Question

FIGURE P39.28 shows a pulse train. The period of the pulse train is $T=2$$\Delta t$, where $\Delta t$is the duration of each pulse. What is the maximum pulse-transmission rate (pulses per second) through an electronics system with a $200kHz$ bandwidth? (This is the bandwidth allotted to each FM radio station.)

Short answer

$f_{\max }=1\times {10}^5\mathrm{Hz}$

Step-by-step solution

part (a) step 1:  Given information

We would like to find the maximum frequency possible for the pulse train. First, we are going to make use of the equation $\Delta f\Delta t\approx 1,$where we are given that the maximum$\Delta f$is 200 KHz ( the bandwidth), and from this, we can find the smallest possible duration of the pulse

$\Delta t=\frac{1}{200\times {10}^3\mathrm{Hz}}=5\times {10}^{-6}\mathrm{s}$

now we can use the fact that the period is$T=2\Delta t,$so the period of the pulse train is

$T=2\Delta t=2\left(5.00\times {10}^{-6}\mathrm{s}\right)=1\times {10}^{-5}\mathrm{s}$

which is the smallest possible period. Thus, the maximum frequency or the maximum pulse- transmission rate is

$f_{\max }=\frac{1}{T}=\frac{1}{1\times {10}^{-5}\mathrm{s}}=1\times {10}^5\mathrm{Hz}$