Keysight 53230 Frequency counter review and bug identification

[maxwell3e10]

Keysight 53230A frequency counter is not a new instrument, there are a few posts discussing it here and even articles published regarding its performance. Nevertheless there is no concise review.  I got it because of the time-stamping capability and here is a brief summary of performance and comparison with HP53310A Modulation domain analyzer.

53230A has time resolution of less than 20 psec. In fact, single edge timestamp RMS of its own 10 MHz reference signal is about 10 psec. It can record up to 1M timestamps at a maximum rate of 1 MHz (for a 10 MHz signal every 10th trigger is recorded). Frequency measurements can be made using either reciprocal method or resolution-enhanced "gap-free" continuous method. I put "gap-free" in quotes because it turns out not be exactly true. Problems with CONT method were pointed out in https://arxiv.org/abs/1604.05076. The counter also has an undocumented RCON method that uses back-to-back reciprocal measurements.

Simple comparison of resolution-enhanced frequency measurements between 53230 and 53310 for equal gate time show that 53230 is significantly worse (histograms have equal span)
However, one has to look more precisely at what constitutes one gate time. This can be done by applying a signal with a square-wave frequency modulation. As can be seen in the figure below, in 53230 only one point is affected by a sharp frequency jump, while in 53310 there are 3 points on the transition.
Making a histogram of such measurements one can determine precisely the weighting function used in resolution-enhanced frequency measurements, as discussed in https://www.eevblog.com/forum/metrology/hp53310a-and-other-counter-allan-deviation/msg2342007/#msg2342007. We see that the weighting function of the two instruments is the same, but 53310 extends over 3 gate time intervals, while 53230 extends only over one gate time.
This can be summarized by the following diagram
.
One can see that 53230 resolution-enhanced measurements are not exactly "gap-free" because the weighting function goes to zero at the edges. This adds phase random walk to the frequency measurements. To obtain optimal results resolution-enhanced measurements need to overlap, so their total weight after averaging subsequent points approaches "Pi" weight, as discussed in https://arxiv.org/abs/physics/0411227v2 So this, I believe, is the origin of poor performance of Allan deviation for CONT method.

To have a fair comparison of standard deviation of individual frequency measurements, one then has to use a 3 times shorter gate time on 53310 relative to 53230. With this scaling the performance of the two counters is then comparable. While '230 has a better raw time resolution, it can only perform time-stamp measurements at 1 MHz, vs. 5 MHz for '310. One can also obtain some improvement by performing linear fitting of the results of time-stamp measurements, which constitutes "Omega" counting method https://arxiv.org/abs/1506.05009  The improvement is supposed to be only sqrt(6.75/6) compared with truncated "Lamda" method, but is actually more than that. Time stamp measurements also allow one to directly look at oscillator phase time: and calculate the Allan deviation of the phase measurements. It starts to deviate from white noise and shows substantial drift at longer times even when the meter is timing its own reference signal (in this case internal high stability timebase)

In terms of user interface, 53230 is somewhat reminiscent of 3446x DMMs, but is not as refined. For example, chart mode can display only 100 points (!) while the histogram mode is limited to 1M points (both of these are much better on 53310). Also one cannot see statistics and histogram on the same screen. In terms of speed, 53230 cannot actually make frequency or time interval measurements as fast as 53310, only record time stamps which then require substantial offline processing afterwards. For example, to find cumulative phase one has to sum up individual time stamp measurements (corresponding to time between sequential triggers) with high precision. It is actually better to convert them to integer numbers using the counter bin size of 10ns/2048=4.88 psec. It would have been more efficient if those integers where reported by the meter, otherwise it is fairly slow to read out 1M double precision floating numbers.

So, in summary the performance of 53230 is somewhat disappointing. It has reasonably good performance metrics in terms of raw time resolution and timestamp speed, although both of these are exceeded by more specialized instruments. But for a general-purpose instrument simple frequency measurements and user interface could be improved.