Voltage and Current Sources (Independent and Dependent Sources)

In the basic circuit tutorials up to this point, we have generally represented a voltage potential by just assigning a node one potential and another node a different potential. In reality, those voltages are produced by something and they are represented symbolically in circuits. By doing this, we also have more freedom with what those sources can represent - AC and/or DC voltage sources, current sources, dependent or independent sources. Let’s go over these different symbols and important things to remember about each one.

First, in general, power sources, both voltage and current sources, are active elements. This means they can generate energy as well as absorb, where passive elements can either only absorb energy (resistors) or store/release energy (capacitors and inductors). Also, these sources will create however much current or voltage necessary to produce the desired effect. This can cause some interesting and potentially dangerous situations.

Also, when learning about Ohm’s Law, we talked about how not everything follows Ohm’s Law and that is the case with power sources. Sometimes there’s the desire to figure out the equivalent resistance of a power source if you know the current through and voltage across it. Please fight that desire, it doesn’t work that way.

Let’s start with a voltage source. By far the most common power source you’ll see in both circuits and your career, if you just learn about this and then come back to this tutorial later for everything else, we won’t judge you. There are three common symbols used to represent a voltage source.

The circle with a plus/minus inside of it is a more generic symbol. This can represent any independent voltage source, whether AC or DC or both. If you don’t know the difference between AC and DC electricity, go check out this tutorial really quick, it’ll be fast and will give you everything you need to move forward with this. The circle with the sinusoid in it means that it is an AC power source but it could also have a DC offset. The other symbol, made up of three lines, typically represents a battery and, as such, can only represent a DC voltage source. If you have a DC source, it’s a matter of preference for which symbol you use but we typically use the circle with the plus/minus with every voltage source just to be consistent.

An ideal voltage source will produce or absorb any current needed to maintain the rated voltage. If there is basically no resistance, then that will be a large amount of current. If there is a huge resistance, then it will be a tiny amount of current. This leads to the danger of voltage sources. If you short circuit the two outputs of a voltage source together, meaning resistance is effectively zero, then the voltage source will attempt to create enough current to maintain that voltage potential, which will result in, effectively, infinite current. While real voltage sources can’t provide infinite current, almost all of them will provide enough current to make you really unhappy.

Now, let’s talk about current sources. When I was in circuits, there was a gentleman who had been a technician for a few decades and he complained that he had never seen current sources in real life, they were stupid, and there was no point in learning about them. Despite his real-life experience, he, of course, was wrong. Different careers take us different places and it’s possible that you will never need to understand current sources in your career. Or it could be you design with them everyday. More likely, it’s somewhere in the middle. They’re mostly used to model things like transistors, op-amps, or specific IC’s so you’ll need them at least a couple times in academia, if nothing else, so let’s learn a bit about them. With that pontificating out of the way…

A current source is a source that provides a set amount of current by varying its voltage. It’s usually represented by the symbol below:

In this case, the idea of a DC or AC voltage doesn’t apply as the current source will produce whatever voltage is necessary to keep a constant current, whether that voltage is positive, negative, or varying. Current sources are pretty straightforward as there are less real-life variations and even if they’re not extremely commonly used, they are relatively simple to work with during circuit analysis.

In contrast to voltage sources, current sources don’t go well with open-circuits. If there is an open circuit between the two nodes of a current source, that ideal current source will attempt to “force” a current by increasing its voltage. Looking at Ohm’s Law, if resistance is infinity and current is any finite number, it means that voltage needs to be infinite as well. Again, as with the voltage source, a real current source won’t be able to create an infinite voltage but it’ll be high enough to cause problems.

Up to this point, we’ve been talking about independent voltage and current sources. Sometimes, there are things like dependent sources, or sources that change their output depending on other parts of the circuit. Their symbols look like this:

On occasion, such as with a current mirror, a power source in real life depends on the voltage or current in another portion of the circuit. This is modeled with dependent power sources. They complicate circuit analysis but they shouldn’t be too scary as they simply replace one bit of math with another.

Also note, that they’re not always dependent on the same thing they’re being generated. For example, a current source could be dependent on a voltage while a voltage source could be dependent on a current. It’s just a mathematical representation. It will cause some things that look odd at first, like 0.5v₁ amps, but it’s perfectly natural. Indeed, there are the four common types of dependent power sources.

• Current-controlled current source
• Current-controlled voltage source
• Voltage-controlled voltage source
• Voltage-controlled current source

When working with dependent power sources, you need to look for the dependent element, or the element that the power source is dependent upon. Make sure that you pay attention to whether it’s dependent on the voltage or the current. When solving the circuit, you can just place the provided relationship into the equation you laid out. Sometimes this will force you down one path of circuit analysis but as long as you’re aware of that fact and proficient at the different types of analysis, it should be straightforward.

For the most part, we assume that power sources are ideal. They can produce infinite current and infinite voltage no matter the load and they provide and absorb power equally well. In basic circuits, this is sufficient. But as you learn more about electronics and deal with real world applications, you’ll see that every part of that sentence is not true. Nothing can produce infinite current or infinite voltage, the load almost always affects the rated voltage or current, and some things can’t absorb power very well or at all. At this point, we won’t go into details on any of these items, it suffices to just be aware that we’re dealing with ideal situations and reality is more complicated.

In this final tutorial before we get into the meaty aspects of circuit analysis with Kirchhoff’s Laws, we learned about voltage and current sources and some of their important features. We touched on the dangers of short-circuiting a voltage source and open-circuiting a current source. We also delved into dependent power supplies and learned a few important items that will become more obviously applicable as we start analyzing circuits.