Quick and Simple Notch Filter for THD Measurements

One important tool that can help extend the capabilities of a distortion measurement setup is a notch filter. The logic behind it is fairly simple, if we are only interested in the distortion components, why should we even feed the fundamental frequency into the measurement setup? By eliminating it (or simply attenuating it sufficiently), we can reduce the harmonic distortion generated by the test equipment as a result of the large tone, effectively extending its capabilities for harmonic distortion measurement. ย There is obviously more than one way of doing it, and in this post I will only describe one wayย  which was a good match for my needs.

I wanted to create a small box that would implement this function for my needs to allow me to extend further the THD measurement setup I have. In its simplest form, using the EMU 0404USB I’m able to measure THD of ~0.001% at 1KHz. By using an external low distortion 1KHz oscillator I was able to extend this down to ~0.0004%. However, I was looking for a way to get down to 0.0001% to allow measurement of high quality DAC’s. Since I know the external oscillator I use has sufficiently low distortion to support these figures, I needed a way to reduce the distortion caused by the input stage and ADC of the EMU. I have considered trying to hack the EMU and improve its input stage, but I expect the ADC will limit me before I can reach the target performance. Therefore I went with the option of removing the fundamental frequency from the signal before feeding it into the EMU, to reduce the distortion it generates.

The simplest way of cancelling some band (or specific tone) in the incoming signal without any other information about its phase is using a notch filter. A notch filter would ideally have an infinite attenuation at the desired frequency, and no attenuation for the rest of the frequency range. However, practical filters have limited attenuation at the desired frequency, and some residual attenuation for the rest of the frequencies. The narrower the attenuation band is the higher the Q (quality factor) of the filter is. Since these filters are very selective, they are typically tuned to give the deepest notch at the frequency of interest. Therefore, it is typically preferred to have one of these filters for each desired frequency instead of making a single filter that will have to be tuned every time the frequency is changed.

For my application, I didn’t look for a very strong notch, as I wasn’t too far out from my target to begin with. I have therefore decided to go with the simpler option rather than the potentially superior performing option, and went for a passive Hall notch filter. There are other options such as making the active version of this filter, or going for a twin-T notch filter, each with its pros and cons. A very good source of information about the Hall notch filter can be found in this article. As always, I’ve decided to make a small PCB out of this and place it in one of the project boxes I’ve used in the past instead of building it on a protoboard. Its just so cheap to get PCB’s printed nowadays, that its easier and faster than soldering with wires. The schematic used is drawn below.

Fig. 1. Schematic of the Circuit

The notch is doubled in this board so that I can either have a single filter for a SE signal, or a dual filter (relative to GND) for a balanced (or pseudo-differential) signal. It is also possible to use each of the filters individually for a stereo signal, or even cascade them with a proper cable for a deeper notch, if needed.
The input has both a 1/4″ TRS connector, as well as a BNC for SE application. If the BNC is used instead of the TRS connector, the TRS jack will short the negative input to GND to reduce noise at the output of the box for the negative pin of the TRS connector. This allows interfacing to a balanced output even if a SE input is used, without excess noise/coupling.
The 5K trimmer is optional (and its value can be increased if desired) for post assembly tuning. Resistors R4-R7 (R11-R14 on the 2nd channel) are meant to be fixed resistors that set the exact frequency of the notch for the actual component values used for the rest of the board. For my application, taking into consideration the value of the capacitors and resistors I’ve had, the optimal value was ~480ohm for the parallel combination of R4||R5, and 2220Ohm for R6||R7, with no trimmer installed. I’ve preferred to have no trimmer installed as they can drift over time. Instead I’ve measured the resistors and capacitors used for R1-R3 and C1-C3, and punched the numbers into the circuit simulator to find the appropriate value for the “TBD” resistors R4-R7.
Since we are looking for a low distortion instrument, all the capacitors used were C0G MLCC’s. I know some people prefer film caps for these applications, but C0G (NP0) MLCC’s are really good enough, and they are small and cheap. I went for 1206 SMD packages for all the components, as they are large enough to solder easily, and have sufficient voltage and power handling rating for the application.

Fig. 2. Assembled PCB

After assembling the PCB I’ve had to “calibrate” it. As I’ve mentioned earlier, its attenuation outside the notch band won’t be 0dB, and I’ve had to quantify it so that I could normalize the measurement after it and extract the information about the input signal. This was also a good chance for me to make sure I didn’t make any mistake in the calculation, and the notch really is placed at 1KHz as I was aiming for.

First, for a reference I’ve measured the transfer function without it, to make sure there are no significant fluctuations in the frequency response of the EMU. Then I’ve measured the frequency response of the PCB with both SE and differential input.

Fig. 3. Direct Loop-Back Frequency Response at -6dBFS
Fig. 4. SE Mode Measurement (additional 6dB attenuation for SE mode)
Fig. 5. Balanced Mode Measurement

From these figures I’ve been able to verify the notch is at the target frequency, and the transfer function matches well with simulation. I’ve taken note of the attenuation at each harmonic of the 1Khz up to 5KHz for future reference when using this unit. To make sure I don’t forget where I wrote this, I though printing this onto the unit would be a good idea ๐Ÿ™‚

Fig. 5. Attenuation Numbers Across Modes and Frequency
Fig. 6. Front Panel
Fig. 7. Rear Panel

I’ve connected it in between the low distortion (SE only) 1KHz oscillator and the EMU input, to measure the resulting distortion and see if the combination of this shallow notch with the EMU will suffice for <0.0001% THD measurement at 1KHz. After normalizing the signal attenuation based on the frequency response of the filter, the most dominant harmonic was the 2nd, and it was -123.2dB below the fundamental. The following harmonics were somewhat lower, with the 3rd at -125.3dB, and 4th/5th below -140dB. Combining the numbers, the THD of this setup is slightly under 0.0001% and therefore meets the target I was aiming for with this cheap and simple circuit.

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