Amplification RPICT7V1 Version 4

UNDER CONSTRUCTION...

Gain formulae

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

Rg = 100000/(G -1)

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

or deducing the gain from the resistor will be using

G = 100000/Rg + 1

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

Vct = Irms*√2/Nt * Rb

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

G = Vadc*Nt/(Irms*2√2*Rb)

Example

Let 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 from the above formulae

G = Vadc*Nt/(Irms*2√2*Rb)
G = 2.896309375

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 choose.

Rg = 51000 Ω

This will produce a Gain of