Issue 284: EQ Answers

PROBLEM 1
Can you name all of the signals in the original 25-pin RS-232 connector?

ANSWER 1
Pins 9, 10, 11, 18, and 25 are unassigned/reserved. The rest are:

Pin Abbreviation Source Description
1 PG - Protective ground
2 TD DTE Transmitted data
3 RD DCE Received data
4 RTS DTE Request to send
5 CTS DCE Clear to send
6 DSR DCE Data Set Ready
7 SG - Signal ground
8 CD DCE Carrier detect
12 SCD DCE Secondary carrier detect
13 SCTS DCE Secondary clear to send
14 STD DTE Secondary transmitted data
15 TC DCE Transmitter clock
16 SRD DCE Secondary received data
17 RC DCE Receiver clock
19 SRTS DTE Secondary request to send
20 DTR DTE Data terminal ready
21 SQ DCE Signal quality
22 RI DCE Ring indicator
23 - DTE Data rate selector
24 ETC DTE External transmitter clock

 

PROBLEM 2
What is the key difference between a Moore state machine and a Mealy state machine?

ANSWER 2
The key difference between Moore and Mealy is that in a Moore state machine, the outputs depend only on the current state, while in a Mealy state machine, the outputs can also be affected directly by the inputs.

 

PROBLEM 3
What are some practical reasons you might choose one state machine over the other?

ANSWER 3
In practice, the difference between Moore and Mealy in most situations is not very important. However, when you’re trying to optimize the design in certain ways, it sometimes is.

Generally speaking, a Mealy machine can have fewer state variables than the corresponding Moore machine, which will save physical resources on a chip. This can be important in low-power designs.

On the other hand, a Moore machine will typically have shorter logic paths between flip-flops (total combinatorial gate delays), which will enable it to run at a higher clock speed than the corresponding Mealy machine.

 

PROBLEM 4
What is the key feature that distinguishes a DSP from any other general-purpose CPU?

ANSWER 4
Usually, the key distinguishing feature of a DSP when compared with a general-purpose CPU is that the DSP can execute certain signal-processing operations with few, if any, CPU cycles wasted on instructions that do not compute results.

One of the most basic operations in many key DSP algorithms is the MAC (multiply-accumulate) operation, which is the fundamental step used in matrix dot and cross products, FIR and IIR filters, and fast Fourier transforms (FFTs). A DSP will typically have a register and/or memory organization and a data path that enables it to do at least 64 MAC operations (and often many more) on unique data pairs in a row without any clocks wasted on loop overhead or data movement. General-purpose CPUs do not generally have enough registers to accomplish this without using additional instructions to move data between registers and memory.

Issue 282: EQ Answers

PROBLEM 1
Construct an electrical circuit to find the values of Xa, Xb, and Xc in this system of equations:

21Xa – 10Xb – 10Xc = 1
–10Xa + 22Xb – 10Xc = –2
–10Xa – 10Xb + 20Xc = 10

Your circuit should include only the following elements:

one 1-Ω resistor
one 2-Ω resistor
three 10-Ω resistors
three ideal constant voltage sources
three ideal ammeters

The circuit should be designed so that each ammeter displays one of the values Xa, Xb, or Xc. Given that the Xa, Xb, and Xc values represent currents, what kind of circuit analysis yields equations in this form?

ANSWER 1
You get equations in this form when you do mesh analysis of a circuit. Each equation represents the sum of the voltages around one loop in the mesh.

PROBLEM 2
What do the coefficients on the left side of the equations represent? What about the constants on the right side?

ANSWER 2
The coefficients on the left side of each equation represent resistances. Resistance multiplied by current (the unknown Xa, Xb, and Xc values) yields voltage.
The “bare” numbers on the right side of each equation represent voltages directly (i.e., independent voltage sources).

PROBLEM 3
What is the numerical solution for the equations?

ANSWER 3
To solve the equations directly, start by solving the third equation for Xc and substituting it into the other two equations:

Xc = 1/2 Xa + 1/2 Xb + 1/2

21Xa – 10Xb – 5Xa – 5Xb – 5 = 1
–10Xa + 22Xb – 5Xa – 5Xb – 5 = –2

16Xa – 15Xb = 6
–15Xa + 17Xb = 3

Solve for Xa by multiplying the first equation by 17 and the second equation by 15 and then adding them:

272Xa – 255Xb = 102
–225Xa + 255Xb = 45

47Xa = 147 → Xa = 147/47

Solve for Xb by multiplying the first equation by 15 and the second equation by 16 and then adding them:

240Xa – 225Xb = 90
–240Xa + 272Xb = 48

47Xb = 138 → Xb = 138/47

Finally, substitute those two results into the equation for Xc:

Xc = 147/94 + 138/94 + 47/94 = 332/94 = 166/47

PROBLEM 4
Finally, what is the actual circuit? Draw a diagram of the circuit and indicate the required value of each voltage source.

ANSWER 4
The circuit is a mesh comprising three loops, each with a voltage source. The common elements of the three loops are the three 10-Ω resistors, connected in a Y configuration (see the figure below).

cc281_eq_fig1The values of the voltage sources in each loop are given directly by the equations, as shown. To verify the numeric solution calculated previously, you can calculate all of the node voltages around the outer loop, plus the voltage at the center of the Y, and ensure they’re self-consistent.

We’ll start by naming Va as ground, or 0 V:

Vb = Va + 2 V = 2 V

Vc = Vb + 2 Ω × Xb = 2V + 2 Ω × 138/47 A = 370/47 V = 7.87234 V

Vd = Vc + 1 Ω × Xa = 370/47 V + 1 Ω × 147/47A = 517/47 V = 11.000 V

Ve = Vd – 1 V = 11.000 V – 1.000 V = 10.000 V

Va = Ve – 10 V = 0 V

which is where we started.

The center node, Vf, should be at the average of the three voltages Va, Vc, and Ve:

0 V + 370/47 V + 10 V/3 = 840/141 V = 5.95745 V

We should also be able to get this value by calculating the voltage drops across each of the three 10-Ω resistors:

Va + (Xc – Xb) × 10 Ω = 0 V + (166 – 138)/47A × 10 Ω = 280/47 V = 5.95745 V

Vc + (Xb – Xa) × 10 Ω = 370/47V + (138-147)/47A × 10 Ω = 280/47 V = 5.95745 V

Ve + (Xa – Xc) × 10 Ω = 10 V + (147-166)/47 A × 10 Ω = 280/47 V = 5.95745 V

The Future of Inkjet-Printed Electronics

Silver nanoparticle ink is injected into an empty cartridge and used in conjunction with an off-the-shelf inkjet printer to enable ‘instant inkjet circuit’ prototyping. (Photo courtesy of Georgia Institute of Technology)

Silver nanoparticle ink is injected into an empty cartridge and used in conjunction with an off-the-shelf inkjet printer to enable ‘instant inkjet circuit’ prototyping. (Photo courtesy of Georgia Institute of Technology)

Over the past decade, major advances in additive printing technologies in the 2-D and 3-D electronics fabrication space have accelerated additive processing—printing in particular—into the mainstream for the fabrication of low-cost, conformal, and environmentally friendly electronic components and systems. Printed electronics technology is opening an entirely new world of simple and rapid fabrication to hobbyists, research labs, and even commercial electronics manufacturers.

Historically, PCBs and ICs have been fabricated using subtractive processing techniques such as photolithography and mechanical milling. These traditional techniques are costly and time-consuming. They produce large amounts of material and chemical waste and they are also difficult to perform on a small scale for rapid prototyping and experimentation.

This single-sided wiring pattern for an Arduino microcontroller was printed on a transparent sheet of coated PET film, (Photo courtesy of Georgia Technical Institute)

This single-sided wiring pattern for an Arduino microcontroller was printed on a transparent sheet of coated PET film, (Photo courtesy of Georgia Technical Institute)

To overcome the limitations of subtractive fabrication, over the past decade the ATHENA group at the Georgia Institute of Technology (Georgia Tech) has been developing an innovative inkjet-printing platform that can print complex, vertical ICs directly from a desktop inkjet printer.

To convert a standard desktop inkjet printer into an electronics fabrication platform, custom electronic inks developed by Georgia Tech replace the standard photo inks that are ejected out of the printer’s piezoelectric nozzles. Inks for depositing conductors, insulators/dielectrics, and sensors have all been developed. These inks can print not only single-layer flexible PCBs, but they can also print complex, vertically integrated electronic structures (e.g., multilayer wiring with interlayer vias, parallel-plate capacitors, batteries, and sensing topologies to sense gas, temperature, humidity, and touch).

To create highly efficient electronic inks, which are the key to the printing platform, Georgia Tech researchers exploit the nanoscale properties of electronic materials. Highly conductive metals (e.g., gold, silver, and copper) have very high melting temperatures of approximately 1,000°C when the materials are in their bulk or large-scale form. However, when these metals are decreased to nanometer-sized particles, their melting temperature dramatically decreases to below 100°C. These nanoscale particles can then be dispersed within a solvent (e.g., water or alcohol) and printed through an inkjet nozzle, which is large enough to pass the nanoparticles. After printing, the metal layer printed with nanoparticles is heated at a low temperature, which melts the particles back into a highly conductive metal to produce very low-resistance electrical structures.

Utilizing nanomaterials has enabled the creation of plastic, ceramic, piezoelectric, and carbon nanotube and graphene inks, which are the fundamental building blocks of a fully printed electronics platform. The inks are then tuned to have the correct viscosity and surface tension for a typical desktop inkjet printer.

By loading these nanomaterial-based conductive, dielectric, and sensing inks into the different-colored cartridges of a desktop inkjet printer, 3-D electronics topologies such as metal-insulator-metal (MIM) capacitors can then be created by printing the different inks on top of each other in a layer-by-layer deposition. Since printing is a non-contact additive deposition method, and the processing temperatures are below 100⁰C, these inks can be printed onto virtually any substrate, including standard photo paper, plastic, fabrics, and even silicon wafers to interface with standard ICs with printed feature sizes below 20 µm.

The Georgia Tech-developed printing platform is a major breakthrough. It makes the cost of additively fabricating circuits nearly the same as printing a photo on a home desktop inkjet printer—and with the same level of simplicity and accessibility.

These advancements in 2-D electronics printing combined with current research in low-cost 3-D printing are enabling commercial-grade fabrication of devices that typically required clean room environments and expensive manufacturing equipment. Such technology, when made accessible to the masses, has the potential to completely change the way we think about building, interacting with, and even purchasing electronics that can be digitally transmitted and printed.  While the printing technology is currently at a mature stage, we have only scratched the surface of potential applications that can benefit from printing low-cost, flexible electronic devices.

Client Profile: Lauterbach, Inc

1111 Main Street #115
Vancouver, WA 98660

Contact:
sales_us@lauterbach.com

LauterbachFeatured Product: The TRACE32-ICD in-circuit debugger supports a range of on-chip debug interfaces. The debugger’s hardware is universal and enables you to connect to different target processors by simply changing the debug cable. The PowerDebug USB 3.0 can be upgraded with the PowerProbe or the PowerIntergrator to a logic analyzer.

Product Features: The TRACE 32-ICD JTAG debugger has a 5,000-KBps download rate. It features easy high-level Assembler debugging and an interface to all industry-standard compilers. The debugger enables fast download of code to target, OS awareness debugging, and flash programming. It displays internal and external peripherals at a logical level and includes support for hardware breakpoints and trigger (if supported by chip), multicore debugging (SMP and AMP), C and C++, and all common NOR and NAND flash devices.

For more information, visit www.lauterbach.com/bdmusb3.html.

Client Profile: Digi International, Inc

Contact: Elizabeth Presson
elizabeth.presson@digi.com

Featured Product: The XBee product family (www.digi.com/xbee) is a series of modular products that make adding wireless technology easy and cost-effective. Whether you need a ZigBee module or a fast multipoint solution, 2.4 GHz or long-range 900 MHz—there’s an XBee to meet your specific requirements.

XBee Cloud Kit

Digi International XBee Cloud Kit

Product information: Digi now offers the XBee Wi-Fi Cloud Kit (www.digi.com/xbeewificloudkit) for those who want to try the XBee Wi-Fi (XB2B-WFUT-001) with seamless cloud connectivity. The Cloud Kit brings the Internet of Things (IoT) to the popular XBee platform. Built around Digi’s new XBee Wi-Fi
module, which fully integrates into the Device Cloud by Etherios, the kit is a simple way for anyone with an interest in M2M and the IoT to build a hardware prototype and integrate it into an Internet-based application. This kit is suitable for electronics engineers, software designers, educators, and innovators.

Exclusive Offer: The XBee Wi-Fi Cloud Kit includes an XBee Wi-Fi module; a development board with a variety of sensors and actuators; loose electronic prototyping parts to make circuits of your own; a free subscription to Device Cloud; fully customizable widgets to monitor and control connected devices; an open-source application that enables two-way communication and control with the development board over the Internet; and cables, accessories, and everything needed to connect to the web. The Cloud Kit costs $149.