标签: sine

I saw a recent product introduction by Cypress Semiconductor tackling a new approach to mobile touch sensor technology, called metal mesh. It said the company is partnering with FujiFilms to bring this technology to a wider range of smartphones as an alternative to traditional indium tin oxide (ITO) and aluminium-doped zinc oxide (AZO) displays. I have been keeping an eye on the display market and I noticed recently a couple of trends recently that seem to me required something other that AZO and ITO based designs. One is the trend towards larger displays in traditional mobiles and tablets and the other was a shift to "up close and personal" wearable electronics. Both will need more flexible display substrates that are less prone to cracking in the case of large screen mobiles and are more flexible and bendable for wearable devices. Talking to Vikas Dhurka, product marketing director for TrueTouch touchscreen solutions at Cypress, I found out that they had spotted the same trends and think that FujiFilm's metal mesh technology is a very promising way to address both issues in a potentially very large market. According to Jennifer Colegrove, Ph.D., president of Touch Display Research Inc., the potential market for flexible and curved displays in which metal mesh would play is estimated to grow from less than 1% market share this year to $27 Billion and 16% market share of global display revenue by 2023 ( figure ).   Figure. Market for up close and personal flexible and curved displays. (Source: Touch Display Research, Flexible and Curved Display Technologies and Market Forecast Report, September 2013) Durkas said metal mesh displays are built using thousands of copper wires, each smaller in diameter than a strand of human hair and offer greater flexibility. In traditional consumer electronics devices, he said, shifting from the traditional indium tin oxide (ITO) based screens to ones based on metal meshes made of copper would not only make them cheaper to produce but make them more noise immune and easier to manufacture. "ITO is an etching process that is expensive, while metal meshes are laid down in a process similar to that of a semiconductor device in a layered fashion," said Dhurka. Based on its assessment of the technology, Cypress Semiconductor has expanded its TrueTouch capacitive touchscreen controller family to include support for metal mesh sensors technology from Fujifilm as an alternative to indium tin oxide (ITO) and aluminium-doped zinc oxide (AZO). Among the reasons for the shift, he said, is that because the metal mesh sensors are copper based they face less resistance in sending signals out to the electronics than existing multi-element based compound materials, making possible brighter and more easily readable displays. But what made Cypress sit up and take notice is that unlike ITO or AZO, metal mesh sensors are bendable, which will be a requirement for many of the personal wearable electronic things that are considering for the next generation of consumer electronics. "ITO is prone to cracking as standard smartphone and tablet screens get larger," said Dhurka, "and in the more curved flexible screen wearable designs that are being considered it is not a viable alternative." But beyond the bendable features, an advantage of metal mesh is that it will allow mobile makers to build lower cost phones with capacitive touch technology. The technology also improves touchscreen sensitivity and delivers robust noise immunity. Because the mesh consists of almost invisible copper wiring with the diameter of a hair, a display built using it is much more transparent than one built with ITO. Unlike ITO, a display fabricated with hair-thin ( 4 micron diameter ) copper wiring can be very dense before transparency is affected, allowing the incorporation of additional electrical redundancy which improves yields and lowers cost. According to Dr. Colegrove, metal mesh-based touch displays will make possible the creation of next generation of aesthetically pleasing wearable devices and things that because they are bendable can be contoured to the curves of human body. "Flexible and curved displays are more ergonomic for the wrist," she said, "and larger-sized flexible displays could fit better and show more information." Cypress is offering the CY3290-TMA500 and CYTK58 TrueTouch Evaluation Kits for developers who want to design their next UI-based products with Fujifilm metal mesh sensors. But Cypress and FujiFilm are not alone in going after this new consumer and mobile display technology. Metal mesh has started shipping in a couple of nextgen touchscreen-based smart phones. And competitors to FujiFilm such as MNTech in Korea and Unipexel are shipping metal mesh to their customers. Also, Atmel has partnered with CIT in the United Kingdom and as of late last year shipped its metal-mesh based XSense line of flexible touch sensors for use in a smartphone and a seven inch display Tablet. Several companies in China are also shipping.

In my seminars, I often tackle why we should understand at least a little electromagnetics theory, even for purely firmware people. But the subject is hard to understand and sometimes harder to believe, which is why the best book on the subject, " High Speed Digital Design, " is subtitled "A Handbook of Black Magic." Why is it important? You'll surely be probing your design with various tools like scopes and logic analysers, and every such probe has some impedance. As speeds get higher, that impedance is ever more likely to corrupt the operation of the device. But "speed" is poorly understood today. We equate clock rate with speed, which is only part of the story. Almost two hundred years ago polymath Jean-Baptiste Joseph Fourier showed that any periodic function can be expressed as the sum of sine waves of different amplitudes and frequencies. A square wave, like a microprocessor clock, is periodic and its Fourier series is:   In other words, a square wave is composed of the sum of the sine of the wave's frequency and each of its odd harmonics. (A harmonic is an integer multiple of the base frequency.) As you can see, no matter what the square wave's frequency is, it has harmonics that go to infinity, though at progressively lower amplitudes. A useful rule of thumb is that for most digital design we can ignore harmonics that exceed: f=0.5/T r Where T r is the square wave's rise time in nanoseconds. Every real-world signal takes time to transition from a zero to a one. Above f the Fourier components are down about 40 dB. Since a picture is worth a million bits, look at the following scope trace:   Figure 1—A square wave with 20 ns rise time. The top trace is a 1MHz square wave, just like a CPU clock. The bottom is an expanded view of the highlighted portion of the same trace. Note that what looks like a nice, quick zero to one transition actually takes quite a bit of time. In this case the rise time is 20 ns. Running 20 ns through the previous formula and it's clear that anything above 25MHz will be so far down we don't have to worry about them. But it does mean that 1MHz signal has important frequency components that far exceed the fundamental. That square wave comes from my scope's waveform generator. To show the Fourier effect more dramatically I built a circuit to improve the signal's rise time by feeding the signal through a fast gate.   Figure 2—Square wave fixer-upper circuit. It is possible to see the individual frequency components predicted by the Fourier series. Most modern scopes can compute the Fourier transform of a signal, as in the following screen capture.   Figure 3—10MHz sine wave The bottom trace is a simple 10MHz sine wave. Above it is the Fourier transform. Unlike a normal scope display where the horizontal axis is time and the vertical volts, the upper one is displayed in units of dB and frequency. In this case the screen's scale is set to 0MHz at the left and 20MHz all the way to the right. Note there's a very strong peak exactly at 10MHz, because 10MHz is the only frequency component in a 10MHz sine wave. Sure, there are some other things running around on that trace due to an imperfect waveform generator and some artifacts of the Fourier transform process. But the ugly stuff is 57 dB lower than the peak. That's 1/500,000 less than the 10MHz peak. Switching from dB to voltage makes this more obvious:   Figure 4—10MHz sine wave in volts. Here's the Fourier transform of the 20 ns rise time square wave:   Figure 5—Spectrum of a square wave with 20 ns rise time. The bottom trace is the 1MHz square wave from the scope's waveform generator, before going to the fixer-upper circuit. Above it is the Fourier transform. In this case the screen's scale is set to 0MHz at the left and 100MHz at the right. Each peak is one of the square wave's odd harmonics from the Fourier series. Unsurprisingly, the highest peak is at the wave's fundamental frequency of 1MHz. At 33MHz the signal is down 38 dB, and quickly rolls off from there. That's close enough to the rule of thumb for practical work. With the fixer-upper circuit the rise time is now 1 ns:   Figure 6—Spectrum of a square wave with 1 ns rise time. This looks different from the previous picture because now the Fourier transform window goes from 0MHz to 500MHz. There are a lot more harmonics displayed. But notice that the 40 dB point is now at 375MHz (the formula predicts 500MHz, again, close enough for a rule of thumb). It's important to remember that this is the spectrum of the same 1MHz signal; all that has changed is the rise time. If your little 8 bit system is clocking at just a few MHz, or even hundreds ofkHz, with sharp edges it may have all of the same high speed issues we usually attribute to much faster circuits. Sounds hard to believe. Some time ago a company asked for help with their 30 year old, 4MHz, Z80 design. A new batch of boards didn't work, though the design was unchanged. It seems the semiconductor vendor had increased the speed of some of the logic. Those gates that used to switch in 15 ns now did it in 5. The company had to redesign this board as a high-speed digital system simply because of the faster rise time. The takeaway is that we can't think of digital signals as we do simple sine waves. They are composed of a lot of harmonics, and, depending on rise time, those harmonics can have a huge effect on the circuit's operation. A 1MHz clock does not necessarily imply a slow circuit.

In my seminars, I usually discuss the importance of understanding at least a little electromagnetics theory, even for purely firmware people. But the subject is hard to understand and sometimes harder to believe, which is why the best book on the subject, " High Speed Digital Design, " is subtitled "A Handbook of Black Magic." Why is it important? You'll surely be probing your design with various tools like scopes and logic analysers, and every such probe has some impedance. As speeds get higher, that impedance is ever more likely to corrupt the operation of the device. But "speed" is poorly understood today. We equate clock rate with speed, which is only part of the story. Almost two hundred years ago polymath Jean-Baptiste Joseph Fourier showed that any periodic function can be expressed as the sum of sine waves of different amplitudes and frequencies. A square wave, like a microprocessor clock, is periodic and its Fourier series is:   In other words, a square wave is composed of the sum of the sine of the wave's frequency and each of its odd harmonics. (A harmonic is an integer multiple of the base frequency.) As you can see, no matter what the square wave's frequency is, it has harmonics that go to infinity, though at progressively lower amplitudes. A useful rule of thumb is that for most digital design we can ignore harmonics that exceed: f=0.5/T r Where T r is the square wave's rise time in nanoseconds. Every real-world signal takes time to transition from a zero to a one. Above f the Fourier components are down about 40 dB. Since a picture is worth a million bits, look at the following scope trace:   Figure 1—A square wave with 20 ns rise time. The top trace is a 1MHz square wave, just like a CPU clock. The bottom is an expanded view of the highlighted portion of the same trace. Note that what looks like a nice, quick zero to one transition actually takes quite a bit of time. In this case the rise time is 20 ns. Running 20 ns through the previous formula and it's clear that anything above 25MHz will be so far down we don't have to worry about them. But it does mean that 1MHz signal has important frequency components that far exceed the fundamental. That square wave comes from my scope's waveform generator. To show the Fourier effect more dramatically I built a circuit to improve the signal's rise time by feeding the signal through a fast gate.   Figure 2—Square wave fixer-upper circuit. It is possible to see the individual frequency components predicted by the Fourier series. Most modern scopes can compute the Fourier transform of a signal, as in the following screen capture.   Figure 3—10MHz sine wave The bottom trace is a simple 10MHz sine wave. Above it is the Fourier transform. Unlike a normal scope display where the horizontal axis is time and the vertical volts, the upper one is displayed in units of dB and frequency. In this case the screen's scale is set to 0MHz at the left and 20MHz all the way to the right. Note there's a very strong peak exactly at 10MHz, because 10MHz is the only frequency component in a 10MHz sine wave. Sure, there are some other things running around on that trace due to an imperfect waveform generator and some artifacts of the Fourier transform process. But the ugly stuff is 57 dB lower than the peak. That's 1/500,000 less than the 10MHz peak. Switching from dB to voltage makes this more obvious:   Figure 4—10MHz sine wave in volts. Here's the Fourier transform of the 20 ns rise time square wave:   Figure 5—Spectrum of a square wave with 20 ns rise time. The bottom trace is the 1MHz square wave from the scope's waveform generator, before going to the fixer-upper circuit. Above it is the Fourier transform. In this case the screen's scale is set to 0MHz at the left and 100MHz at the right. Each peak is one of the square wave's odd harmonics from the Fourier series. Unsurprisingly, the highest peak is at the wave's fundamental frequency of 1MHz. At 33MHz the signal is down 38 dB, and quickly rolls off from there. That's close enough to the rule of thumb for practical work. With the fixer-upper circuit the rise time is now 1 ns:   Figure 6—Spectrum of a square wave with 1 ns rise time. This looks different from the previous picture because now the Fourier transform window goes from 0MHz to 500MHz. There are a lot more harmonics displayed. But notice that the 40 dB point is now at 375MHz (the formula predicts 500MHz, again, close enough for a rule of thumb). It's important to remember that this is the spectrum of the same 1MHz signal; all that has changed is the rise time. If your little 8 bit system is clocking at just a few MHz, or even hundreds ofkHz, with sharp edges it may have all of the same high speed issues we usually attribute to much faster circuits. Sounds hard to believe. Some time ago a company asked for help with their 30 year old, 4MHz, Z80 design. A new batch of boards didn't work, though the design was unchanged. It seems the semiconductor vendor had increased the speed of some of the logic. Those gates that used to switch in 15 ns now did it in 5. The company had to redesign this board as a high-speed digital system simply because of the faster rise time. The takeaway is that we can't think of digital signals as we do simple sine waves. They are composed of a lot of harmonics, and, depending on rise time, those harmonics can have a huge effect on the circuit's operation. A 1MHz clock does not necessarily imply a slow circuit.