Circuit Idea/How to Visualize Voltages in Circuits

voltage diagrams - current loops - IV curves - stage 

Need to Visualize Voltages in Circuits
Voltages, like all electrical quantities, are invisible. To show them, we have somehow to visualize their value and polarity (in circuit theory, voltage polarities are considered unimportant and are represented by arbitrary signs).

The Idea
For the purposes of intuitive understanding, we can represent local voltages in circuits by vertical segments (voltage bars) whose length (height) is proportional to the voltage magnitude. This notion of voltage comes from the well-known water tower hydraulic analogy - a water column with a height proportional to the pressure (the higher the column, the greater the pressure).



Implementation
These bars can represent both single-ended voltages (with respect to the negative rail, ground or positive rail of the power supply) and "floating" voltages. Thus, some of them are firmly "tied" to ground or supply rails, while others are "floating". The relation between the voltage magnitude and the bar length is given by a scale factor with dimension [V/cm].

We can develop various voltage bars (with polarity signs, arrows, etc.) The zero voltage level (of ground) and other typical levels (of supply rails) can be marked by horizontal dotted lines. Positive voltages can be represented by bars drawn above the zero level and negative voltages - by bars below it. The sum of bars representing voltage drops is equal to the supply-voltage bar, which simply represents KVL in a geometric form.

It is preferable to color the voltage bars in red to easily distinguish them from circuit diagrams drawn in black (the red color makes an association with pressure). Also, 3-D voltage pictures can be made, where the circuit diagram is axonometrically drawn and the voltage bars are placed perpendicular to it.

Sophisticated Voltage Pictures
We can create more sophisticated voltage pictures by means of grapnic editors like Corel Draw. Here is, for example, the circuit of a differential transistor amplifier ("long-tailed pair") adorned with voltage bars:



"Live" voltages
We can even make animated circuit tutorials (for example, with Flash animator) with "living"voltage bars that change their height proportionally to the voltage magnitude (you need Ruffle Flash emulator to see Flash movies because Adobe Flash player is no longer supported):



Content is More Important than Form
Of course, content is more important than form... and we can draw circuit diagrams with superimposed voltage pictures even by hand. Here is an attractive "geometrical" representation of the op-amp current-to-voltage converter aka "transimpedance amplifier" drawn by color fiber pens on a white sheet of paper.



Another example of a hand-drawn voltage picture is an ECL gate.



We can impose the voltage picture even on a circuit diagram drawn on the blackboard:



In Circuit Simulation Software
An interesting application of this way of visualizing voltages inside circuits could be in more intuitive circuit simulators (like Falstad) as an attractive form of displaying simulation results.

Voltage Bars vs Voltage Oscillograms
What do voltage bars actually represent? It is a like of a "frozen picture", sort of like an image on the oscilloscope screen without a horizontal sweep. The question arises, "Wouldn't it be better to display oscillograms of the voltages at the points being controlled rather than bars?"

The advantage of bars is that voltages can be easily compared. The bars can be superimposed in height (summed) so that, according to KVL, in a closed loop the sum of all the bars is equal to the largest bar - the applied supply voltage. If they are oscillograms, moments of time must be added because the oscillogram shows within a period the instantaneous values at each point in time. Visualizing with oscillograms has the advantage that only one circuit is needed, whereas here more circuits have to be drawn for different typical voltage values... but the relationships between the voltages are clearly visible. For a comparison, voltage bars are like snapshots (static frames) of individual moments of the circuit operation, whereas the oscillograms are like movies that have all the frames.

What is the benefit of representing voltages by such bars? It gives a very good general idea of circuit operation. A glance at such a circuit with a voltage picture superimposed gives an idea of voltage magnitudes at circuit points. This is an advantage over the numerical representation, which is accurate but abstract.

Helping the Online Learning
ZOOM has a unique feature named "annotation tool" - a pen that can be used to draw on existing web circuit diagrams. It turns out this simple feature can serve as a very powerful didactic technique. See, for example, such a snapshot of the ZOOM whiteborad (really, the picture is not so beautiful... but attractive:-)



We can even draw voltage bars on a picture of a real laboratory setup.