Govt. Exams
Entrance Exams
Nyquist sampling rate = 2 × (maximum frequency) = 2 × 5 = 10 kHz
Z-transform: X(z) = ∑aⁿu[n]z⁻ⁿ = z/(z-a) for |z| > |a|
A causal system does not depend on future values. Only option B satisfies this condition.
From x(t) = 5cos(2πt + π/4), ω = 2π, so f = ω/2π = 1 Hz
Bandwidth of a low-pass filter is defined by its cutoff frequency (-3dB point). At f = fc, magnitude drops to 0.707 of DC gain. Bandwidth = fc = 1 kHz.
The 741 op-amp has a gain-bandwidth product of approximately 1 MHz. This means for a gain of 100 V/V, maximum usable bandwidth is ~10 kHz.
The 741 op-amp has a slew rate of approximately 0.5 V/μs. This limits the maximum output voltage change rate, causing distortion at high frequencies/amplitudes.
Precision op-amps like OP07, OPA2134 are designed with input offset voltages < 1 mV. General purpose op-amps (e.g., 741) have offset voltages of 1-5 mV.
Maximum power transfer theorem states that maximum power is delivered when load impedance equals the complex conjugate of source impedance. For resistive cases, RL = Rs.
An ideal op-amp has infinite input impedance. The voltage follower configuration maintains this high input impedance at the non-inverting input.
