3.4. Noise gain and signal gain

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 R₁ and R₂ becomes V_NI.
Since the current flowing through R₁ (I₁) does not flow to the op-amp, all of I₁ flows through R₂.

I₁ = V_NI / R₁

Hence, the noise voltage at V_O (V_NO) is calculated as:

V_NO = V_NI + R₂ × V_NI / R₁ = V_NI × (1 + R₂ / R₁)

Since the noise gain (A_N) is equal to V_NO/V_NI,

A_N = 1 + R₂ / R₁

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.

Next, the following paragraphs briefly describe the oscillation margin.
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 R₃ is equal to the GND potential at a signal gain of A_V (= V_o/V_i), no current flows through R₃. Hence, A_V = -R₂/R₁, 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 = R₁ // R₃. Hence, A_N = 1 + R₂ / (R₁ // R₃), which is higher than the noise gain for basic inverting amplifiers, A_N = 1 + R₂ / R₁. 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.