Analog filters and specifications swimming: What, I thought I was getting rid of the noise?

Active filters are great – if you need to reduce noise in your signal chain. But, what about the intrinsic noise that the filter’s resistors and amplifiers add to your signal path? We all know the uses of active filters. For instance, a low-pass filter can be used to attenuate noise above a designed-in frequency. You can use a high-pass filter to eliminate low-frequency signals and noise from your system. You also can utilize the bandpass filter in under sampling applications. Finally, the bandstop filter can reject mains frequencies, such as 50 or 60 Hz, or a power supply frequency. All of these filters are designed to eliminate or at least reduce noise in the signal path.

So, what happens to the noise in the passband frequencies of these filters? Actually, your amplifier and resistors create their own intrinsic noise inside and outside of the bandwidths where your filter either passes or reduces noise. You probably don’t care about noise in areas where your filters are rejecting noise, but what about the frequency areas where you are passing signals? Take a look at Figure 1 for examples of low-pass, second-order, filter circuits.

Figure 1. Sallen-Key and multiple-feedback (MFB), second-order, low-pass filters with the noise generators in these circuits (red).

The Sallen-Key filter R₁, R₂, and the operational amplifier (op amp) all generate noise. The resistance voltage noise is equal to Ö(4*K*T*R*BW),

where K is Boltzmann constant (1.38 * 10^-23 J/T)

T is temperature in Kelvin (298.5 K = room temp)

R is your resistor value

BW is the bandwidth of interest

The unit of this calculation is V/ÖHz. The amplifier’s noise specifications can be found in the device’s product data sheet under Input Voltage and Current Noise Density specifications. In the MFB filter, R₁, R₂, R₃, and the op amp generate noise.

Let’s look at a circuit example. A Sallen-Key, fourth-order, low-pass linear phase (0.5 deg) is shown Figure 2.

Figure 2. Gain of 10 V/V, fourth-order, low-pass, Sallen-key filter with a cut-off frequency of 1 kHz and OPA342 voltage and current noise spectral density vs. frequency.

Figure 2 shows a TINA-TI^TM circuit diagram for a fourth-order low-pass filter using the OPA342^[1] amplifier. Texas Instrument’s Analog Filter Designer software determines the resistors, capacitors, and op amp for this circuit. The TINA-TI program creates the rms output-noise and total-output-noise plots. Figures 3 – 4 show these plots for the circuit in Figure 2. The creation of these plots is possible because the OPA342 macromodel accurately models the input current and voltage noise. You can load the file for this reference design here^[2a].

Figure 3 shows the TINA-TI simulated output noise of the circuit in Figure 2. Notice that the x-axis label is frequency and the y-axis label is V /ÖHz.

Figure 3. TINA-TI simulated output noise from Figure 2. Note the peak in noise around the corner frequency of 1 kHz. This peak is an artifact of the filter’s Q and the complex harmonics occurring around the corner frequency. ^[2a]

In Figure 3, the noise throughout the filter’s passband frequency band is about 330 nV/ÖHz. This includes the noise from all of the resistors and both amplifiers. In this graph, you can see a noise peak around the center frequency of 1 kHz.

Figure 4 shows the circuit’s cumulative output noise found in Figure 2. By cumulative I mean that this simulation combines up to a given x-axis frequency. In other words, all of the combined noise below 100 Hz is equal to approximately 3.49 uV rms, and all of the noise below 1 kHz is equal to approximately 13 uV rms.

Figure 4. TINA-TI simulated total-output cumulative noise shown in Figure 2. ^[2a]

The plot in Figure 4 levels off at around 1 MHz. You might notice that the bandwidth of the OPA342 is 1 MHz. With a 16-bit converter (full-scale range = 2.5V) this rms noise is equivalent to one LSB.

This is an interesting way to look at noise. The Operational Amplifier Noise book by Art Kay ^[3] is an excellent how-to-do-it guide, which takes you through the process of noise analysis for your circuit. Also, please download the TINA-TI file ^[4] and play with this circuit yourself. Note that this free software is required to open the attachments. You can also look at the behavior of the MFB fourth-order filter ^[2b]here.

References

1. Download a datasheet for the OPA342

2. TINA-TI files:

a)    Single-supply, Sallen-Key, fourth-order low-pass filter (SS_SK_4P_low-pass.TSC)

b)    Single-supply, MFB, fourth-order low-pass filter (SS_MFB_4P_low-pass.TSC)

3. Operational Amplifier Noise: Techniques and Tips for Analyzing and Reducing Noise, Kay, Art, Newnes, ISBN: 978-0-7506-8525-2

4. WEBENCH Filter Designer

5. “Successful application of Active Filters,” Kuehl, Caldwell, Texas Instruments Tech Day Presentation