Amplification RPICT7V1 Version 4: Difference between revisions
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=Gain formulae= | =Gain formulae= | ||
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Given a desired Gain the Gain resistor Rg can be calculated as follow. | Given a desired Gain the Gain resistor Rg can be calculated as follow. | ||
[[File:Rg_Calc_01.png]] | |||
'''G''' is the Amplification Gain.<br> | '''G''' is the Amplification Gain.<br> | ||
'''Rg''' is the resistor value in | '''Rg''' is the resistor value in Ω. | ||
or deducing the gain from the resistor will be using | or deducing the gain from the resistor will be using | ||
[[File:Rg_Calc_02.png]] | |||
=ADC Full Scale= | =ADC Full Scale= | ||
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Combining ohm's law and the relations of transformation in the CT sensor we can calculate Vct as such | Combining ohm's law and the relations of transformation in the CT sensor we can calculate Vct as such | ||
[[file:math_03.png]] | |||
'''Irms''' - Max rms current required at full scale.<br> | '''Irms''' - Max rms current required at full scale.<br> | ||
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'''Rb''' - Burden Resistor.<br> | '''Rb''' - Burden Resistor.<br> | ||
Combining all formulae together we get the following relation for the Gain. | |||
[[file:math_04.png]] | |||
=Calibration Coefficient= | |||
The calibration coefficient ICAL is calculated as below | |||
[[file:math_05.png]] | |||
=Example= | =Example= | ||
Let calculate the required Gain resistor for the SCT-013-000. | Let's calculate the required Gain resistor for the SCT-013-000. | ||
This CT has 2000 turns. | This CT has 2000 turns. | ||
Nt = 2000 | Nt = 2000 | ||
We will use a 10Ω resistor | We will use a 10Ω burden resistor. Within spec of the CT datasheet. | ||
Rb = 10 | Rb = 10 Ω | ||
We want to measure 100A at full scale. | We want to measure 100A at full scale. | ||
Irms = 100 | Irms = 100 A | ||
and we know that | and we know that | ||
Vadc = 4.096 | Vadc = 4.096 V | ||
Hence we deduce from | Hence we deduce the gain from | ||
G = Vadc*Nt/(Irms*2√2*Rb) | G = Vadc*Nt / (Irms*2√2*Rb) | ||
G = 2. | G = 2.8963093 | ||
This correspond to a resistor of | This correspond to a resistor of | ||
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Rg = 52734.0112 Ω | 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. | Precisely such resistor does not exist. So we will pick a common standard resistor value close to the one calculated here.<br> | ||
We will prefer higher resistor than the one calculated to make sure the 100A are clearly inside the scale.<br> | |||
We will choose. | We will choose. | ||
Rg = | 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 | |||
Latest revision as of 16:21, 18 April 2019
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