Message-ID: <3EA9784E.6080102@virgin.net>
Date: Fri, 25 Apr 2003 19:02:54 +0100
From: "Stewart Bryant" <stewart.bryant@virgin.net>
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To: rsgb_lf_group@blacksheep.org
Cc: "ACT \(E-mail\)" <g4jnt@thersgb.net>, 
 "Tottingham Brian J" <BJTOTTINGHAM@dstl.gov.uk>,
  Linda_Holtby@ntlworld.com
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Subject: Re: LF: A conumdrum for the weekend - Image Can	celling Mixer.
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Silly me, it's called dispersion.

Sorry to waste the bandwidth.

Stewart

Stewart Bryant wrote:
> Andy
> 
> I have a problem with the output 90deg phase shifter. I can see how you
> can shift the LO and the signal by 90deg, but the output from the
> top mixer has sin(A+B) and sin(A-B) signals present. Unless you have
> a frequency sensitive phase shifter, it is only going to shift one
> component by 90deg and the other by some strange ammount.
> 
> Is the phase shifter frequency sensitive?
> 
> Stewart G3YSX
> 
> Talbot Andrew wrote:
> 
>> The following little theoretical problem has occured several times 
>> during my
>> working life, and has cropped up once again, when another engineer here
>> asked me to explain how a radar receiver front end, as shown in the block
>> diagram in a manufacturers data sheet, could possibly work.
>>
>> A well-known supplier of packaged mixers once had the same conumdrum to
>> solve when producing a customised mixer for us. Concern about it 
>> resulted in
>> them developing a special 90 degree network for operating over 0.3 to 
>> 5 MHz,
>> when all that was really needed was a couple of simple designs that 
>> operated
>> at HF/VHF.  If common sense had ruled, the mixer would have been produced
>> much quicker and at less cost.
>>
>> Andy  G4JNT
>> =========================================================
>> Image Cancelling Mixer connundrum.
>>
>> In the classic image cancelling mixer, suppression of one mixer 
>> sideband is
>> obtained by combining two 90 degree shifted input signals with two 90 
>> degree
>> shifted versions of a local oscillator.  The outputs from the two 
>> channels
>> are then added or subtracted depending on which sideband is desired.
>>
>>
>>
>>         ---90---X---------|
>> Signal -|       |        +/- IF
>>         ------------X-----|
>>                 |   |
>>                 90  |
>>                 | - |
>>                   |
>>                Local Osc.
>>
>> If the signal is represented by SIN(A) and the Local Oscillator by SIN(B)
>> then the signal input to the top mixer is now COS(A) as it has passed
>> through a 90 degree phase shift, and its respective LO is COS(B)
>>
>> The mixers multiply the two signals, and from standard trignometric
>> identities taken from any mathematical reference, the products of two 
>> sines
>> can be expressed as a sum and difference equation So the outputs of 
>> the mixers (ignoring the factors of 2 in the trig
>> identities) are :
>>
>> Top       COS(A).COS(B) =  COS(A-B) + COS(A+B)
>> Bottom   SIN(A).SIN(B) =  COS(A-B) - COS(A+B)
>>
>> So the cancellation / reinforcement at the output is obvious. 
>> NOW,  if we move the second 90 degree phase shift to the output of the
>> mixers (the IF) rather than the LO, as shown below, intuition and common
>> sense tells us it should still work since the mixing process is fully
>> reversible and actual direction of signal flow is irrelevant.  
>> Furthermore,
>> many real designs of SSB exciters and receivers prove this really does 
>> work
>> in practice.
>>
>>         ---90---X----90----|
>> Signal -|       |         +/- IF
>>         ------------X------|
>>                 |   |
>>                 | - |
>>                   |
>>               Local Osc.
>>
>> But here is the conumdrum :
>>
>> Keeping the same terminology of Signal = SIN(A), and LO = SIN(B), the 
>> inputs
>> to the top mixer become  COS(A) . SIN(B)
>> and the output given by the product rule :
>> COS(A).SIN(B)     =  SIN(A+B) - SIN(A-B)
>>
>> After the output 90 degree phase shift, the SIN terms beocome COS so we
>> have, in the top output leg :
>> COS(A+B) - COS(A-B)
>>
>> The output from the bottom mixer is, as before :
>> SIN(A).SIN(B)   =  COS(A-B) - COS(A+B)
>>
>> Which is the SAME as in the top leg, and will either cancel or reinforce
>> both sidebands.  So it doesn't appear to work at all !
>> Moving the output 90 degree shift to the lower leg still fails to 
>> cancel one
>> sideband only.
>>
>> So where is the conundrum?    Both forms of image cancelling mixer do 
>> indeed
>> work, and the trig identities can be taken from any reference.
>> ==================================================
>> PS.
>> I do have one rather weak explanation, but it doesn't give that warm cozy
>> feeling expected when theory falls into place!
>> Andy
>>
>>
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>>
> 
> 
> 
>