Amplification RPICT7V1 Version 4

Gain formulae

Given a desired Gain the Gain resistor Rg can be calculated as follow.

G is the Amplification Gain.
Rg is the resistor value in Ω.

or deducing the gain from the resistor will be using

ADC Full Scale

The RPICT7V1 Version 4 uses 4.096V voltage reference for the ADC. Signals are centred on 2.048V. Therefore the waveform can have a max amplitude of 2.048V. We will call this Vadc/2.

Vadc = 4.096V

The relation between the peak voltage from the CT at full scale and the Gain is given by

Vct * G = Vadc/2

Vct - Secondary peak voltage of the CT sensor.

Combining ohm's law and the relations of transformation in the CT sensor we can calculate Vct as such

Irms - Max rms current required at full scale.
Nt - Turn Ratio of the CT sensor. Or number of turns.
Rb - Burden Resistor.

Combining all formulae together we get the following relation for the Gain.

Calibration Coefficient

The calibration coefficient ICAL is calculated as below

Example

Let's calculate the required Gain resistor for the SCT-013-000.

This CT has 2000 turns.

Nt = 2000

We will use a 10Ω burden resistor. Within spec of the CT datasheet.

Rb = 10 Ω

We want to measure 100A at full scale.

Irms = 100 A

and we know that

Vadc = 4.096 V

Hence we deduce the gain from

G = Vadc*Nt / (Irms*2√2*Rb)
G = 2.8963093

This correspond to a resistor of

Rg = 100000/(G -1)
Rg = 52734.0112 Ω

Precisely such resistor does not exist. So we will pick a common standard resistor value close to the one calculated here.
We will prefer higher resistor than the one calculated to make sure the 100A are clearly inside the scale.
We will choose.

newRg = 53600 Ω

This will produce an effective Gain of

newG = 100000/Rg + 1
newG = 2.8656716

Therefore the exact effective full scale current that we can read is

newIrms = Vadc*Nt / (G*2√2*Rb)
newIrms = 101.07 A

The calibration coefficient we will enter in the config will be

ICAL = Nt / Rb / newG
ICAL = 69.8