Logarithmic conformity of frequency weighted flip-flop logarithmic ratemeters for random pulses

Nuclear Instruments and Methods 178 (1980) 285-286 © North-Holland Publishing Company

LOGARITHMIC CONFORMITY OF FREQUENCY WEIGHTED FLIP-FLOP LOGARITHMIC RATEMETERS FOR RANDOM PULSES H.J. F R A S E R Australian A t o m i c Energy Commission, Research Establishment, Private Mail Bag, Sutherland, N S W 2232, Australia

Received 19 May 1980

Calculated errors from a true logarithmic law for frequency weighted flip-flop logarithmic ratemeters are presented. These ratemeters achieve an output that is proportional to the logarithm of input rate by summing the averaged outputs of a chain of N flip-flops which are all set by a common train of random input pulses and reset by different but related clock rates obtained from (+K) clock frequency divider circuits. Errors are given for frequency divider ratios 4, 8, 16, 32, 64 and for two to eight flip-flops.

1. Introduction

calculated errors and ranges which should be useful to designers of these logarithmic ratemeter circuits. The ratemeters discussed are unsuited to the measurement of regularly spaced pulses because it is possible to obtain slow variations in output if the input rate is close to any o f the clock frequencies, also the logarithmic law is not obeyed as it is for random pulses.

The frequency weighted flip-flop logarithmic ratemeter has been shown to be highly accurate [1]. It has the advantage over previous conventional designs that it may be constructed from standard integrated circuit (IC) chips; this results in a welldefined and designable mode o f operation. It also does not require matched resistor-capacitance time constants which is a drawback o f the multiple diode pump ratemeter, nor does it require low leakage components which are necessary in wide range logarithmic diode ratemeters. Calculated error curves have been published elsewhere [1] for the following parameters: K=2,N=15;

K=5,N=

2. Logarithmic conformity error The output voltage VOT of the ratemeter can be obtained from eq. (2) o f the ref. [1 ] and expressed as N 1 - e-K-nx roT= 1 K_nx , (1) n=l

where

10;

K= 10,N=6; K= 10,N=9; where K is the frequency ratio o f the dividers and N is the number o f flip-flops. Since 1974, a number o f complementary metal oxide semiconductor (CMOS) logarithmic ratemeters have been constructed at the Australian Atomic Energy Commission Research Establishment particularly for health survey and area radiation monitoring instruments; it has been recognized that larger division ratios (K > 16) can produce errors o f less than -+5.5% o f a decade which is acceptable for these instruments. A reduction in parts cost is also obtained as fewer dividers and flip-flops are required to cover a given range of rate as K is increased. One objective o f this paper is to present a table of

x=K

random input pulse rate lowest clock frequency to flip-flop "

The limits o f n have been changed from the original equation for ease in programming a calculator to produce the error results. Eq. (1) assumes that the flipflop supply rail is +1 V. The percentage error e is defined as the error in output voltage expressed as a percentage o f one volt; this is the full contribution o f one flip-flop stage and also the incremental output nominally produced b y a K-fold multiplication o f random input rate well within the normal range of the ratemeter. Therefore e% = (1OgKX --

[,'rOT

+A) X 100,

where A is the constant. 285

(2)

286

H.J. Fraser / Logarithmic ratemeters

We now arbitrarily set the error equal to zero for x = Xo = K (N+1)/2 as this rate is well within the nor-

mal range. From eq. (2)

K

A = VoT(Xo) -- (N + 1 ) / 2 ,

+

1-

N n=l

-+e%

(3)

where V o T ( x o ) is the output voltage for x = Xo. The complete expression for the percentage error then becomes

o : 00 ilo .

Table 1 Range of logarithmic ratemeters within stated error bands with K and N as parameters

1 1_:-)

Number of decades of range within -+e for N = 2

4 8 16 32 64

0.06 0.4 2 3.5 5.5

3

4

2.7 4.1 5.4

1.4 3.4 5.5 7.2

5

6

7

2.6 5.7

3.4

8 1.5

2.7 3.6

4.6 7

K-nx

1

(4)

Values o f e from eq. (4) were obtained from a Texas SR56 programmable calculator and the results plotted as error curves. The slope and position of the error curves, relative to the assumed e = 0 at x = Xo, were adjusted to obtain the best fit by inspection. This is equivalent to a slight gain change between VOT and the meter logarithmic scale together with an appropriate dc offset. The maximum error and the number o f decades of range within these error bands are given in table 1. The error bands in table 1 are chosen to enclose all of the deviations from a true logarithmic scale over the ranges indicated. Beyond the end points of these ranges small increments in range result in rapidly increasing errors.

3. Conclusion Table 1 shows that useful logarithmic ratemeters can be made with large values of K. For example, K = 64, N = 2 gives a range o f 3.6 decades within +5.5% error. To illustrate the economy o f design, this ratemeter can be constructed from just two CMOS chips comprising one CD4060 and one CD4013 and one operational amplifier. The performance o f any chosen combination of K and N not shown in table 1 can be evaluated from eq. (4).

Reference [1] H.J. Fraser, IEEE Trans. Nucl. Sci. NS21 (1974) 31.