Tidying up my desk a bit yesterday, I found a circuit on a breadboard I’d left hanging. Months ago I was looking into notch filters for removing mains hum, to clean up a ELF/VLF signal a wee bit. I’d put together a bootstrapped twin-T notch filter, but had got rather frustrated when testing it. I wanted to get a general idea of its response and (assuming it looked ok) tune it to 50Hz.
But I’ve only got a USB port Bitscope oscilloscope (the BS10 mixed-signal model) which does do basic frequency analysis and even has a signal generator built in. Unfortunately there’s no sweep for the sig gen, and the UI is so clunky I wound up making a little generator with an easily-twiddled knob. That still didn’t really give me what I was after in being able to clearly see what was going on.
Anyhow, today I thought I’d take another look. Got everything set up, did some manual sweeping which showed that the component values I’d used were quite a way out (more like 70Hz). But still no clear visualisation of the overall response.
Staring at the desk, pondering what to do next…there’s an Arduino Uno right in front of me. I’ve spent a fair while getting to know the things over the past few weeks. I’d noticed in passing that it had a tone() method, but hadn’t actually played with it. Ok, about 15 minutes later I had this loaded:
void setup (){
}
void loop() {
int i;
for (i = 35; i <= 100; i++) {
tone(11, i);
delay(10);
}
}
A sweep generator!
Ok, its frequency range is limited and it gives a square wave out. So I took the output from pin 11 and fed that to a simple RC filter (15k, 220nF) which took the buzziness down a bit. Stray harmonics aren’t that much of an issue for the current problem, and 35-100 Hz cover the range I’m looking at.
One thing the Bitscope’s waveform generator allows is the fairly accurate setting of frequency. So I set that at 50Hz and put it in one scope input, the output of my notch filter into the other. After a bit of fiddling to get levels reasonably stable, I got this:
The yellow is my 50Hz reference, green the notch filter response. The harmonics on the ref are pretty dire – dunno, I guess it must be clipping. But look at that lovely notch in the green! Around 70 or so Hz, as measured before.
So this setup can help me quickly tune the notch down to where it’s needed. But that isn’t the real triumph here. What I wasn’t sure about is the rest of the response of the active notch. Where the passive notch goes from flat into a 6dB (I think) / octave drop into the notch, this version has noticeable mounds either side. Those are potentially very undesirable. If you look at the 50Hz marker here, my filter as it stands would boost that frequency. While I’m sure I can get the notch in a much better position than this, any drift (maybe due to environmental factors) could be very bad. So at the cost of less sharp notch, I reckon on balance the passive version is probably the one to go for.
PS.
A few hours on, and a bit more progress. I pulled out the active notch circuit, did calculations again and plugged in a passive one. Well, I say passive, am using a TL074 to buffer the signal.
The basic filter circuit is this:
Fc = 1/(2 pi R C)
Using C = 100nF (2C just two of them in parallel) and 33k for each of the two Rs on top, a single 15k for the R/2 I got something looking like a cleanish notch, centred on 47.8Hz. It took a little trial & error. The capacitors are just off-the shelf, ceramic I think, probably 10% tolerance but came from the same batch so should be reasonable well matched. 1% resistors, again off-the shelf, same batch.
I forgot to take a screenshot…
But as I measured previously, the ambient mains hum here also contains a significant amount of 3rd harmonic, ie. 150Hz. So I did the sums again for this.
Ran into a slight snag with my setup though – when sweeping up through a reasonable range for it to go over the 150Hz target, the spectrogram display was all over the place.
But, as an alternative to sweep, you can also test freq response with white noise (or an impulse, but that’s another story). Coincidentally I was playing with a pseudorandom number generator just yesterday (for DOG-1), so knew what to look for. I found one, to which I’ve made minor tweaks –
#define speakerPin 11
unsigned long lastClick;
void setup() {
// put your setup code here, to run once:
pinMode(speakerPin,OUTPUT);
lastClick = micros();
}
/* initialize with any 32 bit non-zero unsigned long value. */
#define LFSR_INIT 0xfeedfaceUL
/* Choose bits 32, 30, 26, 24 from http://arduino.stackexchange.com/a/6725/6628
* or 32, 22, 2, 1 from
* http://www.xilinx.com/support/documentation/application_notes/xapp052.pdf
* or bits 32, 16, 3,2 or 0x80010006UL per http://users.ece.cmu.edu/~koopman/lfsr/index.html
* and http://users.ece.cmu.edu/~koopman/lfsr/32.dat.gz
*/
#define LFSR_MASK ((unsigned long)( 1UL<<31 | 1UL <<15 | 1UL <<2 | 1UL <<1 )) unsigned int generateNoise(){ // See https://en.wikipedia.org/wiki/Linear_feedback_shift_register#Galois_LFSRs static unsigned long int lfsr = LFSR_INIT; /* 32 bit init, nonzero */ /* If the output bit is 1, apply toggle mask. * The value has 1 at bits corresponding * to taps, 0 elsewhere. */ if(lfsr & 1) { lfsr = (lfsr >>1) ^ LFSR_MASK ; return(1);}
else { lfsr >>= 1; return(0);}
}
void loop() {
/* ... */
if ((micros() - lastClick) > 500 ) { // Changing this value changes the frequency.
lastClick = micros();
digitalWrite (speakerPin, generateNoise());
}
}
One tweak to use pin 11 as I’d already got that wired up. The other is rather sweet. The original code had a loop delay of 50 micros, related to the bandwidth. But that again wasn’t very clear on the spectrogram. Was nice white noise, but I’m only interested in the low end here. Making the micros 500, and letting the display accumulate for a minute, produced this:
There’s a nice notch pretty close to 50Hz, plus my new one, near enough at 150Hz (measured at 145Hz). The peak on the left is probably just an artifact of the setup – FFT does that sort of thing. Also the relative shallowness of the second notch I reckon is at least in part to the fact that it uses a linear scale on the spectrogram.
The values I used here were C = 47n, R = 22k, pleasingly standard values (the resistors gived those capacitors calculated at 22.57k, which was handy).
I’ve just got this set up on the breadboard around a TL074 quad op amp, using 3 op amps for unity gain buffers (each with a 1M to ground). Those things have input resistance of 10^12 ohms. So I’m now thinking I might just use one of them as the input stage for an ELV/VLF receiver. The 2N3819 input stage of the BBB-4 receiver I was going to try has a 10M resistor to ground, seems like plenty of leeway for that here. Input buffer, maybe give it variable gain of something like 1-100, to these filters (perhaps adding a little more gain along the way), then use the spare op amp to drive a couple of transistors for a small speaker/headphone level output.
Just trying it with a longish wire at the input, computer speakers at out, still way too much mains-derived noise to hear any natural signals, but the difference between the different stages of the circuit is really noticeable. I’ll have to get it soldered up, battery power, take it up the fields.
And try it when there’s a thunderstorm around 🙂
ELFquake 