# 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.