Is the source internal resistance really a resistance?

I dedicate this story to my students from groups 48 and 49, ITI

Traditionally, at the beginning of the first lab on Semiconductor Devices, I remind my students of Electrical Engineering basics. Of course, I start with electrical concepts such as ideal and real voltage and current sources. And, for the last time, I realized how difficult they are to understand... as soon as I felt that I was still thinking about them starting somewhere in the 70's. Because the bare truth is that we know them... but do not understand them.

Such a fundamental electrical concept is "source internal resistance". I dedicate this post to it in the hope that this will arouse the interest of my students in electrical phenomena.

Classic viewpoint

It is said that "the real voltage source has internal resistance". Thus, it is represented by an electrical equivalent circuit of two elements - an ideal voltage source and a resistor.

However, this creates a misconception of physical resistance, which in fact does not exist. Actually, there is only a varying (dynamic) voltage source whose voltage is not constant but decreases linearly as the load current increases.

Natural voltage source

The reason for this strange behavior can be, as in batteries, chemical. Generally speaking, sources convert some non-electrical energy into electricity. If, for some reason, the current consumed by the load reduces their conversion factor, the voltage across their terminals begins to decrease in proportion to the current. This creates the illusion of physical resistance… but there is no such resistance.

In fact, there is a virtual resistance that is artificially created by changing (decreasing) the voltage when changing (increasing) the current. This is a well-known trick in negative resistance circuits known as negative impedance converters (NICs).

So, the real voltage source is something like a current-dependent voltage source or a current-to-voltage converter. But how do we get a constant voltage source to behave this way?

Equivalent circuit

In the equivalent circuit we use a simple trick - we connect a resistor R in series with a constant voltage source having a maximum voltage. The load current I "creates", according to Ohm's law, a voltage drop V = I.R across the resistor... that is subtracted from the constant voltage... and the resulting output voltage decreases linearly when the current increases.

Thus the combination of a constant voltage source and resistor mimics the varying real voltage source in the famous equivalent circuit. This equivalent real voltage source already has "internal" physical resistance R while the original real voltage source does not have any resistance inside.

So, there is a significant difference between the two sources - original and equivalent, in terms of energy consumption. The former does not dissipate power while the latter dissipates power in the physical resistance... but for the purposes of calculation it does not matter.

It is a pretty silly way to reduce voltage... but it is the only way used in analog electronics. The smart way to reduce voltage is to control the process of energy conversion. For example, if this is a thermal power plant, and we want to reduce the voltage of the generator, we simply reduce the amount of coal supplied... and not to supply the same amount of coal and then to dissipate the excess power in some powerful resistors... But in electronics we have no choice and we reduce the voltage in this "stupid" way... always reaching the ubiquitous circuit of a voltage divider.

So this is the simple truth about real voltage sources - there is a decreasing voltage inside them and not a constant resistance. And this decreasing voltage gives us the illusion of resistance.

Someone will say that wires have resistance.  But they are so short that their resistance is negligible. The connection terminals (for example of a secondary battery) also have a contact resistance ... but it is outside the source. The same is valid for the line resistance...

Mains voltage source

However, in the case of a mains power supply, the line resistance dominates. Since, for us, the voltage source is the wall socket, the line resistance serves as an internal source resistance (the power plant is the source). Thus both circuits - real and equivalent, are the same... and the source resistance is a physical resistance.

Electronic voltage source

In electronics, we use mainly artificial voltage sources (voltage stabilizers). They consist of a constant voltage source (power supply) and electrically-controlled "resistor" (the collector-emitter part of a transistor) in series. In addition, this "resistor" is dynamic (depends not only on the input voltage but on the load voltage as well). An emitter follower is a typical example.

Because of the finite transistor gain, the output voltage slightly decreases when the load current increases. This gives the illusion of constant internal (output) resistance... but actually this is changing (dynamic) resistance.

-------------

An interesting question arose; it is worth asking at ResearchGate.