Previous installments of this blog post series discussed the need to verify SPICE model accuracy and how to measure common-mode rejection ratio (CMRR), offset voltage versus common-mode voltage (Vos vs. Vcm), slew rate (SR), open-loop output impedance (Zo), input offset voltage (Vos) and open-loop gain (Aol). In this sixth and final installment, I’ll cover operational amplifier (op amp) noise, including voltage noise and current noise.

Noise is simply an unwanted signal, usually random in nature, that when combined with your desired signal results in an error. All op amps, as well as certain other circuit elements like resistors and diodes, generate some amount of intrinsic – or internal – noise. In analog circuits, it’s critical to confirm that the noise level is low enough to obtain a clear measurement of your desired output signal. Figure 1 shows an example of input voltage, ideal output voltage and output voltage with noise for a circuit with gain of 3V/V.

**Figure 1: Noise example**

With an accurate model, predicting the noise performance of an op amp circuit becomes quite straightforward. This is very appealing to most engineers, as calculating noise by hand can be cumbersome and difficult.

**Input voltage noise density**

The voltage noise of an op amp is usually given as input voltage noise density (e_{n}) in nanovolts per square root hertz (nV/√Hz), which quantifies how much noise voltage the op amp generates at its input pins for any given frequency. To measure e_{n}, configure the op amp as a unity gain buffer with its noninverting input connected to an AC source Vin. Figure 2 shows the recommended test circuit.

**Figure 2: Input voltage noise density test circuit**

Let’s use this circuit to measure the e_{n} of the OPA1692, a low-noise amplifier from TI. Simply run a noise analysis over the desired frequency range and measure the noise level at node Vnoise with respect to Vin.

In this case, the simulated e_{n} matches perfectly with the data-sheet spec, shown in Figure 3.

**Figure 3: OPA1692 e _{n} result**

**Input current noise density**

Op amps also generate noise currents at their input pins, called input current noise density (i_{n}) and typically given in femtoamperes per square root hertz (fA/√Hz). You can measure this in a similar way to e_{n}, but you will need to perform a simple trick. Some simulators have trouble measuring noise in terms of current, so a current-controlled voltage source converts the current flowing into the noninverting input pin into a voltage. Figure 4 shows the recommended test circuit.

**Figure 4: Input current noise density test circuit**

Let’s use this circuit to measure the i_{n} of the OPA1692. Run a noise analysis over the desired frequency range and measure the noise level at node Inoise with respect to Vin. Keep in mind that the resulting plot will have converted amps to volts due to current-controlled voltage source (CCVS1). Figure 5 shows the results after converting back to amperes.

**Figure 5: OPA1692 i _{n} result**

Again, the noise characteristic matches the data-sheet curve extremely well.

**Total voltage noise**

While knowing the input-referred noise of an op amp is useful, it doesn’t paint a complete picture of your circuit’s overall noise performance. A combination of factors like closed-loop gain, bandwidth and the noise contributions of other circuit elements will affect the total amount of noise that appears at the circuit output. Thankfully, most simulators provide a way to measure this type of noise, called total noise or integrated noise, since it’s the integration of all noise sources over the circuit’s effective bandwidth.

Figure 6 shows a more complex op amp circuit, with the OPA1692 configured for a noninverting gain of 10V/V and an additional resistor-capacitor (RC) filter at the output to limit the effective bandwidth to roughly 150kHz.

**Figure 6: OPA1692 total noise example circuit**

Run a total noise analysis over a wide frequency range (shown in Figure 7) and measure the noise level at node Vnoise in order to find the total root mean square (RMS) noise, which will appear at the circuit output. You are looking for the level at which the total noise curve flattens out to a constant value at high frequency.

**Figure 7: OPA1692 total noise result**

The test result shows that the total noise of the circuit in Figure 6 is equal to 21.15µVrms, or 126.9µVpp. This is what you would expect to measure if you probed the output of this circuit in the real world. However, keep in mind that the random nature of noise means that the actual noise level may be somewhat higher or lower than what you calculated or simulated. For a deeper discussion, watch the TI Precision Labs – Op Amps video series on noise.

Thanks for reading this sixth and final installment of the “Trust, but verify” blog series! I hope you’ve found the information and techniques in this series useful in your pursuit of more accurate SPICE simulations. If you have any questions about simulation verification, log in and leave a comment, or visit the TI E2E™ Community Simulation Models forum.

**Additional resources**

- Download the OPA1692 datasheet.
- Learn more from industry expert Art Kay who literally wrote the book on noise.