The 10 Percent Rule: This rule is a standard method for selecting R 1 and R 2 that takes into account
2.13 Voltage and Current Sources
An ideal voltage source is a two- terminal device that maintains a fixed voltage across its terminals. If a variable load is connected to an ideal voltage source, the source will maintain its terminal voltage regardless of changes in the load resistance. This means that an ideal voltage source will supply as much current as needed to the load in order to keep the terminal voltage fixed (in I = V/R, I changes with R, but V is fixed).
FIGURE 2.50
Now a fishy thing with an ideal voltage source is that if the resistance goes to zero, the current must go to infinity. Well, in the real world, there is no device that can sup- ply an infinite amount of current. If you placed a real wire between the terminals of an ideal voltage source, the calculated current would be so large it would melt the wire. To avoid this theoretical dilemma, we must define a real voltage source (a bat- tery, plug- in dc power supply, etc.) that can supply only a maximum finite amount of current. A real voltage source resembles an ideal voltage source with a small series internal resistance or source resistance rs, which is a result of the imperfect conduct- ing nature of the source (resistance in battery electrolyte and lead, etc.). This internal resistance tends to reduce the terminal voltage, the magnitude of which depends on its value and the amount of current that is drawn from the source (or the size of the load resistance).
In Fig. 2.52, when a real voltage source is open- circuited (no load connected between its terminals), the terminal voltage (VT) equals the ideal source voltage (VS)—
there is no voltage drop across the resistor, since current can’t pass through it due to an incomplete circuit condition.
FIGURE 2.51
FIGURE 2.52
However, when a load Rload is attached across the source terminals, Rload and rs are connected in series. The voltage at the terminal can be determined by using the volt- age divider relation:
V V R
R r
T s
s load load
= +
From the equation, you can see that when Rload is very large compared to rs, (1000 times greater or more), the effect of rs is so small that it may be ignored. However, when Rload is small or closer to rs in size, you must take rs into account when doing your calculations and designing circuits. See the graph in Fig. 2.52.
In general, the source resistance for dc power supplies is usually small; however, it can be as high as 600 Ω in some cases. For this reason, it’s important to always adjust the power supply voltage with the load connected. In addition, it is a good idea to recheck the power supply voltage as you add or remove components to or from a circuit.
Another symbol used in electronics pertains to dc current sources—see Fig. 2.52.
An ideal current source provides the same amount of source current IS at all times to a load, regardless of load resistance changes. This means that the terminal voltage will change as much as needed as the load resistance changes in order to keep the source current constant.
In the real world, current sources have a large internal shunt (parallel) resistance rs, as shown in Fig. 2.52. This internal resistance, which is usually very large, tends to reduce the terminal current IT, the magnitude of which depends on its value and the amount of current that is drawn from the source (or the size of load resistance).
When the source terminals are open- circuited, IT must obviously be zero. However, when we connect a load resistance Rload across the source terminals, Rload and rs form a parallel resistor circuit. Using the current divider expression, the terminal current becomes:
I I r
R r
T s
s s load
= +
From this equation, you can see that when Rload is small compared to rs, the dip in cur- rent becomes so small it usually can be ignored. However, when Rload is large or closer to rs in size, you must take rs into account when doing your calculations.
A source may be represented either as a current source or a voltage source. In essence, they are duals of each other. To translate between the voltage source and current source representation, the resistance value is kept the same, while the voltage of the source is translated into the current of the source using Ohm’s law. See Fig. 2.53 for details.
One way to look at an ideal current source is to say it has an internal resistance that is infinite, which enables it to support any kind of externally imposed potential difference across its terminals (e.g., a load’s resistance changes). An approximation to an ideal current source is a voltage source of very high voltage V in series with a very large resistance R. This approximation would supply a current V/R into any load that has a resistance much smaller than R. For example, the simple resistive current source circuit shown in Fig. 2.54 uses a 1- kV voltage source in series with a 1- MΩ resistor. It
will maintain the set current of 1 mA to an accuracy within 1 percent over a 0- to 10- V range (0 < Rload < 10 kΩ). The current is practically constant even though the load resis- tance varies, since the source resistance is much greater than the load resistance, and thus the current remains practically constant. (I = 1000 V/(1,000,000 Ω + 10,0000 Ω.
Since 1,000,000 Ω is so big, it overshadows Rload.)
A practical current source is usually an active circuit made with transistors, as shown in Fig. 2.54c. Vin drives current through R1 into the base of the second transis- tor, so current flows into the transistor’s collector, through it, and out its emitter. This current must flow through R2. If the current gets too high, the first transistor turns on and robs the second transistor of base current, so its collector current can never exceed the value shown. This is an excellent way of either making a current source or limiting the available current to a defined maximum value.