The DSP task using the sigma-delta analog-to-digital converter model as an example

This example implements the Sigma-Delta analog-to-digital converter (Sigma-Delta ADC) model, which uses the delta-sigma modulation method to achieve high accuracy and resolution in measuring analog signals. It is widely used in various applications requiring high measurement accuracy, such as audio, measuring sensors, etc. (model sigma_delta_adc.engee):

Next, in this example, the work of Sigma-Delta ADC in Simulink and Engee is analyzed, and the results of the work of the two development environments are compared.

First, you need to connect the libraries:

Pkg.add(["Statistics", "CSV"])

   Resolving package versions...
  No Changes to `~/.project/Project.toml`
  No Changes to `~/.project/Manifest.toml`

# Подключение библиотек
using Plots
using CSV
using DataFrames
using Statistics
plotlyjs();

Launching a model implemented in the Engee development environment.

modelName = "sigma_delta_adc"
SDC_model = modelName in [m.name for m in engee.get_all_models()] ? engee.open( modelName ) : engee.load( "$(@__DIR__)/$(modelName).engee");

results = engee.run( modelName )

SimulationResult(
    "analog" => WorkspaceArray{Float64}("sigma_delta_adc/analog")
,
    "SD_ADC" => WorkspaceArray{Float64}("sigma_delta_adc/SD_ADC")
,
    "diff" => WorkspaceArray{Float64}("sigma_delta_adc/diff")

)

Visualization of model outputs

SD_ADC_res_t = results["SD_ADC"].time;
SD_ADC_res_d = results["SD_ADC"].value;
p_adc_da_sl = plot(SD_ADC_res_t, SD_ADC_res_d, legend = false) # Построение графика
plot!(title = "Результаты моделирования в Engee", ylabel = "Цифровой сигнал", xlabel="Время, c") # Подпись осей и заголовка графика

Simulation results in Simulink:

using MATLAB # Подключение ядра MATLAB
mat"cd /user/start/examples/dsp/sigma_delta_adc"
mat"""
    out = sim('sigma_delta_adc');
    sig = getElement(out.yout,1);
    $DA_times = sig.Values.Time;
    $DA_values = sig.Values.Data;
    """; # Запуск Simulink

p_adc_da_sl = plot(DA_times, DA_values, legend = false) 
plot!(title = "Результаты моделирования в Simulink", ylabel = "Цифровой сигнал", xlabel="Время, c")

The models use a variable-pitch solver. It is necessary to "synchronize" the signals. First, let's put the graphs on top of each other.:

plot(SD_ADC_res_t ,SD_ADC_res_d, label = "Engee")
plot!(title = "Сравнение результатов моделирования")
plot!(DA_times, DA_values, label = "Simulink")
#plot!(label = ["Engee" "Simulink"])
plot!(legend = :outertopright,ylabel = "Цифровой сигнал", xlabel="Время, c")

We find the intersection of two vectors with the simulation time:

# 1. Проверяем, что длины массивов согласованы
if length(SD_ADC_res_t) != length(SD_ADC_res_d)
    error("Размеры SD_ADC_res_t и SD_ADC_res_d не совпадают!")
end

# 2. Обрезаем DA_times/DA_values до длины SD_ADC_res_t (если нужно)
new_length = min(length(DA_times), length(SD_ADC_res_t))
DA_times = DA_times[1:new_length]
DA_values = DA_values[1:new_length];

# 3. Находим пересечение временных меток
common_times = intersect(DA_times, SD_ADC_res_t)

if isempty(common_times)
    error("Нет совпадающих временных меток между DA_times и SD_ADC_res_t!")
end

Then, you need to get the values in common points.

# 4. Находим индексы совпадающих элементов (используем целочисленные индексы)
SD_ADC_d = collect(SD_ADC_res_d).value
SD_ADC_t = collect(SD_ADC_res_t).time

da_idx = findall(t -> t in common_times, DA_times)
sd_idx = findall(t -> t in common_times, SD_ADC_t)

# 5. Убедимся, что индексы соответствуют друг другу по времени
if !all(DA_times[da_idx] .== SD_ADC_t[sd_idx])
    error("Несоответствие временных меток после индексации!")
end

# 6. Извлекаем данные
sd_comp_t = DA_times[da_idx]
sd_comp_sl = DA_values[da_idx]
sd_comp_en = SD_ADC_d[sd_idx]

# 7. Проверяем результат
@assert length(sd_comp_t) == length(sd_comp_sl) == length(sd_comp_en) "Размеры выходных массивов не совпадают!"
println("Успешно обработано $(length(sd_comp_t)) совпадающих точек")

Успешно обработано 45 совпадающих точек

Now we can correctly compare the results of Simulink and Engee.:

adc_abs_tol = sd_comp_sl - sd_comp_en;
mean_adc_tol = abs(mean(adc_abs_tol));
adc_rel_tol = (sd_comp_sl - sd_comp_en)./sd_comp_sl;
mean_adc_tol_rel = abs(mean(filter(!isnan,adc_rel_tol)));
println("Средняя абсолютная погрешность вычислений:", mean_adc_tol);
println("Средняя относительная погрешность вычислений, %:", abs(mean_adc_tol_rel*100));

Средняя абсолютная погрешность вычислений:7.2617452174918e-18
Средняя относительная погрешность вычислений, %:9.655960186035709e-15

engee.close( modelName, force=true);

Conclusion

To summarize, this example implements a sigma-delta analog-to-digital converter model. Based on this example, we can draw several conclusions:

Engee is not inferior in accuracy to Simulink
Engee allows you to use the MOS, and thanks to the large library of blocks, we have the opportunity to implement a large functionality of blocks.
And also, if the functionality of Engee is insufficient, we can use the functionality of MATLAB inside Engee

The DSP task using the sigma-delta analog-to-digital converter model as an example

Conclusion

Blocks used in example¶