Complex Feedback Networks

When complex networks are put into the feedback loop, the circuits get harder to analyze because the simple gain equations cannot be used. The usual technique is to write and solve node or loop equations. There is only one input voltage, so superposition is not of any use, but Thevenin’s theorem can be used as is shown in the example problem given below. Sometimes it is desirable to have a low resistance path to ground in the feedback loop. Standard inverting op amps can not do this when the driving circuit sets the input resistor value, and the gain specification sets the feedback resistor value. Inserting a T network in the feedback loop (FIgure 3–7) yields a degree of freedom that enables both specifications to be met with a low dc resistance path in the feedback loop.

Figure 3–7. T Network in Feedback Loop

Break the circuit at point X–Y, stand on the terminals looking into R4, and calculate the Thevenin equivalent voltage as shown in Equation 3–15. The Thevenin equivalent impedance is calculated in Equation 3–16.

Replace the output circuit with the Thevenin equivalent circuit as shown in Figure 5–8, and calculate the gain with the aid of the inverting gain equation as shown in Equation 3–17.

Figure 3–8. Thevenin’s Theorem Applied to T Network

Substituting the Thevenin equivalents into Equation 3–17 yields Equation 3–18.

Algebraic manipulation yields Equation 3–19.

Specifications for the circuit you are required to build are an inverting amplifier with an input resistance of 10 k (RG = 10 k), a gain of 100, and a feedback resistance of 20 K or less. The inverting op amp circuit can not meet these specifications because RF must equal 1000 k. Inserting a T network with R2 = R4 = 10 k and R3 = 485 k approximately meets the specifications.