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. 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.