Issue 262: EQ Answers

Problem 1—The classic two-transistor astable multivibrator is shown below. Typically, R2 and R3 have at least 10 times the value of R1 and R4. This circuit oscillates, with Q1 and Q2 turning on alternately. From the point in time in a cycle where Q1 first switches on, describe what happens until Q2 switches on.

Source: D. Tweed, CC262

Answer 1—Right before the moment Q1 switches on, C1 is charged to VCC – VBE, with its left end positive, and the left end of C2 has just reached +VBE. The right end of C2 is being held at VCE(SAT) by Q2.

Source: D. Tweed, CC262

So, as Q1 begins to switch on, it pulls the left end of C1 low, and this also pulls the right end of C1 low, cutting off Q2. This in turn allows the right end of C2 to rise, emphasizing the turn-on of Q1 by increasing the voltage (and current) at the base of Q1.

Once Q1 is fully on, the right end of C1 is now at VCE(SAT)– (VCC – VBE) (a fairly substantial negative voltage), and C1 now begins to charge in the other direction, through R2. Once the right end of C1 reaches +VBE, Q2 begins to turn on, starting the second half of the cycle.

Problem 2—What determines the time of one half-cycle of the oscillation? Does this depend on VCC?

Answer 2—The time of the half-cycle described previously is the time that it takes the right end of C1 to charge from –(VCC – (VBE + VCE(SAT))) to +VBE.

Now, keep in mind that the capacitor is charging “toward” +VCC, but it gets halted by the B-E junction of Q2 at +VBE. This charging is occuring at a rate determined by the time constant C1 × R2, and we’re basically interested in the time that it takes to move halfway from its starting value to its final value. This works out to –ln(0.5), or 0.693 times the R-C time constant.

As long as VCC >> VBE, the time does not depend on VCC. That isn’t to say, however, that VCC can be arbitrarily large. If it exceeds the reverse-breakdown voltage of the transistors’ B-E junctions, current will flow and perturb the timing.

Problem 3—Recently, a different circuit appeared on the web, shown below. Again, R2 and R3 are significantly larger than R1 and R4. The initial reaction of one observer was that this circuit can’t work, because there’s no DC bias path for either transistor. Is this assessment correct?

Source: D. Tweed, CC262

Answer 3—No, it isn’t. This circuit can oscillate just fine. Again, look at how C1 charges and discharges.

Source: D. Tweed, CC262

If C1 starts out discharged, it will charge through R1 and the B-E junction of Q2. This current will turn on Q2, holding its collector at ground (really VCE(SAT)) and preventing Q1 from turning on.

However, as C1 reaches full charge, the current through it decays below a level that will keep Q2 turned on. When it starts to turn off, its collector voltage rises, which also forces current into Q1′s base through C2. As Q1 begins to turn on, it pulls its collector low, which also pulls the base of Q2 lower, emphasizing its turn-off. The circuit quickly “snaps” to the other state, with Q1 on and Q2 off. C1 is discharged through Q1 and D2 at the same time that C2 begins charging through R4 and Q1′s B-E junction.

Problem 4—What role do R2 and R3 play in this circuit?

Answer 4—R2 and R3 never have more than ±VBE across them; as a result, the current through them is negligible relative to the current through the capacitors. In other words, they’re superfluous.

Question 5—Does the timing of this circuit depend on VCC? If not, what does it depend on?

Answer 5—The time from when one of the transistors turns on to when it turns off is determined by the currents flowing into its base and collector. When the current into the base drops below the value needed to sustain the current into the collector, the transistor begins to turn off, and the circuit feedback then insures that this happens quickly.

Looking at Q2, and ignoring the transient associated with discharging C2 for now, the collector current is set by R4. The initial base current is set by R1, but this decays exponentially with a time constant of R1 × C1.

Therefore, the primary determinant of the half-cycle time period (in addition to the R-C time constant) is the current transfer ratio, or hFE of each transistor. When the base current drops to a value of 1/hFE of the collector current, the transistor begins to turn off.

Since both currents scale in the same way with VCC, it has no direct effect on the timing. There is only a secondary effect if the value of hFE changes with the value of the collector current.

Contributor:  David Tweed



Electronics Engineering Crossword (Issue 262)


3.     CATHODERAYOSCILLOSCOPE—Isn’t a digital ’scope [three words]

6.     PASSBAND—A super-efficient band of frequencies

9.     MESHNETWORKING—Relies on nodes to capture, distribute, and reproduce data [two words]

11.   PYTHON—An open-source programming language that relies of automatic memory management

13.   NORTONSTHEOREM—A formula for linear electrical networks [two words]

15.   TRIMMER—Variable resistors, variable capacitors, or trimmable inductors, for example

18.   DATATRANSFERRATE—Measures data’s speed of travel [three words]



1.     COLUMBSLAW—Electrostatic physics principal [two words]

2.     NOVACEK—Wrote 26 feature articles for Circuit Cellar between 1999 and 2004

4.     CYGWIN—Enables you to “get that Linux feeling on Windows”

5.     ELECTROLUMINESCENCE—Light emission caused by electrical influences

7.     SCHMITTTRIGGER—A comparator with two different threshold voltage levels [two words]

8.     POLARITYSWITCH—Reverses an output signal’s absolute phase [two words]

10.   SIEMENS—Equivalent of amperes per volt

12.   RAREFACTION—Sound wave phase

14.   SLEWRATE—Represents a signal’s maximum rate of change [two words]

16.   QFACTOR—Measures the damping of resonator modes

17.   GERBER—PCB file format

19.   TRIODE—An amp device with three electrodes

20.   SPRAGUE—Known as the “father of electric traction”


Elektor Weekly Wrap-Up: E-Blocks, Embedded Linux, & the Elektor Lab

Last week Elektor staffers provided the Circuit Cellar staff with an E-Blocks kit to open and analyze, introduced a new course on Embedded Linux (along with an affordable Linux board), and gave members a behind-the-scenes look at the Elektor Lab. Let’s review.


Early last week, the Elektor editorial department sent Circuit Cellar staffers an E-Blocks kit to open and review.

E-Blocks: The Elektor Pro PICmicro Starter Kit

So, what are E-Blocks?

E-blocks are small circuit boards. Each contains a block of electronics that you would typically find in an electronic system. The 40 circuit boards in the E-blocks product line use rugged, nine-way, D-type connectors as a connection bus for eight signal lines and earth. Power (5 or 3.3 V) is wired separately. Thus, you can assemble a complete system to be assembled in a matter of minutes.

The system’s functionality can be enhanced further by the addition of more than 40 sensors and accessories.

Systems based on microcontrollers can be programmed using flowcharts, C, or Assembly. Systems based on CPLD/FPGA technologies can be programmed in block diagrams, VHDL or Verilog. A range of CD ROM tutorials, which includes compilers, development tools and manuals, provides support to students who are new to any of these technologies. (Source)

Click here for more information.

Take closer look at the E-Blocks kit. It includes a Microchip Technology PIC16F877A chip, a multiprogrammer board, an LCD board, a switch board, Flowcode, an internal power supply, and documentation.

Embedded Linux Made Easy

Elektor announced last Wednesday an introductory course on Embedded Linux that’s accompanied by a compact circuit board:

In this beginners’ course you will learn where the most important applications and software components, the basis of our Linux system, originate from. You will also learn how the hardware is constructed and how it operates. The next step is to install a suitable Linux development environment on a PC to compile our own source code. By the end of the course you will be able to construct a simple heating controller with a graphical display and data analysis via a browser.

The Linux board features:

  • Two-layer board using readily-available components
  • No special debugging or programming hardware required
  • Fully bootable from an SD memory card
  • Linux pre-installed
  • 180-MHz ARM9 MCU, 8-MB RAM (32 MB optional), 64 MB swap
  • Integrated USB-to-RS-232 converter for console access
  • Relay, external power supply, and pushbuttons for quick testing
  • Four GPIO pins, 3 A/D channels and a PWM channel
  • I²C and SPI buses accessible from Linux
  • USB interface for further expansion

More info.


Circuit Cellar has been publishing workspace writes for the past few weeks. Last week, our colleagues at Elektor gave the world some insight about the Elektor Lab:

Developing electronic circuits necessitates measurement equipment, tools and a good place to work. Many electronics engineers, pro or hobbyist, tinkerers, researchers and other refer to this place as their “Lab”. We at Elektor have our Lab where we develop and test the circuits we publish in the magazine. Over the years, we have collected, (mis)used and destroyed quite a lot of gear, soldering irons and components here, and it is only thanks to regular & rigorous ‘clean-up’ campaigns that we keep our lab workable.

Many of our readers have access to their own often substantial labs, with equipment that sometimes even the NASA would be jealous of. So what does your electronics workspace look like? Our colleagues at Circuit Cellar have begun posting write-ups about workspaces, hackspaces, and “circuit cellars” on their website. If you would like to show off your lab, just send them some pictures and descriptions and they will post it on the Circuit Cellar website. Don’t worry about cleaning up first as our lab is probably in a similar state as yours. (Source)

Email pictures and descriptions of your workspaces, hackspaces, and circuit cellars to our editors. is an Elektor International Media publication.


Issue 262: Full-Featured SBCs at Your Fingertips

Fact 1: Easy-to-use, full-featured SBCs are popping up everywhere. Fact 2: Open-source software is becoming more commonplace each day. (Even Microsoft Corp. has begun taking open source seriously.) Conclusion: It’s an opportune time to be an electronics innovator.

In Circuit Cellar May 2012, Steve Ciarcia surveys some of the more affordable, 32-bit hardware options at your disposal. In “Power to the People” he writes:

While last month I may have implied that 8 bits is enough to control the world, there are significant things happening in high-end, 32-bit embedded processors that might really produce that inevitability. There are quite a few new system-on-chip-based, low-cost, single-board computers (SBCs) specifically designed to compete with or augment the smartphone and pad computer market. These and other full-feature budget SBCs are something you should definitely keep on your radar.

These devices typically have a high-end, 32-bit processor, such as ARM Cortex-A8, running 400 MHz to 1,000 MHz, coupled with a GPU core (and sometimes a separate DSP core) along with 128 MB to 512 MB of DDR SDRAM. These boards typically boot a full-up desktop operating system (OS)—such as Linux or Android (and soon Windows 8)—and often contain enough graphics horsepower for full-frame rate HD video and gaming.

Texas Instruments made a significant splash a few years ago with the introduction of the BeagleBoard SBC (, $149 at the time) with their OMAP3530 chip along with 256-MB of flash memory and 128 MB of SDRAM running Angstrom Linux on a high-resolution HDMI monitor. That board has since been superseded by the BeagleBoard-xM (1,000 MHz and 512 MB) at the same price and supplemented by the BeagleBone board. Selling for just $89, BeagleBone includes a 600-MHz AM3517 processor, 256-MB SDRAM, a 2-GB microSD card, and Ethernet (something the original BeagleBoard lacked).

All of the software for these boards is open source, and a significant community of developers has grown up around them. In particular, a lot of effort has been put into software infrastructure, with a number of OSes now ported to many of these boards, along with languages (both compiled and interpreted) and application frameworks, such as XBMC for multimedia and home-theater applications.

Another SBC that has been generating a lot of buzz lately is the Raspberry Pi board (, mainly because the “B” version is priced at just $35. Raspberry Pi is based on a Broadcom chip, which is unexpected. Broadcom traditionally only gave hardware documentation and software drivers to major customers, like set-top box manufacturers, not to an open-source marketplace. Apparently, the only proprietary piece of software for the Raspberry Pi board will be the driver/firmware for the GPU core. Unfortunately, as I write this, there are a few lingering manufacturing issues, and Raspberry Pi still awaits shipping.

Both the concept and size of an “SBC” are evolving as well. In addition to the bare development boards, a number of interesting second-level products based on these chips has begun to appear. Take a look at A couple of projects in particular are Pandora’s Pandora Handheld and Always Innovating’s HDMI Dongle. The former is a pocket-sized computer that flips open to reveal an 800 × 480 touchscreen and an alphanumeric keypad with gaming controls. Besides the obvious applications as a video viewer, gaming platform, and “super PDA,” I see huge opportunities for this box as a user interface for things like USB-based test instruments.

The Always Innovating HDMI Dongle is amazing for how much functionality they’ve crammed into a small package: it’s no bigger than a USB thumb drive (it also needs a USB socket for power), but it can turn any TV with an HDMI input jack and USB socket into a fully functional, Android-based computer with 1080p HD video playback, games, and Wi-Fi-based Internet access. These dongles might easily become distributed home theater nodes, delivering high-quality video and audio to multiple rooms from a common file server; or, one of the other low-cost SBCs might become the brain of a robot that can see and understand the world around it using open-source computer vision (OpenCV).

While it makes an old hardware guy like me feel less useful, it’s clear that the hardware—or, more specifically, the necessity to always design unique hardware—is no longer the bottleneck when it comes to powerful embedded applications. In a turnaround from decades ago, the ball is now clearly in the court of the software developers.

The applications for these boards and “thumb-thingies” are endless. Basically, they have the hardware muscle to handle anything that a smartphone or pad computer can do for much less. A lot of work has already been done on the OS and middleware layers. We just need to dive in and create the applications! Then it basically becomes a simple matter of programming. Of course, you know how much I personally look forward to that.

Circuit Cellar 262 (May 2012) is on newsstands now. Click here for a free preview of the issue.

Raspberry Pi Now Shipping

Got Raspberry Pi? Probably not. But rest assured. The wait is almost over.

After receiving an inquiry about the status of Raspberry Pi from a Circuit Cellar member earlier today, I decided to do a bit of research. It didn’t take long to figure out that hundreds of thousands of orders have been placed and shipping has begun.

Raspberry Pi (Source: Raspberry Pi Foundation & posted on reported last week that more than 350,000 orders have been placed since February and the next shipments are scheduled for May.

According to an April 18 post by element14′s Sagar Jethani, shipping is underway and “will be made strictly in the order that commitments were received within each region — Europe, Asia, and the Americas.” He added that “Everyone who ordered before 18th April will definitely receive their Raspberry Pi before the end of June. Those placing new orders from today can expect a July delivery.”

I encourage Circuit Cellar members to tell us what they think about Raspberry Pi once their receive their orders. We’ll be happy to review project articles for publication in print or online.

The Raspberry Pi Foundation’s compact (85.60 mm × 53.98 mm × 17 mm) single-bard computer features a Broadcom BCM2835, an ARM1176JZFS, and a Videocore 4 GPU. The ARM GNU/Linux system costs $25.

You can order the Raspberry Pi from element14 and RS Components.

Check out my first Raspberry Pi post for additional information.