Summary: This module discusses actual loads used for measuring the output from a circuit. A load model and examples are provided.

Suppose we want to pass the output signal into a voltage measurement device, such as an oscilloscope or a voltmeter. In system-theory terms, we want to pass our circuit's output to a sink. For most applications, we can represent these measurement devices as a resistor, with the current passing through it driving the measurement device through some type of display.

In circuits, a sink is called a load; thus, we
describe a system-theoretic sink as a load resistance

We must analyze afresh how this revised circuit,
shown in Figure 1, works. Rather
than defining eight variables and solving for the current in the
load resistor, let's take a hint from other analysis (series rules, parallel rules). Resistors
*v-i* relations:

Let
*v-i* relation, the voltage across it is

Thus, we have the input-output relationship for
our entire system having the form of voltage divider, but it
does *not* equal the input-output relation of
the circuit without the voltage measurement device. We can not
measure voltages reliably unless the measurement device has
little effect on what we are trying to measure. We should look
more carefully to determine if any values for the load
resistance would lessen its impact on the circuit. Comparing the
input-output relations before and after, what we need is

Voltage measurement devices must have large
resistances compared with that of the resistor across which the
voltage is to be measured.

Let's be more precise: How much larger would a load resistance need to be to affect the input-output relation by less than 10%? by less than 1%?

We want to find the total resistance of the
example circuit. To apply the series and parallel combination
rules, it is best to first determine the circuit's structure:
What is in series with what and what is in parallel with what
at both small- and large-scale views. We have
*away* from the terminals, and worked
toward them. In most cases, this approach works well; try it
first. The total resistance expression mimics the structure:

Another valuable lesson emerges from this example concerning the
difference between cascading systems and cascading circuits. In
system theory, systems can be cascaded without changing the
input-output relation of intermediate systems. In cascading
circuits, this ideal is rarely true *unless*
the circuits are so *designed*. Design is in
the hands of the engineer; he or she must recognize what have
come to be known as loading effects. In our simple circuit, you
might think that making the resistance
*a circuit cannot be designed in isolation that will
work in cascade with all other circuits*. Electrical
engineers deal with this situation through the notion of
*specifications*: Under what conditions will
the circuit perform as designed? Thus, you will find that
oscilloscopes and voltmeters have their internal resistances
clearly stated, enabling you to determine whether the voltage
you measure closely equals what was present before they were
attached to your circuit. Furthermore, since our resistor
circuit functions as an attenuator, with the attenuation (a
fancy word for gains less than one) depending only on the ratio
of the two resistor values
*any* values for the two
resistances we want to achieve the desired attenuation. The
designer of this circuit must thus specify not only what the
attenuation is, but also the resistance values employed so that
integrators—people who put systems together from
component systems—can combine systems together and have a
chance of the combination working.