Circuit Idea/How to Visualize Operating Point

voltage bars - voltage diagrams - current loops - IV curves - stage 

Need to Visualize the Operating Point
In addition to voltage bars, voltage diagrams, and current loops, we can also visualize circuit operation with superimposed IV curves. The idea of ​​this graphic representation is as follows.

The Idea
By means of equivalent transformations, we can reduce any electrical circuit to two connected to each other 2-terminal parts - a source and a load. Each of them is represented graphically with its IV curve, which represents all possible pairs of the voltage V across and the current I through the part. At a certain moment in time, however, only one of the possible pairs (V,I) acts and it determines the position of only one point A from the graph - the operating point of the circuit. Since the voltage and current are the same for both elements, the operating point is obtained from the intersection of their IV curves drawn in a common coordinate system. The IV curve of the element connected to ground starts at the origin of the coordinate system and is sloped to the right; the IV curve of the other element is offset to the right and sloped to the left. This representation allows to illustrate the operating mode (point) of the circuit.

Implementation
Voltage-to-current converter (resistor) driven by a voltage source. The simplest example that we can graphically represent in this way can be the elementary Ohm's circuit consisting only of a resistor driven by a voltage source - Fig. 1.  Here, the first circuit part consists only of the resistor R connected to ground. Its IV curve is a straight line that passes through the origin of the coordinate system and is inclined to the right. The second part consists only of the voltage source; its IV curve is a vetical line shifted to the right along the abscissa with the value of its voltage VIN.

Voltage divider driven by a constant input voltage. Another more complicated example can be a voltage divider made up of resistors R1 and R2 and driven by a constant input voltage VIN - Fig. 2.



The first circuit part consists only of the resistor R2 connected to ground. Its IV curve is a straight line that passes through the origin of the coordinate system and is inclined to the right. The second part consists of two elements in series - the resistor R1 and the voltage source VIN (we can think of this network as a real voltage source with voltage VIN and internal resistance R1). Its composite IV curve is a straight line shifted to the right along the abscissa with VIN and tilted to the left (we can denote it as VINR1). We superimpose the IV curves of the two elements; the intersection point A determines the current IA flowing through the voltage divider and its output voltage VA.

Voltage divider driven by a varying input voltage. During the circuit operation, some of the circuit quantities change its magnitude (for the divider example, it can be the input voltage or one of the resistances). As a result, its IV curve begins to move, and the operating point slides along the other IV curve. Thus, the moving curve scans the stationary one (the moving one is scanning, and the stationary one is scanned). In the voltage divider example, if the source voltage is changed - Fig. 3, its IV curve VINR1 moves parallel to itself (performs a translation). If the resistance R1 is changing, its IV curve rotates around the origin of the coordinate system; if the resistance R2 is changing, its IV curve rotates around the point VIN on the abscissa.



Sophisticated IV curves
A more complicated example – the classical circuit of an op-amp inverting amplifier, is shown in Fig. 3 in three cases: R1 changes, R2 changes, both change simultaneously and in the same direction. In all three cases, the operational amplifier (until it has reached the supply rails) successfully copes with its main task - to maintain a zero voltage (virtual ground) at its inverting input. For this purpose, it changes its output voltage in the corresponding direction and moves the IV curve of the resistor R2.



"Live" IV curves
We can even make animated circuit tutorials (for example, with Flash animator) with moving IV curves (you need Ruffle Flash emulator to see Flash movies because Adobe Flash player is no longer supported).



Comparison
Let's compare this method of graphical representation of circuit operation with other methods (voltage bars, voltage diagrams and current loops). While they visualize only one electrical quantity - local voltage, distribution of voltage inside a resistor or local current, the intersection of the IV curves (the "operating point") gives the solution of the circuit. Therefore, this method is sometimes called "graphoanalytic method".

It is most often used to calculate non-linear circuits. But here, for the purposes of this heuristic approach, we use it more to visualize circuit operation.