# 5.9: Summary


In this chapter we have taken a closer look at op amp characteristics. First of all, we find that the upper frequency limit is a function of the op amp parameter $$f_{unity}$$, also known as the gain-bandwidth product, and the circuit's noise gain. The higher the gain is, the lower the upper break frequency will be. Op amps are capable of flat response down to DC. If coupling capacitors are used, the lower break frequency may be found by using standard lead network analysis. When stages are cascaded, the results echo those of cascaded discrete stages. The lowest $$f_2$$ is dominant and becomes the system $$f_2$$. The highest $$f_1$$ is dominant and sets the system $$f_1$$. If more than one stage exhibits the dominant critical frequency, the actual critical frequency will be somewhat lower for $$f_2$$ and somewhat higher for $$f_1$$.

In order to make the op amp unconditionally stable, a compensation capacitor is used to tailor the open loop frequency response. Besides setting $$f_{unity}$$, this capacitor also sets the slew rate. Slew rate is the maximum rate of change of output voltage with respect to time. Slewing slows down the edges of pulse signals and distorts sinusoidal signals. The highest frequency that an amplifier can produce without slewing is called the power bandwidth. In order to optimize $$f_{unity}$$ and slew rate, some amplifiers are available without the compensation capacitor. The designer then adds just enough capacitance to make the design stable.

Due to slight imperfections between the input transistors, op amps may produce small DC output voltages called offsets. Offsets may be reduced through proper resistor selection. Simple nulling circuits may be used to completely remove the offset. A variable offset due to temperature variation is called drift. The larger the temperature variation, the larger the drift will be. The transistor mismatch also means that common-mode signals will not be completely suppressed. Just how well common mode signals are suppressed is measured by the common-mode rejection ratio, CMRR. Similar to CMRR is PSRR, the power-supply rejection ratio. PSRR measures how well power-supply noise and ripple are suppressed by the op amp. Both PSRR and CMRR are frequency-dependent. Their maximum values are found at DC and then they decrease as frequency increases.

Finally, noise is characterized as an undesired random output signal. The noise in op amp circuits may be characterized by three components: the thermal noise of the input and feedback resistors, the op amp's input noise voltage density, $$v_{ind}$$, and its input noise current density, $$i_{ind}$$. The combination of these elements requires an RMS summation. In order to find the output noise voltage, the input noise voltage is multiplied by the circuit's noise gain. The ratio of the desired output signal and the noise voltage is called, appropriately enough, the signal-to-noise ratio. Normally, signal-to-noise ratio is specified in decibels.

This page titled 5.9: Summary is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James M. Fiore via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.