Hello and welcome to TI Precision Lab discussing Intrinsic Op Amp Noise Part 3. In this video, we'll continue the noise discussion by doing a full noise calculation for a simple amplifier circuit. 

Before we start to look at the hand calculation, however, let's take a look at a range of different amplifiers and the associated current and voltage noise. Voltage noise is closely related to the device's quiescent current. Voltage noise and quiescent current are inversely proportionate. So amplifiers with high quiescent current tend to have lower noise. For example, comparing the OPA349 to the OPA333, you can see that the amplifier with the higher quiescent current has lower noise. 

Furthermore, bipolar amplifiers tend to have lower noise than CMOS amplifiers for a given current. For example, compare the OPA350 CMOS amplifier to the OPA211 bipolar amplifier. Notice that the bipolar amplifier has lower noise than the CMOS amplifier, even though the quiescent current is higher. 

Current noise, on the other hand, is not related to quiescent current. Current noise is lower for CMOS amplifiers than for bipolar amplifiers. Generally, you will notice amplifiers that have low bias current also have low current noise. This table gives examples that represent the extreme range of noise values for amplifiers. In other words, most amplifiers will be in the range of hundreds of nanovolts per root hertz to one or fewer nanovolts per root hertz for voltage noise and thousands of femtoamps per root hertz to one or fewer femtoamps per root hertz for current noise. 

Let's go back to our example noise calculation. In this example, we will examine an OPA627 in a non-inverting configuration with a gain of 101 volts per volt. The total noise at the output will be the sum of op amp voltage noise, op amp current noise, and resistor noise. We will have to consider both the 1/f region and the broadband region in the noise spectral density curves. We will also have to consider the noise bandwidth and the noise gain of the circuit. 

The curve on the left is the voltage spectral density curve. Remember from earlier videos that it has a 1/f region and a broadband region. The right hand curve is the open loop gain, or AOL curve. The bandwidth of the circuit is only determined by the AOL curve, because there is no other filter. Dividing the OPA637's unity-gain bandwidth of 16 megahertz by our gain of 101, we get a closed loop bandwidth of 158 kilohertz. This can also be seen graphically. 

Now that we have learned all the equations for the op amp voltage noise in the previous videos, let's compute the voltage noise for this example. Inspection of the results shows that the 1/f noise component of 192 nanovolts is not significant in this example compared to the broadband noise component of 2,499 nanovolts. This is fairly typical of wide bandwidth examples. Also note that the results are added using the root sum of squares for a total input referred noise of 2,497 nanovolts. 

Now that we have the op amp voltage noise component, let's compute the effect of current noise. For a non-inverting amplifier, the current noise flows through the parallel combination of R1 and Rf. This relationship can be derived using the same op amp analysis techniques that would be used for a DC current source. The current noise is multiplied by the equivalent resistance to generate an input referred noise voltage. Let's look at the numbers for this example. 

So in this example, the noise current density is very small at just 1.6 femtoamps per square root hertz. The equivalent input resistance is also small at just under 1 kiloohm. Multiplying these together, we get an extremely small noise voltage density of 0.0016 nanovolts per root hertz. 

Converting to rms using the noise bandwidth, we get 0.8 nanovolts rms. For all practical purposes, we could neglect this number, since it is insignificant compared to the voltage noise of 2,497 nanovolts. But we will include it for the sake of completeness. Later on, we will see an example where current noise dominates. 

Let's now finish up by calculating the circuit's resistor thermal noise also called Johnson noise. We use the equivalent resistance to do this, which again is just under 1 kiloohm. And after plugging in our values into the equation from the previous video, we get a result of 2,010 nanovolts rms. This is actually a significant amount of noise. 

So now that we have the op amp voltage noise, the op amp current noise translated to voltage, and the op amp resistor noise, we can add them all together again using the root sum of squares. This gives us the total input referred noise voltage in rms. Notice that the current noise does not contribute significantly to the total noise. 

The OPA627 is a JFET input op amp, which typically has very low input current noise density. In this example, the total input referred noise calculates out to 3,205 nanovolts rms. Multiplying by the gain of 101, we get an output noise voltage of 324 microvolts rms. 

Now, frequently, engineers want to know the peak-to-peak noise. How do we compute this? We can do this by multiplying the rms noise by 6 or 6.6. Remember that noise has a Gaussian distribution. The Gaussian distribution tells us that there is a 99.7% probability that any reading in time is within the limits of plus or minus three standard deviations or 6 sigma. This means that there is a finite probability of only 0.3% that a noise reading will be outside of this limit. 

Sometimes, 6.6 standard deviations is used, because the probability of noise being inside the limits has increased to 99.9%. It is important to remember that the tails of the Gaussian distribution extend to infinity. So there is no number of standard deviations that will produce a 100% probability that all noise is inside of the bounds. Thus 6 or 6.6 are used as good estimates. One final thing to keep in mind is that rms and standard deviation are equivalent for noise signals with no mean value. This is generally true for the intrinsic noise that we are considering. 

Multiplying the rms output by 6 gives us the estimate of peak-to-peak output noise voltage. In this example, the peak-to-peak output voltage noise is 1.95 millivolt peak to peak. In later videos, we will simulate and measure the circuit with the same results. That concludes this video. Thank you for watching. Please try the quiz to check your understanding of this video's content.