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The Inverting Op Amp Stage

The op amp inverting gain stage, also known simply as the inverter, is shown in Figure 1-4. As can be noted by comparison of Figures 1-3 and 1-4, the inverter can be viewed as similar to a follower, but with a transposition of the input voltage VIN. In the inverter the signal is applied to RG of the feedback network, and the op amp (+) input is grounded.
The feedback network resistances, RF and RG set the stage gain of the inverter. For an ideal op amp, the gain of this stage is:
For clarity, these expressions are again included in the figure. Note that a major difference between this stage and the non-inverting counterpart is the input-to-output sign reversal, denoted by the minus sign in Equation 1-5. Like the follower stage, applying ideal op amp principles and some basic algebra can derive the gain expression of Eq. 1-5.
The inverting op amp stage (inverter)
Figure 1-4: The inverting op amp stage (inverter)
The inverting configuration is also one of the more useful op amp stages. Unlike a non-inverting stage however, the inverter presents a relatively low impedance input for VIN, i.e., the value of RG. This factor provides a finite load to the source. While the stage gain can in theory be adjusted over a wide range via RF and RG, there is a practical limitation imposed at high gain, when RG becomes relatively low. If RF is zero, the gain becomes zero. RF can also be made variable, in which case the gain is linearly variable over the dynamic range of the element used for RF. As with the follower gain stage, the gain is ratio dependent, and is relatively insensitive to the exact RF and RG values.
The inverter’s gain behavior, due to the principles of infinite op amp gain, zero input offset, and zero bias current, gives rise to an effective node of zero voltage at the (−) input. The input and feedback currents sum at this point, which logically results in the term summing point. It is also called a virtual ground, because of the fact it will be at the same potential as the grounded reference input.
Note that, technically speaking, all op amp feedback circuits have a summing point, whether they are inverters, followers, or a hybrid combination. The summing point is always the feedback junction at the (–) input node, as shown in Fig. 1-4. However in follower type circuits this point isn’t a virtual ground, since it follows the (+) input.
A special gain case for the inverter occurs when RF = RG, which is also called a unity gain inverter. This form of inverter is commonly used for generating complementary VOUT signals, i.e., VOUT = −VIN. In such cases it is usually desirable to match RF to RG accurately, which can readily be done by using a well-specified matched resistor pair.
A variation of the inverter is the inverting summer, a case similar to Figure 1-4, but with input resistors RG2, RG3, etc (not shown). For a summer individual input resistors are connected to additional sources VIN2, VIN3, etc., with their common node connected to the summing point. This configuration, called a summing amplifier, allows linear input current summation in RF (The very first general-purpose op amp circuit is described by Karl Swartzel in Reference 3 (Karl D. Swartzel, Jr. "Summing Amplifier," US Patent 2,401,779, filed May 1, 1941, issued June 11, 1946), and is titled "Summing Amplifier". This amplifier became a basic building block of the M9 gun director computer and fire control system used by Allied Forces in World War II. It also influenced many vacuum tube op amp designs that followed over the next two decades). VOUT is proportional to an inverse sum of input currents.
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