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measuring small AC noise from cables.....


Hi im studying a circuit&coding which is detecting and measuring very small ac signals using an external 12bit ADC (AD7324) and a dspic microcontroller.

The Measured signal:-

it has a dc offset set to 2.5vdc and a very small variable ac signal rides on the dc offset if is it disturbed, this ac signal need to be measured, and compared with a threshold. if higher than threshold then turn on a led,if lower turn off the led. thats all.

The ac signal is "variable frequency/amplitude" but very small (maybe in milivolts only e.g 220mv) and depends on how the sensor is disturbed.

The circuit:-
the signal feed through op-amp (unity gain), then filters(lowpass & high pass), then another Op amp (unity gain) and then to the external ADC, analog input is set as single ended. in which the analog input range is set to -5 to 5v and using internal Vref set at 2.5v, the conversion is 12 bit. The adc datasheet says that :- 1 LSB = FSR/4096,

The coding:-

reading=reading & 0x1FFF; //mask off channel number;
voltage=(float)reading * ADC_LSB; //convert reading count to voltage (ADC_LSB = 5v/4096)
voltage = voltage-HALF_ADC_FSR; // HALF_ADC_FSR is 5
return voltage;

Ok basically the the circuit and coding will detect a very small variable ac signal as explained but what i dont understand here is:-

The vref is set to = 2.5v, but the software calculates the voltage measurements by multiplying "ADC read value with 5/4096" and then the results is subtract again with 5. whats purpose of this?? how to explain the theory behind this?? what i can know is the step size will be 0.00061v

so from what i understand is , if vref is set to 2.5 volt, the maximum voltage the ADC it can convert is 2.5+- few volts, i just dont get how this formula is used to measure the small ac signal present in the dc offset.....any idea??

i just gv the simple explanation.......hopefully enough to triggers some pointers.... ....anyway after getting the voltage reading it will compared with a adjustable threshold value which calculated using another formula.

an example of a calculated threshold value is = 0.049989, so finally just the coding just check the measured ac signal is higher or lower than the threshold.

So The main question is i dont understand theory behind formula to measure the small the ac voltage reading. the circuit works and can detect any small ac noise presents within the filters range.
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