Core Engineering

Solved Numerical Drills

Two-tier practice for core company technical rounds: type a numeric answer (anything within ±2% passes), then walk the full derivation. Every drill links back to its formula.

ECEQualcommTexas Instruments

Inverting amplifier gain

An inverting op-amp uses Rf = 240 kΩ and Rin = 12 kΩ. Compute the magnitude of the closed-loop voltage gain.

Given

  • Feedback resistor Rf: 240 kΩ
  • Input resistor Rin: 12 kΩ
ECEQualcommISRO

Nyquist rate for a composite signal

A signal contains components at 2 kHz, 5 kHz and 9 kHz. What is the minimum sampling frequency (Nyquist rate) in kHz?

Given

  • Highest frequency component: 9 kHz
ECEQualcommISROBEL

VSWR from load impedance

A 50 Ω transmission line is terminated in ZL = 100 Ω. Compute the VSWR on the line (round to 2 decimals).

Given

  • Line characteristic impedance Z0: 50 Ω
  • Load impedance ZL: 100 Ω
ECEQualcommIntelTexas Instruments

RC low-pass cutoff frequency

An RC low-pass filter has R = 1.6 kΩ and C = 100 nF. Find the −3 dB cutoff frequency in kHz (use π = 3.1416, round to 1 decimal).

Given

  • Resistance R: 1.6 kΩ
  • Capacitance C: 100 nF
ECEQualcommTexas Instruments

Friis received power (dBm)

A transmitter radiates Pt = 100 mW. With unit-gain antennas (Gt = Gr = 1) at d = 1 km at f = 1.8 GHz (λ = 0.1667 m), compute received power in dBm using the Friis equation. (10·log10(Pr) in dBm; λ/(4πd) = 1.326e-8.)

Given

  • Transmit power Pt: 100 mW
  • Wavelength λ: 0.167 m
  • Distance d: 1,000 m
ECETexas InstrumentsBEL

Shannon capacity of a noisy channel

A channel has bandwidth B = 4 kHz and SNR = 30 dB (linear ratio 1000). Compute the channel capacity in kbps (1 decimal).

Given

  • Bandwidth B: 4 kHz
  • SNR (linear): 1,000 ratio