Butterworth order and curves

[Speckie]

Based on the following FFT of the inputs all shorted (In+, In-, and ground) of the AMP01 amplifier. what Butterworth order is it? I used low pass cutoff of 10,000 Hertz (the "1" in the FFT) just to understand the concept of the Butterworth attenuation at both sides (see right side of the following)

Then I changed the gain from 1000 above to 2000, 5000, 10000, 20000, 50000. Why is that as the gain increases, it gets more curve?

2000 gain, 10kHz low pass cutoff

5000 gain, 10kHz low pass cutoff

10000 gain, 10kHz low pass cutoff

20000 gain, 10kHz low pass cutoff

50000 gain, 10kHz low pass cutoff

Why is that at 50000 gain, the shape is curved and unlike the first one at 1000 gain?

 

[LTig]

What you see is the noise of the amplifier at different gains. Only at a gain of 50000 you can see the low pass character of the gain, and it would be a flat falling curve if you use a logarithmic y axis. At lower gains the noise of later stages within the amplifier dominate.

To measure the low pass characteristic you have to feed a signal into the amplifier, either a broadband (white) noise or a frequency sweep. Its amplitude should be sufficiently high so that the amplifier noise does not dominate any more.

 

[Speckie]

What you see is the noise of the amplifier at different gains. Only at a gain of 50000 you can see the low pass character of the gain, and it would be a flat falling curve if you use a logarithmic y axis. At lower gains the noise of later stages within the amplifier dominate.

To measure the low pass characteristic you have to feed a signal into the amplifier, either a broadband (white) noise or a frequency sweep. Its amplitude should be sufficiently high so that the amplifier noise does not dominate any more.

If at lower gains the noise of later stages within the amplifier dominate. Why did you say only at a gain of 50000 you can see the low pass character of the gain? I mean what kind of noise in the later stages at lower gain? And to understand the context, what kind of noise in the later stages at higher gain?

 

[Speckie]

I've been thinking of what you said. You mean the FFT at the initial 1000 gain with half of the amplitude attenuated is not due to the Butterworth filter attenuating all those amplitudes before the cutoff?

If yes (see also my last message). Why is the low frequency amplitude so high in all of them? How do you get the real FFT amplitude of the low frequency if they are 5 times higher than the amplitudes at say 10000Hz?

 

[MaxwellsEq]

I'm struggling to understand what you are trying to do.

By shorting the inputs, you have no signal, is that right? So you are analysing only noise, is that your intention?

 

[Speckie]

Im trying to understand why the noise has those particular FFT amplitudes. I was thinking if there are real signals. It can follow those shapes (amplitudes) too? I thought the Butterworth filter can attenuate them same pattern for noises and signal.

 

[MaxwellsEq]

Im trying to understand why the noise has those particular FFT amplitudes. I was thinking if there are real signals. It can follow those shapes (amplitudes) too? I thought the Butterworth filter can attenuate them same pattern for noises and signal.

Noise is not like a sine wave or music signal and has different characteristics.

Consider a resistor, unless it's at -273 degrees C, it generates broadband noise. The bigger the resistance or temperature, the greater the noise. The noise bandwidth extends up GigaHz and TeraHz ranges (limited by quantum effects.The noise comes from the random oscillations of electrons. So at any zeptosecond time slice, the value of "noise" energy will vary over a large range. It's only when we sample over a period of milliseconds or seconds that we can really assign a value to it. This is completely unlike music or some waves.

This natural noise generation tends towards a 1/f curved.

Because you have terminated the inputs, you are not injecting (e.g) white noise at a significant level such as -20dB which you can measure. Instead you are measuring the sum of all the noises generated by every component including every component in a filter.

 

[Speckie]

Noise is not like a sine wave or music signal and has different characteristics.

Consider a resistor, unless it's at -273 degrees C, it generates broadband noise. The bigger the resistance or temperature, the greater the noise. The noise bandwidth extends up GigaHz and TeraHz ranges (limited by quantum effects.The noise comes from the random oscillations of electrons. So at any zeptosecond time slice, the value of "noise" energy will vary over a large range. It's only when we sample over a period of milliseconds or seconds that we can really assign a value to it. This is completely unlike music or some waves.

This natural noise generation tends towards a 1/f curved.

Because you have terminated the inputs, you are not injecting (e.g) white noise at a significant level such as -20dB which you can measure. Instead you are measuring the sum of all the noises generated by every component including every component in a filter.

But for the AMP01, the 1/f curved is up to 10Hz only:

But in the FFT, why does the 1/f curve even extend to 0.5 or 5000Hz? (noting the scale at bottom is 10^4) Or maybe the huge low frequency noise (all input shorted) is not really 1/f? what then cause it?

 

[NTK]

The noise amplitude spectrum for the first plot (gain 1000) seemed to drop approximately linearly with frequency. So, it can't be 1/f. Can you explain more in detail how you took these measurements and how you get these very high level amplifications (gain 1000 to 50 000)? A schematic of the signal chain would help.

 

[Speckie]

The noise amplitude spectrum for the first plot (gain 1000) seemed to drop approximately linearly with frequency. So, it can't be 1/f. Can you explain more in detail how you took these measurements and how you get these very high level amplifications (gain 1000 to 50 000)? A schematic of the signal chain would help.

View attachment 476183

I used the following bioamplifier. It has a dial for the gains examined: (so what caused the low frequency noise to be high at all gains up to 2500Hz to 5000Hz (0.5 (noting 10^4) in the FFT) and beyond?) Since it is not 1/f noise which is up to 10Hz only.

 

[MaxwellsEq]

Not an audio amplifier

 

[AnalogSteph]

Not exactly, but I would say if you can get a DC to 50 kHz response out of it, that should be quite good enough.

OP, do you yourself a favor and plot loglog (dB over log10(f)).

 

[Speckie]

MaxwellsEQ. Why did you say "Not an audio amplifier"? I just want to know why there are huge noises at low frequency, what cause it if it is not 1/f?

AnalogSteph and others. The BMA-200 is connected to the E1DA Cosmos ADC (grade a) and connected to Audacity (note: the iso module box on top doesn't have PCB inside but just empty box to accept touchproof connectors)

The following is the Matlab code to read the Audacity wave file and plot it FFT. How do you add "plot loglog (dB over log10(f)).". I just copied the code it the internet somewhere (at wiki examples) and don't know what you mean by plot loglog (dB over log10(f)). Btw. What FFT app can I use to plot the FFT real time direct from the E1DA Cosmos ADC (not Audacity since Audacity can't plot FFT like the Matlab output I shared).


[signal1,Fs] = audioread('audiofile.wav');
T = 1/Fs; % Sampling period
signal2 = signal1,1);
W = double(signal2);
signal3=W(500:end);
X = highpass(signal3,70,Fs);
L = size(X, 1); % Length of signal
t = (0:L-1)*T; % Time vector


X = X - mean(X);

plot(t,X);
title('signal');
xlabel('t (seconds)');
ylabel('X(t)');

Y = fft(X);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);

f = Fs/L*(0L/2));
plot(f,P1,'LineWidth',0.05);
title('FFT');
xlabel('f (Hz)');
ylabel('Amplitude');

 

[LTig]

Audacity can plot as well.

 

[Speckie]

Audacity can plot as well.

Audacity real time is only Spectogram

This is the FFT plot in Audacity. It is not real time. I need real time where the FFT can be seen while the amplifier is collecting data. What app can do this?
(The following is for the 50000 gain 10000 Hz bandwidth, I used passband of 100Hz to 10,000Hz to avoid the 60Hz electricity signals) Why is there large peak at lower frequency?? Can one share any Audacity wave test file to see what audio FFT looks like?

 

[NTK]

I don't think too many members here are familiar with bioamplifiers, and I am certainly not one. According to the Wikipedia page, the bandwidth requirement for the typical applications (ECG, EMG, EEG) is in the few hundred Hz.

One possibility I can think of is the drop in maximum gain with frequency (which is typical of amplifiers, especially high gain ones). I found an example gain vs frequency plot here. You can see that the max available gain drops with frequency starting at < ~100 Hz. The max gain at low frequencies (in the case) is ~90 dB = 31 623×, and drops to ~40 dB = 100× at ~10 kHz. May be the lower gains at higher frequencies amplify less of the noise at higher frequencies, and resulted in the high frequency noise not being magnified as much relative to the low frequency noise as gain increases.

If you want to try a "music like" test signal, you can find the AES75 "music noise" in this link.

 

[Speckie]

You mean for pure audio amplifiers. there is no higher noise at low frequency? Do you have examples of noise floor for audio system from 0 to 20000Hz?

 

[NTK]

Here is the regular 1 kHz measurement of a non-switching type amp (that uses the TI LM3886 chip). Ignoring the AC supply noise spikes and the harmonics from the 1 kHz test signal, the noise spectrum is flat.

 

[Speckie]

What equipment do you use to frequency sweep all frequencies in audio?

 

[danadam]

How do you add "plot loglog (dB over log10(f)).".

AFAIK, use "loglog()" function instead of "plot()".

Btw. What FFT app can I use to plot the FFT real time direct from the E1DA Cosmos ADC

RTA tool in REW.
Or Multitone probably too.