Desarrollo experimental

The effect that the parasitic capacitance between the two pixel electrodes has on the converter circuit can be estimated in a similar way to the effect of capacitor ratio errors considered earlier. The way in which this capacitance introduces an error into the final converted voltage can be illustrated with reference to Figure 6-44. During the conversion, when the transistor T% is turned off the voltage V2 should remain constant. However the presence of the capacitance Cc between the two halves of the converter couples any changes in the value of Vj onto the second pixel, thus changing the value of V2. The errors caused by Cc can be quantified by determining the equation for V2 which is iterated during the conversion. For simplicity it is assumed that the transistors are ideal switches with no parasitic capacitance and that the capacitances of the two halves o f the pixel are equal.

Column Gate 1 T T. Gate 2 J T V V

Figure 6-44 Pixel equivalent circuit including capacitance between two half pixels

Consider the operations during one cycle of the conversion from the point at which T% has just turned on. The voltages on the two pixel capacitors are initially equal with a value of V2(i-1). The first capacitor now charges to the voltage representing the next bit of the input data Vi(i). The change in voltage on the first capacitor is coupled onto the second by Cc so that the new value of V2, V2*, is given by the expression below.

C r

C c + C 6-24

Next T1 turns off and T2 turns on so that charge sharing takes place between the two pixel capacitors. The resulting voltage, V2(i), can be calculated using the conservation of charge.

M 0 2 C = ( F z f i - V + { V , ( i ) - V 2 ( i - V ) - ^ 1 c + F ; ( 0 C 6-25

V C r + C J

VzU) = V , ( i Ü 1 + 7 T ^ + V 2 { i - V i

C^ + C y ^ Cr + C> 6-26

The pixel voltage at the end of N conversion cycles can be derived by considering the effect o f iterating equation 6-26 and is given by the equation below.

- I ; 6-27

/ = ]

^CI =

= 1 +

The presence o f capacitance between the two halves of the pixel affects both the gain and the linearity of the conversion. The differential non-linearity can be calculated for a 6-bit conversion using the equation below.

D NL = ^---—---- j —,--- 1 6-28

Mi'"»)

Figure 6-45 shows how the differential non-linearity varies with the ratio of the capacitance between the two half pixels to the capacitance of one half pixel. As the ratio o f the capacitance between the half pixels to the pixel capacitance increases, so does the non- linearity. In order to improve the performance of the converter pixels it would therefore be possible to increase the value of the pixel storage capacitor or to reduce the value of the stray capacitance between the pixel electrodes.

Increasing the value of the storage capacitor is undesirable since the larger capacitor will occupy a greater fraction of the pixel area reducing the aperture o f the display. The higher capacitance would also increase the charging time required by the pixels. The capacitance between the two pixel electrodes can be reduced by increasing their separation. Figure 6-46 shows schematically the arrangement of the electrodes within the display in cross section and plan views. The capacitance between the two pixel electrodes has been calculated using a layout simulation program “Fasterix”^^^''''’®

■c o (U I c o c o Q 0.01 0.0001 0.001 0.01 0.1 R o lio c y c

Figure 6-45 Variation of differential non-linearity with pixel coupling capacitance

g l a s s s u b s t r a t e ITO c o m m o n e l e c t r o d e cell s p a c in g p ix el s e p a r a t i o n g l a s s s u b s t r a t e ITO pixel liquid c ry s ta l la y e r ITO pixel

F igure 6-46 C ross section and plan views of pixel used for cap acitance calculation

The variation of capacitance with electrode spacing is shown in Figure 6-47 and this can be used to calculate the spacing required to achieve a differential non-linearity o f less than 0.5LSB. The value of C JC required is determined from Figure 6-45 and is < 0.009. The capacitance of the half pixels in the second generation design is approximately 0.65pF therefore the value of Cc should be less than 6fF. Using the results shown in Figure 6-47, the gap between the two electrodes should be greater than approximately 12pm. Such a large separation is undesirable due to its impact on the displays aperture if the gap has light masking and its impact on the displays contrast if the gap has no light masking. Increasing the separation of the electrodes therefore looks unattractive as a method of reducing the differential non-linearity. M 0) TJ 2 "o CD CD c 0) Q) "q5 X I CD O c g o o Q _ O Ü 15 14 13 12 10 9 8 7 6 5 4 3 2 0 8 12 14 16 0 2 4 6 10 18 20

Gap between ITO electrodes (urn)

Figure 6-47 Variation o f pixel coupling with electrode separation

Errors in the capacitance of the two half pixels and the presence of the capacitance between the two half pixels both have the same effect on the performance o f the converter. It is therefore possible to compensate for the capacitance between the pixel electrodes by deliberately introducing a difference in the values of the pixel capacitors. To establish the required pixel capacitance ratio it is necessary to calculate the combined effect o f capacitance between the pixels and unequal values o f pixel capacitance on the converted

voltage. Consider again the voltages present during the data conversion. The voltage on C2 after Cl has been charged but before T2 is turned on is given by the expression

V

* = Vi O' - V

( K ( 0 - V 2 Û ' - V )

Cr

Q : + Q

6-29

When T2 is turned on charge sharing takes place between the two pixel capacitors. The resulting voltage, V2(i), can be calculated from the conservation of charge.

F2(0(C'i+Q) “ + (K(0~y^2f^~v) Cr

Cc + C^jC,+Vjii)C, 6-30

6-31

By considering the effect of iterating this equation the voltage at the end of the conversion can be obtained. The pixel voltage after N conversion cycles is given by the equation below.

V p M = Z i=\ (N-i) = C , + C V C + C Kc2 ~ c - C , + Q

To eliminate the differential non-linearity the parameter Kci must be made equal to 1. 6-32

6-33

6-34

2

C , + C 2

In order to simplify the equation the capacitance values can be related to the total pixel capacitance Cy by making the substitutions Ci=KrCx, C2==(l-Kr)CT and Cc=KcCx. This

yields the relationships between Kr and IQ indicated by the equations below and illustrated in Figure 6-48.

K = l - 3 K + 2 K 6-35