- [Narrator] Operational amplifiers got their name because
they can be used to implement mathematical operations.
For example, an amplifier circuit that increases or
decreases the voltage of a signal by some amount of gain
is mathematically equivalent to multiplication and division.
The circuit is multiplying an input voltage by some gain
value to produce a larger or smaller output.
Other op amp circuits exists that can implement
mathematical operations including; addition, subtraction,
integration, and differentiation.
For this video, I'll be focusing on an op amp circuit
that's capable of adding multiple voltages together
known as a summing amplifier.
To create a summing amplifier, I'll begin with the
inverting amplifier configuration.
And then, I'll connect another input resistor to the
op amp's inverting terminal.
The circuit now has two input terminals that I can connect
to different input voltage sources, which are referred to as
Va and Vb.
I'll also give each of the two input resistors their own
unique names referring to them as Ra and Rb.
Since the non-inverting input terminal is tied to ground,
the op amp will change its output voltage in a way that
keeps the inverting input terminal at zero vaults too.
Because the inverting input terminal is held at zero vaults
when there's a positive or negative voltage at the input
terminals that voltage drop will cause current to flow
through the two input resistors.
Which I'll label as Ia and Ib.
Since current doesn't flow into the op amp's input terminals
the current from those two input resistors will both flow
together through the feedback resistor Rf.
The current through Rf will be the sum of the input currents
a and b.
Using Ohm's law again, the output voltage will be equal to
the feedback current times the feedback resistance.
However, since the voltage across the feedback resistor will
drop from left to right, when current flows in the direction
shown here, and the inverting input terminal is held at
zero vaults. The output voltage will be negative.
Just as with the inverting amplifier configuration.
To get an equation for the output voltage based on the input
voltages, I'll begin with the expression for the output
in terms of the feedback current and the feedback
resistance.
I'll substitute the feedback current for the sum of those
two input currents and, according to Ohm's law,
each of those two input currents will be equal to their
corresponding input voltage divided by the input
resistor value.
This equation gives me the output voltage in terms of the
circuit's resistor values and input voltages.
To demonstrate how that equation relates to the circuit
using actual numbers, I'll make all of the resistors in
this circuit one kilohm,
and I'll make the input voltage a one volt and
input voltage b two volts.
Using Ohm's law, one volt across the one kilohm resistor
will produce one milliamp of current for input a.
And two volts across the one kilohm resistor,
will produce two milliamps of current for input b.
Those two input currents will add together,
so that three milliamps will pass through the feedback
resistor, and using Ohm's law one final time,
three milliamps through a one kilohm feedback resistor
will create a three volt drop from the inverting input
terminal to the output terminal,
so the output will be negative three volts.
This circuit is sometimes referred to as a summing invertor
because of the fact that it adds together voltages and
then negates their sum on the output.
Now, one nice thing about this summing circuit is that I
can scale how much each of these input voltages contributes
to its final output sum by adjusting the input resistor
values.
For example, if I increase resistor b from one kilohm
to two kilohm's, by doubling its resistance I cut the
amount of current through it in half.
Now, only two milliamps will flow through the feedback
resistor, so the output voltage changes to
negative two volts.
With this uneven configuration of input resistors,
input b is only contributing half of much of its voltage,
in the total sum, as input a.
This sort of uneven scaling can come in handy when I need
to combine several signals together in different ratios.
Maybe I have a circuit recipe that calls for one part of
signal A and two parts of signal B.
I can mix those signals together in the desired quantities
using the summing amplifier.
I can also adjust the gain that's applied to all of the
signals by changing the value of the feedback resistor.
For example, if I increase the feedback resistor from one
kilohms to three kilohms, the op amp will have to scale its
output voltage by a factor of three,
so that the output current through the feedback resistor
remains the same.
One final thing about summing amplifiers, is that I'm not
limited to having just two input voltages.
I can add as many input resistors as I need and the basic
principle for how the circuit works remains the same.
The equation shown here can be extended to include as
many inputs as you want and will calculate the resulting
output voltage based on each of the input voltages and
their corresponding resistor values.