Other Parts Discussed in Post: TINA-TI

My birthday is this month; every year I remind my friends how much engineers HATE surprises. Whether it’s a surprise in our social lives or a surprise in a project, anything unexpected is unwelcome. In analog circuits, a very unwelcome surprise is the noise produced by active filter circuits. After all, active filters are supposed to remove noise!

All active circuits produce some amount of noise and filters are no different. We can uncover the source of this noise by looking at their noise gain. Noise gain is a term used to describe the amount of amplification that a circuit applies to its intrinsic noise source(s). In a typical op amp circuit, the noise gain is measured from the non-inverting input.

Figure 1 shows the TINA-TITM  simulation circuit I used to measure the noise gain of two 2nd-order, Butterworth, 1kHz low pass filters. One circuit uses the Sallen-Key (SK) topology and the other uses a multiple feedback (MFB) topology. To measure the noise gain of an active filter, the signal input is grounded and a signal source is inserted in series with the op amp non-inverting input.

Figure 1: Circuit configuration for measuring the noise gain of Sallen-Key (top) and multiple feedback (bottom) active filters.

Performing an AC transfer characteristic analysis on the two circuits reveals their noise gain:

Figure 2: The noise gain of 1kHz, Butterworth lowpass filters.  An MFB filter is shown in Blue and the SK filter is shown in red.

Although these two circuits have identical filter characteristics (signal gain and attenuation, Q, corner frequency), their noise gain is quite different! Notice that the MFB filter has a noise gain of 6dB in the pass band because the op amp is in an inverting configuration.

Also notice the increase in the noise gain which occurs near the filter’s corner frequency. The magnitude of this noise gain “hump” is proportional to the quality factor, or Q, of the filter. To illustrate that point, we can compare several SK filters with the same signal gain and corner frequency, but different Q values.

Figure 3: Noise gain comparison of SK low pass filters of differing Q values

Higher Q filters have substantially greater noise gain near their corner frequency and this affects the total integrated noise. I used TINA-TI to simulate the total integrated noise of 3 SK low pass filters in a 10kHz bandwidth, all built with the OPA172. The corner frequency of the filters was identical (1kHz) but their Q values were different. The results are summarized in Table 1.

Table 1: Total integrated noise in a 10kHz bandwidth of SK filters with different Q values.

Engineers often select higher Q filters for their greater attenuation, without considering the increase in noise from the filter itself!

Here is a list of my basic rules for low noise filter design. I tried to implement all these design practices in my most recent TI Precision Design: An Analog, Active Crossover Network for Two-Way Loudspeakers.

Basic Rules for Low Noise Filter Design

• Use the Sallen-Key topology if possible.
• Avoid high Q filters if a low Q filter can do the job.
• Use the lowest resistor values possible as long as you:

1.     Use high quality capacitor types (film or NP0/C0G ceramics). Other types of capacitors may produce distortion, as I show here and here.

2.     Avoid excessively loading the op amp or other circuits.

• Pay attention to the source impedance presented to the op amp. A FET input op amp may provide lower noise when the filter resistor values are large.
• Place low pass filters at the end of the signal path to attenuate the noise of preceding circuits.

Following these rules can help avoid some of the unwanted surprises we engineers have to cope with on a daily basis!

• Hi John

I have a question  regarding noise bandwidth in noise calculation. The noise in table 1 is calculated with a bandwidth of 10kHz, but I noticed that noise gain beyond 10kHz is 0dB (as shown in Fig2) which means that noise beyond 10kHz is not zero. Therefore, I wonder why you don't consider noise beyond 10kHz in noise calculation. I think that noise is influential if GBW of the opamp is high. I don't know what is wrong.

Look forward to your reply. Thanks a lot.

• Ahmet, noise gain is different than signal gain because it is always measured from the non-inverting input of the amplifier as I show in Figure 1. In these two circuits, the noise gain is measured from the point where I have inserted the voltage sources (VG1 in both circuits) however the signal gain would be measured from the filter input (where R2 and R4 are grounded).

• A quick comment on Stephen P's post below. If the values of the two resistors aren't the same, you can put them in either order and you'll get the same filter frequency response for sure.  But the noise properties will be different - easily shown in simulation.  There's a great paper by Peter Billam on optimizing for this - if you can't track it down, mail me at filterwizard@cypress.com and I'll try to dig out my own copy. Noise - and offset - in filters is a fascinating topic, I've covered some facets of it in my Filter Wizard columns.

• Thank you for given information. Higher Q cause higher noise output.  If transfer function is the same effect to  both signal and noise, Is S/N ratio   change for higher Q? or is noise gain diffirent from signal gain?  Regards.

• Stephen,

You bring up really great points about the location of the passive components within the Sallen-Key filter circuit. I will have to do some investigating on how they affect the filter output with a step input (maybe a future blog post?).

b) My two articles listed in the Basic Rules section (rule 3, item 1) examine the effects of capacitor voltage coefficient on signal distortion, but not dielectric absorption. In his book The Design of Active Crossovers, Douglas Self confirms your recommendation for using a high quality capacitor to ground with a comparison of polyester and polypropylene capacitors. However, when I repeated this investigation using ceramic capacitors, the results with mixed dielectric types (C0G and X7R) were still unacceptable, so I avoid recommending that customers try it unless their signal levels are extremely low or they have no other option.

Thanks for reading my blog post and providing some high quality input! I hope you'll come back to the Precision Designs Hub in the future!