When I started writing on my blog, I promised myself that it would not be about personal issues (“my roommate won’t pickup his socks!”) or rants about everyday happenings (“The people at the grocery store are slow!”). But I feel that reviewing the past 25 years of my life is good from a historical perspective and in terms of this blog so readers know more about where I’m coming from.
I am constantly amazed at how lucky I have been. I was born a white middle class male to loving parents and into a great family that encouraged my academic and intellectual achievement. I was also born in the United States of America, in an English speaking community that was voted one of the safest in America throughout my childhood. I’d say this already puts me in the top .1% of the world in terms of being dealt some great cards. Add to that the opportunities I’ve had with the school I was able to attend and the jobs I successfully interviewed for and I can’t think of many better situations. On top of all that, I work at a great company with lots of educational opportunities and I do something I really enjoy.
So not to sound like an Oscars speech, but I would like to thank so many people that made the past 25 years of my life possible. I want to thank my parents and sisters for being there for me and putting up with me. I’d like to thank all of my teachers throughout school that encouraged me, especially my high school physics teacher that inspired me to go into engineering. To all of my friends that are kind enough to click on my blog on a regular basis and give me great feedback on all things in my life, not just this blog. To our pound puppy Lola, who licks my face at every available chance and sits next to me whenever I need a canine friend. And saving the best for last, to my beautiful and brilliant girlfriend, who encourages me every day and loves me even when I’m writing about electronics and trying to explain it to her at 11pm.
That’s all for now. I thought one mushy post interspersed with serious posts wouldn’t be too bad, so I hope you enjoyed. Getting older always seems to have a stigma of life going faster and getting more hectic, but I think of it as more opportunities for learning and meeting new people. I’m sure this year will be another great one. If not, at least I can now rent cars with out that silly under-25 surcharge. Woo!
My friend Trevor has an intriguing post about methods of mapping the brain. This is of interest to me because of how I have been reading “The Singularity is Near” by Ray Kurzweil. Trevor talks about research into “seeing” water flow in the brain, as opposed to glucose or electrical signals or bloodflow. It’s a really cool idea to help understand how the brain works and how it could help humans relate to the world around them.
So why am I interested in the brain? Well, as Ray says, mapping the brain will result in technology beyond anything we could ever imagine for future technology. Using the biologically evolved model of the brain will allow us to leap past prior research in digital and analog technologies to create more advanced computers sooner. This will eventually allow for humans to choose to either become hybrid (biological/machine) beings or even completely machine beings, with transferred knowledge from the biological counterparts. This is also the idea he refers to as “The Singularity”…when human intelligence is surpassed by machine intelligence and machines begin to evolve on their own. Not to worry, he also claims that the machines will consider us “their biological forebears” and they will respect us (and not dominate us and turn us into batteries).
For more reading on/by Kurzweil, be sure to check out The Law of Accelerating Returns, upon which he bases many of his arguments. Some of the ideas he has are pretty radical and optimistic, but they are definitely possible in this lifetime. If you’re not interested in that, make sure you read Trevor’s post (or an part of his blog), it’s quite intriguing.
I have a friend who alerted me to a company out in New Mexico known as Solar Automation. They don’t make solar panels; rather, they make the equipment to make solar panel arrays. However, what I find most intriguing about the company is their concept of Micro-Factories. In the case of Solar Automation, the basic idea is that a small team of people are capable of creating solar arrays by soldering the tiny wires with non-lead solder. This same concept could be expanded to many other applications, including mechanical or auto assembly, textiles, food preparation (already done at caterers, really).
Although it exists on a slightly larger scale, China epitomizes the Micro-Factory model. They have large labor pools using simple equipment to make incrementally more complex equipment. One example might be a board house that hand assembles and solders through-hole part boards. This could instead be done in a large facility with automation on expensive equipment. However, the cost for the equipment would likely mandate a large overall throughput for the factory in order to justify the cost of the equipment. Conversely, a smaller hand soldering operation could easily scale the number of people required to make an order of boards. As for energy savings, there can be higher efficiency with a laborer using a low wattage soldering iron as compared to heating lamps or continuously heating a wave solder machine.
The pivotal point in this argument is whether or not the end product requires increasing complexity in the machines that construct it. Solar is a good example. The panels themselves are not particularly complex, mostly they are tons and tons of PN junctions that convert incident light into flowing electrons. However, the chemicals and the semiconductor processing equipment is very complex.
So what are the benefits of Micro-Factories?
Local workforce – With the exception of a privileged few (non-whiners), no one will contend that the US and the world economy is hitting some tough times. Local jobs are outsourced or cut outright. Mom and pop shop workers are now greeters at WalMart. Why not instead allow lower education workers have a job creating something useful for society and the environment, rather than peddling trinkets made 6000 miles away? Added bonus: Your workers do not have to travel from far away to work, thereby cutting down on costs and emissions.
Simple training – Training is not cheap. If you ask people at Samsung, I was training for roughly a year and a half to do my job (and promptly left for a new one). It takes times to get into the swing of things at companies, no matter the task. Why not make the task simpler? The Solar Automation takes a complicated end process and allows simple training to quickly begin.
Built in quality control (eyes) – While this would hinge on the enthusiasm of the workers (and therefore dependent on myriad other factors), it’s a fact that most computers do not notice something innately wrong with a process. Most people will notice if a solar panel is discolored or if a wire is hanging off where it’s supposed to be connected. Until the day when computers are smarter than humans (and cheaper), people will implement a natural form of quality control.
What are the drawbacks, you ask?
If you give a mouse a cookie (cutter job), he’s going to want benefits – My own views about benefits and healthcare aside, it’s a fact that people expect some form of benefits, most easily represented in business as overhead. It expands beyond healthcare and such (think tables and chairs and other things that people expect from jobs), so you might have to label the job as “an alternative workplace” where compensation is higher (in the event you don’t want to/have to provide benefits). Doesn’t mean you can’t have a productive workplace though.
In the solar example, there are still high material costs (the actual solar cells), so the margins will be squeezed. In general, assembly jobs are meant to be high volume, low margin endeavors, so there are risks when material costs rise; doubly so if your revenues are stagnant (because of contracts or otherwise).
Sometimes it’s still cheaper to ship repetitive jobs overseas or automate a process. That’s all there is to it.
Micro-Factories could be a great way to increase employment, mobilize a stagnant workforce and help cut down on emmissions. I would highly suggest you check out the Solar Automation page and leave comments on other places you have seen similar ideas implemented.
I recently had a high school friend visit and while watching the Olympics and having some beers, conversation turned to China (and the rest of the world). I know, I know, I’ve recently talked about the Olympics and China and such; But this is different. The conversation moved to energy and how it relates to national security, which I also have read about recently in a trade journal. Basically he brought up the astute point that renewable energy needs to be our number one priority in the coming years. We’re not talking 20 or 30 years…we’re talking 2 or 3. Really, it’s that important.
If you think about it, it makes perfect sense. Let’s say America reduces its energy dependence and busts its hump to get renewable energy contributing to say 40% of the country’s need (imagine a breakthrough that would allow this). What happens next? Well, if it was overnight (which it wouldn’t be), oil demand and prices would more than likely fall overnight too. Not to worry, I’m sure somewhere along the way that the demand would be filled by large countries that manufacture goods and want some newly cheap energy. But what about (the) US? In succession, we’d be able to say “Goodbye! No Thanks! Don’t Need it anymore!” to: Iraq…Iran….Russia….Venezuela….and China (though we probably wouldn’t with China, they make our stuff, right?). Almost all of the conflicts the US has with other countries center around oil! I would imagine it’s not going to stop with these countries either. Oil will become the driving force behind global conflicts for years to come, followed only by the fight for potable water. So why not go over the oil barons’ heads and make our own energy and let the wind and sun give us all the power for free?
40% of energy coming from renewable energy? Does the US have the brainpower to achieve that? No, not unless just about every scientist and engineer was capable of dropping what they’re doing and shift all their focus to working on energy. But there’s tons of smart scientists and engineers all over the world. What a break! In fact, there are engineers already doing a lot of this renewable energy work already. So maybe we could achieve two things here…first, the US would get scientists to help develop energy solutions that would allow us to ignore the tyrants of the world; second, the US would continue to maintain our most important resource going to the future: intellectual capital.
For the past 100 years, the US has been a leader in technology because of its innovators. These best and brightest minds created everything from electronic building blocks to the computers in which they were utilized. And now we’ve seen not only jobs going overseas, but a lot of the best minds are popping up outside this country too. Not only that, a lot of the top minds are coming to the US to study and then following jobs home to their native countries. So another solution for the benevolent (or otherwise) forces in the world: lure them to the United States and claim them as our own. While intellectual capital may have been one of our greatest resources that is arguably losing ground to the rest of the world, the US still has something that many other countries do not. What other countries have Hollywood, New York City, Chicago, LA, National parks bigger than certain countries and so on and so forth? Where do people want to move for jobs and stay and live and raise families? I think that the US needs to utilize the drawing power of our entire country, our availability of opportunities and our lifestyles (whether people agree with the decadence of western culture or not).
The future of the world in regards to energy is very uncertain; the US will remain a world power only if we are able to recruit the best minds, keep them here and have them help to create a world run on renewable energy.
The other morning I heard a great story on NPR about people in China and their interest in basketball. I was really interested to learn how they believed basketball allowed them to express their individuality. One of them dreamed out loud of being able to dunk and how this was their ultimate dream of freedom.
Aside from the question of how many different ways there are to dunk, it got me thinking about Chinese culture and how it has contributed to their success over the past 8 years or so. It is no secret that the Chinese culture, and specifically the government, stresses conformity. One might think that this would hinder the technological progress in China, but they are quickly becoming a technology leader in the world (it is important to note that a good deal of the continued success of China is companies outside the country driving progress…but not all of it). Add to that how more and more design work is being offshored, due to the low cost and higher supply of design engineers. A slew of questions have popped up in my mind when I think about these kinds of things.
Does conformity hurt a culture?
I would argue that when it comes to academics and business, conformity helps. In school, this is obvious. If you are in a classroom with 50 other students, every student is expected to know that 2 + 2 = 4. Sure, this is a simple example, but the academic system is usually based upon reaching a solution that someone else (the textbook, your teacher, the government, etc) wants you to reach. Further, the extremely competitive nature of academia in China has parents encouraging this behavior, even outside the structures of academia (no, I am not suggesting that 2 + 2 does not equal 4, nor that you should tell your teacher so to be unique, just that conformity can travel beyond the walls of a school). Academic stress happens in America too, I just feel like it is more ubiquitous in China.
What about in business? This too has some benefits. Think about a production line in China, cranking out iPod after iPod, all made to be the exact same, with the outliers and the bad production techniques tweaked to remove these expensively bad units. The faster each unit can be made the same, the cheaper that unit will be, and the happier the company selling it will be. The concept was created in the wake of World War 2, when the Japanese began to focus heavily on quality control; today, the Chinese benefit from these methods of conformity.
So business and school both seem to be havens for conformity. But what about situations that require some ingenuity? What happens when the product that is made so fast and becomes so cheap and ubiquitous that the public is clamoring for a newer and shinier device? (an iPhone instead of an iPod, for example) Who will create the technology that will drive the next revolution? What about when there are students that rise to the top of their class and go on to get a PhD? What happens when the smartest student goes to the best school and gets the highest degree possible after conforming to all the standards placed before them? Then they stare out into the abyss and try to figure out something new, only to realize that no one is there telling them what they need to figure out. I’m not saying this happens, only that it is an interesting scenario and it begs the question: is absolute conformity a good thing?
Is the academic system set up for failure eventually?
This is an extension of the above idea about PhD students. I know many PhD students (in the US) who tell me about their research being only that which their advisor wants. Further, while they are working on their research, they are hoping and praying that there are not any other students about to publish similar results as their own. Perhaps this is why we see more PhD students who are from outside the US (studying at US schools) or are getting PhDs at international institutions–because the fastest paper published is the most important, not the most creative. Perhaps the conformity aspect of academia extends beyond the simple math equations into the upper echelons of higher education. I think the scariest part is the students who eventually become the teachers. If you think about the rigor involved in obtaining a professorship these days, it can include 1 or more PhDs, multiple post doctorate positions and continual paper publishing throughout one’s career. This basically means that the most astute students of the system (those that best navigate the conformity requirements placed upon them) are the ones that become the teachers. These same people then expect the same (or more!) out of the rising students. One has to wonder when this sort of thing will stop.
Another point about the academic system that confuses me is whether or not the students who exhibit some amount of individuality are more or less successful. I would like to think that those with bright new ideas rise to the top, but I am not so sure that this happens. Perhaps instead the ones that conform the quickest and those with the best advisors do the best. Personally, I have never heard of an academic phenom that did not have a spectacular advisor guiding them through the world of academics.
What is individuality?
Well, the idea is that an individual is capable of defining themselves as different from all other people. Does this happen very often? No, of course not. Even this article I am writing now has been conceived and written about many times over. But I view individuality as the opposite of conformity; it is bucking the norm, even if others do too (some small amount of them, of course. If the majority buck the trend, it becomes the new trend).
How does individualism affect creativity?
Creativity is a nebulous and fickle thing. Further, I don’t think that individuality breeds creativity; instead, I believe creativity breeds individuality. This is important to engineering because without creativity, engineering would essentially stop in its tracks. There would be no new methods, no new products, no intellectual progress. Most importantly (and realistically), there would be no financial gain and therefore no more funding to teach and advance engineering. Of course this also extends outside of engineering; art programs, humanities, economics, language (?)…none of these would be funded if there was no creativity and new ideas. Instead, the money would focus on getting the best value from what is already being made. If this is the case, Seth Godin points out not to follow the money.
Does too much individualism breed a sense of entitlement?
I think it’s important to view the other side of this issue. What happens when students are given the freedom to express themselves and the means to do so? In the extreme cases, I think that students are more prone to laziness, replication (copying others) and a sense of entitlement. Let’s look at an American student as it is interesting to contrast the difference from a Chinese student. Many newly graduating students are demanding higher salaries, more responsibilities and have less experience. Some people justify it (and rightly so), but does that mean we’re worth the more than our last generation? I’m not so sure.
C’mon people, of course the extremes of conformity and individualism will have their faults. Of course there will be some mixing of the two that will produce the best engineers and the best students. However, I would really love to hear from you about your opinions on individuality and conformity.
As promised, this post is a follow up post to explain the real-world behavior of an op amp. Here we will continue to anthropomorphize op amps in order to better understand their behavior and what they “want” to do. Also, we will look at some more complicated (but common) op amp configurations so that they are easily recognizable. Let’s begin.
First, let’s look at the symbol for the op amp:
Whoa-ho! What the heck are those? Last time, there was only 3 lines coming out of the triangle and now there’s five! They’re multiplying!
Really the “D” and “E” inputs are the power inputs to the op amp. This means we are no longer simply dealing with the “ideal” case and are now going to look at the behavior with some realistic expectations. I know that when I was first learning about op amps, I was perplexed by this idea. I thought, “Well what is the point of putting power into an op amp? What do I get for it?” The idea is that as long as the signal at the input (or more accurately the difference between “A” and “B” is smaller than the power at the “D” and “E” terminals, then the op amp can amplify the signal. This gets very useful once you start encountering signals that change over time, or AC signals (as opposed to DC signals). Let’s look at this idea below:
Special thanks to CoolMath.comfor the graphing program!
On the top left, we see a SINE wave, which is one of the simplest time varying signals there is. Amplifying this signal would not shift the signal, but instead would make the entire range of the signal larger. If we used a 4x amplification, then we would get the top right picture with the larger signal. Notice in the bottom picture the overlay of these two signals. They do not SHIFT up, but instead look like they are stretched. The easiest way to think of all this is at the extremes. If in the first picture the highest point was 1 and we had 4x amplification, then the output would be 4. However, the middle point is 0 and that multiplied by 4 is still zero. Hence the reason the overlay shows the extreme highs and lows being “stretched” the most. Also, it is important to note that these are analog signals, so EVERY point in between the extremes is being amplified.
The power coming into the op amp also restricts how much the op amp can amplify a signal. Not only that, but sometimes you don’t even get to go to the limits! Say you have +15 volts attached to “D” and -15 volts attached to “E” (most op amps have lower voltages these days but +/- 15 volts still happens sometimes). Now let’s say you have a 1V signal coming into a non-inverting amplifier (shown below). The gain on this amplifier is set to 15 by making the top resistor 14 times less than the resistor connected to the ground (non-inverting amplifiers have a gain of 1+R(top)/R(gnd)). So our 1 volt signal is placed at the non-inverting input (the plus) and the op amp says “15 volts, coming right up!”. Ah, but the op amp doesn’t quite have it. The op amp outputs 13.4 volts are so and then stops. “But WAIT!” you say, “why can’t this op amp output as much as I wanted? The ideal ones can output INFINITY. Can’t I just get one of those?” The short answer: no, you can’t. Op amps have internal protection circuitry that limits how high the input to the op amp can be in order to protect it from blowing up. Additionally, the op amp must consume some of that power in order to actually amplify the input signal; this will be expounded upon in further posts (the internals of an opamp).
The final point in this continuing discussion about op amps, is known as slew rate. Really it is a discussion of how fast an op amp can go and is limited by capacitance. Inside of any op amp, there is a capacitor, or rather a bunch of components that act together as one capacitor. This creates a required charge time for the internals of the circuit (for a more advanced look at this topic, check out the allaboutcircuits.com article on capacitors and calculus). The end result is that the op amp has some limit to how fast it can “decide” what the output should be. If we think back to the signals above that alter with time, we can imagine a situation where they would vary so quickly that an op amp would not be able to keep up. The end result is that a circuit such as the non-inverting amplifier shown above has some frequency above which it can no longer accurately amplify. This is known as the bandwidth of the circuit and has implications in many audio, measurement and communication industries.
This post discussed some of the real world aspects of op amps. The next post will discuss the internals of the op amp, such as the transistor setups. Imperfections in the silicon and the realities of material science will show us that more of the “ideal” op amp model is not possible in every day life; some potential topics are the input bias currents, the voltage offsets across the input terminals and how they can affect everyday circuits.
Things get old. Things eventually do not work anymore. Even the best engineers cannot design a system for part failures (unless they have triple redundant systems, like NASA). It is for this reason, I have decided to document on my blog the tune up of my Wurlitzer 200A electric piano (seen below) as opposed to the usual analog issues in the workplace today.
I mentioned this piano in my post about keeping it simple, namely not replacing EVERY component, only the ones that require an upgrade/replacement. It is a famous piano that can be heard in many types of music, spanning rock, soul, jazz and more. Similar to the FenderRhodes, the Wurly can be characterized by a darker, more over-driven sound and a built in vibrato (constructed from a simple oscillating circuit).
There are two components on these boards that need to be replaced the most often. The first is transistors, due to thermal stresses when they are over worked. In the case of my Wurly, the power transistors (seen below bolted to the large metal heat sink on the left) have started corroding, but have also had reduced output due to thermal stresses over the years. The board has upwards of 250 V and these transistors are ready to be replaced.
The other element that commonly needs to be replaced are the capacitors (the purple barrels seen above), specifically the electrolytic capacitors. An electrolytic capacitor is constructed by soaking paper in an electrolyte and sandwiching it between two aluminum plates (then attached to the leads of the capacitor). After about 10 years or so, the electrolyte begins to dry out and the capacitor degrades. Sometimes this can lead to a catastrophic breakdown (think “POP” or “BOOM”) or it can just mean that no signals will get through. Whereas I think of capacitors being frequency-dependent resistors (where the lower the frequency, the higher the resistance), these capacitors instead have resistance at ALL frequencies, due to the fact that the dielectric constant has gone from that of electrolyte to that of air. The final effect of all of this is a poorer sound, especially at the higher frequencies that are supposed to “pass through” a capacitor.
I am also hoping this will take care of some of the “hum” sound (most likely from 60 Hz); I’m hoping this will be resolved once the power filtering capacitors are replaced. I think that the ripple current may be higher since the capacitors have slowly degraded. This will impose the 60 Hz from the wall power onto the signal coming from the vibrating reeds (through the capacitive pickup). I also am wondering if the transformer (below) requires replacement, but I think I will replace the capacitors and transistors first.
That’s all for now, I will update more as I actually replace these capacitors. For now, enjoy the pictures and the sound samples (above links to Last.fm).
These are questions that I have asked at two periods in my life. The first time was in my introductory circuits class and around that time I really didn’t care (beer was a priority). The second time was when I dove headfirst back into analog electronics for my new job and had to re-teach myself a lot of things. I really appreciate the opportunity I had to re-learn everything because the second time around, I think I got it right.
OK, so let’s start simple. What is an op amp? Whoa, loaded question. For our purposes here (and just for now), let’s say it’s just a symbol.
To keep things basic, the A & B points are the input, the C point is the output.This symbol is an IDEAL op-amp, meaning it is impossible to construct one and really the expectations for the op amp are unrealistic. But this is the internet and we can do what we want on the internet, so we’ll just use the IDEAL op-amp for now.
OK, so now you know what the symbol is, but what does it mean? Well, the idea is you put two electrical signals into the inputs then the output changes accordingly. It takes the difference between the inputs and amplifies it, hence operational amplifier, or op amp. You may have noticed that input A has a minus symbol and input B has a plus symbol. So let’s say that the input to the minus, or INVERTING, input is 1 (for simplicity’s sake…this site is about analog so that value could be ANYWHERE from 0 to 1 or higher! Just thought I’d mention that). The input to the plus, or NON-INVERTING, input is 0. Now the op-amp is in an unbalanced state. The device is designed so that when this happens, the output goes as negative as it can. For the ideal case, we say this is negative infinity, but that’s not really possible. More on that later.
Conversely, in figure 3, if we put a one on the non-inverting and a zero on the inverting input, the op amp output would go high, infinity for our purposes here. The important thing to know is this:
The op-amp always “wants” both inputs (inverting and non-inverting) to be the same value. If they are not, the same value, the op amp output will go positive or negative, depending on which input is higher than the other. (Throughout this article I will continue to anthropomorphize op amps…best to get used to it now)
Alright, so how do we use this in circuits? If we wanted to find out if two signals were different, we could tie the signals to the inputs of the op amp, but then the output would go to infinity. This would not do us any good. The answer to this and many other questions in the universe is feedback. We are going to take the output and tie it back to the inverting input. Now the circuit looks like this:
First, we assume that the circuit has all points start at zero (point A being the most important). Next, we put a value of 1 (like the picture in figure 2) at the “B” non-inverting input. “WHOA,” says the op amp, “THIS AIN’T RIGHT!” So now the op amp puts its output to as high as it can, as fast as it can. This feeds back from the output (“C”) to the inverting input (“A”). So as the output moves closer to 1, the op amp is happier and backs off the output. When the input at A is the same as at B, the op amp is happy and stays there (but maintains the output of 1). The key here is that the op amp moves as fast as possible to get both inputs to be the same.
Why would someone use a buffer? Well that brings us to the next point about op amps, specifically ideal op amps:
Ideal op amps have infinite impedance (resistance) at their inputs. This means that no current will flow into the op amp.
A common use for a buffer is to supply current to another stage of a design, where the buffer acts as a gateway. So when the buffer “sees” a voltage at the input (“B”), it will output the voltage at “C”, but will also drive that voltage with current (as much as you want for an ideal op amp). This would be useful if you have a weak signal at the input, but want to let some other part of a circuit know about it. Perhaps you have a small sensor that is outputting a small voltage, but then you want to send the voltage over a long wire. The resistance in the wire will probably consume any current the sensor is outputting, so if you put that signal through a buffer, the buffer will supply the necessary current to get the signal to its destination (the other end of the wire).
What if the signal coming from the sensor is too small though? What if we want to make it bigger? This is when we turn the op amp into an amplifier, using resistors. One of the more common ways of doing so is using the inverting input, shown below:
Let’s go over what we know about this circuit. We know that the op amp wants both inputs to be the same. We also know that the non-inverting input is zero (because it’s connected to ground) and so the op amp will want the inverting input to be equal to zero (sometimes known as a “virtual ground”). In fact, since the op amp has feedback through the top resistor (squiggly line if you didn’t know), then the (ideal) op amp will output just about any current and voltage in order to get the inverting input to be equal to zero.
So now our situation. A dashing young engineer hooks up a voltage source to the point “IN” set to 1 volt. This creates a voltage at the inverting input. “WHOA” says the op amp, and then it begins to output a voltage to make the inverting input point equal to zero. Since the input is 1 volt the op amp decides it better do the opposite in order to make the inverting input match the non-inverting input of zero. As fast as it can (infinitely fast for an ideal op amp), it outputs -1 volt. The inputs are both zero and everything is right in the op amp’s world. What about current though? We remember that current cannot flow into the op amp at the inverting input, so any current will be flowing through both resistors. If we have 1 volt at the input and a 1 ohm resistor at the input, then we will have 1 amp of current flowing (according to Ohm’s law V=IR). So when the op amp outputs -1 volt across the top resistor, there is a -1 amp going through it (assuming it is a 1 ohm resistor). The currents cancel each other out at the inverting input and the voltage then equals zero. The place where the currents meet is sometimes called the “summing node”. This is a useful representation when dealing with currents as opposed to voltages.
For the last part of this thought exercise, let’s look at a situation where the resistors at the input and at the top of the circuit are not the same. Similarly to above, the same dashing young engineer puts 1 volt at the “In” node. The resistor is still 1 ohm, so there is 1 A of current flowing through to the summing node. The op amp once again sees this 1 volt and once again says “WHOA, I’m unhappy about this” and starts outputting the highest voltage it can. However, in this situation, the top resistor is now 4 ohms. In order to create the -1 amp that is required to cancel the 1 amp going through the input resistor, the op amp must output -4 volts (remember V=IR). We see that for an inverting op amp configuration, the ratio of the resistance of the top resistor to the bottom resistor determines the gain, or a multiplication factor from the input to the output. Also notice that the output is negative for a positive input, confirming that this is an inverting amplifier.
That’s the basics of it. Check back here for more about op amps, because there is a lot more to be said. Future posts might include other op amp configurations, design considerations and even the dreaded “REAL WORLD”, where the ideal op amp no longer exist.