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**Wideband FM/PM Signals**

Dr. Ali Hussein Muqaibel Electrical Engineering Department King Fahd University of Petroleum & Minerals

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**When do we call it Wideband ?**

Narrowband Otherwise Wideband

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**What is the Bandwidth of Wideband FM?**

Nyquist sampling theorem m(t) with a bandwidth of Bm (Hz), the minimum sampling frequency is 2Bm t = 1/2Bm

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**Bandwidth of the Approximate FM**

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In Frequency Domain It is not delta!

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The estimated BW Using the fact that f = kf mp/2 , the bandwidth in Hz becomes In practice, this bandwidth is higher than the actual bandwidth of FM signals. Consider for example narrowband FM. Using this formula for the bandwidth, we see that the bandwidth is twice the actual bandwidth.

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**Carson’s Rule Special Case where**

Bm = Bandwidth of the Message Signal m(t) in Hz, and = kf mp f = kf mp/2. Special Case For very wideband FM For narrowband FM

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**The Modulation Index (Deviation Ratio)**

For FM/PM, the modulation index or deviation ratio ,β, is defined as Accordingly we may rewrite Carson's rule as

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For PM Similar Rrsults . Notice that the above results can be readily extended for PM: Notice that BWFM depends on the max(m(t)). BWPM depends on the frequency content (change of m(t)) which is related to

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**Examples for Bandwidth Estimation**

On the text book do examples & 5.5 (In the class we start 5.3 then continue 5.3 & 5.4 to see the effect of doubling the amplitude of the message also examine the effect of time expansion/compression. Do example 5.5. Historical Note: Read the historical Note about Edwin H. Armstrong ( )

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Why FM? We started FM with the objective of saving bandwidth but this out to be wrong. So why FM what are the features that make FM applicable? FM can exchange bandwidth for quality Signal to Noise Ration (SNR) α (Transmission bandwidth)2 Recall that AM has limited bandwidth FM has constant amplitude (fixed Power) FM is Immune to nonlinearity. ……..

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