A charge coupled device (CCD) chip has an active area of 14.0 mm 7.00 mm and a r
ID: 1593904 • Letter: A
Question
A charge coupled device (CCD) chip has an active area of 14.0 mm 7.00 mm and a resolution of 8.6 megapixels; the pixels are square. Note that here we are using the binary definition of megapixel:
1 megapixel = 220 pixels = 1,048,576 pixels.
(a) What are the dimensions of the device, expressed in pixels (i.e., x pixels y pixels)? Round to the nearest integer number of pixels.
(b) What are the dimensions of each pixel, in micrometres?
(c) Using your answer in (b) as the plate area, and assuming a dielectric constant of 3.0 and a plate spacing of 1.00 m, what is the capacitance of each pixel cell? (Note: This is a very simplified model of a CCD.)
Explanation / Answer
a) let the area of each pixel is a^2
where a is the side each pixel
Now , as 8.6 megapixels = area of chip
8.6 * (1048576) * a^2 = 14 * 7 *10^-6 m^2
solving for a
a = 3.2966 *10^-6 m
length of chip = 14 mm = 14 *10^-3/(3.2966 *10^-6) pixel
length of chip = 4247 pixel
width of chip = 7 mm = 14 *10^-3/(3.2966 *10^-6) pixel
width of chip = 2123 pixel
the diemnsion of device is (4247 pixel X 2123 pixel)
b)
the dimension of each pixel is 3.2966 *10^-6 m X 3.2966 *10^-6 m
c)
Capacitance = k * epsilon_0 * area/d
Capacitance = 3 * 8.854 *10^-12 * ( 3.2966 *10^-6)^2/(1 *10^-6)
Capacitance = 2.89 *10^-16 F
the Capacitance of each pixel cell is 2.89 *10^-16 F
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