**I had a call from Chris who was asking how his Leak Troughline worked so I decided that maybe it was time for a quick blog article on FM. Frequency Modulation or FM is a system of radio transmission where the carrier amplitude is kept constant whilst the frequency varies about the nominal value. **

**The frequency variation has to convey two pieces of information: - **

**i) Audio frequency which is the number of times per second the carrier frequency oscillates or wobbles either side of it's nominal value.**

**ii) Audio amplitude which is the amount the transmitted frequency shifts above and below the carrier frequency f**_{c} and is known as the frequency swing f_{s} where f_{s} is proportional to the amplitude of the original sound and has a maximal value of 75KHz

**The simplest method of recovering the audio frequency oscillation is shown below: -**

**Above you can see that an RF circuit has been set 'off-tune' to the carrier frequency such that the oscillations correspond to the straight part of one half of the response curve. As the frequency of the FM signal oscillates from f**_{c}-f_{s} to f_{c}-f_{s} and back again the response changes from point A to B and thence back to A. This completes one cycle at audio frequency.

**The amplitude of the AF component in the output depends on the magnitude of f**_{s} and also on the slope of the response curve. The repetition periodicity of the waveform (= 1/frequency) is the time taken for the signal to swing f_{c}-f_{s} to f_{c}+f_{s} and back again.

**To give a worked example consider a carrier frequency of 90 MHz being modulated by an AF signal of 1KHz showing a frequency oscillation of 50KHz - this will show a signal oscillalation of 1000Hz between the limits of 90.05MHz to 89.95MHz and will reach these maxima 1000 times per second.**

**The bandwidth required for FM transmissions is much larger than that needed for AM transmissions. If the modulating (audio) frequency is denoted by f**_{m} then sidebands are formed at f_{c}+/-f_{m} dependant upon the modulation index f_{s}/f_{m}. Theoretically, there will exist an infinate sequence of sidebands but the range can be reduced by operating with minimal frequency oscillations, the maximal allowable of which is denoted the frequency deviation f_{d}. In broadcasting, the magnitude of f_{d} is typically several times greater than the highest transmitted audio frequency. fd can be characterised further by the deviation ratio a value of 5 or higher being preferred where the frequency deviation of 75KHz results from a maximal modulating frequency of 15KHz.

**Consequently, medium waves are unsuitable for FM transmissions as the output would be ruined by phase selective fading, conversely at very high frequencies (VHF) fading and selectivity concerns are much reduced as tropospheric bounce has little effect as only the ground wave reaches the receiver.**