve input] --> B
B --> D[Output = -Rf/Rin × Vin]
D --> E[Amplified and inverted signal]
Without negative feedback, the op-amp compares $V_+$ and $V_-$: - $V_+ > V_-$: Output saturates at $+V_{sat}$ (close to positive supply voltage) - $V_+ < V_-$: Output saturates at $-V_{sat}$
Used in burglar alarms (thermistor/LDR potential divider compared to reference), zero-crossing detectors, and Schmitt triggers.
Digital electronics uses binary logic — signals are either HIGH (1, typically ~5V or 3.3V) or LOW (0, ~0V). Logic gates perform Boolean operations on binary inputs.
| Gate | Symbol | Boolean | Output |
|---|---|---|---|
| NOT | ¬A | $\overline{A}$ | Inverts input |
| AND | A·B | $A \cdot B$ | 1 only if both inputs 1 |
| OR | A+B | $A + B$ | 1 if at least one input 1 |
| NAND | ¬(A·B) | $\overline{A \cdot B}$ | NOT AND — universal gate |
| NOR | ¬(A+B) | $\overline{A + B}$ | NOT OR — universal gate |
| XOR | A⊕B | $A \oplus B$ | 1 if inputs are different |
NAND and NOR are universal gates: Any logic function can be constructed using only NAND gates (or only NOR gates). This is economically efficient in chip manufacturing.
Complex logic circuits combine multiple gates. A truth table lists all possible input combinations and corresponding outputs — essential for analysing and designing logic circuits.
Example — Half Adder: Adds two 1-bit numbers. Produces Sum (S) and Carry (C): - $S = A \oplus B$ (XOR) - $C = A \cdot B$ (AND)
| A | B | Sum (S) | Carry (C) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
A bistable (flip-flop) is a sequential logic circuit with two stable states — it can store one bit of information. The SR (Set-Reset) bistable uses cross-coupled NOR (or NAND) gates.
SR NOR bistable: - S=1, R=0: Output Q set to 1 (Set) - S=0, R=1: Output Q set to 0 (Reset) - S=0, R=0: Q retains previous state (Memory) - S=1, R=1: Indeterminate — avoid this state
The D flip-flop, clocked T flip-flop, and JK flip-flop are more advanced forms used in registers, counters, and memory.
Real-world signals (sound, temperature) are analogue — continuously varying. Computers require digital (binary) signals. An ADC (Analogue-to-Digital Converter) samples the analogue signal at regular intervals (sampling rate) and converts each sample to a binary number.
DAC (Digital-to-Analogue Converter) performs the reverse — converts digital values back to analogue signals (e.g., in audio speakers, function generators).