LOADING EFFECT

EDITOR: B. SOMANATHAN NAIR

1. INTRODUCTION

Consider Fig. 1, which shows a resistive network consisting of a 1-Ω resistor and a 10-kΩ resistor, forming a loop with a voltage source of 100 V. We find that a current I₁flows through the loop whose value is given by

                                                I₁ = 100 V/(10 kΩ+1 Ω)= 0.01 A

In the above computation, we have neglected the 1-Ω resistor in comparison with the 10-kΩ resistor. And the voltage across terminals AB is now found to be

                                                V_AB =0.01 x10 kΩ  = 100 V

We find that the supply voltage and the terminal voltage are the same. Hence we say that there is no loading effect in this case.

As a second step, we add a new resistor of 1 kΩ (1000 Ω) across AB. This new resistor comes in parallel to the 10-kΩ resistor. The equivalent resistance of the parallel combination of the 10-kΩ and 1-kΩ resistors will be 10 k x 1 k/(10 k + 1 k) = 900 Ω . The total loop resistance becomes 900+1 = 901 Ω and the current now flowing through the circuit will be

                                                I = 100/(900+1) = 0.111 A

This new current is much higher than the value of current when the load was 10 kΩ only. The new voltage across AB is

                                                V_AB =0.111 x 900 Ω  = 99.9 V

The output voltage is seen to get decreased slightly from the previous value. Hence there is no loading effect in this case also.

In the third step, we remove the 1-kΩ resistor and add a 100-Ω resistor across the 10-kΩ resistor, as shown in Fig. 3. The equivalent resistance across AB will be

                                    10000 x100/10100 = 99 Ω

We find that the equivalent resistance across AB has drastically reduced in this case. The new circulating current

                                                 I = 100/(99+1) = 1 A

The circulating current is found to be very high. The new output voltage is

                                                            V_AB = 1 A x 99 Ω = 99 V.

Since the output voltage is not reduced, we have negligible loading effect in this case also.

As a fourth step, we remove the 100-Ω resistor and add a 10-Ω resistor in its place as shown in Fig. 4.

The equivalent output resistance in this case is

                                                            10000x10/10010 = 10 Ω  (app.)

The current through the loop

I = 100/11 = 9.09 A

And the voltage  

                                                            V_AB = 9.09x10 = 90.9 V

In this fourth case, we find that the output voltage has really decreased. Therefore, in this case, we state that there is loading effect in the circuit. The output voltage is only 90.9 V. Where has the balance voltage of 100 ‒ 90.9 = 9.1 volt gone? We find that this is dropped across the series 1-ohm resistor, as shown in Fig. 4.

 As a final step, assume that the 10-Ω resistor is removed and we connect a 1-Ω resistor in its place. The equivalent output resistance is now 1 Ω only (10 kΩ parallel to 1 Ω = 1 Ω). The current through the circuit has gone up to the extremely large value of

                                                I = 100/(1+1) = 50 A

and the output voltage is

                                                V_AB = 50x1= 50 V

In this extreme case, we find that the output voltage has very drastically reduced and hence we say that there is serious loading effect in this final case. It can be seen that the remaining part (i.e., half) of the supply of 100 V is dropped in the series resistance of 1 Ω, as shown in Fig. 5.

2. DISCUSSION

From the examples given above, we infer that loading effect is that phenomenon by which the loads added to a network results in an excess flow of current which results in a drastic reduction in the output voltage.

            Loading effect is a sever problem in long ac power distribution lines. Figure 6 shows such a distribution line. In the conventional 230-V distribution lines, several loads of varying ohmic values are connected. If the distribution lines have zero resistance, then there will not be any problem. However, in reality, these wires have resistance which is not negligible. Loads near the supply transformer get full supply voltage since the series resistance of the distribution wires is negligible and hence the loading effect is negligible.

However, for loads far away from the transformer, the resistance of the distribution lines (i.e., series resistance) becomes large. At the same time, the equivalent resistance value of the parallel load resistances across the distribution lines become smaller and smaller as the number of distribution points increase. The net effect is that, at distribution points far away from a distribution transformer, the supply voltage gets drastically reduced. This is the result of loading effect.

Loading effect can be seen to be a very severe problem in power distribution lines, because equipments which need correct and specified supply voltages can not function properly as loading effect reduces the supply voltage drastically.

3. LOADING EFFECT IN ELECTRONIC CIRCUITS

In electronic circuits also loading effect is a very serious problem. Consider a voltage amplifier being connected in between two systems, as shown in Fig. 7. We find that the input impedance Z_i(amp) of the amplifier comes in parallel with the output impedance Z_{o(sys 1)} of the first system. If Z_i(amp) = ∞, then the amplifier will not load that system. However, if Z_i(amp) is low and comparable to Z_{o(sys 1)}, then the effective value of Z_{o(sys 1)} is reduced further and the amplifier draws heavy current from the first system, which affects its performance severely. Hence, amplifiers must have high input impedance, so that they will not load the system to which they are connected to.

Now, consider the output side of the amplifier which is connected to the input of the second system, i.e., System 2 is acting as a load to the amplifier. In this condition, output impedance of amplifier Z_o(amp) comes in parallel with the input impedance Z_{i(sys 2)} of System 2. If Z_o(amp) = 0 (or very low), then System 2 will not load the amplifier as the effective value of the parallel combination of Z_o(amp) and Z_{i(sys 2)} is Z_o(amp) itself. Therefore, we conclude that to avoid loading effect, the output impedance of an amplifier must be ideally zero.

Summarizing, we state that an ideal  voltage amplifier must have infinite  input impedance and zero output impedance to avoid loading effect.