9.3: OTHER CONSIDERATIONS

A myriad of performance characteristics combine to determine the over­all utility of an operational amplifier. The possibilities for modifications that compromise one characteristic in order to enhance another are nu­merous in this type of complex circuit. While the major advantage of the two-stage design centers on its easily controlled dynamics, the topology can be readily tailored to specific applications by other types of modifica­tions. This section indicates a few of the "hidden" features of the two-stage design and points out the possibility of certain types of design compromises.

Temperature Stability

The last section shows that the use of internal feedback to compensate the amplifier under discussion yields an open-loop transfer function in­versely proportional to the transfer admittance of the compensating net­work over a wide range of frequencies. The constant of proportionality for this and other variations of the two-stage design includes the transconduct­ance of either input transistor, and is thus inversely related to temperature if the collector current of these transistors is temperature independent. This relatively mild variation with temperature is tolerable in many applications.

If greater transfer-function stability is required, the input-stage bias cur­rent can be made directly proportional to the absolute temperature. As a result, input-stage transconductance, and therefore the open-loop transfer function, will be temperature independent. A further advantage of this type of bias-current variation is that it partially compensates for input-tran­sistor current-gain variations with temperature and thus reduces input-current changes.

The required bias-current temperature dependence can be implemented by appropriate selection of the total voltage applied to the base-to-emitter junction and the emitter resistor of the input-stage current source (\(Q_3\) in Figure 9.1). It can be shown that the output current from the source will be directly proportional to temperature if this voltage is constant and is ap­proximately equal to the energy-band-gap voltage \(V_{go}\) (see Problem P9.11).

Large-Signal Performance

The analysis of the effects of compensation on amplifier performance has been limited up to now to linear-region operation. It is clear that compen­sation also effects large-signal behavior. For example, an open-loop transfer function similar to that obtained using a \(20-pF\) compensating capacitor could be obtained by connecting a series-connected \(3.6-\mu F\) capacitor and \(500-\Omega\) resistor from the base of \(Q_5\) to ground. However, recovery from over­load might be greatly delayed with this type of compensation because of the time required to change the voltage on a \(3.6-\mu F\) capacitor with the limited current available at this node.

The compensation also limits the slew rate, or maximum time rate of change of output voltage of the amplifier. Consider an output voltage time rate of change \(\dot{v}_O\). If a compensating capacitor \(C_c\) is used, the capacitor current required at the node including the base of \(Q_5\) is \(C_c \doet{v}_O\). The maximum magnitude of the current that can be supplied to this node by the first stage and that is available to charge the capacitor is approximately equal to the quiescent bias current of either input transistor \(I_{C1}\). Thus the slew rate is \(\dot{v}_O (\max) = I_{C1}/C_c\). However, the ratio \(I_{C1}/C_c\) also controls the unity-gain frequency of the amplifier, since this frequency is \(g_{m1}/2C_c = qI_{C1}/2kTC_c\). The important point is that if some consideration, such as the phase shift from high-frequency singularities, limits the unity-gain frequency, it also limits the slew rate if a single capacitor is used to compensate the amplifier.

One way to circumvent this relationship is to add equal-value emitter resistors to both input transistors so that the transconductance of the input stage is lower than \(g_{m1} /2\). Unfortunately, emitter degeneration also degrades the drift of the amplifier. Another more attractive possibility is the use of more involved compensation than that provided by a single capaci­tor. This alternative will be discussed in Chapter 13.

Design Compromises

There are many variations of the basic amplifier topology that result in useful designs, and some of these variations will be illustrated in Chapter 10. Other degrees of freedom are possible by varying quiescent operating current and by changing transistor types. The purpose of this section is to

indicate how these variations influence amplifier performance.
Consider the changes that result from increasing all quiescent operating currents by a factor K. This change can be effected by decreasing all circuit resistors by the same factor. In response to the current change, all internal

transistor resistances will decrease by the same factor, since all are mul­tiples of \(1/g_m\). Current gains of the various transistors do not change sig­nificantly if \(K\) is not grossly different from one. Thus the d-c voltage gain, which is a ratio of transistor and circuit conductances of the amplifier, will not change in response to changes in quiescent current. Input current will increase directly with quiescent current, and drift may increase somewhat because of increased self-heating in the first stage.

The dynamics for the design in question (at least without compensation) are determined primarily by the resistance and capacitance values at the base of \(Q_5\) and at the collector of \(Q_6\). The resistance values at these nodes

decrease by an amount \(K\), since they consist of combinations of transistor and circuit resistances. The capacitance values remain constant, at least for moderate changes from the levels used in the last sections, for the following reason. The capacitances involved are transistor-junction capacitances \(C_{gd}\), \(C_{\mu}\), and \(C_{\pi}\). Capacitances \(C_{gd}\) and \(C_{\mu}\) are current-level independent, while C is the sum of a constant term plus a component linearly proportional to current. For transistor types likely to be used in this circuit, the current-proportional term is not important at levels below \(1\ mA\). Thus an increase in current levels by as much as a factor of 10 from the values indicated in Figure 9.1 does not significantly change critical node capacitances.

The argument above shows that moderate increases in operating current cause proportional increases in the locations of uncompensated open-loop poles. The form of the amplifier uncompensated open-loop transfer func­tion remains unchanged and is simply shifted toward higher frequency. The possibility for increased bandwidth after compensation as a result of this modification is evident.

A second alternative is to change the relative ratios of first- and second- stage currents. An increase in second-stage current relative to that of the first stage has three major effects:

1. Drift increases because second-stage loading becomes more significant.

2. Gain decreases because the input resistance of the second stage de­creases.

3. Bandwidth increases because the second-stage resistances decrease.

Significant flexibility is afforded by the choice of the active devices. The transistor types shown in Figure 9.1 were selected primarily for high values of \(\beta\) and \(1/\eta\). These types result in an amplifier design with high d-c voltage gain, low input current, and low drift. Unfortunately, because of compro­mises necessary in transistor fabrication, these types may have relatively high junction capacitances.

Clearly higher-frequency transistors can be used in the design. In fact, amplifiers with this topology have been operated with closed-loop band­widths in excess of 100 MHz by appropriately selecting transistor types and operating currents. However, the d-c voltage gain for a design using high-frequency transistors is usually one to two orders of magnitude lower than that of the design shown in Figure 9.1. Input current and voltage drift are also severely degraded. Furthermore, many high-frequency transistors have breakdown voltages on the order of 10 to 15 volts, resulting in limited dy­namic range for an amplifier using such transistors.

At times high-frequency types are used for transistors \(Q_4\) and \(Q_5\), with high-gain types used in other locations. This change improves the band­width of the amplifier, but compromises voltage gain and drift because of the lower current gain typical of high-frequency transistors. Since transistors \(Q_4\) and \(Q_5\) operate at low voltage levels, dynamic range is not altered.