Bessel functions and FM sidebands

[ArtemisGoldfish]

I've been wracking my brain trying to remember how to do this, and searching the internet for the past 3 hours hasn't yielded anything useful. Anyways, I have a chart of bessel function values for certain sidebands. If I'm thinking of them correctly, they represent percent of peak voltage at a certain modulation index.

What I'm trying to figure out is, for instance, if you have a 1kW FM transmitter and a modulation index of 2, what is the power of the first sideband? The value on the chart is .5767 for the first sideband at a mod index of 2, but I'm not exactly sure how to apply that, and I don't think it's just a matter of simply multiplying .5767 and 1000W.

Any help is greatly appreciated.

 

[MrAl]

Hi,


Doesnt that pertain to the amplitude? Also, dont you first subtract 1 from the sideband?

In other words, the amplitude of the first sideband would be J(s-1,2)*A which would be J(0,2)*A where
A is the amplitude of the carrier. This would come out to around 0.22 for A=1.

The multiplier is J(s-1,m) where s is the sideband number and m is the modulation index.

You should probably verify this however on the web or perhaps someone else can verify or correct this.

 

[ArtemisGoldfish]

I tried it out in MultiSim (not very indicative of real life, but whatever) and found that it generally worked like I thought it would (value on the Bessel function chart multiplied by the unmodulated carrier power), assuming the simulated spectrum analyzer works correctly.

 

[JimB]

For an FM signal, the total power in the carrier and the sidebands is constant.

So the total power is given by the expression

(J0(M))² +2(J1(M))² + 2(J2(M))³ + ... = 1

Where Jn is the Bessel coefficient, M is the modulation index.

The Bessel coefficient reperesents the voltage, so the Bessel² represents the power.

So, in your example, the power in each of the two first side frequencies will be

0.5756² x 1000 watts = 332 watts.

JimB

 

[ArtemisGoldfish]

For an FM signal, the total power in the carrier and the sidebands is constant.

So the total power is given by the expression

(J0(M))² +2(J1(M))² + 2(J2(M))³ + ... = 1

Where Jn is the Bessel coefficient, M is the modulation index.

The Bessel coefficient reperesents the voltage, so the Bessel² represents the power.

So, in your example, the power in each of the two first side frequencies will be

0.5756² x 1000 watts = 332 watts.

JimB

Immeasurable amounts of thanks, JimB. I knew it had something to do with that.