**18**. About the Author**19**. Introduction**20**. Radio Receivers**21**. Heterodyne receivers (single conversion receivers)**22**. 2IM**23**. Superhet receivers (dual conversion)**24**. Can anything interfere with superhets then? Yes**25**. Conclusion

Here is a more technical article on radio theory that gives the how & why behind interference. It was written by Paul Denny.

Author: Paul Denny

E-Mail: pad@galaxy.nsc.com

Posted to: rec.models.rc

Date: 27 Apr 1995

- Filters
- These are devices that only allow certain frequencies to pass through.
In a radio they are almost always bandpass filters and can roughly be
specified as having a centre frequency and a bandwidth. The ideal filter
(which can be proven not to be realisable) would allow the frequencies within
the bandpass to pass through the filter with no attenuation and stop all
other frequencies from passing through at all. Real filters pass most of the
signal at the centre frequency and gradually reduce the amplitude of the
signal as the frequency moves further away from the centre frequency. Filters
can be made to approach the ideal filter but the closer you get the heavier
bigger and more expensive they become. As filters approach this ideal they are
said to have a higher order. It turns out that for a given order, a filter will
have a narrower bandwidth if its centre frequency is lower (remember this as it
will explain why we have frequecy conversions in radios later). So if a filter
that is small light and cheap has bandwidth of 350khz and centre frequency
of 72MHz an equivalent order filter at 10.7MHz will have a bandwidth of 53Khz
and at 455KHz a bandwidth of 2KHz. So
**filters are easier to make narrowband at low frequencies**. - Mixers
- An ideal mixer takes two input signals and multiplies them to give its
output. This is all they do. Real mixers will introduce gain or loss and more
importantly for this discussion introduce distortion. This distortion
characteristic can be described as a power series so that for an input x the
output will contain (a0 + a1.x + a2.x^2 + a3.x^3 + ....) a0 is the dc offset
at the output a1 is the linear gain a2 is the coefficient for 2nd order
distortion which will produce 2IM a3 is the coefficient for 3IM. The co-
efficients usually decrease very rapidly but the higher power terms increase
faster with increasing x (amplitude) so that (if the gain does not compress)
the 2nd and 3rd order terms eventually exceed the linear term. The smaller the
coefficients of the higher order terms are the more linear the radio is - this
is good for preventing distortion but often bad for increasing noise so mixer
designers try to compromise.
- Amplifiers
- Ideal amplifiers just amplify signals - real ones introduce distortion - see above

- The filter would have to be 20KHz wide at 72MHz which requires a very
expensive high order filter.
- All amplification and demodulation needs to be done at high frequency which requires high power consumption circuitry.

To get around this problem radios use either one intermediate frequency ("if") and are called heterodyne receivers or more than one (usually two) in which case they are called superheterodyne receivers (superhet for short).

fout = fs*floAs you said it can be shown by trigonometry theory that;

cos(2*pi*flo*t)*cos(2*pi*fs*t)=1/2*( cos(2*pi*(flo-fs)*t)+cos(2*pi*(flo+fs)*t)Or the output of the mixer contains frequencies at flo-fs and flo+fs. Now the output of the mixer is put through a filter with a centre frequency at 455KHz and a bandwidth of 20KHz (this is called the channel select filter). This definitely gets rid of the flo+fs terms as they are up at about 144MHz but what gets through? well anything that satisfies the relationship;

flo-fs=+455KHz <strong>or</strong> flo-fs=-455KHzyou may well say what does -455KHz mean? - It is called the image frequency and is actually a positive frequency the same as +455KHz but phase inverted by 180 degrees (or multiplied by -1 if you prefer).

To select your transmission frequency, the receiver crystal is designed so
that flo-fs=+455KHz so flo=fs+455KHz however if the input of the mixer
has a frequency at flo+455KHz (which is fs+910KHz) then you will get an
interference output frequency at 455KHz. You rely on the image filter
(see above) to reject this frequency **before** it gets to the mixer
(once it gets into the mixer there is nothing you can do about it)
however this filter has to be at least as wide as the R/C spectrum
which is channel spacing*number of channels (I think there are
60 channels now? so the image filter is then 1200kHz wide) so a single
conversion receiver can let frequencies 45.5 channels away interfere. whether
the interfering channel is 45.5 channels above or below your channel will
depend whether your receiver uses high side or low side flo injection (this
just means whether flo=fs+455Khz or flo=fs-455KHz respectively). If all
receivers used high side injection then channels 45.5 above you would interfere
with you but you would not interfere with them. For high side injection
receivers you want to be one of the high frequency channels, for low side
injection receivers you want to be one of the low frequency ones.

This effect has nothing to do with 2nd order intermodulation it is due to a lack of image rejection in single conversion receivers.

In summary a single conversion R/C radio will always have poor image rejection and if the image frequency is inside the band of the image filter 910KHz away from your channel you will get interference. 2IM may or may not be a problem if the mixer has either low 2nd order distortion or is well balanced or both then 2IM will be less of a problem. 2IM becomes a problem when the two interfering signals are strong and your signal is weak.

- Someone transmits on the same frequency as you
- Someone transmits on a frequency close to you with a wideband transmitter
(if his transmitter bandwith is 60KHz some of his signal will spill into
your channel if enough energy spills ....)
- 3IM ; the mechanism for this is identical to 2IM but now the cube of the two input signals generate 2f1-f2 and 2f2-f1 ( simply look up the trig for (cos a + cos b)^3 ) if two channels are spaced xHz and 2*xHz away from you 3IM in the first mixer will produce an interferer at the same frequency as you - it cannot be filtered once produced. the image filter will not be able to remove these as they can be any of other RC channels with the correct spacing (note the image filter must allow all the channel through or you would not be able to use all the channels (crystals) available in any set which would be a production nightmare.

A final mechanism for interference is jamming whereby the radio is simply
overloaded by a **very** strong signal that gets through the image filter-
it simply overloads the circuitry.

Cheers - Paul