PB 161619

ZDoulder laboratories

^o. 118

A NOTE ON THE PROPAGATION

OF CERTAIN LF PULSES UTILIZED

IN A RADIO NAVIGATION SYSTEM

BY

J. R. JOHLER

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

technical <Vtcte

No. 118

A NOTE ON THE PROPAGATION OF CERTAIN LF PULSES

UTILIZED IN A RADIO NAVIGATION SYSTEM

by

J. R. Johler

October 27, 1961

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-1-

A NOTE ON THE PROPAGATION OF CERTAIN LF PULSES

UTILIZED IN A RADIO NAVIGATION SYSTEM

by

J. R. Johler

ABSTRACT

Low frequency pulses utilized in a radio navigation system can

be synthesized and analyzed by a specialization of the general theory

of pulse propagation. The analysis technique required to accomplish

such a research is detailed, and the introduction of receiver and

detector circuits into such an analysis is described. The time -difference dispersion correction, or the "discrepancy correction" for

operation of a radio navigation pulse system on either the groundwave time mode or the ionospheric time modes of propagation is

defined.

A NOTE ON THE PROPAGATION OF CERTAIN LF PULSES

UTILIZED IN A RADIO NAVIGATION SYSTEM

by

J. R. Johler

The interest in recent years in low frequencies (LF) has been

inspired by the development of the Loran-C (Cytac) [Frantz, Dean,

and Frank, 1957 ] and other [Schneider, 1955] [Ross, 1959]radio

navigation and/or timing systems. The high reliability and predictability requirements of such systems leads the researcher and

system designer quite naturally to low frequencies.

L1NE _0F — POSITION , At = CONSTANT

Figure 1. Radio navigator 1 s hyperbolic line -of -position.

The principle of radio navigation can be described by the line -of -

position, figure 1. A master transmitter, M, and a slave "transponder",

S, are separated by the length of baseline, d. , which is ordinarily a

b

constant. An observer, O, with a phase -difference indicator compares the phase of a signal transmitted to O directly (i. e. , a transmission with which the distance, d , is associated) with the signal m
-2-

received via the slave, S, (i. e, , a transmission with which the

distance, d, , the slave, S, and the distance, d , are associated), b s

If the phase-difference, Acj>, can be interpreted as a time, in microseconds, (t = 10 cj>/u> at a transmission frequency, f = oo/Zir) then the

time -difference, At, represents the phase measurement, or phase

lock, of the automatic system.

At = —^1— [d, L + d - d ] + C , (1) b s rn s

(where C is the slave (S) coding delay which is a system constant,

and r) /c is the reciprocal of the speed of light). The time difference,

At, as a constant, together with a constant baseline, d , describes a hyperbolic locus of points known as a line -of -position, figure 1. Two

such lines -of -position (which can be generated with the aid of one

additional slave) determine a navigation "fix". The transmission

over the distances, d, , d , d , is accomplished by use of LiF radio

b s m

wave propagation. It is therefore evident that the system designer

is interested in the L.F field, E(oj, d) volts /meter, and in particular

the phase of the field, arg E(oo, d), at frequencies, f = w/2tt propagated

over these distances. The existent Loran-C system employs the

ground-wave mode [Johler, Kellar, and Walters, 1956], [Johler,

Lilley, and Walters, 1959], [Johler, Lilley, and Walters, 19 60] for

transmissions over these distances to the exclusion of the ionosphere

modes. Special instrumentation which utilizes pulse techniques and

special radiated pulse signals, E(t' , d) volts/meter, which can be

readily tagged at a point-in-time where t' is reckoned locally from

the beginning of the pulse, t

1 = t - r\ d/c, is required to achieve the

ground-wave "phase lock" to the exclusion of the ionospheric modes.

Thus it is necessary to consider the influence of the conduction and
-3-

displacement currents in the ground, the curvature of the ground,

and the proximity of the source (induction and electrostatic fields).

It is, therefore, necessary to develop and apply a time correction,

t = t (d), for each distance transmission associated with the system,

c cThe time -difference equation is therefore corrected,

At = ^1 [± + d - d ] + t (d, ) + t (d ) - t (d ) + C (2) -— L b s mJ c b c s cm s ,

to describe the line -of -position with greater accuracy.

Recent proposals [ Doherty, Hefley, and Linfield, I960] have

suggested the employment of the world-wide Loran-C system to move

time around the world by means of such a "phase lock" to an accuracy

of one microsecond or better. The ability of the system to synchronize

to fractional microsecond precision, and the corresponding predictability of the ground-wave mode of propagation imply the feasibility

of this application, hence the notation: Loran-C radio navigation

timing system.

Since the Loran-C radio navigation system employs pulse

techniques, a discussion of the analysis procedures requires special

consideration of the pulse type transmission, E(t' , d) volts /meter.

The general approach [ Johler and Walters, 1959] was developed so

that the CW field, E(oo, d), could be related to the transient field,

E(t' d), and the source, F (t), by a direct evaluation of the Fourier

s transform integral,

00 00 E ( t «, d) = ~ { exp (ia)t») E (W| d) f exp (-iu>t ) F

fl (t) dt do

(3) -00 w

00 or E (tSd) = ~ I exp (icjt») E (w, d) F

g

(u>) doj . (4)

-00
-4-

The complex source function, F (t), introduced to simplify the

operational techniques of analysis, also provided a description of an

"ideal" amplitude envelope for the pulse, |E(t' , d)|, which was propagated simultaneously with the pulse.

The transform of the propagation medium, E(u), d) volts /meter,

is a very complicated function which has been extensively described

in the literature [Bremmer, 1949]. The transform is frequently

represented geometric -optically at LF, such that the total field,

E(oj, d), for the particular case of a vertically polarized dipole source

can be written as the sum of time modes [ Johler, 1961] of propagation, j = 0, 1, 2, 3 • • • , between the ionosphere and the earth,

P

E(w, d)= Y E (o>,d) , (5)

j=0

in which the zero order (j = 0) time mode, E (go, d), is the ground

o wave. Each time mode of propagation, j = 1, 2, 3 • • • or j ^= 0, is,

E.(w, d) = iwd D."

1 C exp (iutc

.) G

1

. G

r

. a. F. C. , (6)

j J J J J J J J

where,

C = I oib2 /4TTKd

3 = (io"

7

)/d, (I

Q

i= 1) (7)

and the local time for the ground wave, t

1

, is, o

t* = t-b , (8) o

b = ti^/c , ^j
-5-

where [Johler, Kellar, and Walters, 1956]

E (co, d) = JE (co, d) j exp [ -i(a)b -1- $ )] , (10) o o c

Q

where c is the speed of light, c ~ 3(10 ) meters /second, and r\ is

the index of refraction of air, T) ~ 1. 000338 typically, and similarly,

the local sky-wave time, or sky-wave delay, t' . (j = 1, 2, 3 • • • ) is,

t*.= t-b. , W J J

b = ti D/c, (j a 1, 2, 3«« ) (12)

J J

The quantity, b. - b, is frequently called the relative sky-wave delay,

figure 2 (relative to the ground wave). The physical length of the ray,

D., can be evaluated geometrically for a reflection at an altitude, h,

J above the surface of the earth of radius, a,

D. = 2j T(a+h) cos <j>. . - a cos t.] , (13)

where cj>. is the angle of incidence of the "ray" on the ionosphere and

T. is the corresponding angle of incidence on the Earth (the subscript

"j" reminds the reader that the equation refers to the particular time

mode under consideration). The angles, <$>. and T., are evaluated

quite simply from the geometry if

• x a -1 • 9 (14) sin <b. . = A. a sin -^-r- , K ^'

cos <|> = A

- 1 [a(l-cos 9/2j) + h] , (15)
sin t. = A." (a + h) sin 0/2j ,

cos t. = A." [a(cos 8/2j - 1) + h cos 9/2j) , J J 1 A. = [2a(a + h) (1 - cos e/2j) + h

2

] ,

(16)

(17)

(18)

where 8 is the angle at the center of the earth subtended by the distance, d, along the surface of a spherical earth, or, simply, d = a0.

t r The factors, G . and G ., refer to the transmitter and receiver

J J vertical antenna patterns respectively, and again the subscript, "j",

is employed to designate the particular time mode under consideration.

t r The vertically polarized Hertzian dipoles reduce to G . = G . = sin T..

Of course other antenna patterns can be introduced by these factors.

The factor, F. [Johler, 1961b], [Wait, 1958], describes the

antenna pattern corrections of the transmitter and receiver antennas

at grazing angles of incidence on the earth and the factor, C.,

describes the effective reflection coefficient for multiple hops or a

single hop between the ionosphere and the Earth [Johler, 1961b],

C, =

1 J'jTX cbr1

1 + A x

I

1 — J\ — X — J\ ^ X

(19) x =

A t = -R T

1 m mm

A- = R T -»- R T

Z e ee m mm

A, = R R

i em -T T + T T

ee mm em me

(20)

where Remand R are the ground-reflection coefficients for vertical
7-

and horizontal polarization and T , T , T , and T ,'are the c ee em me mm

ionosphere reflection coefficients [ Johler and Walters, I960] [ Johler,

1961c] [Johler and Harper, 1962].

Since plane -reflection coefficients, T, are employed in this type

of analysis, the convergence-divergence factor, <x, is necessary to

convert plane-reflection coefficients to spherical-reflection coefficients,

or from the view point of ray theory it is necessary to take account

of ray focusing by the ionosphere and a corresponding defocusing of

rays by the Earth.

As a consequence of the time modes,

p p 00 e (t», d> = y e

j

Wy d) = 2 -h j

exp ^y e

j

(a) » d> F

s

(w) **• j=o j=o -oc (21)

This merely represents the sum of separate Fourier integrals for

each time mode, separated in time by the sky-wave time -mode

delay, t

1 ., figure 2.

Figure 2.

80

129

160 240 320 400 480 560 640 720 800

DISTANCE d/j, STATUTE MILES

257 386 515 644 772 901 1030 1158 1287

DISTANCE d/j, KILOMETERS

Relative sky-wave delay for various model

ionosphere boundary emplacement altitudes, h.
d = 858 MILES

MICROSECONDS

d-v/O MILES

100 MICROSECONDS

-8-

d = 662 MILES

U|=2

Y MICROSECONDS

d = 512 MILES

T3 UJ

"5= 5

Ul v. T «» . \

^fe b

o lAnnnnmtaaAAPI1 lUffW^

a > O / ~ -o TIME

5-* -^ GATE" w

w

57 100 191

41

L

: Q

1 J"

J-' H=2

d=858 MILES

t' MICROSECONDS

d-^0 MILES

100

t

1 MICROSECONDS

H=2-

t

1 MICROSECONDS

(0) NIGHTTIME (b) NIGHTTIME (C) DAYTIME

Figure 3. Observations of time modes with the aid of pulses of

various lengths illustrating the separation of time modes

and the measurement of a point-in-time on the leading

edge of the pxilse with the "amplitude envelope minus the

derivative of the amplitude envelope" method, (August

1953, f = 100 kc/s).

The sum of the time modes is illustrated for various (Cytac)

Loran-C, Radio Navigation System pulses, figure 3. The undisturbed

form of the radiated pulse is shown by oscillograms which were made

at short distances. The action of the propagation medium is evidenced

by the complicated, multiple, superposed pulses observed at great

distances. Thus the oscillogram or amplitude -time function,

Re E(t' , d), observed at great distance, comprises the superposed

From the author' s personal notes on the 1953-1954 preliminary

testing of the Loran-C (Cytac) system.
-9-

time modes, E.(t' , d), j = 0, 1, 2, 3 ' ' ' , apparently added together

according to the complex field specification, E., of each and separated

in time by the sky-wave delay, t

1 ., of each time mode, j. The

approximate area in the amplitude -time plane occupied by each mode

of propagation is shown, figure 3. Areas of overlap in which both

constructive and destructive interference between cycles of the multiple

pulses produces notches and enhancements in the composite pulse

can be observed.

The instrumentation which has been developed for the Cytac and

Loran-C systems is quite capable of elegantly tagging cycles and

minute fractions of a cycle on each of the multiple pulses. The

envelope detector, in effect, forms the difference between the amplitude

envelope, |E(t',d)|, and its derivate, ; JE(t',d)|, and an elaborate

servomechanism seeks out a null point or zero crossing time for the

time -function, thus determining a time -root, T , of the differential

c equation, illustrated, figure 3,

F(t',d)=c

1 |E(t\d)| - c

2

-lrT |E(f,d)|=0, (22)

where c and c are constants which move the point-in-time which

is to be tagged on the oscillogram and which can be set by the operator

to pick out a particular point on the pulse. Both amplitude and time

(phase) can be measured at such a point. Additional techniques to

detect cycles and minute fractions of a cycle under the envelope on

the leading edge of a pulse have also been developed [Frantz, Dean,

and Frank, 1957], and the appropriate time-correction, t , of the

continuous wave, E(co, d), is appropriate in this case.
-10-

The earliest time-root, T = T (d), of this equation, F(t' d) = 0, c c constitutes the dispersion correction for the navigator 1 s line-ofposition (1, 2) for propagation via ionospheric modes, or

At = l± [D.(d

b

) + D.(d

s )-D.,dm) ]+Tc<db) + T

c (ds

)

- T

c (dm

1 + C

S . <">

The ground-wave mode is characterized by negligible dispersion

for the type of pulses employed, T (d) = t (d) + c, where c is a constant which becomes part of the coding delay, C , and of course, the

ray length, D.(d) = d, by definition.

The theory which can predict the behavior of pulses is, therefore,

an important adjunct to a system-prediction analysis. The radiated

field from a step or impulse -cur rent dipole source has been the subject of considerable discussion among theoreticians [ Johler and

Walters, 1959] since such functions are quite simple to evaluate.

Thus the field of a step-function dipole current source can be written

CO E(t*, d) = i f ]E(W| d)

] J

i sin [art* - tfj j

dco , (24) o

TT and the particular case of the ground-wave mode, writing (j) 1 = <j> - —

E (go, d) = |E (oj, d)| exp [ -i <j> 1 is illustrated, figure 4, (d = 1000

o o

L c statute miles). The impulse-source-current dipole (vertical polarization) reduces to the following simple formula,

E(t*,d) = ^ ^

]E(w,d) | jcos [cot* -»]} du . (25)
-11-

The results of a quadrature evaluation [ Johler and Walters, 1959]

[ Johler and Lilley, 1961] of this integral are also illustrated, figure

4, for the ground-wave mode of propagation.

t

1 1 r

VERTICAL ELECTRIC DIPOLE SOURCE

Ioi = l ampere meter (step function) d = 1000 miles

cr = 0.005 mhos /meter

£, = 15

Figure 4. The step and impulse -source current radiation

at a great distance from the source.

These pulses give physical insight into the propagation mechanism,

but are of little assistance to the system designer. More sophisticated

pulses must be developed mathematically and the transfer function of

the system equipment must be considered.

The finite bandwidth of a receiver or filter can be introduced,

equations (3 and 4), by a mutilation of the Fourier transform with

one or more frequency-selective networks. The intervals can then be

evaluated by quadrature methods [Johler and Walters, 1959]. In
-12-

principle, this simplifies the numerical problem of integration, since

the range of integration necessary to achieve convergence of the

integral, already limited by the propagation medium, is further

limited by the operation of the receiver transfer function or filter on

the pulse image. The generalized Fourier transform, for some complicated source function, can then be represented as follows:

f(co,d)= E(co,d) [f

Ssl^) + f Sj>2 ^) + "][^8l(w)f

r8 2^)---]. (26)

f ,(03) f (oj) • • • are source transforms which have been superposed

s, 1 s, c to determine some complicated waveform, f ,(<jj), f (co) ••• are

r, 1 r, d

transfer functions of the frequency-selective network which have

been introduced to mutilate the transform or, in effect, restrict the

frequency spectrum of the pulse.

The damped sinusoid, F (t) = exp (-vt), v = c, + ioo , where c.

s 1 c 1 is the damping and f = cj /2tt is the characteristic frequency, is a

more sophisticated pulse [ Johler and Walters, 1959] which has found

useful application to system studies. It is necessary, however, to

take into consideration the receiver or filter. Perhaps the simplest

case is the following series network:

o

1| r^nnp—

C L

R

The frequency response, f (s), s = iw, of this network can be written:

(A) s

8 + m8 + CL
-13-

The damped cosine source model [Johler and Walters, 1959],

exp (-vt), v = c + iw , c form, f(s), is as follows:exp (-vt), v = c + iaj , can be assumed in such a way that the trans

*(s)

(<* 4- P) a (s+vM8+a)(s+p)

(28)

or,

f(s) = off

A(s+v)

+

v a

- i A(s+a ) A (s+p)

where A is described by the determinant,

1 1 1

A =

and,

a -

v+p

ap

2L

v+a

a+p a+p

va

ap

(29)

R v

L CL

(30)

P = 2L CL

(31)

For the special case,
-14-

^

2

<

L ' CL

j3 = a * (32)

i. e. , a, and (3 are conjugate frequencies. This special case characterizes a "ringing" circuit as a result of the introduction of the oscillatory

terms with frequencies, Im a and Im (3 , which correspond to the resonant

frequency of the circuit. Exponential damping, exp (- R/2Ij), is also

introduced by the circuit. It can, therefore, be concluded that the

effect of a simple series -resonant circuit is the same as the sum of

three oscillatory waves as follows:

E(t«,d) = A E v

(t»,d) + B E a

(t»,d) + C E

3

(t»,d) (33)

where each wave is calculated by published [ Johler and Walters,

1959] quadrature methods at the following complex frequencies:

v = c, + iw

1 c

a = c, + iw

2 r

P

= C

3

" itJ r (34)

where,
-15-

c

2

= c

3 = 2L

R_

L CL

c

3 = 3

- A -* \ T. CL

U) R_ \2 _4_

L <* CL ft)

R ^ 2

< JL

CL

w =

r ft

2 , ±

CL (35)

The constants A, B, and C are defined as follows!

A=A-1 v(3 VCL a(3 af(3

B =A if" vQ

C =A -1

1 -

v(3

a]3 (36)
-16-

_j i i _i_ i.-

80 100 120 Time, t. Microseconds m

Figure 5. Comparison of the calculation of the pulse

observed through an infinite bandwidth receiver

with the calculation of the same pulse observed

through a finite bandwidth receiver, illustrating

the effect of 'narrow band" as compared with

"broad band" receiver.

The more complicated filters, f (<*>), are introduced as a

r mutilation of the Fourier transform, f(w, d), simply by complex

multiplication,

f(u>,d)= E(w ,d)f

s

(co)fr(u>) (37)

The filter transfer function, f (w), can be measured experimentally,

r preferably at precalculated Gaussian frequencies, co [Johlerand
-17-

Walters, 1959], suitable for quadrature methods provided that both

amplitude and phase are measured for each frequency. The Fourier

transform (37) can then be formed and the Fourier integral (3, 4) can

then be evaluated. The results of such a calculation are illustrated,

figures 5 and 6, for two damped sinusoids by a comparison of the

pulse in an "infinite" bandwidth receiver with a receiver of restricted

bandwidth and, as might be expected, the ringing of the filter as a

result of the oscillatory terms (33) is evident.

VERTICAL ELECTRIC DIPOLE SOURCE

f

c = 100 kc

c,* 2.5(10*) v = 0.005 mhos /meter d=50 miles

Time, t,' Microseconds Figure 6. Comparison of the calculation of the pulse

observed through an infinite -bandwidth receiver

with the calculation of the same pulse observed

through a finite -bandwidth receiver.

A useful model for the type of pulse normally employed in radio

navigation systems can be readily synthesized by superposition of

damped sinusoids. For example, the "classical" sine-squared pulse

can be evaluated by redefining the source function,
-18-

7

Re F (t) = exp (-c.t) sin u> t sin w t, Si (38) D c

or,

l 1 Re F

g

(t) = j exp (-c^t) sin u> c

t - % exp (-Cjt) sin (a> c + 2oo p

)t

- 4 exp (-c.t) sin (co - 2 oo )t , 4 P

1 c P (39)

or, the complex source function,

F

g

(t) = \ exp (-vt) - \ exp (-v^) - i exp {-vfl , (40)

can be employed for envelope synthesis, where,

v = c. + ico (as before)

v lie = c. + i (eo + 2 oo ) p

v,= c.+i(u>-2u>), (41)

2 1 c p

Typically, the radio navigation type pulse has a value for c of the

order of oo . It is quite obvious, however, that the transient field,

E(t' , d), for the damped sine-squared source-current pulse is merely

the sum of three waves calculated as previously described damped

sinusoids,

E(t'd) = -^E

v (t«,d) +^- E v (t«,d) + £ E

v (t*,d) .

1 C* (42)
-19-

3«i(r 9

UJ ?ii(r9

iTi >

1/1 iir» H1 o

>

III

-*r 9

1 a. -?xKT

9 <

-SilO"9

-4iKT 9

I6irs

I2xKT {

ITUJ BilO"

1 hi>

(/I 4»i<r' h

n

>

hin_>

i- -4x10-'

i a

:><

-8«K>-'

I2iI0- !

-I6iltr*

8x10-'

6x10"' in

crUJ

4*10-'

i i=hi 2x1ft- 1 niii

ii> II <ihi

-> -2x10-' K

1 a -4il0-' <

-6IKT1

-BiKr1

i i i - |E(t',d)l, THE AMPLITUDET 1 1 ENVELOPE OF THE

! 1 SIGNAL7

1 1

" Re E(t',d), THE SIGNAL- / 1 *^\ \\

/ 1 ^

TN/s

- / 1 \ 1 / J

\ 1 ^y \ \ \ \

/ \ "^ V.

^ \ / 1 / \ \ / 1 / \ I / \W 1

1 1 / y

/ V//

/ y

\y

d = 1000 MILES .

i i i

1

1 i 1 1 1 1 t'(/xsec)

1 1 1——

1

1 1 r

|E(t',d)|, THE AMPLITUDE ENVELOPE

OF THE SIGNAL 7

Re E(t',d), THE SIGNAL -\ /

a =0005 MHOS/m.

f2

= 15

fc

= 100 kc/s

c, = 10*

d = 50 MILES .

tVsec)

- |Fs

(f')|,

1 1 1 1 1 THE AMPLITUDE ENVELOPE OF THE

1 1 SOURCE

1 1 -

-

/A M M

x /

-

-

/ \ v

-

_ / C/^3 - \ \ / 1 1 l 1 1 I / \ \\ / / \ 1 / I 1 1/ M/ ^ v \ 1 y \ 1 \\ y

/ \ / '

d =

;

- Re Fs

(t)

1

, THE SOURCE CURRENT MOMENT

1 1 1 1 1 1 1 1 1

-

10 20 30 40 50 60 70 80 90 100 no

1 {fj. sec)

Figure 7. The damped sine-squared pulse, illustrating a radio

navigation system type of pulse with corresponding

amplitude envelope.
-20-

|E(l',d)|,THE AMPLITUDE ENVELOPE OF THE SIGNAL

ReE(t',d),THE SIGNAL

i (^sec)

I81IO-'. |E(t',d)|, THE AMPLITUDE r—

L ENVELOPE OF THE SIGNAL j—-rr „

ct =0005 MHOS/m

Vf c = IOOkc/s

C, = 3XI0 4

fp = 25 Kc/c

Re Ellld), THE SIGNAL

Figure 8. The damped sine -squared pulse, illustrating a radio

navigation system type of pulse with corresponding

amplitude envelope.
-21-

The results of a radio navigation system pulse synthesis are

illustrated for propagation of a damped sinusoidal sine-squared

source current to a distance of 50 to 1000 miles, figs. 7, 8. Both the

"oscillogram" or observed waveform, Re E(t' , d), and the synthetic

amplitude envelope, |E(t' ,d)|, are illustrated.

REFERENCES

Bremmer, H. , Terrestrial radio waves - theory of propagation,

(Elsevier Publ. Co., New York, N. Y. , 1949).

Doherty, R. H. , G. Hefley, and R. F. Linfield, Timing

potentials of Loran-C. Proceedings of 14th annual frequency

control symposium, Ft. Monmouth, N. J. , sponsored by the

U. S. Army Research and Development Laboratory (June I960)

(proceedings to be published).

Frantz, W. P. , W. N. Dean, and R. C, Frank, A precision

multipurpose radio navigation system, 1957 I.R.E, Convention

Record, Pt. 8, 79-120 (March 18-24, 1957).

Johler, J. R. , On LF ionospheric phenomena in radio navigation

systems, proceedings of AGARD meeting, Istanbul (October

I960), (to be published by Pergamon Press, 1961a).

Johler, J. R. , On the analysis of LF ionospheric propagation,

J. Research NBS 65D (Radio Prop. ) No. 5, p.. 507 (Sept. -Oct. 196lb)

Johler, J. R. , Magneto-ionic propagation phenomena in lowand very low-radiofrequency waves reflected by the ionosphere,

J. Research NBS 65D, No. 1, 53-65 (January-February 1961c).

Johler, J. R. , and J. D. Harper, Jr., Reflection and transmission

of radio wave at a continuously stratified plasma with a high

magnetic induction, J. Research NBS 66D (Radio Prop. ) No. 1 (January-February 1962) (in publication at time of printing).
-22-

Johler, J. R. , W. J. Kellar, and L. C. Walters, Phase of the

low radiofrequency ground wave, NBS Circular 57 3, U. S.

Government Printing Office, Washington 25, D. C. (June 26,

1956).

Johler, J. R. , and C. M. Lilley, Ground conductivity determinations at low-radiofrequencies by an analysis of spheric

signatures of thunderstorms, J. Geophy. Research 66, No. 10

(October 1961) (in publication at time of printing).

Johler, J. R. , C. M. Ldlley, and L. C. Walters, Low- and very

low -radiofrequency tables of ground wave parameters for the

spherical earth theory: The roots of Riccati' s differential

equation, NBS Technical Note No. 7, PB 151366, U. S. Dept.

of Commerce, Office of Technical Services, Washington 25,

D. C. (February 1, 1959).

Johler, J. R. , C. M. Lilley, and L. C. Walters, Amplitude

and phase of the low- and very low-radiofrequency ground wave,

NBS Technical Note No. 60, PB 161561, U. S. Dept, of Commerce, Office of Technical Services, Washington 25, D. C.

(June 1, I960).

Johler, J. R. , and L. C. Walters, Propagation of a groundwave pulse around a finitely-conducting spherical earth from

a damped sinusoidal source current, I. R. E. AP-7 , No. 1,

1-10 (January 1959).

Johler, J. R. , and L. C. Walters, On the theory of reflection

of low- and very low-radiofrequency waves from the ionosphere.

J. Research NBS 64D, No. 3 269-285 (May-June I960).

Ross, J. M. , Propagation field test, Appendix D (unci. ) Navigation, guidance, and control system for drone aircraft, 6th

quarterly progress report to U. S. Army Signal Research and

Development Laboratory, Ft. Monmouth, N. J. , (September - November 1959), Contract No. DA 36-039 SC-78020, Motorola,

Inc. , Scotsdale, Arizona.
-23-

Schneider, A. B. , Phase variations with range of the groundwave signal from CW transmitters in the 70-130 kc/s band,

J. British Inst. Radio Engineers 12, No. 3, 181-184 (March

1955).

Wait, J. R. , A. M. Conda, Pattern of an antenna on a curved

long surface, I. R. E. Trans AP-6, No. 4, 348-359 (October

1958).

U. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL RUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover.

WASHINGTON, D.C.

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Office of Weights and Measures. BOULDER, COLO.

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Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.