Simulating op amp noise
Previously I discussed how to use a spreadsheet to visualize an op amp's Noise to help pick the lowest noise for any source resistance .
In this article we will use Texas Instruments capable SPICE like simulator called Tina-TI  and the Visualization techniques described earlier to help design a fairly optimum circuit like one I had to recently work with.
Why use TI's simulator when there are so many others to choose from? One Word: “Models.” No, this doesn't mean op amp models, but rather a very cleverly done set of Voltage and Current Noise Models that are easy to use and simulate both the flat broadband portion of the noise and also the 1/f region very well. Tina also has an essentially “One Button” simulation for noise that produces noise spectral density plots and total integrated output noise which really speeds up the circuit design process.
I will Let TI's Art Kay describe how to setup these noise sources and run the simulations as Art has done a masterful job of this and his presentations are easily found on the web .
These Voltage and Current noise models are added to an ideal op amp's input, then three parameters are added to each model and we have a very accurate simulation of any op amp's Voltage and Current noise and as an added bonus we get a complete integrated noise plot as well!
A Sample Design Problem
This design required that a gain-of-three, non-inverting amplifier be placed between an existing resistive source that has a resistance of 3500 Ohms. The sensor output is 0 to 5 volts so the amplifier output will be 0 to 15 volts. The amplifier load is high impedance. The overall circuit's small-signal bandwidth is to be around 500 Hz. The basic problem is to design this interface amplifier for very low additive noise. Figure 1 shows the basic circuit.
Figure 1: The basic circuit as drawn in Tina. R1 simulates the resistance of the low noise sensor OP2 is a generic op amp model that does not include a noise model, the noise sources used to model the real op amp's Voltage and Current noise are provided by TI's macromodels Vn1 and In1. Reference 3 describes exactly how to set the simulations up in Tina to measure op amp noise.
The first part of the design is easy, that is setting the feedback resistor's value. Since the amplifier output is such a high voltage we will pick the feedback resistor to limit the current required to drive the feedback to around 2.5 mA. This then sets the feedback resistor value of Figure 1 to 4000 Ohms and the input resistor is then found to be 2000 Ohms to get the required gain.
Note that the feedback resistors also add noise, but in this example, the parallel resistance they present to the negative input is less than half the value of the source resistance, so they will be ignored for now. In the simulation that follows they will not be ignored, so we will get a final accurate result.
How To Start?
Nearly every engineer who has set about designing their first low-noise amplifier has searched data sheets for low Voltage Noise devices. Then the realization hits that as the source resistance increases the Current noise starts to become a factor and may even dominate the total amplifier's noise.
In a previous article  I described how to visualize an op amp's total noise versus source resistance and introduced a concept of Ropt or the optimum source resistance for any given amplifier.
This is preferable to making tables of device Vn and In values and trying to decide which will produce the lowest noise.
Op amp Noise Comparison @ 10 Hz
LT1028 Vn = 1 nV/rt-Hz In = 4.7 pA/rt-Hz
AD8675 Vn = 3.5 nV/rt-Hz In = 0.3 pA/rt-Hz
Table 1: Which amplifier will produce lower noise total in our proposed circuit - the Linear Technology LT1028 or the Analog Devices AD8675? It's very difficult to tell from data sheet parameters alone.
Using the Visualizer however and the likely candidate is easy to spot (Figure 2).
Figure 2: Plotting the LT1028 and the AD8675 noise at 10 Hz together on the Visualizer Spreadsheet  provides immediate results. The sensor's source resistance was also drawn on this graph as a red vertical line at 3.5 k Ohms. At this source resistance value the AD8675 can be seen to be clearly the lower total noise amplifier, even though its data sheet Voltage Noise value is 3.5 times that of the LT1028.
An interesting item to note in Figure 2 is the Ropt values that are plotted for each op amp. At 10 Hz the Ropt of the LT1028 is 210 Ohms and the Ropt of the AD8675 is about 12k Ohms.
As was discussed previously, in most circuit configurations, operating at or below Ropt will give the lowest total noise in an actual circuit like this. From the Ropt values we can narrow the choice also as the Ropt of the LT1028 is way too low for the circuit we are working on even though it is commonly thought of as the lowest voltage noise op amp on Earth, at least that's the way I always think of it.