Video Laboratory: Web report and ADC, DAC simulation

Länge: 01:06:27

0:0:0 Save Webpage.zip file 0:1:10 Extract files 0:2:20 Start LTSPICE 0:3:15 Downloaded LTSPICE files 0:4:20 0 0:4:20 Directories 0:5:18 Copy group directory and change name 0:5:52 0 0:5:52 Open our .html report file 0:7:31 Open with Notepad++ 0:8:41 Webpage in Browser 0:9:28 HTML content 0:14:31 HTML slide Overview 0:16:56 Installation of webpage template 0:24:4 Start with LTSPICE 0:25:45 LTSPICE files 0:26:51 Copying of LTSPICE files, New slide 0:28:31 Insert image 0:30:3 LTSPICE simulation started 0:31:41 Add voltage source with pulse and ramp 0:32:31 Ramp voltage 0:34:20 Automatic Webpage update 0:35:26 Update report 0:35:36 Simulation starts 0:37:56 Output voltage for each code? 0:38:42 Cursor measurement 0:39:6 .measure statements 0:43:21 Measurement file saved and executed 0:44:21 Execute measurement file 0:45:12 Output voltage results 0:46:50 Copy bitmap of output, irfanview, save 0:47:56 HTML <img> tag 0:49:22 Comment into report 0:53:14 Enable local file load for Firefox 0:55:21 about:config privacy_file_unique_origin 0:57:50 Real DAC example 1:0:26 Simulation started with levels 1:2:6 Setting up level measurements 1:4:44 Measurement results 1:6:36 Look at INL and DNL calculation 1:9:36 Zip your folder.

Video 4. Lecture: Spectral test

Länge: 01:06:27

0:0:0 0 0:1:33 Signal to noise ratio 0:2:5 Quantization error 0:3:40 ADC Dynamic Range SNR = N · 6.02 dB 0:6:18 ADC Dynamic Range SNR = N · 6.02 dB´+ 1.76 dB 0:8:30 ENOB = (SNR -1.76 dB)/6.02 dB 0:9:15 Signal to quantization noise numbers 0:14:32 Aliasing 0:15:42 Filtering prevents aliasing 0:18:18 Nyquist zones 0:18:42 Data converter classification: Nyquist, oversampling, undersampling 0:22:33 ADC Error simulation with FFT 0:25:22 Frequency noise table 0:27:52 Signal to noise ratio example 0:30:32 u(t) = 0.5 + 0.5 sin(ω t) 0:31:42 SQNR 0:35:36 Distributing noise over NFFT/2 bins: 10 log(NFFT/2) 0:39:2 Noise level estimation not possible only calculation 0:40:42 Signal to distortion 0:42:17 fsignal equal fsampling/2 0:45:42 Non integer number of periods 17.6 causes bleeding 0:47:15 Windowing split signal to adjacent bins 0:50:2 Kaiser and Nutall, simulation guides measurement 0:52:10 Power of 2 number of periods causes pattern in spectrum 0:53:42 Prime number of periods 0:56:47 Noise and signal, amplitude and level 0:59:2 INL, DNL non linearity error and FFT harmonic 1:2:47 Single distortion 1:9:2 FFT Challenges 1:10:14 Why Web application and not Matlab, Excel, C program 1:11:47 FFT Application spectrum

Quantization error can be modeled adding an extra signal ε_q to the original signal.

Root mean square value for quantization error is calculated with the integral over one period T, when the quantization error goes from \( +\frac{T}{2} \) to \( -\frac{T}{2} \):
\( \overline{\epsilon_{q}^2} = \frac{1}{T} \int_{- \frac{T}{2}}^{+\frac{T}{2}} ( k \cdot t )^2 dt \)
with \( k = - \frac{LSB}{T} \) giving \( T = - \frac{LSB}{k} \):
\( \overline{\epsilon_{q}^2} = - \frac{k}{LSB} \int_{+ \frac{LSB }{2 \cdot k}}^{- \frac{LSB}{2 \cdot k}} ( k \cdot t )^2 dt = - \frac{k^3}{LSB} \left( - \frac{LSB^{3}}{8 \cdot 3 \cdot k^3} - \frac{LSB^{3}}{8 \cdot 3 \cdot k^3} \right) = \frac{LSB^2}{12}\)
\( \epsilon_{q} = \frac{LSB}{\sqrt{12}} \)

\( SQNR = 20 \cdot log \frac{\frac{1}{\sqrt{2}} \frac{LSB \cdot 2^{N}}{2}}{\frac{LSB}{\sqrt{12}}} dB = 20 \cdot log \frac{\sqrt{12}\cdot 2^{N}}{2 \cdot \sqrt{2}} dB \)
\( SQNR = 20 \cdot log \left( 2^{N} \sqrt{\frac{3}{2}} \right) dB = N \cdot 20 \cdot log (2) dB + 20 \cdot log \left( \sqrt{\frac{3}{2}} \right) dB \)

\( SQNR = 6.02 \cdot N dB + 1.76 dB \)

Having a sampling frequency f_S gives a frequency spectrum from 0 to f_S/2.
Only this range of interested is highlighted in the figures.
The number of sampled points N_FFT gives the minimum frequency and the frequency resolution:
f_min = f_step = f_S * 2 / N_FFT
The figure shows a linear scaling of the frequency x-axis.
Most of the time a logarithmic frequency scaling is used.

Experiments using 8 bits resolution:
16 times the number of ADC levels are used as number of samples for FFT.
2⁸ · 16 = 4096 samples for FFT.

Aliasing

- Number of periods 4096+17 = 4113

Bleeding

- Non integer number of periods shows bleeding.

Windowing

- Windowing reduces bleeding. The signal peak is distributed over some bins and the magnitude a little reduced.

Noise pattern

- Non prime integer number of periods shows noise pattern.

DNL, INL and spectral analysis

Errors: Sine amplitude 0.01 is 1 %. It is expected to loose more than 1 bit.
INL is -2.5 and could be centered.
FFT without windowing shows a signal level at f_signal of -9 dB and a harmonic at 2 f_signal with -48 dB.
This gives an ENOB of (-9 dB - (-48 dB) - 1.76 dB) / 6.02 dB = 6 bits.

White noise

A noise of 0.01 shows no clear steps in the transfer characteristic any more.
As expected the random INL will vary with every simulation run. Maximum absolute INL is around 3.
FFT without windowing shows a signal level at f_signal of -9 dB and a total noise level of -34 dB.
This gives an ENOB of (-9 dB - (-34 dB) - 1.76 dB) / 6.02 dB = 4 bits.

Single distortion in INL, DNL

What happens with the error, if there is one bad conversion.
8 bits and 17 periods simulation.
Distortion start 0.49, distortion length 0.0036 and distortion amplitude of 0.004.
INL and DNL is 0.9 LSB. Noise floor is 58.13 dB compared to 58.23 dB.
Distortion start 0.49, distortion length 0.0078 and distortion amplitude of 0.01.
From INL and DNL the value of -2 LSB is critical. Noise floor is 56.88 dB compared to 58.23 dB.
Very precise INL, DNL and FFT measurements are needed to catch missing codes.

Amplitude modulation

Windowing is like amplitude modulation spreading the power:
ω is ω + δ and ω - δ