From: "Joel Kolstad" on Tues, Nov 29 2005 6:53 pm

"Scott" wrote in message

Wouldn't it be easier to use a frequency counter? If one is not available,
but a general coverage HF receiver or transceiver with a digital readout is
available, you could zero beat the oscillator, note the reading on the
display, cause the oscillator to shift to your other frequency, zero beat
that signal, note the display reading and subtract to find the difference in
frequency.

I'm told that 'zero beating' typically has accuracy not much better than some
tens of Hz due to the limited lower frequency response of the human ear... has
anyone tried zero beating a signal from above and below and taking the average
to get what might be a more accurate frequency estimate?

On zero-beating very low beat rates: The only perceived problem is
the stability of the receiver and manual control of finding an
"exact" zero-beat. Other than that, cranking up the audio level
will let you know - by the background hiss intensity changes
during zero beat - when the zero point is reached. With manual
tuning and a crystal-controlled BFO that could be done to about
+/- 0.1 Hz if the receiver is kept at an even temperature and
power line voltage kept stable. [the metrologist's patience is a
factor there as well]

There is a problem with modern receivers using PLL or DDS sub-
system tuning: The resolution of the control system (typically 10
Hz on HF receivers). That limits the precision of zero-
beating...unless the beat difference itself is measured with a
counter.

"Time interval averaging" has been used for 3 decades in frequency
and time interval counters to increase accuracy limits caused by the
+/- one count on the display. Statistically, that can be improved
by a factor of the square-root of the number of times it is
measured. For example, taking the square-root of 100
measurements will increase the accuracy by 10 times; 10,000
measurements will increase by 100 times, etc. That averaging is
automatic on base ten displays in modern frequency counters
made since the 1970s.

Example of determining accuracy of frequency standards beat against
WWVB on 60 KHz: An early H-P WWVB receiver and strip-chart
recorder read-out for phase difference against WWVB. A nice little
overlay scale was provided to lay on the strip-chart recording.
Find the slope of the phase comparison plot on the overlay and
determine the error of the local standard down to Parts Per Billion
no problem. [extreme example of "low-frequency" zero-beat...:-)]



Two years in Standards Lab at Ramo-Wooldridge Corp. in early 1960s.