Topband: Polarity and Phase

[Jim Brown]

On Wed, 14 Apr 2004 18:45:11 -0400, Tom Rauch wrote:

>I'm going to make one last comment on this because although I'm pretty busy
>this is really a fascinating thing for me also, and very difficult to
>understand!

No problem. When you have time to think about it, I'll try to help you
get your head around it. This is stuff that we in the pro audio world
have had to spend a lot of effort understanding thoroughly. The sound
spectrum covers nearly 10 octaves -- 160 through 10 meters is only 4
octaves -- so we have pay careful attention to the differences between
time, phase, and polarity. 

But here are some examples that might help. Consider a video camera
sending its broadband data down the 75 ohm transmission line to its
monitor. Let the transmission line be 300 meters long with a Vp of .66.
 There are an infininte number of frequencies in that signal, but sync
is down and white is up. If you invert the polarity (by adding an
inverting gain stage somewhere in the chain), sync and black goes up
and white goes down. ALL of the frequency content is inverted, but the
signal takes the same amount of time to get from one end to the other,
regardless of the polarity. And, of course, the video monitor would
have trouble syncing on the signal, but if it could (perhaps the video
and sync are transmitted separately and you only inverted the video),
the image would be negative.   

The entire signal at the far end of the line is DELAYED by 0.66 usec
(assuming Vp is constant with frequency). The phase difference between
one end of the line and the other will be different for each frequency
that makes up that video signal -- in fact, it will be directly
proportional to frequency.  But as long as the Vp is constant, the line
is terminated, (and the line loss is constant with frequency), the
waveform gets to the other end in without distortion. 

Consider a transmission line that is the delay line for a multiband
antenna array covering 160, 80, and 40 meters. If the line is 1/2 wave
(180 degrees) on 80, it will be 1/4 wave (90 degrees) on 160 and a full
wavelength (360 degrees) on 40. It's the same line, and the same Vp.
That's phase shift created by delay, and the phase shift is
proportional to frequency (and inversely proportional to wavelength).
In this example,  an 80 meter sine wave is, indeed, inverted from one
end of the line to the other.   

But if you create an inversion of the sine wave by inverting the
polarity (reversing the wires), a sine wave of ANY frequency is
inverted. To see this on a scope, of course, you need a sine wave that
is purposely distorted so that one side is slightly flat-topped. That's
how the pro audio guys keep track of polarity. 

And why do audio guys care?   For one thing, because most audio
waveforms are asymmetrical (remember the polarity flippers to get
another few % modulation of AM broadcast transmitters?), and some
asymmetrical waveforms sound different if the polarity of the system
(from recording to reproduction) is wrong in a good sound system. An
obvious example is a bass drum that sucks instead of kicks, but voices
and some musical instruments are also affected. 

But also because we have complex loudspeaker systems in living rooms,
churches, stadiums, theaters, and concert halls. These systems use
arrays of loudspeakers, we use delay systems (digital) to align
loudspeakers with each other, and to account for the acoustic time of
flight of sound through air.