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Unformatted text preview: 3 Frequency Modulation The other common form of analog data transmission that is familiar to most people is called frequency modulation (FM). In the previous section, the message signal was multiplied with the carrier, modulating its amplitude in order to be transmitted (this amplitude modulation). With FM, the frequency of the carrier is modulated (varied) was the message changes. FM is what is used to transmit the majority of radio broadcasts. It is generally preferred over AM because it is less sensitive to noise, and it is in fact possible to trade bandwidth for noise performance. The advantages of FM come at the expense of increased complexity in the transmitter and in the receiver. This having been said, we will see a simple FM receiver is actually no more complicated (to build) than its AM counterpart. Conceptually, FM is pretty simple. If me are sending a message m ( t ), we send a higher frequency wave when the amplitude of m ( t ) is high, and a lower frequency wave when the amplitude is low. The example below shows a square wave message, and the corresponding FM signal. The message here is called m b ( t ). The b stands for binary - the example signal happens to only have two values - and differentiates this example from the case of a general message to which is discussed shortly. t 1-1 ) ( t m b t 1-1 ) ( t s FM High amplitude High frequency Low amplitdue Low frequency Figure 70: We can see that when the message m b ( t ) has a high (1) amplitude, the frequency of the modulated signal s FM ( t ) is high. When m ( t ) goes low (-1), the modulated signal frequency is reduced. Mathematically, we could describe this as s FM ( t ) = A cos(2 π [ f c + k f m b ( t )] t ) . (38) The A in front of this equation is just a constant which tells us the signal amplitude. The constant k f is called the frequency sensitivity. It tells us how much the signal frequency changes as as the message changes. From both the equation and Fig. 70, we can see that the 62 effective frequency of the cosine wave s FM ( t ) is f w ( t ) = f c + k f m b ( t ). This translates into f w = f c + k f ,m b = 1 (Higher Frequency) = f c − k f ,m b = − 1 (Lower Frequency) . What about for an arbitrary message m ( t ) ? We want the frequency of our cosine wave to be f w ( t ) = f c bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright + k f m ( t ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright . Carrier frequency Change due to message (39) The next page or so of math culminates in Eq. 43 which tells us how to get the FM signal. Intuitively, we might think that the FM signal would be determined using Eq. 38. This is in fact incorrect. To get this right, we need to step back and think about the meaning of frequency and phase. Let’s start with an analogy from linear motion. If we define position x ( t ) and velocity v ( t ), we know the relationship between them is v ( t ) = d dt x ( t ) . (40) That is to say that velocity is the time rate of change of position. To obtain position, fromThat is to say that velocity is the time rate of change of position....
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- Summer '09