Circuit Analysis

The complexities of single-supply op amp design are illustrated with the following example. Notice that the biasing requirement complicates the analysis by presenting several conditions that are not realizable. It is best to wade through this material to gain an understanding of the problem, especially since a cookbook solution is given later in this chapter.

The previous chapter assumed that the op amps were ideal, and this chapter starts to deal with op amp deficiencies. The input and output voltage swing of many op amps are limited as shown in Figure 4–7, but if one designs with the selected rail-to-rail op amps, the input/output swing problems are minimized. The inverting circuit shown in Figure 4–5 is analyzed first.

Figure 4–5. Inverting Op Amp

Equation 4–1 is written with the aid of superposition, and simplified algebraically, to acquire Equation 4–2.

As long as the load resistor, RL, is a large value, it does not enter into the circuit calculations, but it can introduce some second order effects such as limiting the output voltage swings. Equation 4–3 is obtained by setting VREF equal to VIN, and there is no output voltage from the circuit regardless of the input voltage. The author unintentionally designed a few of these circuits before he created an orderly method of op amp circuit design. Actually, a real circuit has a small output voltage equal to the lower transistor saturation voltage, which is about 150 mV for a TLC07X.

When VREF = 0, VOUT = -VIN(RF/RG), there are two possible solutions to Equation 4–2.

First, when VIN is any positive voltage, VOUT should be negative voltage. The circuit can not achieve a negative voltage with a positive supply, so the output saturates at the lower power supply rail. Second, when VIN is any negative voltage, the output spans the normal range according to Equation 4–5.

When VREF equals the supply voltage, VCC, we obtain Equation 4–6. In Equation 4–6, when VIN is negative, VOUT should exceed VCC; that is impossible, so the output saturates. When VIN is positive, the circuit acts as an inverting amplifier.

The transfer curve for the circuit shown in Figure 4–6 (VCC = 5 V, RG = RF = 100 kΩ, RL = 10 kΩ) is shown in Figure 4–7.

Figure 4–6. Inverting Op Amp With VCC Bias

 

Figure 4–7. Transfer Curve for Inverting Op Amp With VCC Bias

Four op amps were tested in the circuit configuration shown in Figure 4–6. Three of the old generation op amps, LM358, TL07X, and TLC272 had output voltage spans of 2.3 V to 3.75 V. This performance does not justify the ideal op amp assumption that was made in the previous chapter unless the output voltage swing is severely limited. Limited output or input voltage swing is one of the worst deficiencies a single-supply op amp can have because the limited voltage swing limits the circuit’s dynamic range. Also, limited voltage swing frequently results in distortion of large signals. The fourth op amp tested was the newer TLV247X, which was designed for rail-to-rail operation in single-supply circuits.

The TLV247X plotted a perfect curve (results limited by the instrumentation), and it amazed the author with a textbook performance that justifies the use of ideal assumptions. Some of the older op amps must limit their transfer equation as shown in Equation 4–7.

The noninverting op amp circuit is shown in Figure 4–8. Equation 4–8 is written with the aid of superposition, and simplified algebraically, to acquire Equation 4–9.

When VREF = 0, VOUT = VIN (RF/RG), there are two possible circuit solutions. First, when VIN is a negative voltage, VOUT must be a negative voltage. The circuit can not achieve a negative output voltage with a positive supply, so the output saturates at the lower power supply rail. Second, when VIN is a positive voltage, the output spans the normal range as shown by Equation 4–11.

The noninverting op amp circuit is shown in Figure 4–8 with VCC = 5 V, RG = RF = 100 kΩ, and RL = 10 kΩ. The transfer curve for this circuit is shown in Figure 4–9; a TLV247X serves as the op amp.

Figure 4–8. Noninverting Op Amp

 

Figure 4–9. Transfer Curve for Noninverting Op Amp

There are many possible variations of inverting and noninverting circuits. At this point many designers analyze these variations hoping to stumble upon the one that solves the circuit problem. Rather than analyze each circuit, it is better to learn how to employ simultaneous equations to render specified data into equation form. When the form of the desired equation is known, a circuit that fits the equation is chosen to solve the problem. The resulting equation must be a straight line, thus there are only four possible solutions.