Microelectronic circuits

Map of content for microelectronic circuits — how semiconductor physics gives rise to devices (diodes, MOSFETs, BJTs), and how those devices are biased and combined into amplifiers, op-amps, and signal-processing circuits. The path: semiconductor physics → pn junction → diodes and their circuits → MOSFET and BJT operation → DC biasing → small-signal models → single-transistor amplifiers → operational amplifiers → frequency response.

Signal and circuit preliminaries

The vocabulary for the signals these circuits process and the basic tools used to analyze them.

Signal — the general concept; the time-varying quantity an amplifier acts on.
Sinusoid — the test signal for everything; AC analysis is sinusoidal steady state.
Amplitude (signal) — peak, peak-to-peak, and the size of a swing.
Phase (waveform) — the shift between input and output a circuit introduces.
Frequency and period — the rate and its reciprocal.
Root mean square — the effective DC-equivalent value used for power and ripple.
Capacitive reactance — $1/ (ω C)$ ; why coupling and bypass caps are frequency-dependent.
Voltage divider — the most-reused result in biasing and small-signal analysis.
Fourier series — harmonic decomposition; the basis for talking about distortion and spectral content.

Semiconductor physics

Why silicon conducts the way it does, and how doping turns it into a controllable material.

Semiconductor — material between conductor and insulator; conductivity set by doping and temperature.
Intrinsic semiconductor — pure, undoped silicon; the baseline.
Energy bands (solids) — valence and conduction bands; the band picture of conduction.
Bandgap — the energy gap an electron must cross to conduct.
Direct and indirect bandgap — why some materials emit light and silicon doesn’t.
Hole (semiconductor) — the absence of an electron, treated as a positive carrier.
Electron-hole pair generation and recombination — how carriers are created and destroyed.
Intrinsic carrier concentration — $n_{i}$ ; the equilibrium carrier density in pure material.
Mass-action law — $n p = n_{i}^{2}$ ; ties electron and hole densities together.
Doping — adding impurities to set carrier type and concentration.
Donor and acceptor dopants — the impurity atoms that make n- and p-type.
N-type semiconductor — electron-majority material.
P-type semiconductor — hole-majority material.
Majority and minority carriers — the dominant and trace carriers in doped material.
Drift and diffusion current — the two transport mechanisms behind every device equation.

The pn junction

What happens when n-type meets p-type — the structure underneath every diode and transistor.

PN junction — the metallurgical junction; the foundational device building block.
Built-in voltage — the equilibrium potential barrier across the junction.
Depletion region — the carrier-free zone of fixed charge at the junction.
Depletion region width — how the zone widens and narrows with bias.
Forward bias — lowering the barrier so current flows easily.
Reverse bias — raising the barrier so the junction blocks.
Reverse saturation current — the tiny leakage $I_{S}$ under reverse bias.
Minority-carrier injection — the mechanism of forward conduction.
Reverse breakdown — the high-reverse-voltage conduction Zeners exploit.

Diodes

The two-terminal device built from a single pn junction, and the models used to analyze it.

Diode — the device; one-way valve for current.
Diode equation — $I = I_{S} (e^{V / n V_{T}} - 1)$ ; the exact exponential law.
Exponential diode model — using the full equation directly.
Iterative diode analysis — solving the transcendental diode equation numerically.
Ideal diode model — the on/off switch approximation.
Constant-voltage-drop model — the 0.7 V approximation for hand analysis.
Diode small-signal resistance — $r_{d} = n V_{T} / I_{D}$ ; the diode’s incremental resistance.
Zener diode — a diode operated deliberately in reverse breakdown.
Zener dynamic resistance — the non-ideal slope of the Zener breakdown region.
Zener voltage regulator — the canonical Zener application: a stable reference voltage.
Light-emitting diode — a forward-biased direct-bandgap junction that emits photons.
Photodiode — a reverse-biased junction that converts light into current.

Diode application circuits

Rectifiers, regulators, and waveform-shaping circuits built from diodes.

Rectifier — converting AC to unidirectional current; the front end of a DC supply.
Half-wave rectifier — passes one half-cycle.
Full-wave rectifier — uses both half-cycles.
Center-tapped full-wave rectifier — the two-diode transformer-based version.
Bridge rectifier — the four-diode version, no center tap needed.
Peak rectifier — adding a capacitor to hold the peak; the peak detector.
DC value of a rectified waveform — the average output of a rectified signal.
Conduction angle — the fraction of the cycle the diode actually conducts.
Ripple voltage — the residual AC on the filtered DC output.
Peak inverse voltage — the maximum reverse voltage a diode must survive.
DC power supply — transformer → rectifier → filter → regulator, end to end.
Clamper circuit — shifts a waveform’s DC level by a fixed amount.
Limiter circuit — clips a waveform above or below a set level.
Voltage doubler — a clamp plus a peak rectifier that outputs ~2× the peak.
Voltage reference — a stable fixed voltage independent of load and supply.

MOSFET — structure and operation

The voltage-controlled transistor that dominates modern electronics.

Field-effect transistor — the FET family; current controlled by a field, not a base current.
MOSFET — the metal-oxide-semiconductor FET; the workhorse device.
NMOS transistor — the n-channel device.
PMOS transistor — the p-channel complement.
CMOS — complementary NMOS+PMOS; the dominant logic and analog technology.
Gate oxide — the insulating layer that makes the gate draw no DC current.
MOSFET channel — the inversion layer that carries drain current.
Threshold voltage — $V_{t}$ ; the gate voltage at which the channel forms.
Overdrive voltage — $V_{O V} = V_{GS} - V_{t}$ ; the effective gate drive.
Channel pinch-off — when the channel narrows to zero at the drain.
MOSFET regions of operation — cut-off, triode, saturation; which model applies.
MOSFET cut-off region — no channel, no current.
MOSFET triode region — the resistive (ohmic) region.
MOSFET saturation region — the amplifying region.
MOSFET square-law — $I_{D} \propto V_{O V}^{2}$ ; the saturation current law.
MOSFET transfer characteristic — $I_{D}$ vs $V_{GS}$ ; the device’s input-output curve.
MOSFET transconductance parameter — $k_{n} = μ_{n} C_{o x} (W / L)$ ; the process/geometry factor.
Body effect — how the substrate (body) voltage shifts the threshold.
Channel-length modulation — the finite output resistance in saturation.

MOSFET — DC biasing

Setting the transistor’s operating point so it amplifies.

MOSFET DC analysis — solving for the bias point with the large-signal model.
MOSFET biasing — the goal: a stable operating point in saturation.
MOSFET large-signal model — the DC model used to find the Q-point.
Voltage-divider bias — the standard four-resistor bias network.
Drain-to-gate feedback bias — single-resistor feedback biasing.
Diode-connected MOSFET — gate tied to drain; acts as a two-terminal nonlinear resistor.

BJT — structure and operation

The current-controlled transistor: two coupled pn junctions.

Transistor — the three-terminal amplifying device, in general.
Bipolar junction transistor — the BJT; current controlled by base current.
NPN transistor — the n-p-n structure.
PNP transistor — the p-n-p complement.
BJT operating modes — cut-off, active, saturation; set by the two junction biases.
BJT active mode — the amplifying mode (EBJ forward, CBJ reverse).
BJT cut-off mode — both junctions reverse-biased; the off state.
BJT saturation mode — both junctions forward-biased; the fully-on switch state.
BJT collector current — $I_{C} = I_{S} e^{V_{BE} / V_{T}}$ ; the controlling exponential.
Common-emitter current gain — $β = I_{C} / I_{B}$ ; the big current-gain factor.
Common-base current gain — $α = I_{C} / I_{E}$ ; the near-unity factor.
Early effect — base-width modulation; the BJT’s finite output resistance.
Early voltage — $V_{A}$ ; the parameter that quantifies the Early effect.

BJT — DC biasing

Establishing a stable collector current.

BJT DC analysis — solving the bias network for the Q-point.
BJT large-signal model — the DC model (constant $V_{BE}$ , $β$ ) for bias calculations.
Emitter resistance — $r_{e} = V_{T} / I_{E}$ ; the intrinsic emitter resistance used in biasing and small-signal work.

Small-signal modelling

Linearizing a nonlinear device around its Q-point so AC analysis becomes linear circuit analysis.

Operating point — the DC bias point (Q-point) everything is linearized about.
Linearisation around an operating point — the Taylor-expansion idea behind small-signal models.
Small-signal analysis — the procedure: kill DC sources, replace devices with their models.
Small-signal model — the linear equivalent circuit of a device.
Transistor signal notation convention — uppercase/lowercase/subscript rules for DC, AC, total.
MOSFET small-signal model — the linearized MOSFET.
MOSFET hybrid-pi model — the $g_{m} v_{g s}$ + $r_{o}$ form.
MOSFET T-model — the equivalent form with the source resistance explicit.
MOSFET transconductance — $g_{m} = \partial I_{D} / \partial V_{GS}$ ; the MOSFET’s gain engine.
MOSFET output resistance — $r_{o} = 1/ (λ I_{D})$ ; from channel-length modulation.
BJT small-signal model — the linearized BJT.
BJT hybrid-pi model — $g_{m} v_{b e}$ with $r_{π}$ and $r_{o}$ .
BJT T-model — the alternative with $r_{e}$ explicit.
BJT transconductance — $g_{m} = I_{C} / V_{T}$ ; the BJT’s gain engine.
BJT input resistance — $r_{π} = β / g_{m}$ ; the resistance looking into the base.
Resistance reflection rule — how a resistance at one terminal is scaled when seen from another.

Single-transistor amplifier configurations

The standard ways to wire one transistor as an amplifier, and what each is good for.

Single-transistor amplifier configurations — overview: which terminal is input, output, common.
Voltage-transfer characteristic — output vs input DC curve; gain is its slope in the active region.
Input and output resistance (amplifier) — the loading parameters that decide cascading behaviour.
Discrete-circuit MOSFET amplifier — a full MOSFET amplifier with biasing and coupling.
Discrete-circuit BJT amplifier — the BJT equivalent.
Common-source amplifier — high voltage gain; the MOSFET workhorse stage.
Common-gate amplifier — low input resistance, good high-frequency behaviour.
Source follower — unity gain, low output resistance; the MOSFET buffer.
Common-emitter amplifier — high voltage gain; the BJT workhorse stage.
Common-base amplifier — low input resistance; the BJT current buffer.
Emitter follower — unity gain, low output resistance; the BJT buffer.
Source degeneration — a source resistor that trades gain for linearity and stability.
Emitter degeneration — the BJT equivalent.
Cascode amplifier — CE/CS stacked with CB/CG; high gain and bandwidth, beats the Miller effect.
Coupling capacitor — blocks DC between stages while passing the signal.
Bypass capacitor — shorts a bias resistor at signal frequencies to restore full gain.

Operational amplifiers and feedback

The idealized high-gain differential amplifier and the feedback circuits built around it.

Operational amplifier — the high-gain differential building block.
Ideal op-amp model — infinite gain, infinite input resistance, zero output resistance.
Virtual short and virtual ground — the consequence of high gain plus negative feedback.
Negative feedback — feeding output back to stabilize gain and trade it for bandwidth and linearity.
Open-loop gain — the raw, no-feedback gain $A$ .
Closed-loop gain — the feedback-set gain that’s nearly independent of $A$ .
Inverting amplifier (op-amp) — gain $- R_{f} / R_{1}$ ; the canonical config.
Non-inverting amplifier (op-amp) — gain $1 + R_{f} / R_{1}$ ; high input resistance.
Voltage follower (op-amp) — unity-gain buffer.
Buffer amplifier — isolating a source from a load.
Summing amplifier — weighted addition of several inputs.
Difference amplifier — amplifies the difference of two inputs.
Instrumentation amplifier — the high-CMRR, high-input-impedance difference amplifier.
Op-amp integrator — output proportional to the time integral of the input.
Op-amp differentiator — output proportional to the time derivative.
Differential and common-mode signals — decomposing two inputs into difference and average.
Common-mode rejection ratio — how well the amplifier ignores the common-mode part.
Op-amp output saturation — clipping when the output hits the supply rails.

Op-amp non-idealities

Where the real op-amp departs from the ideal model.

Input bias current — the small DC current the inputs actually draw.
Input offset voltage — the small input mismatch that appears as a DC output error.
Slew rate — the maximum output rate of change; a large-signal speed limit.
Full-power bandwidth — the highest frequency for a full-amplitude undistorted output, set by slew rate.

Frequency response and the Miller effect

How gain rolls off with frequency, and why.

Frequency response — magnitude and phase of gain vs frequency.
Amplifier frequency response — the low/mid/high-band picture for transistor amplifiers.
Transfer function — $H (s) = V_{o} / V_{i}$ ; the s-domain description of the gain.
Bode plot — log-magnitude and phase vs log frequency; the standard visualization.
Decibel — the logarithmic gain unit.
Cutoff frequency — the −3 dB corner where gain falls to $1/ 2$ of midband.
Lowpass filter — the high-frequency roll-off behaviour.
Highpass filter — the low-frequency roll-off from coupling/bypass caps.
RC lowpass filter — the single-pole low-pass; the model for the high-frequency limit.
RC highpass filter — the single-pole high-pass; the model for the low-frequency limit.
Filter (signal processing) — the general frequency-shaping concept.
Miller effect — a feedback capacitance multiplied by the gain; the dominant high-frequency limiter.
Gain-bandwidth product — the gain × bandwidth constant; the fundamental speed/gain tradeoff.

The signal-analysis machinery here — Transfer function, Bode plot, Frequency response, filters, and the Fourier series — is developed in full in Signals and systems; this course applies it to transistor and op-amp circuits. The AC math (complex impedance, phasors, the $s$ -plane) rests on the complex analysis in Mathematical methods. Digital logic is where this meets the gate level: CMOS, NMOS transistor, and PMOS transistor are the transistor-level substrate that digital gates are built from, and the Voltage-transfer characteristic is the bridge between the analog device curve and the digital logic level. The underlying device physics — PN junction, Depletion region, carrier drift and diffusion — is the circuit-side counterpart of the field theory in Electromagnetics.

Idriss Rami — Notes

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