How to Calculate and Solve for Transfer Function (Sensitivity) | First Order Instruments | Dynamic Characteristics of Instruments
Last Updated on January 18, 2021
The image above represents transfer function.
To compute for transfer function (sensitivity) | First Order Instruments, three essential parameters are needed and these parameters are Static Sensitivity (k), Time Constant (u) and Differentiation Value (d / dt) (D).
The formula for calculating transfer function:
c = k / 1 + uD
Where:
c = Sensitivity
k = Static Sensitivity
u = Time Constant
D = Differentiation Value
Let’s solve an example;
Find the sensitivity when the static sensitivity is 24, the time constant is 16 and the differentiation value is 10.
This implies that;
k = Static Sensitivity = 24
u = Time Constant = 16
D = Differentiation Value = 10
c = k / 1 + uD
c = 24 / 1 + 16 x 10
c = 24 / 1 + 160
c = 24 / 161
c = 0.149
Therefore, the transfer function (sensitivity) is 0.149.
Calculating for the Static Sensitivity when the Transfer Function (Sensitivity), the Time Constant and the Differentiation Value is Given.
k = c (1 + uD)
Where;
k = Static Sensitivity
c = Sensitivity
u = Time Constant
D = Differentiation Value
Let’s solve an example;
Find the static sensitivity when the transfer function (sensitivity) is 12, the time constant is 8 and the differentiation value is 4.
This implies that;
c = Sensitivity = 12
u = Time Constant = 8
D = Differentiation Value = 4
k = c (1 + uD)
k = 12 (1+ (8)(4))
k = 12 (1 + 32)
k = 12 (33)
k = 396
Therefore, the static sensitivity is 396.
Calculating for the Time Constant when the Transfer Function (Sensitivity), the Static Sensitivity and the Differentiation Value is Given.
u = (k / c – 1) / D
Where;
u = Time Constant
c = Sensitivity
k = Static Sensitivity
D = Differentiation Value
Let’s solve an example;
Find the time constant when the transfer function (sensitivity) is 8, the static sensitivity is 40 and the differentiation value is 2.
This implies that;
c = Sensitivity = 8
k = Static Sensitivity = 40
D = Differentiation Value = 2
u = (k / c – 1) / D
u = (40 / 8 – 1) / 2
u = (5 – 1) / 2
u = 4 / 2
u = 2
Therefore, the time constant is 2.
Calculating for the Differentiation Value when the Transfer Function (Sensitivity), the Static Sensitivity and the Time Constant is Given.
D = (k / c – 1) / u
Where;
D = Differentiation Value
c = Sensitivity
k = Static Sensitivity
u = Time Constant
Let’s solve an example;
Find the differentiation value when the transfer function (sensitivity) is 12, the static sensitivity is 84 and the time constant is 6.
This implies that;
c = Sensitivity = 12
k = Static Sensitivity = 84
u = Time Constant = 6
D = (k / c – 1) / u
D = (84 / 12 – 1) / 6
D = (7 – 1) / 6
D = 6 / 6
D = 1
Therefore, the differentiation value is 1.
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the transfer function (sensitivity) | First Order Instruments.
To get the answer and workings of the transfer function (sensitivity) | First Order Instruments using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
Web – https://www.nickzom.org/calculator-plus
To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.
Now, Click on instrumentation under Materials and Metallurgical
Now, Click on Dynamic Characteristics of Instruments under Instrumentation
Now, Click on Transfer Function (sensitivity) | First Order Instruments under Dynamic Characteristics of Instruments
The screenshot below displays the page or activity to enter your values, to get the answer for the transfer function (sensitivity) | First Order Instruments according to the respective parameters which is the Static Sensitivity (k), Time Constant (u) and Differentiation Value (d / dt) (D).
Now, enter the values appropriately and accordingly for the parameters as required by the Static Sensitivity (k) is 24, Time Constant (u) is 16 and Differentiation Value (d / dt) (D) is 10.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the transfer function (sensitivity) | First Order Instruments and presents the formula, workings and steps too.
