# RADIO COMPONENTS & INTERFERENCE V1.00

Contents:

(From Max Feil)

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
Posted to: rec.models.rc
Date: 27 Apr 1995

# Introduction

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

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:

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

2. 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 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.

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:

1. Someone transmits on the same frequency as you

2. 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 ....)

3. 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.

# Conclusion

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