Quote of the Day
It's a Baptist school where atheist professors teach Jewish students St. Thomas Aquinas.
— David Brooks on the University of Chicago
If you are wondering about how fiber optics works, this is the best tutorial I have seen.
Quote of the Day
It's a Baptist school where atheist professors teach Jewish students St. Thomas Aquinas.
— David Brooks on the University of Chicago
Quote of the Day
Crush your enemies. See them driven before you. Hear the lamentations of their women.
— Conan the Barbarian's response to a Mongol general asking 'What is best in life?'
My wife and I put on a Christmas-themed duvet cover last night using the technique shown in this video. The approach reminds me of some topology demonstrations. The method worked as advertised.
Quote of the Day
The gem cannot be polished without friction, nor man perfected without trials.
— Chinese Proverb
I find the subject of Antarctica very interesting and I read as much as I can about it – especially articles about the science being done there. I recently was reading an article about Jerri Nielsen, a doctor who developed breast cancer while over-wintering at the South Pole Station (Figure 1), and the difficulties encountered trying to rescue her. As I researched her rescue in more detail, I read a web page that mentioned that the South Pole is limited to a few hours a day of contact with the outside world through satellite communication. I was wondering why this was true and I started to look around the web. I found an FAQ answer that was interesting and worth analyzing here.
Here is the answer on an FAQ that got me curious.
What kind of satellites does the South Pole Station use?
The South Pole Station uses high inclination geosynchronous satellites. Specifically, TDRSS and GOES. Inclination is an orbital parameter that describes the amount of north-south movement a satellite makes in its orbit over 24 hours. When the value is great enough (roughly 8.7 degrees), the geosynchronous satellites are visible at South Pole.
I will show why the satellite's inclination must be about 8.7° for the South Pole Station to communicate with a satellite.
I want to confirm that a satellite inclination of "roughly 8.7 degrees" will put a satellite right on the horizon when viewed from the South Pole. My analysis will be strictly geometric and I will ignore the effects of refraction. You can include the effects of refraction (example), but it complicates the analysis without providing much additional insight into the problem.
Figure 2 shows how some geosynchronous satellites make a figure-eight ground track over the equator in their orbits.
Figure 3 gives you an idea of just how far away the South Pole station is from everything. I have heard US military folks say that Antarctica is the most difficult logistics challenge in the world.
Figure 4 shows the geometry of the satellite-antenna situation at the South Pole.
Using the geometric picture of Figure 4, I can solve numerically for the satellite inclination that will provide a view from the South Pole.
I compute an inclination value of 8.6°, which is very closely to the value of "roughly 8.7 degrees" stated in the quote.
I was able to confirm the satellite inclination statement made in the quote I located on an FAQ. I now understand why the South Pole Station can only get high-bandwidth data transfers for a limited period each day. I have read that a terrestrial fiber link is in the works for Antarctica, so this problem may be resolved in a few years.
Unfortunately, Jerri Nielsen eventually succumbed to cancer in 2009, but had survived 11 years after her ordeal in Antarctica. Here is her video obituary.
Quote of the Day
Life appears to me too short to be spent in nursing animosity, or registering wrongs.
— Charlotte Bronte
I just read an interesting article written by Isaac Asimov (Figure 1) on the creative process. The article was previously unpublished, but has many ideas in common with the ideation folks today.
I saw a well-done list that summarizes Asimov's paper in an Electronic Cooling magazine editorial and I will include the list here.
Quote of the Day
You must have long term goals to keep you from being frustrated by short term failures.
— Charles C. Noble
Since I am always looking for good examples to use for training folks in the use of Excel, I thought I would generate my version of this chart using Excel. Here is what I came up with – I modified the format just a bit because I was not totally happy with how JP Morgan did it. Also, I wanted the assumed interest rate to be programmable and I wanted to be able to modify the yearly contributions. I guess I cannot leave anything alone.
I have attached my Excel workbook for generating this chart.
Quote of the Day
Propose to any Englishman any principle or instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it.
— Charles Babbage, an early computer pioneer who struggled to convince backers that computers had any future.
I was raised in a devout Catholic home and nuns were a big part of my youth. For example, I had to watch every nun movie ever made (e.g. Figure 1), and I attended regular religious education, which was often conducted by nuns.
I have not had any contact with nuns as an adult, with the exception of encountering nuns protesting my workplace when I was working for a defense contractor (Honeywell). That was an interesting experience.
I have not thought about nuns as managers until I read this blog post. I really liked Sister Rosemarie Nassif's ten commandments of leadership. Here they are.
I was reading an article on Stumbleupon that got me thinking about the size of the planets on a more imaginable scale – the distance between the Earth and moon.
Here is a video that shows what the other planets would look like from Earth if they orbited around us at a distance equal to that of the moon's distance.
His is a picture that shows the distance between the Earth and the Moon.
The following picture shows that all the planets, properly oriented, could fit between the Earth and moon. Because the planets are spinning, they tend to flatten at the poles. This drawing assumes that we do not line up the largest diameters.
Here is the sum of diameters that I came up with using WolframAlpha. It is close to what the image artist came up with.
Name | Diameter (km) |
Mercury | 4,879 |
Venus | 12,104 |
Mars | 6,771 |
Jupiter | 138,350 |
Saturn | 114,630 |
Uranus | 50,532 |
Neptune | 49,105 |
Total | 376,371 |
Everyday, I work on delivering fiber-based, video access equipment to service providers. The increased demand for High-Definition Television (HDTV, Figure 1) has increased the need for fiber in the video distribution network. Today, fiber optic cable is often used to deliver the video signal to "green yard furniture" (Figure 2) in local neighborhoods that convert the light to electrical form for distribution using copper-based technologies, like cable TV or DSL.
Figure 2: Green Yard Furniture (Source).
Increasingly often, optical fiber is being used to deliver the video directly to the home – this is the focus of my work. As part of preparing some tutorial material on video distribution, I needed to explain how these distribution networks are configured. There was some interesting math involved in this work that I thought would be interesting to share here.
In this post, I will look at how optical video transmission performance is determined by two key parameters, composite RMS OMI and channel peak OMI (defined below). These parameters are difficult for customers to understand, but critical to the performance of their networks.
A relationship will be determined between these two parameters that is used every day in my lab to setup video systems. This analysis will uses some basic probability theory and calculus to derive a useful result.
There are two basic types of video transmission:
The video data is shipped in digital form like any other internet data. This is being rolled out now and is the future of television. IP-based video subscribers receive only the channels that they are watching. This service is only now being deployed and it will take years before everyone gets access to it.
RF-based video broadcasts multiple channels on the fiber in a manner similar to how over-the-air channels are broadcast – every channel gets a frequency assignment in the band from 54 MHz to 1003 MHz. Each video channel is encoded in an analog form (e.g. NTSC or QAM), summed together, and that sum used to modulated a laser. The video signal itself is carried on a separate wavelength, usually 1550 nm.
This post will focus on the RF-based approach. This approach is becoming less common, but there are still tens of millions of people who watch TV using this technology.
I have been told every year over the last 15 years that RF-based video is going to die in the next two years. I expect to retire in ten years with tens of millions of people still watching RF-based video. Change comes slowly in the access network.
Figure 3 shows the basic video distribution network.
In Figure 3, a large number of electrical channels go into the laser and the same number of electrical channels come out of each home's optical receiver. In this respect, it is similar to how an over-the-air broadcast works.
Aspects of these definitions may require some additional background for those unfamiliar with amplitude-modulated system. See Appendix A for some additional background on these systems.
In theory, you could make the laser bias large enough to ensure that the input cannot be negative. However, there are limits to the amount of power you can transmit down a fiber because of nonlinearities like SBS. Also, higher laser power means MUCH higher cost.
The loss of signal, while short, creates a distortion in the television signal. We refer to this distortion as clipping-induced distortion.
Most cable systems support two OMI levels: one for analog channels and one for digital channels. QAM256 is the most common type of digital channel and it is usually set at 50% of the analog level.
The amount of clipping-induced distortion is related to the composite RMS OMI. The number of channels that can be transmitted on a single wavelength is a function of the channel peak OMI, the number of channels, and allowed composite RMS OMI for a given level of clipping induced distortion. I will be investigating this relationship closely.
The factor of two appears because the channel peak OMI must be converted to an RMS value for the composite calculation. If all the OMI values are the same (e.g. an all analog system), then .
Equation 1 shows formula for the amount of power that was present in the electrical signal but is clipped from the optical signal. You will note that the integral involves the optical power squared and not just the power. This has to do with a subtlety of optical systems in that a milliWatt of optical power produces so many milliAmps of electrical current in the receiver. This means that the electrical signal power produced by the receiver, which is related to the square of electrical current, is proportional the square of the optical power. To compute the electrical power that was clipped, we need to compute the integral of the optical power squared times the probability of clipping, which is Equation 1.
Eq. 1 |
where
For this analysis, I am going to assume that the system performance is limited by clipping-induced distortion. Figure 5 shows my derivation for the power that was clipped from the original signal (highlighted in yellow).
Figure 6 shows how to derive the Carrier-to-Clipped Power of the composite system as a function of the composite OMI. Note that σ represents the standard deviation of the optical power and σ2 represents the electrical power of the information content of the video signal, which is called the signal power.
The equation highlighted in yellow is well-known in the industry as the Saleh equation (ref: A. A. M. Saleh. Fundamental limit on number of channels in subcarrier-multiplexed lightwave CATV system. Electron. Letters, 25(12):776-777, 1989). You will sometimes see this equation in a slightly different form (see Appendix B).
Clipping-induced distortion is only one of a number of noise source in a video system (e.g. RIN, thermal, shot), but it is often a dominant one. Figure 7 shows an example of OMI calculations for a commonly used system configuration consisting of:
There is some debate on the actual CNR requirements. The FCC minimum CNR is 43 dB, which produces a picture with quality comparable to that of an old VHS tape player. A few service providers use 46 dB, but most use 48 dB.
As mentioned earlier, this level is typically set at half of the analog level for QAM256, i.e. 1.9% = 3.8%/2.
We typically set clipping induced distortion to a level at 10 dB less than the required CNR level of 48 dB.
The calculation shows that we just meet our minimum requirements with 80 analog and 33 digital channels.
I frequently am asked why RF-based video has to be setup a certain way or it just does not work well. Hopefully, these calculations show where some of the odd ball formulas come from and that deriving them is not simple.
We generally test the AM-VSB channels using a unmodulated carriers. We can model the optical power present in this test configuration as shown in Equation 2.
Eq. 2 |
where
Equation 2 can be thought of as using optical power to represent the voltage of the original television signal, i.e. , where vVideo(t) is the voltage of the original television signal.
The optical receiver contains a photodetector that generates a current proportional to the input optical power. This means that we can express the detector's output current as shown in Equation 3.
Eq. 3 |
where
In general, there are on the order of 80 analog video channels multiplexed on a single laser output. We can think of vReceived(t) as the sum of a large number (~80) independent, identically distributed, random variables. Because of the central limit theorem, vReceived(t) is well-modeled as a Gaussian random process with mean R·P0 and variance of (the variance equals the signal power). Note that the channel power x(t) does not enter into this equation because its mean value is defined to be 1.
We define the composite modulation index (µ) as the standard deviation (σ) normalized to the signal mean of vReceived(t), R·P0, which I show in Equation 4.
Eq. 4 |
Some folks like to express CNR as a negative dB value and with a numeric constant for a leading coefficient (example). Figure 7 shows how to derive this expression.
Christmas is coming and the engineers are decorating their cubes. Here is an example – excuse the photo quality from my old phone.
My idea of a great Christmas decoration is the one shown below from a Japanese mall. I love Godzilla, but I am sure that my wife will not let me build one of these and put it in our house. She keeps saying that I do not have the proper Christmas spirit ...
I like it when instructors use physical models to illustrate how things work. I was watching this video on submarine design when I saw a physical model used to illustrate how a submarine launches a missile. The demonstration is excellent. I have included a snippet from this video that contains the demonstration below.