Embed Size (px)
Citation preview
.
..
.
..
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
..
.
.
.
..
.
.
.
.
.
.
.
..
.
.
.
.
.
.
..
.
Topics in Physics:
1. Ohm’s Law and VI Characteristics
The Fundamental Law of George Simon Ohm
Integral form: V = IR
Differential form: dV = R dI
V is voltage measured in volts (V)
I is current measured in amperes (A)
R is resistance measured in ohms ()
This law is a linear relationship between two physical parameters,
voltage and current.
Ohm’s Law for a Linear Resistor
V = IR
+ -I V
R
V
I
V
IR = V/I
Ohm’s Law for a Non-Linear Resistor:a Diode
dV = R dI
+ -IV
V
I I = I(V)R(V) = dV/dI
Reverse Forward
Questions:
1. Is the value of R a function of either voltage or current in the linear resistor?
2. Is the value of R a function of either voltage or current in the diode?
3. In which direction is the diode resistance the greatest? The least?Please notice that the roles of x-axis and y-
axis in the VI characteristics have been reversed from the normal algebra
convention. Electrical engineers sometimes think in different ways than algebra
students!
Answer to Question #1:
R is independent of voltage and current in the linear resistor. R = V/I.
Answer to Question #2:
R is a function of position along the diode characteristic,and it is different at every point. R = dV/dI.
Answer to Question #3:
R is smallest in the diode forward direction and largest in the reverse.
How are Diodes Made?
Chemical impurities (dopants) are added to an otherwise pure,refined
material (silicon) to render it either p-type or n-type.
The material is then melted and ‘drawn’ into a single crystal from
which slices are cut. A second dopant layer is then diffused into the crystal
slice to create a semiconductor junction device.
The junction device is then encapsulated in the opaque material
epoxy. BUT if the junction is left exposed to light, something
interesting happens:
The diode becomes an energy transducer - a solar cell, transforming
light into electricity! The VI characteristic moves from power
dissipation only into a power generating region.
V
I
Power is either generated or dissipated, depending on the
quadrant you are in.
1ST Quadrant:
Dissipation
3D Quadrant:
Dissipation
2ND Quadrant:
Generation
4TH Quadrant:
Generation
IV
Dark Characteristic Light Characteristic
I
V Power Generating Region
Power Dissipating
Region
Power Dissipating Region
The VI characteristic of a solar cell is usually displayed like this:
V
IV
I
The coordinate system is flipped around the voltage axis.
Questions:
1. Electrical power is the product of voltage and current: P = VI. Is power a function of position along the solar cell characteristic, or is it a constant everywhere along the curve?
2. What is the power at the intercepts?
3. If power is not a constant along the curve, then where is it minimum and where is it maximum?
4. What is the minimum power?
Answer to Questions #1 - #4:
Power is a function of position along the VI characteristic. At the
intercepts, it is minimum - zero - increasing to a max near the knee of
the curve.
2. Solar Cells Parameters and Their Significance
Every engineering and scientific system is characterized by a set of
parameters - a parameter space. We will now look at a set of solar cell
parameters used in the daily business of making, testing, and using solar
cells.
Set #1: ISC , PMAX , VOC
(0.5V, 0 mA) V I = 0 mW
(0.43 V, 142 mA) V I = 61 mW
ISC
VOC
PMA
X(0V, 150 mA)
V I = 0 mW
Some typical values
The short circuit current ISC is a linear function of sunlight intensity. The open circuit voltage VOC is not.
(VOC is weakly dependent on temperature.) Recall from Part I
that sunlight intensity is measured in terms of a solar constant with
units such as mW/cm2.
Questions:
1. What is the voltage at ISC ? Why is this value called the “Short Circuit Current”?
2. What is the current at VOC ? Why is this value called the “Open Circuit Voltage”?
3. What shape does the curve P = IV have on the VI plane? (Think Analytical Geometry!)
4. How does this shape help you to understand that the value of PMAX is at the knee of the curve and not somewhere else?
5. The nominal distance from the sun to the earth is 150 million km. The nominal distance from the sun to Mars is 230 million km. If the solar constant at 1 A.U. is 136.7 mW/cm2, what is it at Mars?
6. A solar cell has ISC = 150mA on earth under ideal sunlight conditions. Under ideal sunlight conditions on Mars, what short circuit current would this cell produce? (Mars’ power system designers must worry about such things!)
I = ISC
R = 0
Does it surprise you that the current at short circuit is not infinite? Or that a current can flow with no voltage? Where does the energy originate?
Answer to Question #1:
I = 0
R =
Answer to Question #2:
+
_V = VOC
Answer to Questions #3 and #4:
The curve P=VI is a rectangular hyperbola in the VI plane. There is a family of such curves in the plane,
but only ONE is tangent to the solar cell characteristic. The point of
tangency is PMAX. This relationship is shown on the next page.
ISC
VOC
Hyperbola for P = PMAX
Point of tangency
Voltage at max power
Cu
rren
t at
max p
ow
er
Answer to Questions #3 and #4 (cont’d):
Answer to Question #5:
Mars = {(136.7) (150/230)2
}mW/cm2
= 58mW/cm2
Answer to Question #6:
ISC = {150 (58/136.7)}mA= 64 mA on Mars
Set #2: RS , RSH
ISC
VOC
The slopes of these lines are characteristic resistances.
RSH
RS
Questions:
1. Which resistance is higher, the measurement at ISC or the measurement at VOC ?
Remember: R = V/I !
2. Physically, what do you think these resistances represent?
3. As a solar cell designer, what is your preferred ideal value?
Answers to Questions #1 - #3:
The resistance at ISC is extremely high. In an equivalent circuit model of a solar cell, it represents a shunt resistance.
The resistance at VOC is extremely low. In an equivalent circuit model of a solar cell, it represents a series resistance.
Both of these resistances are internal, and represent energy dissipation mechanisms in the cell.
Ideally, a designer would like zero series resistance and infinite shunt resistance.
ISC
RS
RSH
RLOAD
Equivalent circuit for a solar cell with load. Internal resistances RS and RSH represent power loss mechanisms
inside the cell.
Cell
Cell
ISC
RS = 0
RSH =
RLOAD
The ideal solar cell would have no internal losses at all! What would the VI characteristic of THIS cell look like?
ISC
VOC
RSH =
RS = 0
The Ideal Solar Cell
Notice that the area under the rectangle = PMAX for the ideal cell.
For this cell,PMAX = VOC ISC
ISC
VOC
The Ideal Solar Cell
ISC
VOC
Set #3: Fill Factor
In fact, PMAX/(ISC VOC) measures the cell’s quality as a power
source. The quantity is called the “Fill Factor.”
Can you see why?
Questions:
1. What is the ideal fill factor?
2. Can the ideal cell ever be built? Why or why not?
3. For a cell with these parameters:
(0V, 150mA), (0.43V, 142mA), and (0.5V, 0mA)
calculate the fill factor.
Answer to Question #1:
The ideal fill factor is unity. Why?
Answer to Question #2:
An ideal cell might be approximated, but never actually built. Nature is never ideal as humans think about “ideal.”
Answer to Question #3:
The fill factor is:
(0.43V 142mA)/(0.5V 150mA) = 0.81 = 81%
Well, there it is - we’ve taken another step. Those of you that are interested in pursuing this topic still further can study circuit design. Solar arrays are
usually wired in series-parallel configurations to achieve desired VI characteristics. Zener diodes, power
converters, etc. all become part of the design. After all, the raw power of the
array has to be tailored to fit the user’s needs. In space, the effects of
on-orbit eclipses, surface charge buildup and dissipation, and a variety
of other issues all become factored into the designer’s palate.
I hope that you have enjoyed this two-part series and that some of you will further pursue education in electrical
engineering or solid state physics.
Best Wishes!!!
Do you have any questions or topics you would like to discuss?
