# Confusion with non-ideal current and voltage source models

I have a confusion with the following explanation of non-ideal voltage and current sources: These above doesn't look like the Thevenin or Norton models since the plots are non linear. Can someone explain the meaning of these graphs in a simpler fashion?

• What textbook did this come from? I’m assuming they are just trying to point out that real sources have impedance. May 23, 2020 at 19:02
• Whatever it does mean, I'm pretty sure it's not very useful. May 23, 2020 at 19:03
• Unless I am missing something, those plots look completely absurd. Is this from a textbook? Take the 1st -- The "curvy" parts are in the "low I_th" area which is where you'd think it'd be pretty "good" i.e. straight. And what are V_ref, I_ref? I'm as confused as you are! May 23, 2020 at 19:04
• I think I understand. But I also think this "general" model of his is so simplistic and tries to apply to too many things that it is essentially useless. It's more effort to try and understand than just reading on to the more specific examples that he gives (like the resistive divider). May 23, 2020 at 19:14
• @pnatk That Figure 1.3 seems to be the plot of a diode junction used as a "voltage source" which the author does not seem to say. Thus in "V_th" the "th" means "threshold" not "Thevenin". The thing is, an ideal V or I source has the Thevenin/Norton resistance/conductance of zero, and a 1st approximation to a practical one is that it's not zero, may change value, etc. May 23, 2020 at 19:17

This is probably from a textbook on IC design, or on circuit design with an emphasis on ICs.

They are assuming particular types of non-ideal voltage and current sources. The black bands in the resistive elements are likely intended to indicate the nonlinearity of these elements.

For the voltage source, they are considering a diode as the "typical" non-ideal voltage source you might want to model.

And for the voltage source they are considering a current mirror circuit as the "typical" non-ideal current source you might want to model.

Both of these are not actually power generators. They need power from the external circuit and that's why they don't work well near 0 V output (for the current source) or 0 current output (for the voltage source).

Non-ideal power generators (like a chemical cell or electro-mechanical generator) would have very different characteristics.

The two weird and unexplained pictures show only one of the possible ways of making voltage and current sources - by using non-linear elements (without applying negative feedback). They are named "practical" in the sense "they are not ideal".

## Voltage source

Static voltage divider. The simplest voltage source with desired constant voltage VREF can be made by a voltage divider supplied by a voltage source with constant voltage V > VREF. This humble electric circuit consists of two resistors (R1 and R2) in series. Both voltage drops VR1 and VR2 can be used as output voltage but, as a rule, the voltage drop VR2 across the grounded resistor (R2) is used. This voltage divider is "static" since its transfer ratio (gain) is constant - R2/(R1 + R2)... and this is the problem. If this was illustrated by another picture from this source, it would mystically say "the output voltage depends very much on the external parameters". For example, if V is not stable and varies, VREF will vary as well.

Dynamic voltage divider. The clever idea encrypted in the upper picture is to make the voltage divider dynamic. For this purpose, the "static" resistor R2 is replaced by a "dynamic" (self-variable) resistor R2dyn having a property to keep the voltage drop across itself constant. I am not sure what is its "official" name (if there is one at all) but it can be named with a descriptive name like "voltage-stabilizing dynamic resistor"... or "voltage-stable non-linear resistor"... or simply "voltage stabilizer"...

Operation. The dynamizing trick is simple and intuitive... and can be easily demonstrated by an ordinary variable resistor (rheostat). When, for some reason, the supply voltage V decreases, the current I decreases as well… and VREF (VOUT) should decrease. But the "clever" dynamic resistor R2 senses this change and increases its resistance to compensate the current decrease. As a result, VREF = Idec.R2inc = const. In other words, the voltage drop across R2dyn is a function of two oppositely varying input variables... and because of that it does not change.

Range. Dynamic resistors are passive devices (in the sense they do not produce energy). So their IV curve passes through the coordinate origin and can be roughly represented by two sections. The first is (almost) horizontal and not interesting for this application. The second becomes (almost) vertical "beyond Ith" (minimum current) and is useful for this application.

Implementation. Once revealed the concept, we can see many specific implementations of this idea by semiconductor devices having such a behavior - various diodes. So, the IV curve in the upper picture belongs to a diode.

## Current source

Static current source. The simplest current source with desired constant current IREF can be made by a resistor R in series to a voltage source with constant voltage V. This current source is "static" since its internal resistance (R) is constant... and this is the problem. If this was illustrated by another picture from this source, it would mystically say "the output current depends very much on the external parameters". For example, if the supply voltage V or the load voltage VL… or both vary, IREF will vary as well.

Dynamic current source. The clever idea encrypted in the lower picture is to make the current source dynamic. For this purpose, the "static" resistor R is replaced by a "dynamic" (self-variable) resistor Rdyn having a property to keep the current through itself constant. Again, I am not sure what is its "official" name (if there is one at all) but it can be named with a descriptive name like "current-stabilizing dynamic resistor"... or "current-stable non-linear resistor"... or simply "current stabilizer"...

Operation. The dynamizing trick is also simple and intuitive... and can be easily demonstrated by a variable resistor (rheostat). When, for some reason, the supply voltage V decreases or the load voltage VL increases, the effective "current-creating voltage" across Rdyn decreases… and IREF (IOUT) should decrease. But the "clever" dynamic resistor Rdyn senses this change and decreases its resistance to compensate the current decrease. As a result, IOUT = Veffdec/Rdyndec = const. In other words, the output current IREF is a function of both input variables (voltage and resistance) that changes in the same direction... and because of that their ratio - the current, does not change.

Range. These dynamic resistors are also passive devices (they do not produce energy). So their IV curve passes through the coordinate origin and can be roughly represented by two sections. Now the first is (almost) vertical and not interesting for this application. The second becomes (almost) horizontal "beyond Vth" (minimum voltage) and is useful for this application.

Implementation. Once revealed the second concept, we can see many specific implementations of this idea by semiconductor devices having such a behavior - now various transistors. So, the IV curve in the lower picture belongs to a transistor (it is the so-called "output characteristic").

Finally, let me just add that when I come across such "explanations", I feel happy that I was not forced to take an exam in such lectures...