From: mkfeil@bcrki9.bnr.ca (Max Feil)
Subject: Radio Interference (technical)
Organization: Bell-Northern Research
Date: Mon, 14 Sep 92 21:04:50 GMT

Here is a great technical description of the issues being discussed in a
related thread. It was not written by me.


 From:       'galaxy.nsc.com!pad@gatech.uucp'
 Subject:    Radio interference

Max,

I have read your posting and appreciate your efforts to explain the problems 
people have with R/C gear, however I feel that while some of the conclusions
are correct some are not and the explanations are not really accurate. I know
that you are not an RF engineer so please do not take this as a flame - I work
as an RF engineer and have attempted to explain my view of what is going on
and I hope you will find the following constructive. If this email generates
questions on your behalf please feel free to email me.

RADIO COMPONENTS

To understand what is happening in a radio you need to understand what the
following components do;

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

Radio Receivers

The big problem that your airplane has is to know which transmitter to
listen to - at the aerial *every* radio transmission is present - other R/C
channels, pagers, local radio stations, t.v., C.B. etc etc. The receiver tries
to achieve this by by using filters to remove everything except the frequency
band that you are transmitting on. The simplest way to do this would be to
put a filter directly after the aerial that stopped everything but your
transmission band. Your signal could then be amplified and demodulated with no 
further ado. This type of radio is called a tuned radio frequency reciever
or TRF for short. This is such a simple idea - why don't more people use it?
Well for the fllowing reasons;

i) The filter would have to be 20KHz wide at 72MHz which requires a very
expensive high order filter.

ii)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).

Heterodyne receivers (single conversion receivers)

Heterodyne recevers work like this; All signals go into the aerial and a low 
order filter selects frequencies +/- about 600khz either side of the centre
of the R.C. band. This filter is called the image filter and you should note
that it allows *all* the R/C channels through (yes I know! read on...).
They then go to a mixer which multiplies all the incoming signals by the
crystal frequency of the receiver (called the local oscillator with frequency
"flo"). For every input frequency "fs" to the mixer the output contains ;

                fout    =       fs*flo

As 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  **or** flo-fs=-455KHz

you 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.

2IM

As we have seen - any signals at 455KHz coming out of the mixer get through
the channel select filter. If the mixer circuitry has 2nd order distortion
(a2*x^2) then an input of a + b will be distorted to a^2 + a*b + b^2 
the square terms of this quadratic can be ignored (they are easy to filter)
so that the effect of 2IM is to multiply input signals together which are
then multiplied by the local oscillator. the effect of this is that large 
signals 455KHz apart at the input to the mixer generate 455KHz at the *input*
to the mixer -whether these get to the output and cause interference depends
on the mixer type - a good balanced mixer will attenuate these signals before
to the output.

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.


Superhet receivers (dual conversion)

These have 2 intermediate frequencies. The first mixer now has an output 
image frequency 21.4MHz away (2*10.7MHz) these are easily filtered by the
image filter between the aerial and the first mixer. 2IM products need to
be 10.7MHz apart and these are similarly easily filtered by the image filter.
So now all we do is filter at 10.7MHz and detect our signal right? well if 
the filter you used was 20KHz wide then yes you could do this but such filters
are expensive and the circuitry at 10.7MHz still requires fairly high power.
So a superhet filters at 10.7MHz with a cheap filter that is about 100khz
wide. After this filter you simply mix the signal with a local oscillator
whose frequency is fs+455KHz (sound familiar?) the output is filtered at 455KHz
with a bandwidth of 20khz to select your signal the image frequency at this 
if is 910KHz but the filter at 10.7MHz has removed it - so no interference 
from images  or 2IM.

Can anything interfere with superhets then? Yes ;

If a transmitter transmits on your frequency it will fairly obviously 
interfere if its strong enough. The interfering signal must be substantially
higher to interfere with an fm system than an am system (this applies to any
of the interferers listed above or below which is why fm systems are less
prone to interference - all else being equal). This situation will arise if:

i) Someone transmits on the same frequency as you

ii) 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 ....)

iii) 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.


I hope you find this of some value - I may have made some errors (after all
I'm only human!) but I think its mostly correct and if you disagree with
any of it or have any questions I will be happy to answer them.

Cheers - Paul


 

--
Max Feil  mkfeil@bnr.ca | Disclaimer:
Bell-Northern Research  |   What do I know? I'm just a Nerd on the Big Ranch.
P.O Box 3511 Station C, |
Ottawa, Ontario, Canada.| "Enrich The Soil, Not EveryBody's Goal" Peter Gabriel