A Helpful Word about Voltage
Several students had some difficulty with the problems on the homework
that had voltage sources in the feedback loops of op amps. After one
student explained to me his way of thinking about the voltage sources,
I have some comments that I hope will help resolve the difficulties. I
will use this circuit as my example:
It seems that many students have the idea that voltage sources "put"
their values onto the attached nodes. In my circuit here, for example,
the 3-V source puts a value of 3 onto the wire above it, and that same
value propagates up to the other elements. Or, in other words, it puts
a 3 onto node a.
This can be a useful way to think about voltage sources, and we can get
correct values of node voltages this way, as long as we do it right.
The problems come in when we have two voltage sources connected to the
same node, and the values they put don't match:
Here we have the 3-V source putting a 3 onto node a,
and the 2-V source putting a 2 onto the same node. What went wrong?
To resolve the problem, we need to remember that the value of a voltage
source is the
difference between the
potentials at its terminals. That means that we cannot use the value to
determine the node voltage at one of its terminals until we already
know the node voltage at its other terminal. Let's try the example
problem again, keeping this fact in mind.
First, we see that node c is
grounded, so its node voltage is 0. Now that the node voltage at one
terminal of the 3-V source is known, we can use the value to find the
node voltage at the other terminal:
The node voltage propagates along all the wires that make up node a, up to the terminal of the 2-V
source. Given a's node
voltage, we use the value of 2 V to find b's node voltage:
In summary, remember that the values of voltage sources are the differences between the node
voltages at their terminals.