Intermediate Electronics interview questions

150 questions with answers (ELE-151 to ELE-300). Try each one aloud before reading the answer.

Semiconductor Physics

ELE-151 · Why does the conductivity of an intrinsic semiconductor increase with temperature?

More electrons gain enough energy to cross the band gap, and nᵢ ∝ T^(3/2)·e^(−E_g/2kT) rises exponentially. This outweighs the drop in mobility.

ELE-152 · What is the Einstein relation?

D/μ = kT/q = V_T. It links diffusion coefficient and mobility; V_T ≈ 25.9 mV at 300 K.

ELE-153 · What is the conductivity formula for a semiconductor?

σ = q(nμₙ + pμₚ), with resistivity ρ = 1/σ. In doped material, the majority term dominates.

ELE-154 · How is the built-in potential of a PN junction found?

V_bi = V_T·ln(N_A·N_D/nᵢ²). For typical Si doping it is about 0.6–0.8 V.

ELE-155 · How does doping affect depletion width?

W = √(2ε(V_bi + V_R)/q · (1/N_A + 1/N_D)). The depletion region extends mostly into the more lightly doped side and widens with reverse bias.

ELE-156 · What is the difference between direct and indirect band gap semiconductors?

In direct band gap materials (GaAs, GaN), electrons recombine radiatively without a phonon, so they emit light efficiently and suit LEDs and lasers. Si and Ge are indirect, so radiative recombination is weak.

ELE-157 · What is the Hall effect used for in semiconductors?

A current-carrying sample in a magnetic field develops a transverse voltage. Its sign shows the carrier type, and the Hall coefficient R_H = 1/(nq) gives the carrier concentration; combined with conductivity it gives mobility.

ELE-158 · Silicon is doped with N_D = 10¹⁶ cm⁻³. What is the hole concentration?

n ≈ 10¹⁶ cm⁻³, so p = nᵢ²/n = (1.5 × 10¹⁰)²/10¹⁶ = 2.25 × 10⁴ cm⁻³.

ELE-159 · How does the Fermi level shift with doping?

For N-type, E_F − E_i = kT·ln(N_D/nᵢ), moving toward the conduction band. For P-type, E_i − E_F = kT·ln(N_A/nᵢ), moving toward the valence band.

ELE-160 · What is carrier lifetime?

The average time an excess minority carrier exists before recombining. It sets diffusion length and switching speed; shorter lifetime means faster but leakier devices.

ELE-161 · What is the difference between junction capacitance and diffusion capacitance?

Junction (depletion) capacitance comes from the charge in the depletion region and dominates under reverse bias. Diffusion capacitance comes from stored minority carriers and dominates under forward bias, growing with current.

ELE-162 · What is a degenerate semiconductor?

A very heavily doped semiconductor in which the Fermi level enters the conduction or valence band, so it behaves almost like a metal. Tunnel diodes and ohmic contacts use it.

ELE-163 · Why does mobility decrease at high temperature and high doping?

At high temperature, lattice (phonon) scattering increases. At high doping, ionized impurity scattering increases. Both shorten the mean free time between collisions.

Diodes & Rectifiers

ELE-164 · Compare half-wave, center-tapped full-wave and bridge rectifiers.

Half-wave uses one diode with PIV = V_m. Center-tapped uses two diodes and a center-tapped transformer with PIV = 2V_m. Bridge uses four diodes, needs no center tap, and PIV = V_m. Full-wave types double the ripple frequency.

ELE-165 · What is the ripple frequency of half-wave and full-wave rectifiers on 50 Hz mains?

Half-wave ripple is 50 Hz. Full-wave (center-tap or bridge) ripple is 100 Hz.

ELE-166 · What are the maximum rectification efficiencies of half-wave and full-wave rectifiers?

40.6% for half-wave and 81.2% for full-wave, with a resistive load and ideal diodes.

ELE-167 · What is the average DC output of half-wave and full-wave rectifiers?

V_dc = V_m/π ≈ 0.318V_m for half-wave and 2V_m/π ≈ 0.637V_m for full-wave, ignoring diode drops.

ELE-168 · How do you estimate ripple with a capacitor filter?

Peak-to-peak ripple ≈ I_load/(f·C) for half-wave and I_load/(2f·C) for full-wave, where f is the mains frequency.

ELE-169 · How do you design the series resistor of a Zener regulator?

R = (V_in(min) − V_Z)/(I_Z(min) + I_L(max)), so the Zener stays in regulation at worst case. Then check Zener power at V_in(max) and minimum load.

ELE-170 · What is the small-signal resistance of a diode?

r_d = nV_T/I_D. At 1 mA and n = 1, r_d ≈ 26 Ω.

ELE-171 · How does a silicon diode's forward voltage vary with temperature?

At constant current, it falls by about 2 mV/°C. This is why diodes and V_BE junctions serve as temperature sensors.

ELE-172 · What is reverse recovery time?

The time a conducting PN diode takes to stop conducting after being reverse biased, while stored minority charge is removed. It causes switching loss and EMI in fast circuits.

ELE-173 · What is a voltage doubler?

A diode-capacitor circuit that produces a DC output of about 2V_m from an AC input of peak V_m. Examples are the half-wave (Villard plus clamp) and full-wave (Delon) doublers.

ELE-174 · What is a varactor diode?

A reverse-biased diode used as a voltage-variable capacitor, since depletion capacitance falls as reverse voltage increases. It is used in VCOs and electronic tuning.

ELE-175 · Why does a bridge rectifier output have two diode drops?

In each half-cycle, current flows through two diodes in series, so the output peak is about V_m − 1.4 V for silicon diodes.

ELE-176 · What is a tunnel diode?

A very heavily doped diode with a thin junction, where quantum tunnelling produces a negative-resistance region in the forward characteristic. It is used in very high-frequency oscillators.

BJT

ELE-177 · Why is voltage-divider bias more stable than fixed bias?

The divider fixes the base voltage and the emitter resistor sets I_E ≈ (V_B − V_BE)/R_E, almost independent of β. The emitter resistor also provides negative feedback against temperature drift.

ELE-178 · What is the stability factor S of a bias circuit?

S = ∂I_C/∂I_CO, the sensitivity of collector current to leakage current. Fixed bias has S = 1 + β (poor); voltage-divider bias with a large R_E approaches S ≈ 1 + R_B/R_E (good).

ELE-179 · What is the transconductance of a BJT?

g_m = I_C/V_T. At I_C = 1 mA and 300 K, g_m ≈ 1/26 Ω ≈ 38.5 mS.

ELE-180 · What is r_π in the hybrid-π model?

The small-signal base-emitter resistance, r_π = β/g_m. With β = 100 and I_C = 1 mA, r_π ≈ 2.6 kΩ.

ELE-181 · What is the voltage gain of a CE amplifier?

With the emitter bypassed, A_v ≈ −g_m(R_C ∥ R_L ∥ r_o). With an unbypassed R_E, A_v ≈ −R_C/(r_e + R_E), where r_e = V_T/I_E.

ELE-182 · Fixed bias: V_CC = 12 V, R_B = 470 kΩ, R_C = 2.2 kΩ, β = 100. Find the Q-point.

I_B = (12 − 0.7)/470k ≈ 24 µA, I_C = βI_B ≈ 2.4 mA, and V_CE = 12 − 2.4 mA × 2.2 kΩ ≈ 6.7 V. The transistor is in the active region.

ELE-183 · What is the difference between DC and AC load lines?

The DC load line uses DC resistances (R_C + R_E) and shows all possible DC Q-points. The AC load line passes through the Q-point with slope set by the AC load (e.g. R_C ∥ R_L), and determines maximum undistorted swing.

ELE-184 · What is the condition for a BJT to be in saturation?

I_B > I_C(sat)/β_min, where I_C(sat) ≈ (V_CC − V_CE(sat))/R_C. Designers overdrive with a forced β of about 10–20 to ensure saturation.

ELE-185 · Why is the CE output 180° out of phase with the input?

An increase in base voltage raises I_C, which increases the drop across R_C and so lowers the collector voltage.

ELE-186 · What is the effect of removing the emitter bypass capacitor?

Gain drops to about −R_C/R_E, but it becomes stable and largely independent of β. Input impedance rises, linearity improves and bandwidth increases, because of local negative feedback.

ELE-187 · What is the output resistance of a BJT?

r_o = V_A/I_C, where V_A is the Early voltage. With V_A = 100 V and I_C = 1 mA, r_o = 100 kΩ.

ELE-188 · What is the transition frequency f_T?

The frequency at which the common-emitter short-circuit current gain falls to 1. f_T ≈ g_m/(2π(C_π + C_μ)), and β(f) ≈ f_T/f above the β cutoff.

ELE-189 · What is a current mirror?

A circuit in which a diode-connected transistor sets a V_BE that is copied to a matched transistor, so the output current mirrors a reference current. It is used for biasing and active loads in ICs.

FET & MOSFET

ELE-190 · What is the difference between a BJT and a MOSFET?

A BJT is current-controlled, with low input impedance and a bipolar conduction mechanism. A MOSFET is voltage-controlled, with very high input impedance, unipolar conduction and near-zero static gate current, which makes it dominant in digital ICs.

ELE-191 · What is the MOSFET square-law equation in saturation?

I_D = ½μₙC_ox(W/L)(V_GS − V_th)², ideally independent of V_DS. With channel-length modulation, multiply by (1 + λV_DS).

ELE-192 · What is the MOSFET drain current equation in the triode region?

I_D = μₙC_ox(W/L)[(V_GS − V_th)V_DS − V_DS²/2]. For small V_DS it acts as a resistor, R ≈ 1/(μₙC_ox(W/L)(V_GS − V_th)).

ELE-193 · What is the transconductance of a MOSFET in saturation?

g_m = 2I_D/(V_GS − V_th) = √(2μₙC_ox(W/L)I_D). It grows only as the square root of current, unlike a BJT where it is proportional to I_C.

ELE-194 · What is channel-length modulation?

In saturation, increasing V_DS shortens the effective channel, so I_D rises slightly. It is modelled by λ, giving output resistance r_o ≈ 1/(λI_D).

ELE-195 · What is the body effect?

A source-to-body voltage raises the threshold voltage: V_th = V_th0 + γ(√(2φ_F + V_SB) − √(2φ_F)). It reduces gain in source followers and stacked transistors.

ELE-196 · What is the JFET transfer equation?

I_D = I_DSS(1 − V_GS/V_P)², where I_DSS is the drain current at V_GS = 0 and V_P is the pinch-off voltage.

ELE-197 · How does a CMOS inverter work, and what is its dynamic power?

A high input turns on the NMOS and off the PMOS, pulling the output low, and vice versa. Dynamic power is P = αC_L·V_DD²·f, where α is the activity factor.

ELE-198 · Why do power MOSFETs need dedicated gate drivers at high frequency?

The gate must be charged with total gate charge Q_g quickly; the required current is I ≈ Q_g/t_switch. For example, 50 nC in 50 ns needs about 1 A, which a logic pin cannot supply.

ELE-199 · What is the voltage gain of a common-source amplifier?

A_v = −g_m(R_D ∥ r_o ∥ R_L). With source degeneration R_S, it becomes about −R_D/(R_S + 1/g_m).

ELE-200 · Why is the gain of a MOSFET source follower less than 1?

A_v = g_m R_S/(1 + (g_m + g_mb)R_S), so it is always below 1. The body effect (g_mb) and finite r_o reduce it further, typically to 0.7–0.9.

ELE-201 · What is a logic-level MOSFET?

A MOSFET whose R_DS(on) is specified at a low gate voltage such as 4.5 V or 2.5 V, so it can be driven directly from logic outputs. Standard MOSFETs are specified at about 10 V.

ELE-202 · What is subthreshold conduction?

Below V_th, drain current does not stop but falls exponentially with V_GS, about one decade per 60 mV or more at room temperature. It sets leakage in digital ICs and is used in ultra-low-power analog design.

Amplifiers & Feedback

ELE-203 · Why use negative feedback in amplifiers?

It stabilises gain against device variation, increases bandwidth, reduces distortion and noise from inside the loop, and controls input and output impedances. The cost is lower gain.

ELE-204 · What is the closed-loop gain of a feedback amplifier?

A_f = A/(1 + Aβ), where Aβ is the loop gain. When Aβ ≫ 1, A_f ≈ 1/β, set only by the feedback network.

ELE-205 · How does voltage-series feedback change input and output impedance?

Input impedance rises by (1 + Aβ) and output impedance falls by (1 + Aβ). The result is a better voltage amplifier, as in the non-inverting op-amp.

ELE-206 · What sets the low and high cutoff frequencies of a discrete amplifier?

Coupling and bypass capacitors set the low cutoff by forming high-pass sections. Device capacitances (C_π, C_μ, C_gs, C_gd) and wiring capacitance set the high cutoff.

ELE-207 · How does cascading identical stages affect bandwidth?

For n identical single-pole stages, upper cutoff f_H(n) = f_H·√(2^(1/n) − 1). Two stages reduce it to about 0.64f_H.

ELE-208 · How is CMRR improved in a differential amplifier?

By using a constant current source (high output resistance) in place of the tail resistor, matching transistors and resistors, and using active loads. CMRR ≈ g_m·R_tail for a simple pair.

ELE-209 · What is crossover distortion, and how is it reduced?

In a class B push-pull stage, neither transistor conducts for inputs smaller than about ±0.7 V, causing a dead zone. Class AB biasing (diodes or a V_BE multiplier) and overall negative feedback reduce it.

ELE-210 · What are the advantages of a push-pull output stage?

Even-order harmonics cancel, DC core saturation is avoided in transformer designs, and efficiency is higher because each device conducts for only about half the cycle.

ELE-211 · What is a cascode amplifier?

A common-emitter (or common-source) stage followed by a common-base (or common-gate) stage. The low input impedance of the second stage suppresses the Miller effect and raises output resistance, giving high gain and wide bandwidth.

ELE-212 · What is bootstrapping?

Feeding the output signal back to the bottom of a bias resistor so both ends move together, making the resistor appear much larger to the signal. It raises input impedance in emitter followers and audio drivers.

ELE-213 · What is noise figure?

NF = 10 log₁₀(SNR_in/SNR_out) in dB, the degradation in signal-to-noise ratio caused by an amplifier. An ideal noiseless amplifier has NF = 0 dB.

ELE-214 · What are gain margin and phase margin?

Gain margin is how far loop gain is below 0 dB where loop phase reaches −180°. Phase margin is 180° plus the loop phase where loop gain is 0 dB. About 45°–60° phase margin gives good stability with limited overshoot.

Op-Amps

ELE-215 · What are the properties of an ideal op-amp?

Infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth, infinite CMRR and slew rate, and zero offset and noise.

ELE-216 · What is a virtual short in an op-amp?

With negative feedback and very high gain, the circuit forces V+ ≈ V−. No current flows into the inputs, yet they sit at the same potential. If V+ is grounded, V− is a "virtual ground".

ELE-217 · What is the output of a difference amplifier?

With matched ratios R₂/R₁ on both inputs, V_out = (R₂/R₁)(V₂ − V₁). Resistor mismatch directly degrades CMRR.

ELE-218 · Why use an instrumentation amplifier?

It gives very high input impedance on both inputs, high CMRR and a gain set by a single resistor. For the three-op-amp type, G = (1 + 2R/R_G)(R₃/R₂). It suits bridge and sensor signals.

ELE-219 · What is full-power bandwidth?

The highest frequency at which a sine of peak V_p can be produced without slew limiting: f_max = SR/(2πV_p). For a 741 (0.5 V/µs) at 10 V peak, f_max ≈ 8 kHz.

ELE-220 · An op-amp has GBW = 1 MHz. What is the bandwidth at a closed-loop gain of 100?

For a non-inverting amplifier with noise gain 100, bandwidth ≈ GBW/gain = 1 MHz/100 = 10 kHz.

ELE-221 · How is the effect of input bias current reduced?

Add a resistor at the non-inverting input equal to the DC resistance seen by the inverting input (R_in ∥ R_f), so equal bias currents create equal drops. What remains is due to offset current.

ELE-222 · Why does a practical integrator need a resistor across the capacitor?

Without it, DC gain is the open-loop gain, so offset voltage and bias current integrate until the output saturates. A large shunt resistor limits DC gain to −R_f/R_in.

ELE-223 · Why not use an op-amp as a comparator?

Op-amps are compensated for linear operation, so they are slow to come out of saturation and have limited slew rate. Their outputs are not logic-compatible, and some have input clamp diodes that limit differential input.

ELE-224 · What is a precision rectifier?

An op-amp circuit with a diode inside the feedback loop, so the high loop gain cancels the diode drop. It rectifies millivolt-level signals that an ordinary diode could not.

ELE-225 · What is a rail-to-rail op-amp?

An op-amp whose input common-mode range and/or output swing extends close to both supply rails. It matters in low-voltage single-supply systems.

ELE-226 · How is an op-amp biased on a single supply for AC signals?

The non-inverting input is held at a mid-supply reference (e.g. V_CC/2 via a divider and bypass capacitor), and AC coupling capacitors are used, so the signal swings around mid-rail.

ELE-227 · How does a logarithmic amplifier work?

A diode or transistor in the feedback path of an inverting amplifier gives V_out ≈ −V_T·ln(V_in/(R·I_s)), because junction current is exponential in voltage. It is temperature-sensitive and needs compensation.

Oscillators & Waveform Generators

ELE-228 · How does an oscillator start without an input?

Circuit noise or the power-up transient contains energy at the oscillation frequency. The loop gain is designed slightly above 1, so that component grows until nonlinearity reduces gain to exactly 1.

ELE-229 · How is amplitude stabilised in a Wien bridge oscillator?

Gain must settle at exactly 3. Nonlinear elements such as an incandescent lamp, thermistor, back-to-back diodes or a JFET AGC adjust gain automatically with amplitude.

ELE-230 · What is the frequency of a Colpitts oscillator?

f = 1/(2π√(L·C_eq)), where C_eq = C₁C₂/(C₁ + C₂).

ELE-231 · What is the frequency of a Hartley oscillator?

f = 1/(2π√(L_eq·C)), where L_eq = L₁ + L₂ + 2M for coupled inductors with mutual inductance M.

ELE-232 · What are the series and parallel resonances of a crystal?

In series resonance, the motional L, C and R resonate and impedance is minimum. In parallel (anti-) resonance, slightly higher in frequency, the motional arm resonates with the shunt capacitance and impedance is maximum.

ELE-233 · What are the frequency and duty cycle of a 555 astable?

f = 1.44/((R_A + 2R_B)C), and duty cycle = (R_A + R_B)/(R_A + 2R_B). The duty cycle is always above 50% in the basic circuit.

ELE-234 · What is the pulse width of a 555 monostable?

T = 1.1RC, from the capacitor charging from 0 to 2/3 V_CC (T = RC·ln3).

ELE-235 · How can a 555 astable achieve 50% or lower duty cycle?

Add a diode across R_B so the capacitor charges through R_A only and discharges through R_B. With R_A = R_B, duty is about 50%; the diode drop causes slight error.

ELE-236 · What are the thresholds of an inverting op-amp Schmitt trigger?

With feedback divider β = R₂/(R₁ + R₂) from output to the non-inverting input, thresholds are ±βV_sat. Hysteresis width is 2βV_sat.

ELE-237 · How is a triangle-wave generator built?

An integrator feeds a Schmitt trigger, whose square output drives the integrator back. The integrator ramps up and down between the Schmitt thresholds, giving a triangle and a square wave simultaneously.

ELE-238 · What is the frequency of a ring oscillator?

An odd number N of inverters in a loop oscillates at f = 1/(2N·t_pd), where t_pd is the propagation delay per stage.

ELE-239 · What does the Clapp oscillator improve over the Colpitts?

It adds a small capacitor in series with the inductor that dominates the tank frequency. Transistor and stray capacitances then have little effect, improving frequency stability.

Combinational Logic

ELE-240 · How do you build an XOR gate with NAND gates?

Four NAND gates: N1 = (AB)', N2 = (A·N1)', N3 = (B·N1)', Y = (N2·N3)' = A⊕B.

ELE-241 · How many 2:1 multiplexers are needed for an 8:1 multiplexer?

Seven, arranged as a tree of 4 + 2 + 1. In general, N − 1 2:1 muxes build an N:1 mux.

ELE-242 · How do you implement a Boolean function with a multiplexer?

Connect the input variables to the select lines and tie each data input to 0 or 1 according to the truth table. With one fewer select line, data inputs become 0, 1, X or X'.

ELE-243 · What is the difference between ripple-carry and carry-look-ahead adders?

A ripple-carry adder passes carry stage by stage, so delay grows linearly with width. A carry-look-ahead adder computes carries in parallel from generate (G = AB) and propagate (P = A⊕B) signals, so it is faster but uses more gates.

ELE-244 · What is a static hazard, and how is it removed?

A momentary glitch at the output when one input changes and the output should stay constant, caused by unequal path delays. A static-1 hazard in SOP is removed by adding the redundant consensus term covering adjacent K-map groups.

ELE-245 · What are don't-care conditions?

Input combinations that never occur or whose output does not matter, marked X. They can be treated as 0 or 1 in K-maps to form larger groups and simpler logic.

ELE-246 · What is a magnitude comparator?

A circuit that compares two binary numbers and outputs A > B, A = B and A < B. Equality uses XNOR of each bit pair; the inequalities are decided by the most significant differing bit.

ELE-247 · What does a BCD to seven-segment decoder do?

It converts a 4-bit BCD digit (0–9) into seven outputs that drive the segments a–g of a display. Inputs 10–15 are usually don't-cares.

ELE-248 · How does a parity generator and checker work?

A generator XORs the data bits to produce an even or odd parity bit. The checker XORs all received bits including parity; a nonzero result (for even parity) shows a single-bit error.

ELE-249 · What is propagation delay and the critical path?

Propagation delay is the time from an input change to the resulting output change. The critical path is the longest-delay path through a circuit and limits its maximum operating speed.

ELE-250 · What are fan-in and fan-out?

Fan-in is the number of inputs a gate has. Fan-out is the number of gate inputs one output can drive while still meeting logic levels and timing.

ELE-251 · How is overflow detected in two's complement addition?

Overflow occurs when the carry into the MSB differs from the carry out of the MSB (V = C_in,MSB ⊕ C_out,MSB). Equivalently, two operands of the same sign give a result of the opposite sign.

ELE-252 · When is the Quine-McCluskey method preferred over K-maps?

For functions with more than about five or six variables, where K-maps become impractical. It is a tabular, algorithmic method suited to computer implementation.

Sequential Logic

ELE-253 · What is the race-around condition in a JK flip-flop?

With J = K = 1 on a level-triggered JK, the output toggles repeatedly while the clock is high if the pulse is longer than the propagation delay. Edge triggering or a master-slave arrangement prevents it.

ELE-254 · How do you convert a JK flip-flop to a D flip-flop?

Connect J = D and K = D' through an inverter. Then D = 1 sets and D = 0 resets.

ELE-255 · How is the maximum clock frequency of a synchronous circuit found?

T_clk ≥ t_clk-to-Q + t_logic(max) + t_setup (plus margin for skew and jitter). f_max = 1/T_clk(min).

ELE-256 · What is metastability?

When a flip-flop's input changes within its setup-hold window, the output can hang at an intermediate level for an unpredictable time before resolving. It is a risk whenever asynchronous signals are sampled.

ELE-257 · What is a two-flip-flop synchronizer?

Two flip-flops in series clocked by the destination clock. The first may go metastable, but it gets almost a full clock period to resolve before the second samples it, which greatly reduces failure probability.

ELE-258 · What limits the maximum frequency of a ripple counter?

Delays accumulate through the chain, so for N stages, f_max ≈ 1/(N·t_pd) if the full count must settle before the next clock.

ELE-259 · What are the characteristic equations of JK, D and T flip-flops?

JK: Q⁺ = JQ' + K'Q. D: Q⁺ = D. T: Q⁺ = T⊕Q.

ELE-260 · What is an excitation table used for?

It lists the flip-flop inputs needed to produce each present-to-next state transition. It is used when designing counters and state machines.

ELE-261 · What is clock skew?

The difference in clock arrival times at different flip-flops. Positive skew (capture clock late) eases setup but worsens hold; negative skew does the reverse.

ELE-262 · How is a hold violation fixed?

By adding delay (buffers) in the data path or reducing clock skew. Slowing the clock does not help, because the hold check does not depend on clock period.

ELE-263 · What is an LFSR?

A linear feedback shift register whose input is an XOR of selected taps. With a primitive polynomial, an n-bit LFSR cycles through 2ⁿ − 1 states, used for pseudo-random sequences, CRC and BIST.

ELE-264 · What is the difference between one-hot and binary state encoding?

Binary encoding uses ⌈log₂N⌉ flip-flops for N states. One-hot uses N flip-flops with exactly one high, which needs simpler next-state logic and is faster, and is common in FPGAs.

Power Supplies & Regulators

ELE-265 · What are the ideal conversion ratios of buck, boost and buck-boost converters?

In continuous conduction: buck V_out = D·V_in, boost V_out = V_in/(1 − D), and inverting buck-boost V_out = −V_in·D/(1 − D), where D is duty cycle.

ELE-266 · What is the inductor ripple current in a buck converter?

ΔI_L = (V_in − V_out)·D/(f_sw·L) = V_out(1 − D)/(f_sw·L). Designers typically target 20–40% of rated output current.

ELE-267 · What is the difference between CCM and DCM?

In continuous conduction mode, inductor current never reaches zero. In discontinuous mode, it falls to zero for part of each cycle, which happens at light load, changes the conversion ratio and alters loop dynamics.

ELE-268 · Why do some LDOs require output capacitors with specific ESR?

Older PNP-pass LDOs have a low-frequency output pole that needs a zero from capacitor ESR for phase margin. Too low an ESR (e.g. some ceramics) or too high can cause oscillation.

ELE-269 · How do you calculate power dissipation in a linear regulator?

P = (V_in − V_out)·I_load + V_in·I_q. For 9 V to 5 V at 0.5 A, P ≈ 2 W.

ELE-270 · How is junction temperature estimated?

T_j = T_a + P·θ_JA, where θ_JA is junction-to-ambient thermal resistance in °C/W. With a heat sink, θ_JA = θ_JC + θ_CS + θ_SA.

ELE-271 · What is synchronous rectification?

Replacing the freewheeling diode in a converter with a MOSFET switched in antiphase. The I²R_DS(on) loss is much lower than the diode's V_F·I loss, especially at low output voltages.

ELE-272 · How does a flyback converter work?

When the switch is on, energy is stored in a coupled inductor (the "transformer"). When it turns off, the energy transfers to the secondary through a diode. It provides isolation and multiple outputs with few parts.

ELE-273 · How does a series-pass transistor regulator improve on a plain Zener regulator?

The Zener sets the base voltage of an emitter follower, so the load current flows through the transistor and the Zener only supplies base current. Output is V_Z − V_BE and load regulation improves.

ELE-274 · How is the LM317 output voltage set?

V_out = 1.25 V × (1 + R₂/R₁) + I_ADJ·R₂, where 1.25 V is the reference between OUT and ADJ. I_ADJ is about 50 µA and is usually negligible.

ELE-275 · What is the trade-off in choosing SMPS switching frequency?

Higher frequency allows smaller inductors and capacitors and faster transient response, but increases switching and gate-drive losses and can worsen EMI. Lower frequency is more efficient but needs bulkier magnetics.

ELE-276 · What is soft-start?

Gradually ramping the regulator reference or duty cycle at power-up. It limits inrush current into output capacitors and prevents output overshoot.

Filters & Passive Networks

ELE-277 · Compare Butterworth, Chebyshev and Bessel filters.

Butterworth has a maximally flat passband. Chebyshev has a steeper roll-off with passband ripple. Bessel has nearly linear phase (constant group delay) and the best pulse response, but the slowest roll-off.

ELE-278 · How does filter order affect roll-off?

An nth-order filter rolls off at 20n dB/decade (6n dB/octave) beyond cutoff.

ELE-279 · What is a Sallen-Key filter?

A popular second-order active filter topology using an op-amp (often as a unity-gain buffer), two resistors and two capacitors. It is simple and has low sensitivity at modest Q.

ELE-280 · What are the gain and phase of an RC low-pass filter at its cutoff frequency?

The gain is 1/√2 (−3 dB) and the phase shift is −45°.

ELE-281 · How is bandwidth related to Q in a resonant circuit?

BW = f₀/Q. A circuit with f₀ = 1 MHz and Q = 50 has a bandwidth of 20 kHz.

ELE-282 · What is the Q of a series RLC circuit?

Q = (1/R)√(L/C) = ω₀L/R. At resonance, voltage across L or C is Q times the source voltage.

ELE-283 · State the superposition theorem.

In a linear network with several independent sources, the response is the sum of responses to each source acting alone, with other voltage sources shorted and current sources opened.

ELE-284 · What is the charging equation of an RC circuit?

v_C(t) = V(1 − e^(−t/RC)) for charging from zero, and v_C(t) = V₀e^(−t/RC) for discharging.

ELE-285 · What is a twin-T notch filter?

A passive network of two T sections (R-C-R and C-R-C) giving deep attenuation at f₀ = 1/(2πRC). Its Q is low unless the network is bootstrapped with an op-amp.

ELE-286 · What is the time constant of an RL circuit?

τ = L/R. Current reaches about 63.2% of its final value in one time constant.

ELE-287 · Why are inductors avoided in IC and low-frequency filters?

At low frequencies, inductors are large, heavy, lossy, nonideal and pick up magnetic interference. Active RC filters provide the same responses with op-amps, resistors and capacitors.

ELE-288 · What is the delta-to-star (Δ–Y) transformation?

Each star resistor equals the product of the two adjacent delta resistors divided by the sum of all three: R₁ = R_ab·R_ac/(R_ab + R_bc + R_ac). For equal resistors, R_Y = R_Δ/3.

Practical Electronics, PCB & Measurement

ELE-289 · What determines PCB trace width?

Current-carrying capacity for an acceptable temperature rise, copper thickness (1 oz ≈ 35 µm), allowable voltage drop, controlled-impedance requirements and manufacturing limits.

ELE-290 · What is a ground loop?

A loop formed when equipment is grounded at multiple points with differing potentials. Circulating currents, often at mains frequency, add hum and noise to signals.

ELE-291 · What is star grounding?

Connecting all ground returns to a single common point so high-current returns do not share impedance with sensitive signal returns. It is common in audio and power circuits.

ELE-292 · Why combine bulk and small decoupling capacitors?

Bulk electrolytic or tantalum capacitors supply low-frequency, large-charge demand. Small ceramics with low ESL handle high-frequency transients. Together they keep supply impedance low over a wide frequency range.

ELE-293 · What is probe compensation?

Adjusting a trimmer capacitor in a 10× probe so its RC divider matches the scope input. Using the scope's square-wave calibrator, the waveform should have flat tops, with no overshoot or rounding.

ELE-294 · Why does a long oscilloscope ground lead cause ringing?

The ground lead inductance (around 1 nH/mm) resonates with probe capacitance, adding ringing and overshoot to fast edges. A short spring ground tip fixes it.

ELE-295 · What is a Kelvin (four-wire) measurement?

Separate pairs of wires carry the test current and sense the voltage, so lead and contact resistance drop out of the measurement. It is used for low resistances and current shunts.

ELE-296 · What oscilloscope bandwidth is needed for a measurement?

Use about 3–5 times the highest signal frequency. For edges, the scope's rise time ≈ 0.35/BW should be several times faster than the signal's rise time.

ELE-297 · What is a thermal relief pad?

A pad connected to a copper plane through narrow spokes. It limits heat flow so the joint can be soldered properly, while keeping the electrical connection.

ELE-298 · What is controlled impedance on a PCB?

Designing trace width, dielectric thickness and stack-up so traces have a specified characteristic impedance (e.g. 50 Ω single-ended, 90 or 100 Ω differential). This prevents reflections on high-speed signals.

ELE-299 · What is switch debouncing?

Mechanical contacts bounce for milliseconds, producing multiple edges. Debouncing uses an RC filter with a Schmitt trigger, an SR latch with a changeover switch, or software delay to give one clean transition.

ELE-300 · What is component derating?

Operating parts well below their maximum ratings (voltage, current, power, temperature) to improve reliability and lifetime. An example is a 50 V capacitor on a 24 V rail.

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