EE Fundamentals: Series and Parallel, Part 1

In the last EE Fundamentals segment I covered Ohm’s Law and the measurements that make up the bulk of electrical theory: voltage, current, and resistance. I figured the next logical step is to start with the building blocks of circuit analysis. This entry will look at the various ways resistors can be connected in a circuit. This is a two part entry with the first part focusing solely on the way the resistance varies with these connections. The second part will look at the way voltages and currents change depending on the orientation.

Circuits are often connected in series, in parallel, or in series-parallel. When you start talking about circuit topologies these fundamentals break down somewhat, but from a hobbyist perspective these three connection types are likely the only ones you will ever need.

Series Connection

Connecting components in series means you are essentially chaining the end of one component onto the beginning of another. When you connect resistors in series from one end of a voltage source to the other, you create a pathway for current to flow and thus produce a series electric circuit. Figure 1 shows what I am talking about assuming the connecting wires are perfect conductors (i.e. zero voltage drop across them). 

Figure 1. A series circuit

 

The total resistance of a series circuit like the one above is equivalent to the sum of all the resistances in the circuit (assuming those are the only two components present). Figure 2 shows two series circuits that have different resistances.

 

 

Figure 2. Adding resistances in a series circuit

As you can see, when a new resistor is added the circuit resistance increases by the nominal rating of the resistor. In the first circuit, the equivalent resistance is 15 kohms. The second circuit adds another 10k resistor in series with the other two creating an equivalent resistance of 25 kohms. Therefore, we can express the equivalent resistance (in ohms) of a series circuit as the sum of the all the resistances present or (where n = total number of resistances in the circuit):

Parallel Connection

Parallel circuits are the ones that I find people have the most difficulty understanding because conceptually they are not as simple as connecting one component after another like series circuits. Instead, components are said to be in parallel if they share the same electrical connection points throughout the circuit. Figure 3 illustrates this concept more clearly. 

 Figure 3. A parallel circuit

As you can see, three resistors are connected to both the positive battery terminal and ground.

To find the total resistance in a parallel circuit, you have to add the inverse of each resistance together and then take the inverse of the sum. The reason this is necessary becomes apparent in the voltage and current relationship, but I don’t want to get into any proofs in this entry. The total resistance in a parallel circuit can be expressed (where n = total number of resistances in the circuit):

 

Figure 4 shows an example of a parallel circuit as well as a demonstration of how to find the total resistance. Interesting fact about resistances connected in parallel, the total resistance of the circuit will always be less than any individual resistance in the circuit. Therefore, you can effectively reduce the total resistance of a circuit by adding a low value resistor in parallel with your circuit. The equation below shows how this works in practice. 

 

 Figure 4. A 2.5 kohm equivalent circuit

Series-Parallel Connection

 A series-parallel connection is merely a combination of the two types of connections we have already gone over. All of the rules still apply from each connection.

This type of connection is used in almost every circuit out there. It is pretty rare to find a circuit that is just a parallel or just a series connection. The only difficultly in dealing with these types of circuits is identifying the individual connections within the whole and being able to sort them out. Figure 5 shows an example of a series-parallel circuit.

 Figure 5. A series-parallel circuit

Let’s break down Figure 5. The two 10k resistors are connected in parallel with each other but in series with the 5k resistor. To simplify the circuit, we can condense the two 10k resistances into the equivalent resistance seen by the source using the methods mentioned earlier.

The equivalent circuit now looks like Figure 6 below. The circuit resistance is unchanged, but we made the circuit more intuitive by reducing the parallel branches into one resistor. Now, it looks like a simple series circuit where we can add the two 5k resistances together to get the equivalent circuit resistance.

 Figure 6. The series equivalent circuit of Figure 5

Some Final Notes

The total resistance of a circuit can change depending on “who” is viewing the circuit. In the classic teaching example, a DC source (battery) is placed in a series-parallel circuit and you try to find the equivalent resistance. What is often left off is that they are looking for the equivalent resistance as seen by the source, also called the “input resistance”. For reference, every example I have cited so far has been asking for the input resistance.

However, in cases like amplifier design both the input and the output resistance can be critically important. The “output resistance” is the resistance of the circuit as seen by the load. The same rules we have looked at in this entry apply for both input and output resistance, but you must shift your perspective from the power supply to the load receiving the power.

Pop Quiz

Let’s see how much you have learned. I put together a simple series-parallel circuit below and I would like to know the equivalent resistance as seen by the input terminals (where the arrow is). Leave your answers in the comment boxes. The numbers represent the value of the resistor they are closest to in ohms. Good luck!

The Loss of Legends

Sad news to report as the electronics industry has lost two of its design legends. Jim Williams, an analog circuit designer with Linear Technology (LTC), and Bob Pease, an analog circuit designer with National Semiconductor (NSC), both died suddenly just over a week apart. Jim (63) suffered a severe stroke on Friday June 10^th and passed away early Sunday morning. His funeral was held this past weekend with several senior engineers in attendance. As it turns out, Bob Pease (70) was among the crowd of mourners. While driving home from the service Bob lost control of his car and hit a tree. There are ongoing investigations into whether he may have suffered a heart attack or stroke, which could have contributed to the crash.

To say these guys were analog circuit designers trivializes their impact on the electronics world. They were world renowned experts in their field. In an age where more engineers are relying on circuit simulation software as their crutch, they relied on their intuitive understanding of electronics to turn analog design into an art form. Here’s a hint for anyone unaware – analog design is hard. It’s really hard. There are guys who spend their whole lives designing analog circuits but are lost when they look at a schematic of a Pease or Williams original. What adds to their mystique is how they easily they would explain away the most complex circuits. Both men had a knack for making the impossible seem trivial and that is where their greatness lies.

I have only become aware of these two within the last year, but the few articles and papers I have been able to get my hands on blew me away. To celebrate the lives of these two extraordinarily talented engineers, let’s take a closer look into their careers.

Jim Williams

Jim Williams spent a year and a half at Wayne State University in Detroit studying psychology before dropping out. He took a job with the MIT Nutrition Lab shortly afterward where he would build circuits for their test equipment and experiments. Jim was introduced to electronics by a neighbor who loved design and collected oscilloscopes in his garage but had no formal education in the subject.

After 10 years of working at MIT and doing some consulting work on the side for various electronics and integrated circuits manufacturers, like Analog Devices, Jim went to work with National Semiconductor out in Silicon Valley in 1978. He was a mainstay in the linear integrated circuits group while at NSC but by 1982 he had moved on to become the first applications engineer at the then start up company Linear Technology. Since that time, Jim has written dozens of application notes for LTC (“Switching Regulators for Poets” is a personal favorite – check out the last page to see why)  and over 60 articles on Analog Design for Electronics Design News (EDN), a website/magazine dedicated to circuit design. He helped build Linear Technology into one of the biggest analog electronics components suppliers in the world from the ground up.

In 1992, Jim won EDN’s “Innovator of the Year” award for his work in analog design. Jim was touring around companies and campuses in more recent years giving lectures on analog design to students and younger engineers. LTC even featured him in a few of their testing methods videos on YouTube.

He has written over 350 publications on analog circuit design including a book co-authored with the co-founder of LTC Bob Dobkin due to be released later this year. In 2002 he was elected into the Electronic Design Hall of Fame with the likes of Tesla, Turing, Shannon, and Widlar.

Jim was still working at LTC at the time of his death as their “Staff Scientist” citing that he only had two fears in life “sickness and retirement…in that order “.

Bob Pease

Bob Pease graduated from MIT with a degree in electrical engineering in 1961. He took a job designing vacuum tube amplifiers and voltage-to-frequency converters at a company called Philibrick Researches. In 1976, Pease migrated to Silicon Valley to work at National Semiconductor where he remained until retiring in 2009 (he remained a technical consultant for National Semiconductor right up until his death).

Like Jim Williams, Pease wrote articles for EDN and even received his own column called “Pease Porridge”, where he would reflect on electronics, life, and whatever he wanted. By 1992, his column won the Certificate of Merit from the Jesse H Neal Awards Committee of American Business Publications. Pease also wrote a book called “Troubleshooting Analog Circuits” that has become a best-selling electrical engineering text and is now in its 14^th printing. I have only read selected sections, but I can tell it is a quality read and a great reference for any engineer.

During his years at NSC, Bob Pease became the face of the company by touring the world and participating in analog design seminars. By the time he retired, Pease had personally designed more than 20 integrated circuits and held 21 patents. His ICs found their way onto the Apollo spacecraft and were used on medical missions to Mount Everest. One of his most famous designs, the LM337 negative voltage regulator, has sold over 135 million copies in its lifetime.

Pease managed to evolve with the times and started hosting an online electronics show called “Analog by Design” shortly after the turn of the century, which featured engineers from National Semiconductor and other agencies discussing the nuances of good analog design. Bob Pease was also a member of the inaugural class of engineers for the Electronic Design Hall of Fame in 2002.

**UPDATE**  National Semiconductor has posted a memorial video on their website, which is definitely worth checking out if you want to get a sense of this guys personality. Click here to check it out.

I haven’t been around this industry long enough to really grasp the body of work these two men established during their lifetime. In the short while I have had to study their work I have been amazed at what they were able to build without any of the fancy test equipment we have today. Their understanding of electronics and their willingness to impart their knowledge have elevated these two men into electronics legend.

To Bob and Jim, thank you for everything you gave to the electronics community and for all those you inspired, and continue to inspire, to be better. Rest in peace.

New Multimeter

Why invest your money when you buy multimeters! My new BK Precision 2709B multimeter showed up about two weeks ago and I have just gotten around to playing with it. This meter actually won Dave Jones’ $100 multimeter shootout on the EEVBlog (check out the two part video if you are interested in getting an above average meter). Before this meter I had a cheap $20 Chinese meter that I used for college projects and labs so I figured it was time to upgrade. It’s truly amazing the difference quality equipment makes. A little while back I got my first temperature controlled soldering iron (Hakko FX-888) and my work with it has been so much better than anything I did with my cheap Radio Shack iron.

Now for some specs that I really liked about this meter:

True RMS: This meter can measure the true root-mean-squared (RMS) value of any input waveform. Some meters can measure RMS, but they assume the input waveform will be a sine wave so measuring a signal with any other shape will give you inaccurate results. This feature is especially helpful in switching converters because you need RMS voltages for calculating efficiency and selecting components with the right tolerances.

Micro-amps Range: Having a micro-amps range meter is probably going to be a luxury with most designers who don’t work on embedded systems, but one my interests is digital power so I think it may come in handy in the future. For general purpose applications, a micro-amps scale is useful to determine the leakage current of components or the quiescent current of integrated circuits (the current need to make sure the ICs are on even if they aren’t doing anything relative to the system).

3 ¾ Digit Display: Many people get this concept confused when it comes to LCD displays in electronics meters. The first piece is pretty simple: the integer number used for the number of digits represents the number of LCD digits that can display 0-9. So a three digit display can display 999 at the maximum.

Now for the confusing part. The fractional piece usually refers to the most significant digit. Typically you will see a rating like 3.5 digits, which means the maximum the meter can display is 1999 (not 4999 or 5999 like you might think). This meter has a 3 and ¾ digit display so you can get readings up to 5999. As far as I know there are no real defined parameters for these digits outside of using 0.5 to indicate a maximum of 1 as the most significant digit.

0.5% Accuracy: Another term that often gets misused when it comes to multimeters is accuracy. There are actually several accuracy ratings that a multimeter gets because of all the different measurements that it is capable of making (DC volts and amps, AC volts and amps, temperature, etc.). My understanding is that the DC accuracy measurements are the ones most often expressed as the accuracy of the meter because most devices will use DC power.

Accuracy is given as a percentage +/- a few counts, which means you are getting a combination of the measurement accuracy plus the resolution of the LCD display. This meter has a rating of 0.5% + 2 counts. So, for example, if you are measuring a 5V signal, the measurement could be anywhere between 4.975V and 5.025V, but what would actually be displayed on the screen is 4.973V to 5.027V.

Like everything in electronics, the best choices fit the needs of the application. In my case, power conversion requires accurate DC voltages and currents as well as RMS values so DC accuracy and true RMS were important when I chose this meter. I will admit  the fact that Dave Jones gave it his thumbs up helped a lot too, but it ultimately came down to what I needed and the fact that I had seen an in depth review of it somewhere else.

I didn’t really have any specific goal in mind for this post other than to show off my new meter, but my hope is that some of this will be useful in the future. If you want to learn more about multimeters – how they work, what to buy, what to look for – check out the EEVblog and look for any episode with “multimeter” in the heading. Dave Jones is the king of meters as far as I am concerned. He does some really great tutorial blogs on how they work and what to look for when you are buying.

7-Segment Display Demo

In my last post I talked about the 7-segment display and its popularity among digital displays. For the first time in this blog, I figured I would build up a sample circuit just as a small demo to prove what I am talking about actually works in practice. 

 Figure 1. My demo 7-segment circuit layout

In the picture above, I have wired up a simple 7-segment display using the CD4511BE driver IC from Texas Instruments (see my last post for some data sheet diagrams about the chip’s operation). The breakdown of the functional blocks goes like this:

Pink – These are the input switches that allow for any binary number from 0-9 to be entered into the 7-segment driver IC. The resistors closest to the switches are known as pull down resistors because they make sure the voltage seen by the IC is either 0V or 5V (0 or 1). You can enter the binary number using the switches as shown in Figure 2. From left to right, the number translated to 5 in decimal (0101 in binary).

Figure 2. Input switch terminal used to control  the display

Blue – The CD4511BE chip from Texas Instruments. This chip is the brains of the system. It interprets the inputs from the switches and sets the appropriate outputs high according to its internal logic (see the truth table from my last post).

Yellow – Current limiting resistors are used on each of the seven outputs from the IC to protect the chip from trying to source to much current and keeping the led from running away and burning out. In this case, I used 470 ohm resistors to limit the current based on a 2V turn on voltage of the LEDs in the 7-segment and 5V coming from the IC on each output lead.

Red – A 7-segment display using red LEDs. There are several different colors available, but each will require certain voltages and current limiting resistors. If you are ever trying to figure out which resistor to use, I suggest looking up a current limiting resistor calculator online if you don’t want to deal with equations.

There really isn’t too much more to say in this post. Just as an example, Figure 3 shows the output of the 7-segment display using the input from Figure 2. 

 Figure 3. The 7-segment display as a result of the inputs from Figure 2

My goal with this small segment was to introduce a relatively simple electronic system because, as I have said, I am basing my scoreboard design on this layout.

As a side note, if you start bread boarding circuits, I highly suggest color coding your wires so you know what is what. In Figure 1, I used the power and ground convention of red and black respectively (*NOTE: DO NOT ASSUME THIS IN HOUSE WIRING!! Black is often the hot wire and you could get yourself killed if you don’t know what you are doing). I used yellow wires for the inputs from the switches and green as the outputs to the 7-segment display. In some cases, I attached a resistor directly to the output of the IC so a green wire was not necessary. This all may seem like a diversion from the main topic, but I have found these small tips very useful in circuit design.