Encyclopedia of Electrical Engineering
Voltage Divider Supply (Loaded and Unloaded)
When the term loaded is used to describe voltage divider supply, it refers
to the application of an element, network, or system to a supply that draws
current from the supply. In other words,
the loading down of a system is the process of introducing elements
that will draw current from the system. The heavier the current, the
greater is the loading effect.
Recall from internal resistance of voltage source that the application of a load can affect the
terminal voltage of a supply due to the internal resistance.
Voltage $V_a$ is unaffected by the load $R_{L_1}$ since the load is in parallel
with the supply voltage E. The result is $V_a = 120 V$, which is the same
as the no-load level. To determine $V_b$, we must first note that $R_3$ and $R_{L_3}$
are in parallel and
$$R'_3 = R_3 || R_{L_3} = 30 Ω || 20 Ω= 12 Ω.$$
The parallel combination gives
$$R'_2 = (R_2 + R'_3) || R_{L_2} = (20 Ω + 12 Ω) || 20 Ω$$
$$= 32 Ω || 20 Ω = 12.31 Ω$$
Applying the voltage divider rule gives
$$V_b = {(12.31 Ω)(120 V) \over 12.31 Ω + 10 Ω} = 66.21 V$$
versus 100 V under no-load conditions.
Voltage Vc is $$Vc = {(12 Ω)(66.21 V) \over 12 Ω + 20 Ω} = 24.83 V$$ versus 60 V under no-load conditions. The effect of load resistors close in value to the resistor employed in the voltage divider network is, therefore, to decrease significantly some of the terminal voltages. If the load resistors are changed to the 1 kΩ level, the terminal voltages will all be relatively close to the no-load values. The analysis is similar to the above, with the following results: $$V_a = 120 V$$ $$V_b = 98.88 V$$ $$V_c = 58.63 V$$ If we compare current drains established by the applied loads, we find for the network in Fig. 2 that $$I_{L_2} = {V_{L_2} \over R_{L_2}} ={66.21 V \over 20 Ω }= 3.31 A$$ and for the 1 kΩ level, $$I_{L_2} = {98.88 V \over 1 kΩ} = 98.88 mA < 0.1 A$$ As demonstrated above, the greater the current drain, the greater is the change in terminal voltage with the application of the load.
Fig. 1: Voltage divider supply.
No-Load Conditions
Through a voltage divider network such as that in Fig .1, a number of different terminal voltages can be made available from a single supply. Instead of having a single supply of 120 V, we now have terminal voltages of 100 V and 60 V available - a wonderful result for such a simple network. However, there can be disadvantages. One is that the applied resistive loads can have values too close to those making up the voltage divider network. In general, To demonstrate the validity of the above statement, let us now examine the effect of applying resistors with values very close to those of the voltage divider network.Loaded Conditions
In Fig. 2, resistors of 20 Ω have been connected to each of the terminal voltages. Note that this value is equal to one of the resistors in the voltage divider network and very close to the other two. Fig. 2: Voltage divider supply with loads equal to the average value
of the resistive elements that make up the supply.
of the resistive elements that make up the supply.
Voltage Vc is $$Vc = {(12 Ω)(66.21 V) \over 12 Ω + 20 Ω} = 24.83 V$$ versus 60 V under no-load conditions. The effect of load resistors close in value to the resistor employed in the voltage divider network is, therefore, to decrease significantly some of the terminal voltages. If the load resistors are changed to the 1 kΩ level, the terminal voltages will all be relatively close to the no-load values. The analysis is similar to the above, with the following results: $$V_a = 120 V$$ $$V_b = 98.88 V$$ $$V_c = 58.63 V$$ If we compare current drains established by the applied loads, we find for the network in Fig. 2 that $$I_{L_2} = {V_{L_2} \over R_{L_2}} ={66.21 V \over 20 Ω }= 3.31 A$$ and for the 1 kΩ level, $$I_{L_2} = {98.88 V \over 1 kΩ} = 98.88 mA < 0.1 A$$ As demonstrated above, the greater the current drain, the greater is the change in terminal voltage with the application of the load.
Ladder Networks
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