_{NI}) as a difference in voltage between V_{IN(+)} and V_{IN(-)}, it is not significant whether V_{NI} is inserted in series with V_{IN(+)} or V_{IN(-)}.

Figure 3-13 shows an inverting amplifier, and Figure 3-14 shows a noninverting amplifier. Both the inverting and noninverting amplifiers have an equivalent input noise source (V_{NI}) inserted in series with the V_{in(-)} input of the ideal op-amp. These amplifiers have a signal gain of A_{V} as discussed in Sections 2.4 and 2.5.

Using the principle of superposition, signal and noise sources can be considered separately. Let’s calculate the gain for the noise source. At this time, V_{i} is regarded as being short-circuited according to the principle of superposition.

Since the V_{IN(+)} input is grounded in Figure 3-13, the V_{IN(-)} input can also be regarded as being grounded. Therefore, the potential at the intersection of R_{1} and R_{2} becomes V_{NI}.

Since the current flowing through R_{1} (I_{1}) does not flow to the op-amp, all of I_{1} flows through R_{2}.

I_{1} = V_{NI} / R_{1}

Hence, the noise voltage at V_{O} (V_{NO}) is calculated as:

V_{NO} = V_{NI} + R_{2} × V_{NI} / R_{1} = V_{NI} × (1 + R_{2} / R_{1})

Since the noise gain (A_{N}) is equal to V_{NO}/V_{NI},

A_{N} = 1 + R_{2} / R_{1}

In this way, the gain of the noise generated in an op-amp might be different from that of the signal gain. This gain is called a noise gain.

This concept of noise gain can be used as follows:

- Converting the equivalent input noise into output noise
- Calculating the effect of the input offset voltage on the output
- Calculating the oscillation margin

As described above, the concept of noise gain is important for circuits using an op-amp.

Except for oscillators, oscillation means an unwanted fluctuation of a signal at an unintended frequency. A source of oscillation such as unwanted noise circulates through a feedback loop, developing into oscillation, as described in Section 2.3.

The source of oscillation is random noise. It is applied as a difference in voltage between the V_{IN(+)} and V_{IN(-)} inputs of an op-amp. In other words, it is the equivalent input noise voltage (V_{NI}) discussed above.

It is important to determine the oscillation immunity based on the noise gain. As described above, the noise gain of typical inverting and noninverting amplifiers can be calculated using the signal gain equation for noninverting amplifiers.

The concept of the noise gain can be used to provide a margin for oscillation (i.e., increase the noise gain).

Figure 3-16 shows an example of increasing the oscillation margin without changing the signal gain with an inverting amplifier.

Let’s consider V_{i} and V_{NI} separately using the principle of superposition.

(V_{NI} is regarded as being short-circuited when considering V_{i} whereas V_{i} is regarded as being short-circuited when considering V_{NI}.)

From the concept of a virtual short, both the V_{IN(-)} and V_{IN(+)} inputs are regarded as being grounded.

Therefore, since the voltage across R_{3} is equal to the GND potential at a signal gain of A_{V} (= V_{o}/V_{i}), no current flows through R_{3}. Hence, A_{V} = -R_{2}/R_{1}, which is identical to the equation for a basic inverting amplifier.

Since V_{i} is short-circuited at a noise gain of A_{N} (= V_{o}/V_{NI}), V_{i} = R_{1} // R_{3}. Hence, A_{N} = 1 + R_{2} / (R_{1} // R_{3}), which is higher than the noise gain for basic inverting amplifiers, A_{N} = 1 + R_{2} / R_{1}. This means that this circuit provides a larger oscillation margin than a basic inverting amplifier.

However, since the concept of the noise gain is exactly the same as that of the input offset voltage, the oscillation margin increases at the expense of an increase in input offset voltage.

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3. Electrical characteristics

3.3. Internal noise of an op-amp

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