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A signal applied to a CRO has a rising time of 0.5 ╬╝ s. Its bandwidth is:
0.2 MHz
0.07 MHz
0.7 MHz
0.05 MHz
0.7 MHz
The bandwidth of a Cathode Ray Oscilloscope (CRO) is related to its rise time (trтАЛ) by a constant factor known as the rise-time bandwidth product. For a first-order system, the relationship is given by the product BW├ЧtrтАЛтЙИ0.35.
The bandwidth of a Cathode Ray Oscilloscope (CRO) is related to its rise time (trтАЛ) by a constant factor known as the rise-time bandwidth product. For a first-order system, the relationship is given by the product BW├ЧtrтАЛтЙИ0.35.
BW=trтАЛ0.35тАЛ тАФ Fundamental relation between Bandwidth and Rise Time
BW=0.5├Ч10тИТ60.35тАЛ=0.7├Ч106┬аHz=0.7┬аMHz тАФ Calculation for the given value
The rise time is defined as the time taken by a signal to transition from 10% to 90% of its final value. A smaller rise time indicates a faster circuit response, which inherently requires a wider frequency bandwidth to accurately reproduce the high-frequency components of the signal's sharp edges.
The constant 0.35 is derived from the step response of a single-pole low-pass filter (RC circuit).
Rise time is measured in seconds (s) and Bandwidth is measured in Hertz (Hz).
For high-speed digital signals, the actual constant may vary slightly based on the filter topology.
Allows quick estimation of system capabilities.
Provides a direct link between time-domain and frequency-domain specifications.
Assumes a simple first-order system behavior.
Does not account for overshoot or ringing in the step response.
Designing and testing oscilloscope probes.
Characterizing the high-frequency response of analog amplifiers.
Given trтАЛ=0.5╬╝s=0.5├Ч10тИТ6s.
Option B (0.07 MHz) results from incorrect decimal placement.
Option D (0.05 MHz) represents a miscalculation of the frequency constant.
C is correct тАФ The bandwidth is calculated using the formula BW=trтАЛ0.35тАЛ, resulting in 0.7┬аMHz.
Always remember the 0.35 constant for BW├ЧtrтАЛ problems in instrumentation; it is a standard simplification for most test equipment specifications.
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