Time： 2019-01-17 17:57:41

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Previous installments of this article series discussed the need to verify SPICE model accuracy and how to measure the output impedance, small-signal bandwidth, and input-referred errors of operational amplifier (op amp) models. In part 4, I’ll show you how to verify the noise behavior of op amp models, including input voltage noise spectral density (e_{n}) and input current noise spectral density (i_{n}). I’ll also demonstrate a total noise simulation that provides the integrated root-mean-square (RMS) noise of a complete op amp circuit.

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. Noise from the outside world, called extrinsic noise, may also couple into your circuit. This includes 50 Hz or 60 Hz noise from AC power lines, or high-frequency electromagnetic interference (EMI) from mobile phones and other wireless devices. Unfortunately, extrinsic noise is difficult to predict and analyze, so this article will focus on intrinsic op amp 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. For a hypothetical circuit with a voltage gain of 2 V/V, **Figure 1** shows the input voltage, ideal output voltage and output voltage with noise.

**Figure 1** Noise example

Broadband noise, also known as white noise or thermal noise, is the most common noise phenomenon affecting op amp circuits. Broadband noise is made up of contributions from a broad spectrum of fundamental frequencies ranging from 1 kHz and higher. Just how white light can be divided with a prism into its component colors, you can think of white noise in terms of its component frequencies. The representation of a noise source in terms of its component frequencies is called noise spectral density, a topic I’ll explore in more detail later.

**Figure 2** illustrates how a collection of sinusoids at various frequencies combine to create white noise. The plot on the right shows what white noise looks like in the time domain. This is what you would see if you measured noise with a lab oscilloscope or ran a transient noise simulation in SPICE.

**Figure 2** Frequency components of white noise

With an accurate SPICE model, predicting the noise performance of an op amp circuit with simulation becomes a simple task. This is an appealing prospect to many engineers, as performing a complete op amp noise calculation by hand, including the effects of all noise sources and the circuit’s bandwidth, can be an involved process.

**Input voltage noise spectral density – e _{n}**

The input voltage noise spectral density, or e_{n}, is the first type of intrinsic op amp noise, and the type that’s usually of most concern when performing noise analysis. Let’s revisit a simplified small-signal model of an op amp, shown in **Figure 3**. Input voltage noise spectral density is modeled as an error voltage source (e_n) connected in series with the noninverting input. This error voltage has a specific characteristic over frequency, as specified in the typical characteristic curves in an op amp data sheet.

Voltage noise is input-referred, so e_n is amplified by the closed-loop gain of the op amp circuit, along with the differential input signal (Ve), to create the total output voltage (Vout). Since both the noise and the desired input signal are amplified, you must take extreme care when designing high-gain circuits.

**Figure 3 **Simplified input-referred voltage noise model

Voltage noise spectral density over frequency is specified in an op amp data sheet with a curve like the one shown in **Figure 4**. The curve represents the op amp’s voltage noise contribution at each fundamental frequency in the measured range and is usually given in units of nanovolts per square root hertz (nV/√Hz).

Engineers unfamiliar with noise analysis may wonder why such a complex unit is used to quantify op amp noise. The reason is because the measured noise of a circuit is highly dependent on its bandwidth. Noise calculations frequently involve integrating the behavior of noise sources over a specific frequency range, and the units of nanovolts per root hertz simplify to the RMS voltage after calculating the integral.

Op amp noise is a deep subject, and detailing how to perform complete noise calculations is beyond the scope of this article. For a more complete journey into the topic, including techniques for reducing noise in op amp circuits, watch Texas Instruments’ (TI) eight-part TI Precision Labs – Op Amps video series on noise.

**Figure 4** Typical e

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