Let's summarize what we did to solve for the output of the inverting amplifier.  Each step we took was simple, but they combine to give us a powerful method that we can use when we examine other operational amplifer circuits, so it will be worthwhile to review the process to be sure that we understand the approach.

• We assumed that the circuit operated in such a way that the output was not at the exact limits set by the power supply.  If we have a +12 and -12 volt set of supplies, this would probably mean that the output was llimited to somewhere betwwen -10 or -11 volts and +10 or +11 volts.  In other words, we assumed that the amplifier was operating somewhere within its linear range and was not saturated.  That's what we really mean when we say that the output is some reasonable voltage.  If you try to push the output voltage too high or too low, it may be possible to do that, and what is possible is set by the power supply you use.

• You can't make the output be bigger than around 11 volts if you use a power supply voltage of +12 and -12 volts.  Larger power supply voltages allow larger output ranges up to the point where the chip gets fried.  (Fried is a technical description of what happens when an electrical element is operated at voltages and/or currents above rated limits.)

        We need to be more specific about what we mean when we say the output is "reasonable".  Whenever you use an operational amplifier you need to use two power supplies.  Often you use a +12v and a -12v supply, although +/-15v is also common.  Whatever the power supply, the output of the operational amplifier is limited by the supply you use.  Usually the limit is within a volt or so of the power supply voltage, so if the supply voltage is +/-12v, you might be able to drive the op-amp up to 10.8v (or something like that) and down to -10.8v.  (And, it's not always symmetrical so you need to be careful.)  If your circuit tries to make the op-amp output voltage 17.3 v in that situation, you aren't going to see that voltage.  You'll get 10.8 instead.  When that happens, you say that the op-amp is saturated.  Otherwise, when everything is copasetic, and the amplifier is not saturated, you say that the op-amp is operating in the linear range.

        When the op-amp is operating in the linear range, then there is an expression for the output voltage in terms of the gain.

where:

• V₊ = voltage at the non-inverting input,

• V_- is the voltage at the inverting input,

• Gain = gain of the operational amplifier.

        The gain of a 741 operational amplifier is typically well over 100,000.  So, if the output is limited to something like ten (10) or eleven (11) volts, the input difference, V₊ -V_-, can't be more than about 100mv (microvolts).

          The inverting amplifier is an important - and often used - operational amplifier circuit.  It can also be viewed as a prototype circuit that is a starting point for more complex and even more interesting circuits.  You need to be sure that you remember the assumptions and analysis techniques you use to figure out the output voltage in this circuit.  Here is a summary.

• Assuming:

• Infinite gain

• No current into the input terminals (infinite input resistance)

• Then,

• The inverting input is a virtual ground, and the voltage there is assumed to be zero when the non-inverting input is connected to ground.

• Write KCL at the inverting input.

• Solve for the output voltage.