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ATM has, however, emerged from the flames in other ways. Today many service providers see ATM as an ideal aggregation technology for diverse traffic streams that need to be combined for transport across a WAN that will most likely be IP-based. ATM devices then will be placed at the edge of the network, where they will collect traffic for transport across the Internet or (more likely) a privately owned IP network. Furthermore, because it has the capability to be something of a chameleon by delivering diverse services across a common network fabric, it is further guaranteed a seat at the technology game. It is interesting to note that the traditional, legacy telecommunications network comprises two principal regions that can be clearly distinguished from each other: the network itself, which provides switching, signaling, and transport for traffic generated by customer applications; and the access loop, which provides the connectivity between the customer s applications and the network. In this model, the network is considered to be a relatively intelligent medium, whereas the customer equipment is usually considered to be relatively stupid. Not only is the intelligence seen as being concentrated within the confines of the network, so too is the bulk of the bandwidth because the legacy model indicates that traditional customer applications don t require much of it. Between CO switches, however, and between the offices themselves, enormous bandwidth is required.

When doing problems of this kind, remember to use the capacitive reactance values for X C, and not the capacitance values. This means that, if you are given the capacitance, you must use the formula for X C in terms of capacitance and frequency and then calculate the phase angle. You should get angles that come out negative or zero. This indicates that they re RC phase angles rather than RL phase angles (which are always positive or zero).

Problem 14-2

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Problem 14-4 Suppose the capacitive reactance in an RC circuit is 3800 and the resistance is 7400 . What is the phase angle Find the ratio X C /R = 3800/7400. The calculator display should show you something like 0.513513513. Find the arctangent, or tan 1, getting a phase angle of 27.18111109 on the calculator display. Round this off to 27.18 . Problem 14-5 Suppose an RC circuit works at a frequency of 3.50 MHz. It has a resistance of 130 and a capacitance of 150 pF. What is the phase angle First, find the capacitive reactance for a capacitor of 150 pF at 3.50 MHz. Convert the capacitance to microfarads, getting C = 0.000150 F. Remember that microfarads go with megahertz (millionths go with millions to cancel each other out). Then:

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What will be the capacitive reactance of the above capacitor, if the frequency decreases to zero That is, if the source is dc In this case, if you plug the numbers into the formula, you ll get zero in the denominator. Mathematicians will tell you that this is a no-no. But in reality, you can say that the reactance will be extremely large negatively, and for practical purposes, negative infinity.

X C = 1/(6.28 3.50 0.000150) = 1/0.003297 = 303 Now you can find the ratio XC /R = 303/130 = 2.33. The phase angle is equal to the arctangent of 2.33, or 66.8 .

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