Dynamic convergence of random scan multi-beam cathode ray tubes

Attainment of exacting dynamic convergence or beam registration is realized in a multi-gun, multi-colored cathode ray tube display system which maintains beam superposition across the display area of the cathode ray tube regardless of scanning direction or scanning rate. The system is particularly effective in maintaining exacting convergence in random scanned displays wherein scanning direction and scanning rates vary considerably. Inherent lag differences in convergence force fields as compared to deflection force fields is compensated and corrected by the summation of each of the horizontal and vertical scan signals with a signal representing the sign and magnitude of the rate of change thereof and with this summation being applied to convergence signal development circuitry rather than the scan signal per se being applied as in conventional known convergence systems.

This invention relates generally to cathode ray tube display systems and 
more particularly to an improved convergence system for a multi-beam 
colored cathode ray tube display. 
In the prior art, multi-beam cathode ray tubes, such as multi-colored, 
shadow-mask cathode ray tubes, provided useful display systems only when 
they were operated in a synchronously repetitive raster scan mode as 
exampled in the television industry. When employing shadow-mask cathode 
ray tubes to display graphical data, it became necessary to first write 
the graphical data into a memory and subsequently read that data from the 
memory in synchronism with the raster scan. This process was cumbersome 
and the displayed graphical data suffered in quality and resolution. 
Subsequently, as described in my U.S. Pat. No. 4,200,866, it was found 
that shadow-mask, multi-color cathode ray tubes might be employed in 
conjunction with a stroke writing display technique where X and Y 
deflection signals are generated to cause the beam to write as one would 
with a pencil, resulting in what might be termed a random scan display 
system, that is, the beam was caused to be deflected in any direction as 
one would write with a pencil and was not limited to the fixed scanning 
direction and rate defined by raster scanned displays. 
Some type of convergence system for the plural beams employed in 
multi-color, shadow-mask cathode ray tubes has always been necessary 
since, in order for the shadow-mask to perform properly in maintaining 
color registration, it is necessary that the simultaneously emitted plural 
beams impinge at the same spatial point or opening in the shadow-mask 
throughout the entire display surface, so that each beams is caused to 
fall on its predetermined adjacent phosphor color of a phosphor group or 
triad, thereby providing a selective multi-color display. In the 
television industry, convergence has long been employed by developing a 
convergence signal as a composite of signals derived from the respective 
horizontal and vertical sweep signals. A commonly employed method, for 
example, has been to apply representative horizontal and vertical scan 
signals to passive LC networks to develop, for convergence purposes, a 
signal approximating a composite of parabolic waveforms at the horizontal 
and vertical frequencies. Good approximations of these waveforms have been 
derived from the representative horizontal and vertical scan signals and 
applied to the beam convergence couplers of the cathode ray tube through 
suitable amplifiers and transformers. This has been possible since, in the 
raster scan display system employed in standard television, the scanning 
rates, both horizontal and vertical, are of known fixed values determined 
by the respective horizontal and vertical frequencies in the composite 
video signal. Since the directions and rates of the deflection scans are 
constant, convergence signals have been obtainable from relatively simple 
electronic operations on the respective horizontal and vertical waveforms. 
With the advent, however, of random scan (as opposed to raster scan) 
multi-color graphical data, as defined in my U.S. Pat. No. 4,200,866, it 
was discovered that a new form of dynamic convergence was necessary to 
maintain beam superposition across the display area of the cathode ray 
tube. It was discovered that the known convergence techniques function 
properly only when the beams were scanned in a single direction at a fixed 
rate (as in the raster scan display system widely employed theretofore). 
While improved dynamic convergence systems for color cathode ray tube 
displays, as described in Oswald U.S. Pat. No. 4,095,137, are designed to 
improve the convergence in a cathode ray tube display system employing a 
raster scan technique, it was found that even such a system, providing 
independent adjustment of the convergence of each beam within each of four 
quadrants of the display face independent of the other beams, did not 
achieve proper beam convergence throughout the display area on the face of 
the cathode ray tube when the beams were scanned in a random fashion as 
when stroke written imagery was displayed. 
Accordingly, the primary object of the present invention is to provide an 
improved dynamic convergence system for a multi-beam, multi-color cathode 
ray tube display system employing a shadow mask and upon which random scan 
display techniques are imposed. 
A further object of the present invention is to provide a dynamic 
convergence system for a multi-beam, shadow-mask cathode ray tube display 
system by means of which exacting convergence may be maintained without 
the restriction that the beams be scanned in a fixed direction at a fixed 
rate. 
The present invention is featured in the provision of the development of 
dynamic convergence signals for the plural beams of a multi-color cathode 
ray tube display system which is applicable whether the cathode ray tube 
display is raster scanned, random scanned, or alternately, both raster 
scanned and random scanned. 
A further feature of the present invention is the provision of a dynamic 
convergence or beam registration signal generation scheme for a cathode 
ray tube display system wherein the scan rate and scan direction are 
considered in the generation of the convergence or registration signals.

FIG. 1 depicts a mult-beam color cathode ray tube display system wherein a 
scan generator 10 develops horizontal scan signals 11 and vertical scan 
signals 12. Each of the horizontal (X) and vertical (Y) scan signals are 
applied through deflection amplifiers and lines 13 and 14 respectively to 
the deflection yoke 15 of a multi-beam color cathode ray tube 16. In 
addition, for the purpose of developing dynamic convergence signals, the 
horizontal scan signal 11 is applied as a first input to a dynamic 
convergence signal generator 16 and the vertical scan signal 12 is applied 
as a second input to the dynamic convergence signal generator 16. 
Convergence signal generator 16 develops plural convergence signal outputs 
17, 18, 19, and 20 for application to the convergence yoke 21 of the 
cathode ray tube 16 for the purpose of developing signal force fields for 
each of the red, green and blue beams associated with the cathode ray tube 
16 prior to main deflection of the beams by the X and Y deflection signals 
inputted to the deflection yoke on lines 13 and 14. The present invention 
is directed to an improved dynamic convergence signal generator 16 for use 
in the system generally depicted in FIG. 1. 
During development of the stroke written (random-scanned) shadow-mask 
cathode ray tube display system as defined in my U.S. Pat. No. 4,200,866, 
it was discovered that known convergent techniques function properly only 
when the beams were scanned in a single direction at a fixed rate. Since 
the present invention is primarily directed to the use of random scan 
techniques, known convergence techniques were found to be incapable of 
maintaining proper convergence control throughout the display area. To 
overcome this detriment is the subject of the present invention. 
In order to maintain proper convergence of multi-beam, shadow-mask cathode 
ray tubes, it is necessary to apply independent convergence 
(pre-deflection) force fields on each of the plural electron beams as 
described by the general equation (1) C=a.sub.1 +f(X)+f(Y)+f(XY), where 
a.sub.1 represents the static field to provide center-of-screen 
convergence, f(X) represents the lateral dynamic field, f(Y) represents 
the vertical dynamic field, and f(XY) represents the diagonal dynamic 
field. The terms X and Y in the general convergence equation of (1) 
correspond to the scan signals which develop the main deflection force 
fields. 
Now, because the dynamic convergence force fields are generally parabolic, 
and the dynamic deflection force fields are basically linear, the 
rate-of-change of force between the convergence and deflection fields are 
unequal. In fact, it was discovered that these rate-of-change inequalities 
caused the developed convergence force fields to greatly lag the 
deflection force fields at the extremities of the display area, and that 
the amount of lag was dependent upon scan rate (dX/dt, dY/dt), deflection 
direction, and beam position (X or Y). 
With reference to FIG. 2, current waveforms depicting those utilized to 
develop the deflection and convergence magnetic force fields in an 
electromagnetic deflection/convergence multi-beam cathode ray tube display 
system are shown. 
FIG. 2 illustrates a deflection current waveform 22 as an essentially 
linear function and a typical parabolic convergence current waveform 23. 
FIG. 2 illustrates that rate of change inequalities exist between the 
deflection and convergence fields as depicted by the respective different 
time rates of change of these current waveforms at a chosen point as 
defined by the dashed line 24. It is noted that, since the convergence 
current waveform 23 is parabolic in nature and the reflection waveform 22 
is linear in nature, the time rate of change of the convergence current 
(di.sub.C /dt) varies differently than the time rate of change of the 
deflection current (di.sub.D /dt). Further, the inequalities which exist 
between the deflection and the convergence fields is essentially dependent 
upon scan direction, scan rate, and beam position. With reference to FIG. 
5, the effect that these inequalities have on convergence in a multi-gun 
cathode ray tube was discovered by deflecting the red and green beams in a 
multi-beam colored cathode ray tube both to the right and subsequently, 
both to the left. A delta gun tube was utilized and FIG. 5 depicts the 
positions of the blue gun 25, the red gun 26, and the green gun 27. For 
purposes of the experiment, the red and green beams were scanned first in 
a direction from left to right as depicted in the uppermost portion of 
FIG. 5. It is noted that the beam trace 28 of the beam from the red gun 26 
(as depicted in dashed line in the uppermost portion of FIG. 5) 
illustrates convergence with the trace 29 of the green gun 27 (shown in 
solid line in the uppermost portion of FIG. 5) only in the central portion 
of the screen. It was further discovered that when the red and green beams 
were scanned in the opposite direction, from right to left, as depicted in 
the lower portion of FIG. 5, that the red beam trace 28' and the green 
beam trace 29' again experience convergence only in the center portion of 
the screen. However, in this situation, it is noted that the particular 
traces cross oppositely from that depicted in the upper portion of FIG. 5. 
Central convergence again was exhibited, but in this case, the red beam 
trace 28' appeared above the green beam trace 29' in the right-hand 
portion of the figure, with the opposite situation occurring in the 
left-hand portion of the figure. This phenomena illustrated that the 
direction of scan had an effect an convergence and that, due to the 
relative different positions of the red and green guns with respect to the 
resulting traces on the cathode ray tube face, the rate and direction of 
the scan which resulted in the traces had something to do with the 
convergence situation. Accordingly, utilizing the same convergence system, 
the rate of change of the horizontal scan waveform which was utilized to 
obtain the traces in FIG. 5 was obtained from differentiating the 
horizontal scan waveform, and this rate of change was added (summed) with 
the respective scan signal. When this rate of change (anticipation factor) 
was added to the scan waveform prior to application to the circuitry 
developing the convergence signals in the system employed, the 
misconvergence depicted in FIG. 5 was remedied for both left-to-right 
scans and right-to-left scans. 
Thus it was discovered that by predistorting the scan position signal with 
a signal representative of scan rate and direction prior to application to 
the convergence generation circuitry employed, precise convergence could 
be maintained at all positions on a cathode ray tube display surface 
regardless of scan rate or direction. As will be further discussed, the 
utilization of random scan display techniques on such a cathode ray tube 
results in scanning rates which vary considerably depending upon the 
particular direction in which the beam is scanned at any moment and thus 
it was surmised that stroke or random scan display techniques could be 
made possible and successful on multi-beam cathode ray tube display 
systems with precise maintenance of convergence. 
FIG. 3 depicts a typical deflection coil linear amplifier as it was 
utilized in the system, resulting in the waveforms depicted in FIG. 5. 
This same linear amplifier configuration was utilized to drive the 
convergence coils of the cathode ray tube employed. With reference to FIG. 
3 the signal input 30 is applied as input to an operational amplifier 31 
with the output 32 therefrom applied through deflection or convergence 
coil 33 and a coil current sensing resistor 34 to ground. Resistor 35 
between the output and input of the operational amplifier provides damping 
feedback, while resistor 36 applies the voltage developed across the coil 
current sensing resistor 34 as a stabilizing feedback to the input of the 
operational amplifier. If the input signal 30 is a deflection signal, the 
output is depicted as being V.sub.D =L(di.sub.D /dt)+i.sub.D R. With a 
convergence input signal, the output may be expressed as V.sub.C 
=L(di.sub.C /dt)+i.sub.C R. In either case, the Ldi/dt term developed 
across the deflecting coil 33 provides damping feedback stabilization. 
This same signal, however, inserts a time lag between the input signal 30 
and the developed output force field in the deflection or convergence 
coil. Since the convergence field is a parabolic of the deflection field, 
the convergence field exhibits a different lag than the deflection field. 
This phenomena may be examined mathematically as follows: 
Referring to FIG. 3, output deflection voltage may be expressed as: 
EQU V.sub.D =L(di.sub.D /dt)+i.sub.D R; (2) 
and, for a convergence input signal, the convergence voltage may be 
expressed as: 
EQU V.sub.C =L(di.sub.C /dt)+i.sub.C R. (3) 
The convergence signal current i.sub.C may also be generally expressed as a 
parabolic function of deflection current: 
EQU i.sub.C =a.sub.1 i.sub.D +a.sub.2 i.sub.D.sup.n. (4) 
Differentiating expression (4) obtains: 
EQU di.sub.C /dt=a.sub.1 (di.sub.D /dt)+a.sub.2 ni.sub.D.sup.n-1 (di.sub.D 
/dt). (5) 
Substituting the expression for di.sub.C /dt of (5) into (3): 
EQU V.sub.C =L[a.sub.1 (di.sub.D /dt)+a.sub.2 ni.sub.D.sup.n-1 (di.sub.D 
/dt)]+i.sub.C R. (6) 
Now, comparing the deflection voltage expression (2) with the convergence 
voltage expression (6), the bracketed time differential term of (6) is 
seen to increase with respect to the parenthetical term of (2) as the beam 
is scanned from the center to the edge of the display surface, and, since 
these terms define the respective lags introduced, the lag of V.sub.C 
varies differently than the lag of V.sub.D and the convergence force field 
exhibits a greater lag at the display extremeties than the deflection 
force field. 
In accordance with the present invention, the lag differential exhibited by 
the convergence force field is eliminated by applying a deflection scan 
vector term to the convergence signal development circuitry. Stated 
otherwise, the convergence lag is neutralized by adding an anticipator 
term to the convergence signal development circuitry to compensate for the 
inherent convergence signal lag. The anticipator term is the time rate of 
change of the scan signals employed in the system as generally depicted in 
FIG. 4. With reference to FIG. 4, scan signal 37, either horizontal or 
vertical, is shown as being applied through an operational amplifier 38 
and further through a differentiator 39 with scan signal at 40 and the 
time rate of change thereof at line 41 being applied to a summing network 
42 to develop an output signal 43 which may be expressed as V.sub.D 
+k(dv.sub.D /dt). In accordance with the present invention, this summation 
signal (the scan signal plus the time rate of change thereof) is applied 
to the convergence generation circuitry of the system, rather than the 
scan signal per se. 
It is to be appreciated that in a raster scan system, the scan rates are 
constant and thus rate taking of the scan signal prior to the development 
of a convergence signal as employed in the present invention may be 
compensated by a fixed system design. Referring to FIG. 6, there is 
graphically illustrated the variation in scan or deflection rates that are 
experienced in a random scanned system. Bearing in mind that in a raster 
scan system, the rate of change of the vertical deflection signal is a 
constant as well as that of the horizontal deflection signal, FIG. 6 
illustrates that an extremely wide variation of rates of change of 
deflection is experienced in a random scan system. FIG. 6 depicts 
graphically the center 44 of a cathode ray tube display face as defined by 
the X and Y axes of the display face. It is noted that the X deflection 
may vary from a negative value of X to zero at the center 44 to a positive 
value of X in the right-hand portion of the screen. Likewise, the vertical 
or Y deflection signal may vary from zero at the center 44 to a positive 
value at the upper half of the display face to increasingly greater 
negative values in the lower portion of the display face. Assuming a 
vector 45 is caused to be displayed on the cathode ray tube face, it is 
noted that the rate of change dY/dt of the vertical deflection signal is 
positive and is greater than the rate of change dX/dt of the horizontal 
deflection signal which is also positive. If the same vector is flipped 
over to be displayed as vector 46 in the lower right-hand portion of the 
screen, it is noted that the rate of change dY/dt of the vertical 
deflection signal is still greater than the rate of change dX/dt of the 
horizontal deflection signal, but in this case, the rate of change of the 
vertical deflection signal is a negative rate of change while that of the 
horizontal deflection signal dX/dt is a positive signal. Now referring to 
the display vector 47 in the upper right-hand portion of the screen which 
is depicted as being at 45 degrees from the X axis of the display, it is 
noted that the rate of change of the vertical deflection signal dY/dt is 
equal to the rate of change of the horizontal deflection signal dX/dt. A 
horizontal vector as depicted by 48 represents a positive rate of change 
of the X deflection signal while that depicted by vector 49 in FIG. 6 
represents a negative rate of change of the horizontal deflection signal. 
It may then further be stated that a display vector of less than 45 
degrees from the horizontal axis results in the rate of change of the 
vertical deflection signal being less than that of the horizontal 
deflection signal. Also depicted is a display vector 50 in the upper 
left-hand portion of the display screen wherein the beam is caused to go 
from a position X1 to a position X2 resulting in a positive rate of change 
dX/dt of the X deflection signal and that here the position X2 may be 
defined as -X.sub.1 + the integral of dX/dt(t). It is readily apparent 
then that in a random scanned multi-color cathode ray tube display system 
the sign of the deflection signals, the rate of change of the deflection 
signals and the sign of the rate of change of the deflection signals 
varies constantly as symbology is traced on the display faceplate. 
A simplified embodiment of the present invention, showing the signal flow 
for the corrected convergence implementation of a delta-gun cathode ray 
tube is shown in FIG. 8. With reference to FIG. 8, inputs 51 and 52 
represent the respective horizontal and vertical scan signals applied to 
the deflection coil amplifiers of a cathode ray tube. The horizontal scan 
signal 51, (designated X) is seen to be applied directly as an input to a 
linear amplifier 53 which develops a horizontal deflection signal for 
application to the horizontal deflection coil 55 of the cathode ray tube. 
Likewise, the vertical scan signal 52 (designated Y) is applied as an 
input to a linear amplifier 56 which develops an output 57 for application 
to the vertical deflection coil 58 of the cathode ray tube. The 
convergence circuitry in accordance with the present invention is depicted 
functionally in the lower portion of the diagram. Here the horizontal scan 
signal 51 is applied as an input to a differentiator 59 to develop an 
output 60 representing the time rate of change (dX/dt) of the horizontal 
scan signal. This rate signal 60 is applied as a first input to a summer 
61. A second input to the summer 61 comprises the horizontal scan signal 
51, such that the output 62 from the summer 61 represents the summation of 
the horizontal scan signal and the time rate of change thereof. 
Similarly, the vertical scan signal 52 is applied through a differentiator 
63 which develops an output signal 64 definitive of the time rate of 
change of the vertical scan signal. The vertical scan signal 52 and the 
time rate of change 64 of the vertical scan signal are applied as 
respecitve inputs to a summer 65 the output 66 of which comprises the 
summation of the vertical scan signal and the time rate of change thereof. 
Now in accordance with the equation (1) above, it is noted that the 
convergence signal is generally expressed as a summation of a function of 
X and a function of Y and a function of the cross product of X and Y. 
Accordingly in FIG. 8, the outputs from the two summation circuitries 61 
and 65 are utilized in place of the scan signals per se to develop a 
convergence signal of the form of equation (1) above. Output 66 of 
summation circuitry 65 is applied as respective first and second inputs to 
a multiplier 67 to develop an output 68 which may be expressed as 
(Y+dY/dt).sup.2. Similarly, the output 62 from summation circuitry 61 is 
applied as respective first and second inputs to a multiplier 69 to 
develop an output signal 70 which may be expressed as (X+dX/dt).sup.2. 
Additionally, output 66 from summer 65 is applied as a first input to a 
multiplier 71 and outut 62 from summer 61 is applied as a second input to 
multiplier 71 to develop a cross-product output which may be expressed as 
(Y+dY/dt)(X+dX/dt). The convergence signal here comprises the summation of 
the squares of the horizontal scan signal with anticipation, the vertical 
scan signal with anticipation, and the cross-product of these two signals 
each with anticipation. Thus outputs 68, 72 and 70 from multipliers 67, 71 
and 69 are applied as respective inputs to each of further signal summers 
73, 74, 75 and 76 with the output from summer 73 being applied to the red 
radial convergence coil 77, the output from the summer 74 being applied to 
the green radial convergence coil 78, the output from the summer 76 being 
applied to the blue radial convergence coil 79 and the output from the 
summer 76 being applied to the blue lateral convergence coil 80. 
Since the invention as thusfar described was implemented using a delta-gun 
shadow-mask cathode ray tube, where none of the three electron beams 
passes through the center of the main deflection force fields, the 
required convergence force field magnitudes are different for each 
quadrant of the display area. It was necessary therefore to separate each 
quadrant of convergence signal to achieve independent control for each 
quadrant of the display. The four quadrants of the display under 
consideration are depicted functionally in FIG. 7 wherein the general 
equation for convergence is expressed as C=a.sub.1 +f(X)+f(Y)+f(XY). FIG. 
7 depicts that in the upper right portion of the display screen both the X 
and Y deflection signals are positive. In the lower left quadrant of the 
display, both the X and Y deflection signals are negative. In the upper 
left-hand portion of the display area, the X deflection signal is negative 
while the Y deflection signal is positive, and in the lower right portion 
of the display screen, the X deflection signal is positive and the Y 
signal is negative. In the embodiment which was caused to be constructed, 
the general equation to describe the convergence for the random scan 
multi-beam cathode ray tube display may be expressed as follows: 
EQU C=a.sub.1 +a.sub.2 (X.sub.R).sup.2 +a.sub.3 (X.sub.L).sup.2 +a.sub.4 
(Y.sub.T).sup.2 
EQU +a.sub.5 (Y.sub.B).sup.2 +a.sub.6 (XY.sub.LB)+a.sub.7 (XY.sub.LT) 
EQU +a.sub.8 (XY.sub.RB)+a.sub.9 (XY.sub.RT) 
where 
X.sub.L =(X+k.sub.1 (dX/dt)) LEFT 
X.sub.R =(X+k.sub.1 (dX/dt)) RIGHT 
Y.sub.T =(Y+k.sub.2 (dY/dt)) TOP 
Y.sub.B =(Y+k.sub.2 (dY/dt)) BOTTOM 
FIG. 7 depicts four independent convergence signals, one for each of the 
four quadrants of display wherein it is to be noted that certain terms of 
the general equation expressed above are zero as determined by the 
polarity of the X and Y deflection signals. 
A specific implementation for a convergence system of a delta-gun 
multi-color cathode ray tube, taking into consideration independent four 
quadrant control, is depicted functionally in the block diagram of FIG. 9. 
With reference to FIG. 9, horizontal scan, signal 51 (designated X) and 
vertical scan signal 52 (designated Y) are again applied as respective 
inputs to the convergence signal development circuitry. The horizontal 
scan signal input 51 is applied through a differentiator 81 to obtain the 
time rate-of-change thereof, with a predetermined portion thereof as 
determined by potentiometer 82 being applied as a first input 83 to a 
summing circuit 86. The horizontal scan signal 51 is additionally applied 
through an operational amplifier 84 to develop an amplified scan signal 85 
as a second input to summing circuitry 86. The output 87 from summing 
circuitry 86 thus comprises the summation of the horizontal scan signal X 
and the time rate-of-change thereof. As above discussed, this signal 
polarity is dependant upon the particular quadrant in which the beam is 
located and the direction in which the beam is moving. The output 87 from 
summing network 87 is separated into quadrant-oriented signal paths by 
application thereof through diode members 88 and 90. The output 89 from 
diode 88 responds to positive output signals 87 from summer 86 and is 
designated X.sub.R corresponding to horizontal scan signal of a positive 
sign, corresponding to the right-hand portion of the display screen. The 
output 87 from summer 86 is also applied to an oppositely polarized diode 
90 to develop an output 91 corresponding to negative signals only, 
designated X.sub.L, corresponding to the left-hand portion of the display 
screen. It is to be noted that, in accordance with the present invention, 
each of the signals X.sub.R and X.sub.L corresponds to the summation of 
horizontal scan signal and its time rate of change. 
Similarly, in the lower left-portion of the diagram of FIG. 9, the vertical 
scan signal 52 is seen to be applied through a differentiator 92, with the 
output from the differentiator applied to potentiometer 93 to develop an 
output 94 comprising a selected magnitude of the time rate of change of 
the vertical scan signal. This time rate of change 94 is applied as a 
first input to a summing circuit 97. The vertical scan signal 52 is 
additionally amplified to an operational amplifier 95 to provide a 
deflection signal input 96 to summer 97. The output 98 from the summer 97 
comprises the summation of the vertical scan signal and its time rate of 
change. Output 98 is applied through a diode member 99 to develop an 
output 100 corresponding to positive signals only and is designated 
Y.sub.T since they correspond to vertical scan signals in the upper half 
of the display screen. Output 98 from summer 97 is applied to an 
oppositely polarized diode member 101 to develop an output 102 designated 
Y.sub.B, corresponding to negatively signed vertical scan signals 
experienced in the bottom portion of the display screen. 
In accordance with the present invention, the convergence signal comprises 
summations of the square of each of the horizontal and vertical scan 
signals along with the cross products thereof. For the four-quadrant 
independent arrangement depicted in FIG. 9, eight multipliers are employed 
for this purpose. Multiplier 103 is seen to receive signals corresponding 
to positively signed horizontal scan signals X.sub.R as respective first 
and second inputs to develop an output 111 corresponding to 
(X.sub.R).sup.2. Multiplier 104 receives X.sub.1 (negatively signed 
horizontal scan signal) as respective first and second inputs to develop 
an output 112 corresponding to (X.sub.L).sup.2. In the lower portion of 
FIG. 9, multiplier 109 receives positively signed vertical scan signal 
Y.sub.T as respective inputs thereto to develop an output 117 designated 
(Y.sub.T).sup.2 while multiplier 110 receives negatively signed vertical 
scan signals Y.sub.B as respective first and second inputs thereto to 
develop an output 118 designated (Y.sub.B).sup.2. The four multipliers 
105, 106, 107, and 108 centrally depicted in FIG. 9 develop the 
cross-product terms in accordance with the present invention. Multiplier 
105 receives X.sub.L and Y.sub.B as respective first and second inputs to 
develop an output 113 designated XY.sub.LB. Multiplier 106 receives 
X.sub.L and Y.sub.T as respective inputs thereto to develop an output 
signal 114 designated XY.sub.LT. Multiplier 107 receives X.sub.R and 
Y.sub.B as respective first and second inputs thereto to develop an output 
signal 115 designated XY.sub.RB. Multiplier 108 receives X.sub.R and 
Y.sub.T as respective first and second inputs thereto to develop an output 
signal 116 designated XY.sub.RT. The outputs from all of the multipliers 
are independently summed to provide a convergence signal for each of the 
four convergence coils associated with the cathode ray tube. Again, it is 
noted that, depending upon the quadrant within which deflection is being 
experienced, certain of these multiplier outputs will be zero. 
Accordingly, the outputs 111-118 of multipliers 103-110 are respectively 
applied through potentiometers to develop an output summation for 
application independently to each of the four convergence coil amplifiers 
of the display system. Output 111 from multiplier 103 is applied to a 
potentiometer 122, the output 123 of which corresponds to a.sub.2 
(X.sub.R).sup.2. Output 112 from multiplier 104 is applied to a 
potentiometer 124 to develop an output 125 corresponding to a.sub.3 
(X.sub.L).sup.2. Output 113 from multiplier 105 is applied to a 
potentiometer 126 to develop an output 127 corresponding to a.sub.6 
XY.sub.LB. Output 114 from multiplier 106 is applied to a potentiometer 
128 to develop an output 129 corresponding to a.sub.7 XY.sub.LT. Output 
115 from multiplier 107 is applied to a potentiometer 130 to develop an 
output 131 corresponding to a.sub.8 XY.sub.RB. Multiplier 108 develops an 
output 116 which is applied to a potentiometer 132 to develop an output 
133 corresponding to a.sub.9 XY.sub.RT. Output 117 from multiplier 109 is 
applied to a potentiometer 134 to develop an output 135 corresponding to 
a.sub.4 (Y.sub.T).sup.2. Output 118 from multiplier 110 is applied to a 
potentiometer 136 to develop an output 137 corresponding to a.sub.5 
(Y.sub.B).sup.2. In addition, as depicted in the upper portion of FIG. 9, 
a dc voltage source 119 is applied to potentiometer 120 to develop an 
output 121 corresponding to a.sub.1. 
The output convergence signal is obtained by a summation of the outputs 
from all the potentiometers of the summation network 140 (designated 
.SIGMA.) at common connection 139. This convergence signal is 
independently developed and applied to each of the convergence coil 
amplifiers associated with the cathode ray tube, only one of which is 
depicted in FIG. 9, comprising operational amplifier 141 and convergence 
coil 142. It is noted that with the arrangement of FIG. 9 independently 
adjustable convergence signals are obtainable independently for each of 
the four quadrants of display as depicted generally in FIG. 7. 
An implementation of the system functionally depicted in FIG. 9 is 
illustrated in block diagram form in FIG. 10 and schematically in FIGS. 
11, 12, and 13. With reference to FIG. 10, development of the squares and 
cross-products of the X and Y scan signals (each of which include rate 
enhancement) is again shown functionally on an independent four quadrant 
basis, where the algebraic sign of the scan signals is considered in 
developing the convergence signal which is applied in common to each of 
the convergence coils associated with the cathode ray tube. FIG. 10 
illustrates the X scan signal 51 being inputted to an X.sup.2 convergence 
signal generator 143. Signal generator 143 develops output signals X.sub.R 
on line 89, X.sub.L on line 91, +X.sub.R.sup.2 on line 111, -X.sub.R.sup.2 
on line 111', +X.sub.L.sup.2 on line 112, and -X.sub.L.sup.2 on line 112'. 
It may be noted that the X.sub.R.sup.2 and X.sub.L.sup.2 signals are 
outputted as both plus and minus polarities and, as before, the subscripts 
R and L refer to the right and left portions of the display screen 
respectively. In the lower portion of FIG. 10, the Y scan signal 52 is 
inputted to a Y.sup.2 convergence signal generator 144 which develops six 
output signals. Y.sub.B is outputted on line 102, Y.sub.T is outputted on 
line 100, +Y.sub.T.sup.2 is outputted on line 117, -Y.sub.T.sup.2 is 
outputted on line 117', +Y.sub.B.sup.2 is outputted on line 118, and 
-Y.sub.B.sup.2 is outputted on line 118'. As previously considered, the 
subscripts B and T define vertical scan signals in the respective bottom 
and top halves of the display screen. 
Cross-products of the X and Y signals on a four-quadrant basis are 
developed by four XY convergence signal generators 145, 146, 147, and 148. 
The X.sub.L output 91 from the X.sup.2 convergence signal generator 143 is 
applied as a first input to each of XY convergence signal generators 145 
and 146. The X.sub.R output 89 from X.sup.2 convergence signal generator 
143 is applied as a first input to each of XY convergence signal 
generators 147 and 148. The Y.sub.B output 102 from Y.sup.2 convergence 
signal generator 144 is applied as a second input to each of XY 
convergence signal generators 146 and 148. The Y.sub.T output 100 from 
Y.sup.2 convergence signal generator 144 is applied as a second input to 
each of XY convergence signal generators 145 and 147. Convergence signal 
generator 145 develops outputs 114 and 114' comprising respective 
oppositely polarized cross-products of X.sub.L and Y.sub.T, designated 
+XY.sub.LT and -XY.sub.LT respectively. Convergence signal generator 146 
develops oppositely polarized outputs 113 and 113' corresponding to the 
cross-products of X.sub.L and X.sub.B and designated +XY.sub.LB and 
-XY.sub.LB respectively. Convergence signal generator 147 develops 
oppositely polarized outputs 116 and 116' corresponding cross-products of 
X.sub.R and Y.sub.T and designated +XY.sub.RT and -XY.sub.RT respectively. 
Similarly, convergence signal 148 develops oppositely polarized outputs 
115 and 115' corresponding to the cross-product of X.sub.R and Y.sub.B and 
designated +XY.sub.RB and -XY.sub.RB respectively. The sixteen outputs 
from the convergence signal generators 143, 145, 146, 147, 148, and 144 
are applied to each of four signal summing networks designated .SIGMA. and 
identified by reference numeral 140. As in the system of FIG. 9, each of 
the summing networks 140 comprises a plurality of potentiometers by means 
of which levels of the signals making up the composite convergence signal 
may be individually and selectively adjusted. The outputs from the signal 
summers 140 are individually applied to each of the convergence coils 
associated with the cathode ray tube. Depicted in FIG. 10 are a red radial 
convergence coil, a green radial convergence coil, a blue radial 
convergence coil, and a blue lateral convergence coil. 
The X.sup.2 convergence signal generator circuitry 143 and the Y.sup.2 
convergence signal generator circuitry 144 of the system of FIG. 10 are 
comprised of identical circuitries as depicted schematically in FIG. 11. 
Circuitry of FIG. 11 accepts either the X scan input 51 or the Y scan 
input 52 and functions in either case to add the time rate of change of 
the scan input signal thereto to the scan input signal per se prior to 
utilization thereof in developing the convergence signal formulation. FIG. 
11 depicts the circuitry schematically, when utilized with the X scan 
signal input reference numerals, without parentheses, and when utilized 
with Y scan input signals, reference numerals are indicated 
parenthetically. Considering first the utilization of the circuitry with X 
scan input signal 51, the deflection signal is seen to be applied to an 
operational amplifier 84 to develop an output 86 which is a function of 
the X scan signal per se. Additionally the X scan input signal 51 is 
applied to a second operational amplifier circuitry 81 which develops a 
signal proportional to the time rate of change of the X scan signal. The 
time rate of change of the scan signal and the scan signal are added at 
common junction 86 and applied to a further operational amplifier to 
develop an output 87 which may, as previously discussed, carry either a 
positive sign or a negative sign. A stearing diode 88 passes positively 
polarized signals only to develop a signal on line 89 which is expressed 
as: 
EQU X.sub.R =X+k(dX/dt) 
Negatively polarized summation signals 87 are passed through stearing diode 
90 to develop an output on line 91 defined as: 
EQU X.sub.L =X+k(dX/dt). 
The X.sub.R output signal on line 89 is applied as respective first and 
second inputs to a four-quadrant multiplier 103 the output of which is 
passed through an operational amplifier 149 to develop an output 111' 
defined as -X.sub.R.sup.2. The output 111' is applied as input to a still 
further operational amplifier 150 to develop an output 111 defined as 
+X.sub.R.sup.2. 
In a similar fashion, the X.sub.L signals developed on line 91 are applied 
as respective first and second inputs to a four-quadrant multiplier 104 
which provides an input to an opertional amplifier 151 which outputs a 
signal on line 112' defined as -X.sub.L.sup.2. Output 112' is additionally 
applied as an input to a further operational amplifier 152 which develops 
an output 112 defined as +X.sub.L.sup.2. 
The circuitry of FIG. 11, as employed for the Y.sup.2 convergence signal 
generator 144 of FIG. 10 develops in response to the Y scan signal input 
52, output signals corresponding to Y.sub.T and Y.sub.B as well as 
-Y.sub.T.sup.2, +Y.sub.T.sup.2, -Y.sub.B.sup.2 and +Y.sub.B.sup.2, where 
Y.sub.T and Y.sub.D are each defined as Y+k(dY/dt). 
Now with reference to FIG. 10 the X.sub.R, X.sub.L, Y.sub.B, and Y.sub.T 
outputs from the X.sup.2 and Y.sup.2 convergence signal generators 143 and 
144 are shown to be applied in various cross-product combinations as 
inputs to XY convergence signal generators 145, 146, 147, and 148. Each of 
these XY convergence signal generators is comprised of identical circuitry 
as depicted schematically in FIG. 12. The X.sub.L, X.sub.R, Y.sub.T, and 
Y.sub.B inputs to the XY convergence signal generator circuitries of FIG. 
12 are outputted from FIG. 11 and these outputs are comprised of 
quadrantal polarized scan signals each having added thereto the time rate 
of change thereof. As utilized in the system of FIG. 10, the circuitry of 
FIG. 12 functions as XY convergence signal generator 145 when connected to 
receive inputs X.sub.L and Y.sub.T designated in FIG. 12 as inputs 1 . 
The cross-product permutations outputted from the circuitry of 12 when 
employed with inputs 1 are designated as outputs 1 . Similarly when the 
circuitry of FIG. 12 is utilized as the XY convergence signal generator 
146 of FIG. 10, inputs are designated 2 and outputs are designated 2 . 
When utilized as XY convergence signal generator 147, the circuitry of 
FIG. 12 receives inputs 3 and develops outputs 3 when utilized as XY 
convergence signal generator 148, the circuitry of FIG. 12 receives inputs 
4 and develops outputs 4 . The circuitry comprises a four-quadrant 
multiplier 145-148, the output of which is applied to an operational 
amplifier 153 which develops negatively polarized cross-product output 
permutations 114', 113', 116', and 115', depending upon the particular 
input signal pair applied. These negative output signals are applied to a 
further operational amplifier 154 which inverts the input thereto to 
develop positively polarized output signals 114, 113, 116, or 115 
depending upon the input signal pair applied. 
As is thus far discussed, the circuitry of FIGS. 11 and 12, as used in 
plural applications in the system defined in FIG. 10, develop the sixteen 
output signals depicted from the convergence signal generator blocks of 
FIG. 10. As previously discussed, these sixteen output signals are applied 
independently to each of four signal summation devices each of which 
develops an output signal for application to a particular one of the 
plural convergence means associated with the cathode ray tube. Summation 
devices designated by reference numeral 140 and the associated convergence 
coil drivers are identical in nature and depicted schematically in FIG. 
13. It is noted that each of the convergence coil drivers of FIG. 13 
receives the squared term signals developed in FIG. 11 and the 
cross-product signals from FIG. 12 as inputs to a plurality of 
potentiometers. Each of the squared terms and the cross-product terms is 
applied to an associated potentiometer, with the positive term being 
applied to one end of the potentiometer winding and its corresponding 
negatively polarized term is applied to the other end of the potentiometer 
winding, thus permitting a full range of adjustment of the output from 
that potentiometer about zero potential. The outputs from all of the 
potentiometers are summed in common junction 139 and applied to an 
operational amplifier associated with the coil driver, thus a full range 
of independent adjustment is permitted on a quadrantal basis for each of 
the plural convergence coils associated with the cathode ray tube. 
The present invention is thus seen to provide a means for exacting 
convergence adjustment for a particular cathode ray tube. The general 
convergence equation described herein is implemented in a four-quadrant 
manner which permits the tailoring of the composite convergence waveform 
to any particular cathode ray tube. The insertion of the scan rate and 
direction signals into the convergence system of the multi-gun cathode ray 
tube display system described herein achieves precise convergence 
regardless of position, rate or deflection direction of the cathode ray 
tube beams. Specifically, the invention relates to the development of 
convergence force fields which are a function of the X and Y scan signals 
and their respective time rate of change. Although described with respect 
to analog circuitries and implementation techniques, the invention is 
likewise applicable to digital or hybrid implementation techniques. 
Further, although the invention is described with respect to 
electromagnetic convergence and deflection techniques, it is equally 
applicable to electrostatic implementations and is further applicable 
whether or not the signals are quadraturized into their respective 
quadrants of the display and whether the quadrantization occurs before, 
after, or during convergence signal development. Although particularly 
applicable to random scanned displays wherein scanning rates exhibit a 
wide variation, the invention is applicable whether the display is raster 
scanned, random scanned or alternately both raster scanned and random 
scanned as is presently employed in display systems wherein for example a 
map-like presentation may be random scanned using stroke writing 
techniques and time shared with a raster scanned display of weather radar 
information. 
Although the present invention has been described with respect to a 
particular embodiment thereof, it is not to be so limited as changes might 
be made therein which fall within the scope of the invention as defined in 
the appended claims.