CRO Bandwidth Calculation

The problem involves calculating the bandwidth of a Cathode Ray Oscilloscope (CRO) given the observed rise time of a signal, the signal's actual rise time, and a constant K.

Rise Time Analysis

The observed rise time ($T_{obs}$) in a CRO is affected by both the actual signal rise time ($T_{sig}$) and the CRO system's rise time ($T_{CRO}$). The relationship is given by:

$ T_{obs}^2 = T_{sig}^2 + T_{CRO}^2 $

We are given:

• $T_{obs} = 15\mu s$
• $T_{sig} = 12\mu s$

We need to find the CRO's rise time ($T_{CRO}$):

$ T_{CRO}^2 = T_{obs}^2 - T_{sig}^2 $

$ T_{CRO}^2 = (15\mu s)^2 - (12\mu s)^2 $

$ T_{CRO}^2 = 225 \mu s^2 - 144 \mu s^2 $

$ T_{CRO}^2 = 81 \mu s^2 $

$ T_{CRO} = \sqrt{81 \mu s^2} = 9 \mu s $

Bandwidth Calculation

The bandwidth (BW) of the CRO is related to its rise time ($T_{CRO}$) by the formula:

$ BW = \frac{K}{T_{CRO}} $

Given:

• $K = 0.35$
• $T_{CRO} = 9 \mu s = 9 \times 10^{-6} s$

Now, calculate the bandwidth:

$ BW = \frac{0.35}{9 \times 10^{-6} s} $

$ BW \approx 0.03888... \times 10^6 Hz $

$ BW \approx 38.89 \times 10^3 Hz $

$ BW \approx 38.89 KHz $

Rounding to the nearest option, the bandwidth is approximately 39 KHz.