Negative Feedback Op-Amp for Reliable Gain

Key Takeaways

• Negative feedback op-amps use a feedback pathway to ensure reliable performance under expected operating conditions.

• A few idealized assumptions are necessary to illustrate that the total gain of the negative feedback op-amp network is the reciprocal of the feedback gain.

• An op-amp network without negative feedback is more liable to fluctuations and may perform unexpectedly.

Negative feedback op-amps are a common amplification network topology.

Amplification of signals is essential when dealing with the small signals produced by system transducers when interfacing with the outside world. However, amplification generally requires negative feedback paths to relate the output and input signals for enhanced reliability and established performance. The negative feedback op-amp is the more common implementation method, but it’s worthwhile to investigate why this is the case.

Op-Amp Performance With and Without Negative Feedback

The Motivation for Negative Feedback Op-Amps

Op-amp networks can take on countless forms, but there are two essential formats (we’ll ignore the voltage follower for this article): non-inverting and inverting amplifiers, with the difference being which of the differential inputs connect to ground and the voltage input. While some might conflate negative feedback with an inverting op-amp and negative gain, both inverting and non-inverting op-amp networks utilize negative feedback. The innate design of the op-amp necessitates the general application of negative feedback: op-amps have high gain but low gain stability and linearity that make amplification less reproducible, introducing reliability issues. Negative feedback trades total gain for more efficient gain characteristics and reduced output impedance, but the exact advantages differ between inverting and non-inverting networks:

• Non-inverting op-amps have higher input impedance to buffer and isolate circuit blocks.

• Inverting op-amps reduces distortion by keeping the differential inputs close to ground.

Negative feedback's universal importance becomes clearer when considering the idealized amplifier, which assumes the differential inputs have the same potential with no current flow into or out of the nodes. These assumptions have three direct consequences:

1. The input impedance approaches infinity.

2. The output impedance equals zero.

3. The open loop gain (the ratio of output values to input values, typically voltage) approaches infinity. 

While a zero potential difference on the differential inputs is impractical (besides a trivial case of connecting the inputs), negative feedback aims to reproduce this idealized requirement with a negligible value. Then, nodal analysis can calculate the non-ideal closed-loop gain to model the amplifier network’s actual gain accurately.  An op-amp that doesn’t utilize negative feedback performs entirely differently and generally has a reduced scope of applicability. Typically, the open loop voltage will be much too high for linear applications, the impedances will be appreciably high and low on the input and output, respectively (yet lack any modification capability), and the bandwidth will shrink considerably as the gain-bandwidth product remains constant while the gain increases. The difference between the gain and bandwidths owes to the forward attenuation factor, which varies for every closed-loop gain value.

Constructing an op-amp network with negative feedback creates a feedback path where the signal's gain (G) is the output over the input. A fraction of the output signal returns to the inverting terminal of the op-amp as the error signal (the difference of the source minus the input), which amplifies according to the feedback-loop gain (ꞵ). The new input signal multiplied by the amplifier's open-loop gain (A) produces the amplifier's output signal, and the process continues. This relationship provides an impetus for general network analysis via nodal analysis:

When the open-loop gain is appreciably high (as mentioned, theoretically approaching infinity), the equation simplifies to

This relationship shows that the closed-loop gain is independent of the open-loop gain (provided the closed-loop gain is “infinity enough”  to fulfill the above simplification). The amplification of the negative feedback network depends only on the topology and the quality of the circuit elements.

Benefits of Negative Feedback and Frequency Considerations

Incorporating negative feedback into an op-amp network offers tremendous benefits:

• Stable gain to promote reliability.

• Linearity forms a proportional response from input to output.

• Frequency dependence may or may not be independent of the highest frequency component. As a result, the bandwidth of input signals can drastically affect the circuit's performance if tuned for a specific pole.

• Tying high input and low output impedance minimizes the effects of a change in the gain of the amplifier network.

• Low noise sensitivity ensures the inherent randomness of signal fluctuations do not meaningfully impact the signal output.

The frequency response of the negative feedback op-amp is worth exploring further. Across its bandwidth, a negative feedback op-amp will not experience a uniform gain for all frequencies but will operate as a low-pass filter around a dominant pole frequency. The effects of frequency on the negative feedback are most noticeable at the extent of the bandwidth. At low frequencies, the op-amp will enter saturation quickly for very low amplitude signals due to the high gain; high frequencies, meanwhile, allow for an undistorted output voltage signal as the gain decreases. Saturation, in effect, overrides any derived output equations of the op-amp, making a carefully tuned amplifier network perform unexpectedly.

Cadence Solutions Simplify Simulation and Accelerate Production

Negative feedback op-amps are a fundamental amplification topic and the basis for their reliability and expected operation. As shown with nodal analysis, the signal amplification is proportional to the reciprocal feedback loop gain, which trivializes analysis for many circuits under ideal assumptions. While these assumptions are generally accurate, manufacturing may require more comprehensive modeling to capture circuit behavior. Cadence’s PCB Design and Analysis Software suite includes PSpice for quick construction and powerful analysis of time-variant, steady-state, and transient responses with an intuitive toolset. Simulation results can then seamlessly translate to OrCAD PCB Designer for an accelerated, constraint-driven layout with a unified ECAD ecosystem.

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