SU1746357A1 - Device for measuring pulse width - Google Patents

Description

A booster is connected to the output of the first adder, the first oscillator of the control pulse, the input of which is connected to the switch output, and the output are connected to the inputs of the second generator of the control pulse, to the control input of the first control key, the input of the second inverter amplifier, the output of which is connected to the second input of the second adder, as well as the third block of amplitude ratios, the first input of which is connected to the output of the third adder through the first expander of the pulse duration, the second variable the resident, the second control key and the exponential amplifier; the second input of the multiplier is connected to the generator output of a linearly varying voltage through the amplifier; the control input of the second control key is connected to the output of the second generator of the control pulse, whose input is connected to the output of the first generator control pulse, and the second input of the third block of amplitude ratios is connected to the output of the second control key via the fifth pulse width expander, the first amplifier-inverter, input is connected to the output of the first squarer and an output - to an input of the first adder, the output of the first control pulse generator is connected with the control inputs of the pulse duration extender.

Other technical solutions with similar features have not been found in the patent and scientific literature. Indeed, although the blocks listed above, which are part of the proposed device, are known and used earlier, but in the proposed device, as a result of their new connection, they possess in aggregate new properties. So. for example, in a known device, the signal from the output of the adder is fed to the input of the extremum indicator, so that the position of the extremum determines the duration of the measured pulse. In the proposed device, by introducing a relationship block, one of the inputs of which is connected to an adder in a known device through an exponential amplifier and a control key, and the second through a multiplier, the second input of which is connected to an output voltage generator , the proposed device acquires a qualitatively new, previously unknown property — to use for increasing the accuracy of measuring the pulse duration not only the amplitude of the signal at the output of the adder, as It was

in the known device, but also to use the information contained in the ratio of the areas under the signals generated by the above method from the output

adder signal.

1 shows a block diagram of the device; 2-21 are timing diagrams showing the kind of transformations to which the distorted is subjected.

0 multiplicative noise pulse during the passage of various elements of the proposed device; Figures 22-33 show the dependences of the gain in the accuracy of measuring the pulse duration by the proposed device as compared with the known device on the signal-to-noise ratio; Fig.34-37 - typical implementations of the processes at the outputs of some blocks of the proposed device.

0 The device contains a switch 1. a control pulse generator 2, a linearly varying voltage generator 3 (GLINE), blocks 4, 16 and 21 of amplitude ratios, quadrants 5 and 23, amplifiers 5 inverters 6. 14 and 17, adders 7, 24 and 26, logarithmic amplifier 8, second control pulse generator 9, controllable extenders 10, 13, 15, 25 and 28 pulse widths (integrators), amplifier 11, controllable keys 12 and 19, multipliers 18 and 20, band-pass filter 22 , exponential amplifier 27. Position I of switch 1 corresponds to the operation of the device (with Merenii shiroko5 bandpass interference level) when the generator 2 a control pulse is triggered by the leading edge of the measured pulse. Position II of the switch 1 corresponds to the operation of the device (with a high level of interference) when

0 the control pulse generator 2 is triggered by a pulse synchronized with the leading edge of the measured pulse. When the device operates in mode II, it is most effective. The blocks forming the device are realized on the basis of standard radio engineering devices, elements and measuring devices manufactured using both the traditional element base and the element base of microelectronics.

The input terminal of the device through the switch 1, the first generator 2 of the control pulse, the generator 3 of the linearly varying voltage is connected to

5 first inputs of blocks 4 and 16 amplitude ratios, inputs of the third amplifier-inverter 17 and amplifier 11. The second input of the first block of amplitude ratios is connected to the input terminal through the second expander 13 of the pulse duration

and the first controllable key 12. The output of the first amplitude ratio unit is connected to the first input of the first adder through the first quadrant 5 and the first amplifier-inverter 6 connected in series. The second input of the first adder 7 is connected to the output of the second amplitude ratio unit 16, the second input of which connected to the output of the controlled key 12 through the third pulse-width expander 15, the second quadrant 23 and the band-pass filter 22. The first input of the third adder 26 is connected to the output of the first p The multiplier 18, one of the inputs of which is connected to the output of the third amplifier inverter 17, and the second through a logarithmic amplifier 8 with the output of the first adder 7. The second input of the third adder 26 through the fourth expander 25 of the pulse duration is connected to the output of the second adder 24, the first input which is connected through the second amplifier-inverter 14 to the output of the first generator 2 of the control pulse. The second input of the second adder 24 is connected to the output of the second quadrant 23. The output of the third adder 26 through an exponential amplifier 27 is connected to the input of the second control switch 19, the control input of which is connected to the output of the first generator 2 of the control pulse through the second generator 9 of the control momentum. The output of the second control key 19 is connected to the output of a fifth controllable pulse width expander 28 and the first input of a multiplier 20, the second input of which is connected to the output of amplifier 11, and the output of the multiplier 20 is connected to the block 21 via a first control extender 10 amplitude ratios, the second input of which is connected to the output of the p of the extender 28 pulse duration. The control inputs of the first control key 12, the expanders 10, 13, 15, 25 and 28 of the pulse duration are connected to the output of the first generator 2 of the control pulse. The measured value of the pulse duration, distorted by multiplicative interference, is the output value of a block of 21 amplitude ratios.

The device works as follows.

The pulse duration meter receives the additive mixture x (t) S (t} + n (t) of the pulse S (t) and the broadband jitter n (t). The measured pulse is distorted by parasitic amplitude modulation so that it can be described by formula

с / чл- fU0 + | (t), m 5 (g) - {0,, W

where Do is the amplitude of the undistorted part of the pulse; Ј (t) describes the random law of amplitude modulation and has a power spectrum concentrated in the frequency range - Q / 2; Q / 2, and the multiplicative distortions are assumed to be fast, so that Qru / 2rt 1. When the input signal exceeds a certain level (switch 1 in position I) or when a pulse synchronized with the leading edge of the measured pulse (switch 1 in position II) is received, the generator 2 of the control pulse generates the control signal X2 (t) (Fig. 2). ). The duration of the first positive pulse in the control signal is produced equal to the longest possible duration of the measured pulse T. The distance from the trailing edge of the positive pulse to the front face of the second (negative) pulse Tind is chosen minimal but sufficient to read the measurement results. Thus, Tind is the time of indication. The duration of the second (negative) pulse is chosen to be minimal, but sufficient to control the circuit blocks. In the initial state (before switching on the generator 2 of the control signal) the keys 12 and 19 are closed, the control signal at the inputs of the expanders 10,13,15,25 and 28 pulse durations, the input of GLINE 3, the generator 9 of the control pulse, the amplifier-inverter 14 is missing. When a positive pulse of the control signal X2 (t) appears, the key 12 opens and remains open for a period of time T, In this time interval, the pulse extender 13 and the bandpass filter 22 receive the additive mixture x (t) S (t) + n ( t). where S (t) is described by formula (1), a n (t) is a wideband interference. Band-pass filter 22 has a bandwidth equal to the Q / 2 band occupied by the power spectrum of the parasitic amplitude modulation of the measured pulse (1), and must provide the transmission coefficient K22. As a result, at the output of block 22, we have a signal

)

(2)

In this case, the signal (2) at the output of block 22 differs from the input mixture of the measured pulse and the additive noise x (t) only in that all spectral components of the additive noise n (t) suppressed outside

frequency band -Q / 2; Q / 2, and the amplitude is changed to K22 times.

The pulse width expander 13 is an integrator with a long time constant, at the output of which a signal is generated

t

X13 (t) / x (t) dt. (3)

about

Next, the signal xia (t) is fed to the first input of block 4 amplitude ratios, to the second input of which the signal xs (g) is output from the output of GLINE 3

xs (g) Csg. (4)

Thus, at the output of the amplitude ratio block, a signal X4 (t) is formed, equal to

X4 (r) jfx (t) dt / K3 r.

After squaring the signal X4 (g) by the quad 5 and passing through the inverter amplifier 6, the first input of the adder 7 receives the signal

hb (t) (t) dt / K3rf (6)

OU

where Kb is the gain factor of the amplifier - inverter 6.

The second input of the adder 7 receives the signal xie (g) from the output of the block 16 amplitude ratios, equal to

xie (t) x15 (t) / xs (t), (7)

where xs (t) is the output signal of GLIN 3 (4), and the signal xis (t) is formed from the signal X22 (t) (2) by squaring the quad squared 23 and then integrating the pulse width expander 15. In this way ,

X15 (t) / x222 (t) dt, (8)

about

but

t -i

xie (g) / x22 (t) dt / (K3 t) (9)

about

At the output of the adder 7, an output signal x (t) is formed, equal to the sum of the signals xv (t) i1b (g)

XT (t) - / x222 (t) dt / (K3T) - (t) dt / (Kr. Ooe

(ten)

Next, the signal x (t) is fed through a logarithmic amplifier 8 to one of the inputs of the multiplier 18, the second input of which receives the signal xi (t), formed by the amplifier-inverter 17 from the output

signal (4) CLAY 3. Thus, the signal xta (t) arriving at the first input of the adder 26 has the form t

5 xie (t) x222 (t) dt / (K3r) o

 x (t) dt / (K3r |. (11)

about

The other input of the adder 26 receives a signal x25 (t) from the output of the pulse width expander 25, whose input signal is the sum of the signal from the output of the square x2z (1)

x23 (t) x222 (t) (12)

15 and the signal xz (t) -Ki4, formed from the control signal X2 (t) by the amplifier-inverter 14, i.e.

X25 (T) / X222 (t)). (13)

20 °

The output signal x2b (t) of adder 26 is the sum of the signals xie (t) (11) and

X25 (T) (13)

g

25

thirty

X26 (T) (t) about 7G

-KzPP {/ x222 (t) dt / (K3r) o (t) dt / (K3rf}.

(14)

From the output of the adder 26, the signal (14) is fed to an amplifier 27 with an exponential dynamic characteristic, which forms the output signal x2 () of the form t

X27 (g) exp K27 X26 (g) exp {Kzj / (xZ22 (t) o -K14) dt - KZ T In {/ X222 (t) dt / (K3 T)

r

-K6 {/ x (t) dt / (K3T) 2}}, (15)

about

From the output of the exponential amplifier 27 to the subsequent blocks of the circuit, the signal enters through the control key 19, which opens with a delay of Ti T relative to the leading edge of the positive pulse of the control signal X2 (t), where TI is the minimum possible

duration of the measured pulse. The delay is provided by the fact that the generator 9 of the control pulse generates a control signal different from zero in the interval Hz T (Fig. 3).

The multiplier 20 forms the product X2o (t) of the signal хц (t) obtained from the output signal of the GLINE by the gain Kc times the amplifier 11 and the signal xtg (r) from the output of the key 19

X20 (r) xii (t) xi9 (g}

KzKtsgh 9 (g) .1y

v 0,. (sixteen)

In this way, the input signals of the X20Y IX19 (t) begin to arrive at the input of the integrators 10 and 28 after the time TL so that when Ti t T the signals are formed at the outputs of the integrators.

At the output of the integrator 10

 / X2o (r) dr; integrator output 28

X28 (t) JX19 () d G. T1

As a result, a signal is formed at the output of the relationship block 21

X2l (t) xio (t) / X28 (t). (19)

This signal depends on time only for t T. When t T, this signal is a constant value that is numerically equal to the measured value of the duration of the input pulse. If the output signal of the proposed device X2i (t) is expressed through the input mixture of impulse and interference x (t), then in the time interval from T to T + Tind we get

(17)

(18)

; ".

To / ,, fteiptajj Wt-t,)

tL 0

JUfMft X -, §

 l §zfL «f- | f rt

s sin (I.t. / g; 9.1, / i

rt, -Kjctt KfilnfajlJxft-l,) o Loo

 Ј "% fo / t fc ftJl / fo

. ".

Thus, X21 (T) is the measured value of the unknown duration of the input pulse.

After the end at time T of the positive impulse of the control signal X2 (t), the keys 12 and 19 are closed, the formation of the linearly varying signal GLIN 3 is stopped, and the negative impulse of the control signal at the time T + Tind is reset (zeroed), integrators 10, 13, 15, 25 and 28. Thus, the meter is brought to its initial state and is ready for operation.

The accuracy of the measurement of the pulse duration in the proposed device depends on the choice of the coefficients Кз, Кб, Кц, Ki4, K22 and К27, which determine the mode of operation of the corresponding units. Analysis of the measurement accuracy in the proposed device, as well as the results of the noise immunity theory, show that the greatest accuracy in measuring the pulse duration is achieved with the values of the coefficients ...

1746357

12

40

45 50

55

Кз о2 / К222; ;

K27 K222 / No,

where K22 is selected depending on the specific operating conditions of the meter in such a way as to coordinate the dynamic ranges of the input signal-to-noise mixture

and used typical blocks. Here cr is the average power (dispersion) of additive interference in the –Q / 2 frequency band; Q / 2, multiplicative interference, M0 is the one-sided spectral density of additive broadband noise.

Additionally, the operation of the proposed device can be done using the 5 time diagrams shown in Fig.3-21. For the sake of consistency, these diagrams are shown for the case of the absence of wideband additive interference, which in the proposed device is suppressed both by frequency filtering by block 22 at the input of quad, 23 and so by temporal averaging in expanders 10, 13,15 , 25 and 28 pulse durations (integrators), as well as the deactivation of 5 integrators 25 and 28 for the time Ti. Such suppression of broadband additive interference, as follows from the theory of potential noise immunity, reduces its effect on the accuracy of the pulse width measurement to the maximum.

Figure 4 shows (conditionally) the measured pulse (2) with a duration gi. Figure 5 presents (by a solid line) the signal at the output of the expander 13 of a pulse duration of 35 pulses with an accuracy of an amplitude multiplier. Here, the dotted line shows the linearly varying voltage produced by GLINE 3. FIG. B shows the result of dividing the solid line by the dotted line of FIG. 5. Fig. 7 shows (up to an amplitude multiplier) the result of raising the signal x-j (t) to the square by the square 5, and in Fig. 8 the signal hb (t) at the output of the inverter amplifier 6.

The output of the band-pass filter 22 (Fig. 9) differs from the input signal S (t), shown in Fig. 4, only in amplitude. FIG. 10 shows (up to an amplitude multiplier) the signal at the output of the quadrant 23 and the signal xi4 (t) at the output of the inverter amplifier 14. Figure 11 shows the signal X24 (t), which is the result of the addition of the signals x2zM and xn (t) adder 24. After integrator 25, the transformed signal with multiplicative interference is approximately as shown in FIG. 12. According to FIG. 1, the signal X23 (t) c of the output of the quadrant 23 is also fed to the pulse width expander 15, the output signal of which XIB (t) is shown in FIG. 13. In FIG. 14 shows the output signal xie (g) of the amplitude ratio block 16, which is the ratio of the signal xis (t) shown in FIG. 13 and the xs signal (O, represented in Fig. 5 by a dashed line. The output signal xt (d) of the adder 7 is equal to the sum of the signals xb (t) shown in Fig. 8 and the signal xie (t) shown in Fig. 14 , is shown (up to an amplitude multiplier) in Fig. 15. The output signal xs (t) of a logarithmic amplifier 8, obtained by logarithmizing the signal x (t), is shown in Fig. 16. The same figure shows (up to an amplitude multiplier) output signal XIT (inverter amplifier 17. The result of multiplying xie (t) signals xv (t) and xie (t) shown on 16 is shown in Fig. 17. Fig. 18 shows the result of summation by block 26 of signals X25 fr) shown in Fig. 12 and xn (t) shown in Fig. 17. Output signals of the exponential amplifier hat (t) and key X19 (t) are presented respectively in Fig. 19 and 20. At the same time in Fig. 20, the dotted line shows the output signal xn (g) of amplifier 11. Fig. 21 shows the output signal X2o (t) of multiplier 20. The total time axis is on all The drawings show how the timing of the operation of the circuit blocks is related in time. From the theory of potential noise immunity, it follows that in the absence of broadband additive interference, the ratio of the integrals of the signals X20 (t) and xi9 (t) formed by the ratio block 21 at time T is close to the duration of the measured pulse ru. Thus, the measured value of the pulse duration is the ratio of the areas under the curves shown in Figs. 21 and 20, respectively. In the absence of broadband interference, this is the area ratio, although close to the true value of the impulse duration Ti. but still somewhat different from him. The known device as the measured value of the pulse duration uses the position of the maximum signal X2b (g) at the output of the adder 26 (Fig. 18). Therefore, in the absence of broadband interference, the known device provides an accurate measurement of the duration. However, the known device for measuring uses only one sign of the signal X26 (t) - amplitude. The proposed device uses to refine the measurement also the area under the curves formed by blocks 19 and 20. Thus, in contrast to the known device, the proposed device for measuring the pulse duration uses two signs of the generated signal — amplitude and

area under the curves. The use of two signs in the proposed device, instead of one in the known, allows to increase the accuracy of measuring the duration in the presence of interference. In addition, the exponential

0, amplifier 27 substantially sharpens the peak of the generated signal in the vicinity of the true value of the pulse duration, as illustrated in Figs. 18-20. This aggravation also makes it possible to increase the accuracy of measurements. In the presence of broadband interference, the exponential amplifier also significantly sharpens the peaks of the output signal of block 26, due to the effect of interference. This is tantamount to expanding the spectrum.

0 interference As a result, integrators 10 and 28 more effectively smooth out (suppress) broadband interference. Therefore, in the presence of broadband interference, the accuracy of measuring the pulse duration in

5 the proposed device is always higher than in the known device. In the absence of broadband interference, the use of an additional feature (the area under the peak) and additional smoothing of the pulse, implemented by integrators 10 and 28, is unnecessary and does not improve the accuracy of measuring the pulse duration.

To confirm the efficiency of the device when measuring the pulse duration against the background of broadband interference, a comparative analysis of the accuracy of the pulse width measurement by the proposed device compared with the known device using the methods of mathematical modeling of both devices on a computer is performed. Figures 22-30 show the dependences of the relative mean square error of the measurement of the pulse width p V / Gu, where V is the average square error

5 measurements, from the value of the signal-to-noise ratio by power Q for two values of the ratio Ti / T 0.01 and Ti / T 0.1, three values of the ratio q (0.1; 1; 10) and three values of fi QrM / 2 n (// 10,

0 50, 100). When constructing a dependency, Gp T / 2 is assumed. In these drawings, the obtained experimental values of the normalized square error of measuring the pulse duration in a known device (A - at Ti / T 0.01; x - at Ti / T 0.1) and the proposed device (0 - at Ti / T 0.01; y - at Ti / T - 0,1).

For individual values of the parameters Ti / T, q, //, Q, the table shows the experimental values of the gain b -

(Vn is the average square of the measurement error in the known device) in the accuracy of measuring the pulse duration with the proposed meter as compared with the known device.

As can be seen from Figs. 22-30 and the table, the gain in accuracy of measuring the pulse duration can reach large values, for example, d 18.4 dB with a signal-to-noise ratio Q - 20 dB, T1 / T 0.01, q 0.1, / g 10i 5 16dBprT1 / T 0,1.d-0,1, / 100.

Figures 31-33 show the averaged (by the values of the ratio Ti / T 0.01; 0.02; 0.1) the experimental dependences of the magnitude of the gain on the signal-to-noise ratio. From the above results it can be seen that the use of the proposed device provides a significant positive technical effect. With large and moderate values of the power of the broadband interference. Even with very low power interference, for example, when the signal-to-noise ratio Q is 10-15 dB, the proposed device provides a gain in measurement accuracy of about 1 dB.

In order to further clarify the reasons for the gain in accuracy of the estimated duration in the proposed device compared to the known, consider the output signals of blocks 26 and 19 in the presence of wideband interference. Figures 34-37 show the experimentally obtained, in the process of modeling on a computer, the output signals of these blocks. The curves of FIGS. 34 and 35 correspond to a signal-to-noise ratio of 5 dB, and the curves in FIGS. 36 and 37 correspond to a signal-to-noise ratio of 10 dB. From the comparison of FIG. 18 and FIGS. 34 and 36, as well as FIGS. 19 and FIGS. 35 and 37, it can be seen how strongly the broadband interference distorts the output signals of the respective blocks.

Let us consider in more detail Figures 34 and 35, where the following notation is accepted: Gu is the true value of the pulse duration; t is the position of the maximum maximum of the output signal of block 26, which coincides with the position of the maximum maximum of the output signal of block 19; t is the output of block 21 calculated for the curves shown in these drawings. The value of r is the result of measuring the pulse duration in a known device; the value of t is the result of measuring the pulse duration in the proposed device with the same specific implementation of a random broadband interference. Directly from FIGS. 34 and 35 it follows that the measurement error

(t - gi) in the proposed device is significantly less than the measurement error (t - gi) in the known device. Indeed, the known device is not

during the measurement, it takes into account no signs of the signal at the output of block 26, except for its amplitude. At the same time, in the proposed device, in the process of integration, blocks 10 and 28 additionally smooth the curve x0 (g) (Fig. 35). Taken together, there is a gain in measurement accuracy. Indeed, on the curve of FIG. 34, at the point t, the output signal of block 26 slightly exceeds the signal,

5 for example, at point r, which is substantially closer to g than r. However, the known device records the position of point r and takes this value as the measured value of the pulse duration,

0 regardless of the presence of other pulses. The proposed device analyzes the entire signal at the output of block 19 in more detail, which makes it possible to increase the measurement accuracy.

5 Fig. 36 and 37 show a specific type of signals at the outputs of blocks 26 and 19, respectively, for a signal-to-noise ratio Q -10 dB. From the comparison of Figs. 34 and 35 and Fcg.36 and 37, it can be seen that with an increase in the signal-to-noise ratio, the output signals of these blocks become more rugged. Again, from the analysis of the curve in Fig. 37, it follows that the measurement error () of the pulse duration in the known device is substantially

5 is larger than the measurement error (t - g) in the proposed device.

Claims (1)

Apparatus of the Invention A device for measuring the pulse duration, comprising a switch, 0 two control pulse generators, linear voltage generator, multiplier, three controlled pulse extender, quad, amplifier-inverter, two adders, amplifier, 5 two controllable keys, a bandpass filter, an exponential amplifier, the first amplitude ratio block, the first input of which is connected to the output of the first controlled pulse width expander, 0 the first input of which is connected to the output of the first multiplier, the first input of which is connected to the output of the second controlled key, and the first input of the third controlled extender of the duration 5 pulse, the output of which is connected to the second input of the first amplitude ratio block, the output of which is the output of the device, the first input bus of which is connected to the first input of the switch and the first input of the first control key, the output of which is through the series-connected band-pass filter, first quad , the first adder, the second controlled expander pulse duration, the second adder, an exponential amplifier connected to the first input of the second controlled key, the second input of which is connected to you the second generator of the control pulse, the input of which is connected to the second inputs of the first, second and third controlled pulse extenders, the second input of the first controlled key, the output of the first generator of the controlled pulse and the generator of the linearly varying voltage, the output of which through the amplifier is connected to the second input of the first multiplier, the second input bus is connected to the second input of the switch, the output of which is connected to the input of the first generator of the control pulse, the output The first inverter amplifier is connected to the second input of the first adder, characterized in that, in order to improve the measurement accuracy of the pulse width, distorted by parasitic amplitude modulation under the conditions of additive broadband interference of high and moderate power, two blocks of amplitude ratios are entered into it, controlled pulse width extender, the second quad is a two inverter amplifier, the third adder, a logarithmic amplifier, 1g, multiplier multiplier, the second input of which is connected to the output of the transducer The second inverter amplifier, whose input is connected to the second inputs of the second and third amplitude ratio blocks and the generator output of a linearly varying voltage, the output of the third amplitude ratio block through a series-connected second quadrant, second amplifier-inverter, third adder, logarithmic amplifier, second multiplier connected to the second input of the second adder, the output of the first controlled key is connected to the first input of the fourth controlled expander pulse width, the second input to torogo connected to the output of the first generator yn. equalizing pulse, the input of the first inverter amplifier, the second input of the fifth controlled pulse width expander, the output of which is connected to the first input of the first adder, the output of the fourth controlled pulse width extender connected to the first input of the third amplitude ratio unit, the output of the fifth controlled the pulse width expander is connected to the first input of the second amplitude ratio block, the output of which is connected to the second input of the third adder. W) Fig 2 V B Fig.Z B g Fig4 FI.5 t g W) Hnm FIG. 7 Mr. T  t FIG. eight T t Fig.9 /, j / Wi about yu FIG Xx FIG & g TL FIG. TO H ®К / 7 Fig 18 or G -AND rttti Vui.HI No g,  / Fig. 21 g g g g FIG. 20 G0 G -thirty th -is th -5О 3Fig.gy -20 -15 -10- Shy ° 5W Q5 iO UAS AS -JO -20 -15 -10 -EfmO5 iO im   - -tqbff 5 -35  20 15 -i0Vut.B5 ° -58 -20 -15 -10-Зфм О5iO QM 510 fa  fs -10 WH -20 -15 -10 -5 m 0 FIG. 29 s 10 or 6 iO Q. & s fin CO CO J $ & fc1 "four ABOUT -20 -15 10 -50510 Q4S lPt / hL and Ab 20 -15 -10 -5О Fig.ZZ Yu Q & "Vi t i fc to YU "MX