Page 500 - Instrumentation Reference Book 3E

Digital frequency and period/time-interval measurement 483

counters often employ both methods, using the
Narrow Wide hysteresis
conventional method to obtain the high reso-
lution at high frequencies.
The period, TI, of the input wave is calculated
from
1
--JFxArL T.--= Gating period
f; Number of cycles of input waveform
1-
\ \ / Iz,,c x 10-7
-
False countscaused by -
noise I11
(a) with a relative resolution of kl in nose.
The accuracy of frequency counters is limited
Measured
by four factors. These are the system resolution,
and trigger, systematic, and time-base errors.
Hysteresis t Trigger error (TE) is the absolute measurement
band error due to input noise causing triggering which
is too early or too late. For a sinusoidal input
waveform it is given by
Pulse
duration 1
(b) TE = -f- (input signal to noise ratio)
Figure 20.76 (a) The use of hysteresis to reduce the 76
effects of noise; (b) timing errors caused by hysteresis. and for a non-sinusoidal wave
Peak-to-peak noise voltage
of cycles of the input waveform. The frequency of TE=& Signal slew rate
the input waveform is thus calculated as
Systematic error (SE) is caused by differential
Number of cycles of input waveform propagation delays in the start and stop sensors
A= Gating period or amplifier channels of the counter; or by

Ili errors in the trigger level settings of the start
= - 10-7 H~ and stop channels. These errors can be removed
x
%SC
by calibration. The time-base error (TBE) is
caused by deviation on the frequency of the
The relative resolution of the reciprocal method is crystal frequency from its calibrated value. The
- lo-’
10-7 -*-=*- 1 causes of the deviation have been considered
above.
Gating time f, nose The relative accuracy of frequency measure-
ment is given by
independent of the input frequency, and thus it is Resolution of J; TE
possible to provide high-resolution measurements f - i Relative TBE
for lowfrequency signals. Modern frequency .A ts

Table 20.10 Quartz oscillator characteristics
Stnbilitji against Uncoipipensated Twiperatuw Oven
coinpensated stabilized
Aging: E4 h n.a. n.a.
lmonth <5 x 10-7 <I x 10-7
/year <5 x 10-6 <I x 10-7
Temperature: 0-50°C ref. to f23”C <I x so-5 <1 x 10-6
Change in measuring and supply mode: <3 x 10-7 <5 x 10-8
linehnt. battery/ext. D.C. 12-26V
Line voltage: &IO% <1 x 10-3 <i so-9 <j x
Warm-up time to reach within lo-’ of final value n.a. n.a <15min
~~
-‘:After 4S h of continuous operation.