[ARC5] HF Converter - feeding mixer with a square wave?
Tom Lee
tomlee at ee.stanford.edu
Thu Mar 17 23:23:40 EDT 2022
Yes, this involves the issue I've brought up a few times in this thread.
A nonlinear thing can produce mixing. But that is not the same as "all
mixer are inherently nonlinear." All mixers seek to approximate a
multiplication. A nonlinear element can produce multiplication as a
common byproduct of being nonlinear, but it's a very crude way to go
about it. A practical drawback of using a nonlinearity is that you get a
bunch of additional components besides the desired sum or difference term.
An amplitude modulator is indeed a mixer, as you surmise, one whose
linearity must be good in order to provide low distortion.
To understand the maths details underlying a multiplier-as-mixer, all
you need is the trigonometric identity that Leslie Smith just kindly
provided. It shows that you get sum and difference frequencies -- and
only sum and difference frequencies -- out of a multiplier. That's what
an ideal mixer provides.
To understand how a nonlinearity may produce multiplication, choose the
simplest nonlinearity to start: A quadratic. If you have two inputs, x
and y, and square their sum, you get the sum of x^2 and y^2 (we're not
interested in those), as well as a cross-product, 2xy. There's your
multiplication. But you see, we get it incidentally. It comes with terms
we don't need (and ultimately do not want). It gets worse when you
consider that real nonlinearities are more complicated than a pure
quadratic. What we want is just the multiplication, but we get a lot of
other crud. Mixers based on nonlinearity are the result of compromise,
but are very popular in early radio circuits because of their
simplicity. That popularity became improperly generalized as a
universality, hence the poorly-written papers and textbooks declaring
that "all mixers are based on nonlinearity."
The class of nonlinearity-based mixers remains popular among hobbyists,
either in homage to early design practice, or because of the appealing
simplicity of 1- or 2-tube (or zero-tube) implementations. And, as many
successful products attest, their performance can be more than
satisfactory for a great many applications. But when you need the
maximum dynamic range, you seek to approach the ideal of emulating a
multiplier to the best of your ability. When multi-carrier telephony was
being developed, it became apparent that the nonlinear-based mixers were
never going to be satisfactory, and thus the now-familiar four-diode
multiplier was developed (using copper-oxide rectifiers -- pre-silicon
solid-state devices!). Cellphones have the same extreme dynamic-range
demands, and that's why you only see double-balanced mixers based on
multiplication in that application.
-- Cheers,
Tom
--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
350 Jane Stanford Way
Stanford University
Stanford, CA 94305-4070
http://www-smirc.stanford.edu
On 3/17/2022 19:46, 1oldlens1 wrote:
> You have another person confused. My understanding has always been
> that a mixer was fed with signals of two different frequencies and put
> out both frequencies plus the sum and difference frequencies. My
> understanding so is this requires the circuit to be non-linear. If
> not why does a straight piece of wire do this? I am away from Home
> and can't look at my books.
> Note that a mixer and an amplitude modulator behave in much the same
> way. What am I missing?
>
>
>
> Sent from my Galaxy
>
>
> -------- Original message --------
> From: Mike Feher <n4fs at eozinc.com>
> Date: 3/17/22 7:18 PM (GMT-08:00)
> To: 'Bob kb8tq' <kb8tq at n1k.org>
> Cc: 'ARC-5' <ARC5 at mailman.qth.net>
> Subject: Re: [ARC5] HF Converter - feeding mixer with a square wave?
>
> The most ideal mixer is a multiplier. And it is linear. The math has
> not changed in hundreds of years except maybe for the case of zero
> divided by zero. When I was young, I wanted to be a professor and
> tutored my classmates many math and EE courses. Always got frustrated
> when what was obvious to me, I could not make a few of them
> understand. So, I turned out to be just an EE who put in 50 years
> working for the DOD one way or the other. This will be my last post on
> the subject as there have been way too many already. Obviously, Tom
> has a lot more patience than I, and I hope you try to understand what
> he is telling you. 73 – Mike
>
> Mike B. Feher, N4FS
>
> 89 Arnold Blvd.
>
> Howell NJ 07731
>
> 848-245-9115
>
> *From:* Bob kb8tq <kb8tq at n1k.org>
> *Sent:* Thursday, March 17, 2022 9:40 PM
> *To:* Mike Feher <n4fs at eozinc.com>
> *Cc:* Tom Lee <tomlee at ee.stanford.edu>; ARC-5 <ARC5 at mailman.qth.net>
> *Subject:* Re: [ARC5] HF Converter - feeding mixer with a square wave?
>
> Hi
>
> Oddly enough pretty much everything we used was in the form of notes
>
> from the prof. The explanation was that the last time they had done “ a
>
> course like this” was back in the early 1950’s. At the point I was there
>
> (the 1970’s) the textbook world had not caught up.
>
> Bob
>
>
>
> On Mar 17, 2022, at 9:16 PM, Mike Feher <n4fs at eozinc.com> wrote:
>
> Bob –
>
> Can you reference the book that you used during your studies? 73 –
> Mike
>
> Mike B. Feher, N4FS
>
> 89 Arnold Blvd.
>
> Howell NJ 07731
>
> 848-245-9115
>
> -----Original Message-----
> From: arc5-bounces at mailman.qth.net <arc5-bounces at mailman.qth.net>
> On Behalf Of Bob kb8tq
> Sent: Thursday, March 17, 2022 9:12 PM
> To: Tom Lee <tomlee at ee.stanford.edu>
> Cc: ARC-5 <ARC5 at mailman.qth.net>
> Subject: Re: [ARC5] HF Converter - feeding mixer with a square wave?
>
> Hi
>
> At least when I took the course in school on this stuff, the basic
> definition of “linear” was indeed that the output was the input
> times a constant. Anything other than that was “non-linear”. This
> is at the root of the conversation about mixers being non-linear.
> If that *is* you definition of linear then mixers must be non-linear.
>
> Bob
>
> > On Mar 17, 2022, at 9:09 PM, Tom Lee <tomlee at ee.stanford.edu
> <mailto:tomlee at ee.stanford.edu>> wrote:
>
> >
>
> > Think about how one actualy uses a multiplier as a mixer, Bob.
> The input-output relationship of relevance is that between the IF
> output and the RF input. That is supposed to be linear, right?
> That is, the output should be a constant times the input, just as
> you yourself stated as the requirement.
>
> >
>
> > --Tom
>
> >
>
> > --
>
> > Prof. Thomas H. Lee
>
> > Allen Ctr., Rm. 205
>
> > 350 Jane Stanford Way
>
> > Stanford University
>
> > Stanford, CA 94305-4070
>
> > http://www-smirc.stanford.edu <http://www-smirc.stanford.edu/>
>
> >
>
> > On 3/17/2022 17:45, Bob kb8tq wrote:
>
> >> Hi
>
> >>
>
> >> If you accept the definition that a “linear” circuit *only*
> produces
>
> >> the input times some constant ( = the gain ) then anything that
>
> >> multiplies must be non-linear.
>
> >>
>
> >> If you look at a different definition, then of course, they can
> be linear.
>
> >> It’s just a mater of what your base definitions are.
>
> >>
>
> >> Bob
>
> >>
>
> >>> On Mar 17, 2022, at 8:13 PM, Tom Lee <tomlee at ee.stanford.edu
> <mailto:tomlee at ee.stanford.edu>> wrote:
>
> >>>
>
> >>> (Just to clarify, this was posted in response to Bob Nickels,
> not to
>
> >>> Mike St. Angelo -- sorry for the confusion, Mike!)
>
> >>>
>
> >>> --Tom
>
> >>>
>
> >>> --
>
> >>> Prof. Thomas H. Lee
>
> >>> Allen Ctr., Rm. 205
>
> >>> 350 Jane Stanford Way
>
> >>> Stanford University
>
> >>> Stanford, CA 94305-4070
>
> >>> http://www-smirc.stanford.edu <http://www-smirc.stanford.edu/>
>
> >>>
>
> >>> On 3/17/2022 12:16, Tom Lee wrote:
>
> >>>> I wish people would stop repeating the claim that mixers are
> inherently nonlinear. That’s completely false. It is true that
> nonlinear things can produce mixing, but that’s a side effect, not
> an inherent property!
>
> >>>>
>
> >>>> Good mixers have to be linear. You want the IF output to be
> proportional to the RF input.
>
> >>>>
>
> >>>> We treat mixer nonlinearity in much the same way as we treat
> amplifier nonlinearity. It is an undesirable property and
> considerable effort is expended to minimize it.
>
> >>>>
>
> >>>> Tom
>
> >>>>
>
> >>>> Sent from my iThing; please forgive the typos and brevity
>
> >>>>
>
> >>>>> On Mar 17, 2022, at 11:39, MICHAEL ST ANGELO
> <mstangelo at comcast.net <mailto:mstangelo at comcast.net>> wrote:
>
> >>>>>
>
> >>>>> Bob,
>
> >>>>>
>
> >>>>> Enjoyed that article and the one about the Si5351 Quadrature
> oscillator. Have the tried feeding the Si5351 to the SA612 instead
> of an Epson? It gives the the ability of easily changing frequency.
>
> >>>>>
>
> >>>>> The SA612 and Si5351, what a pair for experimenters.
>
> >>>>>
>
> >>>>> Mike N2MS
>
> >>>>>
>
> >>>>>> On 03/17/2022 1:05 PM Robert Nickels <ranickels at gmail.com
> <mailto:ranickels at gmail.com>> wrote:
>
> >>>>>>
>
> >>>>>>
>
> >>>>>>> On 3/17/2022 11:10 AM, Phillip Carpenter wrote:
>
> >>>>>>> Can you please share the circuit diagram of your universal
> converter board that you used with the BC-453 receiver?
>
> >>>>>> I've added an article about it to my website:
>
> >>>>>> https://tinyurl.com/mrj7rndd <https://tinyurl.com/mrj7rndd>
>
> >>>>>>
>
> >>>>>> The 4.7uH/100pF values shown work for 40 meters, or calculate
>
> >>>>>> your own - I use a 10uH fixed inductor and 150-180pf
> capacitor for 75-80 meters.
>
> >>>>>>
>
> >>>>>> 73, Bob W9RAN
>
> >>>>>>
>
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