First, I would point out that you can read additional diode parameters BV, Ibv and Cjo directly from the LED datasheet as "Reverse Current" Ir at Vr and as "Capacitance" C.
Adding to W5VO's great answer, I somewhat streamlined the process for myself the following way:
I used the graph type of XY scatter plot as lines only on OpenOffice (YMMV with Excel, etc.) and set the minima and maxima of the axes manually, e.g. (X,Y)=(1.4-4.0, 0.01-50.0).
After the first three columns of sampled datapoints Vf_sampled, If_sampled as well as the If_estimate with the Schokley diode equation, I added a fourth one for a calculated Vf_estimate. Remember, that Rs is a series resistance (see image at the bottom) and the If_estimate actually gives us the current to use here, so one can simply calculate the column cells as:
Vf_estimate = Vf_sampled + (If_estimate * Rs).I could now add a third curve, in which I used the new fourth column (Vf_estimate) as the X coordinate and the third column (If_estimate) as the Y coordinate, and which I could now easily match against the first curve (the data sampled from the graph on the datasheet). Note that I didn't want to simply replace the second curve since the straight line was quite helpful in my estimates.
I'm sure I'm somewhat repeating W5VO here, but it bares reminding of the role of the constants Is, Rs and N in terms of the curve shape (in our log-lin scale):
- Is only affects the position of the curves (up/left or down/right).
- N affects the curve slopes as well as the positions (since it's a linear coefficient and the curves always go through the origin, which is always outside the scale).
- Rs defines the curvature (the progressive rightward sweep) of the new third curve (since it's a linear term).
- Things I found that may be of use:
- You may find that the second curve (the straight line) needs to be very slightly steeper and to the up/left than it would seem from the sampled data, because the curvature due to Rs starts from the origin.
- You can get fairly accurate sampling by zooming in to the datasheet (assuming PDF), taking a screencap and opening it in your favourite drawing program. You can then use e.g. the selection or straight-line tool to measure the distance in pixels between the interval lines and the distance of the datapoint to the lower-value interval line. For linear axes, that fraction translates to easy data values.
- XY scatter plot allows you to use arbitrary datapoints. You can get away with less samples than with equidistant sampling. You can choose to only sample the data at the points where it is easiest and where strictly needed. For example, on a semilog scale you can sample at the interval lines of the logarithmic scale. If you need to, you can still have more points (rows) for the estimated curves. (At least OpenOffice graphs seem to ignore the points for which there is no Y-coordinate.)
- Note the scale of the units you are estimating/graphing/trying to find (e.g. milliamperes) and remember that SPICE generally uses the bare units (amperes).
- Check which metric prefixes (m, p, u, etc.) your SPICE simulator accepts. Using the E-notation (e.g. 1234E-12) may be simpler.
- Editing the cell range for the graph seemed to always reset the (new) third curve so that I had to re-add the data range to X-coordinates and re-change the third column as its Y range. Take that into consideration when adding more points or modeling multiple LEDs on the same graph - make such changes all at once. (Changing the data within the cells obviously didn't trigger the reset.)
- Curved interpolation on the graph may lead you astray.
- Straight line segments may also mislead, since the corresponding datapoints end up in different locations and the linear interpolation doesn't track the logarithmic nature of the curve. (All the datapoints of the sampled curve and the new third curve should be outside of the straight line segments of the other.)
AFAIK, our model for the LED is essentially an Rs resistor and Is/N estimate diode in series: (-R->-D-)
simulate this circuit – Schematic created using CircuitLab
