# What are opamps?

### **Negative Feedback Systems and Its Effects**

##### Negative Feedback System

Although opamps are high voltage gain amplifiers, virtually no opamps carry out standalone amplification.

This is because it is difficult to control the open gain variations and narrow-band amplification factor.

Therefore, a negative feedback circuit is typically used.

The diagram at right shows an example of a negative feedback system.

Configuring a negative feedback circuit provides the following benefits.

[Advantages of Negative Feedback Circuits]

- Widens the region (bandwidth) where the gain of the amplifier circuit becomes constant
- Minimizes the effects of opamp open gain variation
- Suppresses distortion

##### 1.Widens the region (bandwidth) where the gain of the amplifier circuit becomes constant

First off, determine the transfer function, which relates the output to the input of the model.

A_{O} ： Opamp Open Gain (Open Loop Gain)

β ： Feedback Factor

1+βA(s) ： Amount of Feedback

Loop Gain ： βA(s)

In addition, as shown by the following equation, the opamp has a transfer function for 1st order lag.

The above frequency characteristics illustrate the relationship of the formula above.

Applying negative feedback will reduce the gain and amount of feedback, showing that ω_{O} will expand to ω_{O}(1+βA_{O}).

##### 2.Minimizes the effects of opamp open gain variation

Next, assuming that the open gain of the opamp in the transfer function equation (relating the output to the input) is sufficiently large (A_{O}>>1), the gain of the negative feedback circuit at low frequencies can be approximated to 1/β.

In other words, when the open gain of the opamp is large, the gain of the feedback circuit is determined solely by the feedback ratio (regardless of the gain).

As a result, the amplification factor of the amplifier circuit (i.e. inverting amplifiers) at low frequencies is solely determined by the external resistance.

Also, in the case the open gain is sufficiently large (A_{O}>>1), the effects of open gain (based on temperature characteristics and production variations) is small, even with some fluctuations.

##### 3.Suppresses distortion

A feedback circuit with error elements is shown in the figure below.

Here the error elements generated by the opamp are V_{D}.

Elements such as distortion, error voltage, and noise are included.

The transfer function including distortion is shown at the equation at right.

As shown here, as the gain increases V_{D} becomes smaller, and we can see that the error is mitigated.

Conversely, listed below are some disadvantages in configuring a negative feedback circuit.

[Drawbacks of Configuring a Negative Feedback Circuit]

- Lower amplification factor compared with open gain

- Feedback may cause the circuit to oscillate