# Forum

## CWAP Chapter 2 Errata - Shannon-Hartley Theorem

• By blackmonjd - edited: November 29, 2016

Update: I'm referring to the Certitrek Edition CWAP-402 which I purchased from this site just a few weeks ago.

Sorry if this is a duplicate post, but I tried to search and didn't find anything else. In the definition of terms in the Shannon-Hartley Theorem, the bandwidth should be in just hertz, not kilohertz. So when calculating the capacity of a 20 MHz wide channel, you should use 20000000 not 20000.

• I don't have the book so I can't comment directly, but was there a "constant of proportionality" in the equation that corrected the equation, or does the calculation come up with the wrong answer ?

By itself, just a multiplying prefix would not invalidate the answer.   i.e. 20 MHz, 20000 kHz, and 20000000 Hz are still the same value.

• By blackmonjd - edited: November 29, 2016

I suggested this as errata, because all other definitions of the Shannon-Hartley Theorem simply relate channel capacity in bits per second to channel bandwidth in hertz. However, on page 116 we are told,

C = B log2 (1 + S/N)

C is the channel's capacity in bits per second (bps). B is the channel's bandwidth in kilohertz (kHz).

There was no reference to a proportionality constant, and when terms of an equation are specified with a certain magnitude, then it is assumed one would us the value at that order of magnitude, not covert to order of magnitude 0.

In short, if providing the channel bandwidth in kilohertz, then we do not get the channel capacity in bps. So if, for example, you say B = 20 MHz and SNR = 15, and convert B to kilohertz, then you just plug in everything as the book states, you get

C = 20000 * log2 (1 + 15) = 80000 bps or 80 kbps

That's off by an order of magnitude. If we plug in the channel bandwidth in hertz, then we get 80 Mbps. My point is that we can use kilohertz, but then we should expect an answer in kilobits. Likewise, we can use a a value in megahertz and get an answer in megabits.

• Understood.

I agree

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