[ARC5] The maximum power transfer theorem. [Was: Receiver input impedance...)

Mon Oct 20 16:08:21 EDT 2014

Les,

Richard is a nice bloke. It's just that understanding noise in any kind of
receiver system or sensor front end can be downright confusing.  Entire
engineering books have been written about it.  Permit me to take a stab at
explaining it a bit further and hopefully not add to the confusion or
confuse myself in the process ;-)

Most treatments consider the signal source to have the thermal noise of an
ideal resistor; in our case that is usually 50 ohms but it doesn't have to
be. It is straightforward to calculate this thermal noise and it is a very
small number.  Any other input noise source is ignored so right away you
know that your real world QRN is going make things different. The job of a
sensitive receiver is to add as little noise as possible above and beyond
that of the signal source.  Receivers have many different sources of
internal noise, but an attempt is made to model them as a single equivalent
noise resistance.   One then matches the signal source resistance to this
equivalent receiver noise resistance in order to minimize the
figure-of-merit (Noise Figure, NF).  The match that minimizes NF is not
going to be the same match that transfers maximum power from the signal
source to the receiver.  The designer has to decide what he wants most.  If
you are building a crystal diode receiver (no active devices) you darn well
better be using maximum power transfer, but when active devices are
involved you have a choice. It's been said that gain is cheap so what
you're usually after is a good S/N ratio without compromising the dynamic
range.
Unless you live in a quiet location and spend most of your time on 10M and
above, shooting for a super low NF is not productive.  The one exception
would be the use of a small well-shielded receiving loop because these
loops have a very low output.

BTW, the math deals with power calculations and correlations between
different noise sources.  We use voltage as our representation because it
is more convenient, but noise power is where it's at.

There.  I think I have successfully added to the confusion.

Dennis AE6C

On Mon, Oct 20, 2014 at 12:14 PM, Leslie Smith <vk2bcu at operamail.com> wrote:

>   Hello Richard,
>   After reading your last posting, below, I'm trying to figure whether
>   you're a nice bloke (informative) or a nasty bloke (giving
>   mis-information)!
>   So I'm going to spend what spare time I have today thinking about the
>   impedance matching theorem, and how it relates to radio signals (that
>   transfer voltage not power).
>   It's a long time since I read about this, and anyway, I'm not sure I
>   every really understood the deeper meaning of the theorem.
>
>   I'm quite certain power stations don't dissipate 1/2 the power
>   supplied to the national grid!
>   If my memory is correct, at maximum power transfer, 1/2 the power is
>   dissipated in the generator!
>   I think your posting depends on similar thinking - the receiver is
>   interested in "seeing" voltage, not power.
>   But, if that's true, don't we want a good impedance match to get
>   voltage transfer?   (Hmmm .... tick, tick, tick)
>   (I should have listened more carefully in Physics 101).
>
>   73 de Les Smith
>   vk2bcu at operamail.com
>
>   PS.  I'm writing 100 times:  I must listen carefully in my physics
>   101.
>   I must listen carefully in physics 101 ...
>   I must not look out the window in physics 101.
>   I must not be distracted by beautiful women during physics lectures
>   ....
>   (Physics lectures were held just before lunch, and the building was
>   near the cafeteria.  All  the "girls" walked past the window.  Bad
>   planning, I think.)
>
>   (This is getting difficult ....)
>
>
> On Tue, Oct 21, 2014, at 05:37, Richard Knoppow wrote:
> >
> > ----- Original Message -----
> > From: "Fuqua, Bill L" <wlfuqu00 at uky.edu>
> > To: <kgordon2006 at frontier.com>; "ARC5"
> > <arc5 at mailman.qth.net>
> > Sent: Monday, October 20, 2014 10:10 AM
> > Subject: Re: [ARC5] Receiver input impedance...
> >
> >
> > >  Generally, impedance matching is not very useful at below
> > > 30 MHz, especially below 10 MHz due to the atmospheric
> > > noise. Any signal you can receive must be above the
> > > atmospheric noise.
> > > That is why ferrite antennas are just fine for AM
> > > broadcast receivers, but useless for transmission of
> > > signals. Reciprocity still applies it is just that you
> > > don't need much sensitivity at low frequencies.
> > > 73
> > > Bill wa4lav
> >
> >    Well again the important thing at the receiver is to
> > maximize the ratio of signal _voltage_ to noise voltage.
> > Power transfer is of little importance so impedance matching
> > is not very critical. Generally, if the receiver impedance
> > is higher than the source impedance of the antenna and
> > feeder it will be good for SNR. However its not a simple
> > relationship because part of the receiver noise is the
> > equivalent noise resistance. This is mostly generated in the
> > input device whether its a tube or solid state. This becomes
> > very important at frequencies much beyond about 30 mhz and
> > maybe below that too.
> >
> >
> > --
> > Richard Knoppow
> > Los Angeles
> > WB6KBL
> > dickburk at ix.netcom.com
> >
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