n electrical signal for con- version to an optical signal. Under intensity modulation the light signal is turned on and off to represent binary values of 1 and 0. The modulated carrier is given by E(t) = E m (t) COS (2IIf t) where E = energy level of the output signal = energy level of the input signal Light Sources and Detectors m(t) = the modulating signal = the optical carrier frequency = time Because optical power is emitted in proportion to the forward bias, this power will take the shape of the input current. Thus, when the input current has a waveform of m(t) that represents binary information, the resulting optical signal will resemble a burst of light when m(t) rep- resents a 1 and will be absent when m(t) represents a 0. While this trans- lates to the presence and absence of light, it is also worth noting that the linear relationship between input current and light output makes it pos- sible to use LEDs with an analog input. When used with an analog input, an LED can typically support modulation rates of up to 20 MHz. Comparison between an LED and a Laser Diode In concluding our discussion of LEDs, let's compare their operational characteristics to those of a laser diode. Although we discuss the latter in the next subsection, we can note that the LED has a high coupling loss that results in less optical power flowing into a fiber. In addition, because of the longer pulse rise and fall times, the LED operates at a lower data transmission rate than does a laser diode. Because of the greater optical dispersion of the LED, it is used with multimode fiber. Although these factors limit the use of LEDs, it is also important to note that they are relatively inexpensive in comparison to a laser diode. In addition, they have a higher reliability and use multimode fiber, which can be 3 to 5 times less expensive than single-mode fiber. Hence we can paraphrase Mark Twain and say that the death of LEDs for use in opti- cal networking is greatly exaggerated. Lasers A second device used as a light source with optical f