11.4. DC Stabilization with the Feedback Resistor
The dc output voltage can be set close to zero with negative feedback for normal operation as a linear amplifier as illustrated in Fig. 11.7. A portion of the output voltage is applied back to the input as the voltage across Ry. This is
Equation 11.13
Figure 11.7. Opamp dc stabilized with feedback resistor network. The output voltage is applied back to the input to then drive the output toward a smaller value. The voltage across Ry will be about equal to Voff and VO is forced to near zero.
(Dc VO is used, as this is a no-signal or bias state under consideration.) This voltage will cancel most of Voff, such as to drive VO close to zero if Rf is small enough compared to Ry. The value of VO for a given Rf can be obtained as follows: A loop equation at the input side (Fig. 11.7) gives
Equation 11.14
The opamp circuit is a dc amplifier. Therefore, the input – output relation holds for dc as well as for signals. Thus, V∊ = VO/avo such that
Equation 11.15
and
Equation 11.16
where the approximation usually applies and is equivalent to V∊ = 0.
For example, with Voff = 1 mV and AvNI = 100, Vo ≈ –0.1 V. This would be a very satisfactory dc state for using the circuit as an amplifier. Also, the approximation of the right-hand side of (11.16) is quite valid. Note that without the feedback network, VO = –avoVoff = –40,000 · 1 mV = –40 V. Assuming that the power-supply voltage is, for example, ±15 V, the output is locked at VO ≈ –15 V and the linear gain relation does not apply. In our project with the opamp, we determine Voff from a measurement of VO and the application of (11.16).