This document discusses the dynamic characteristics of instruments. It describes how instruments can be classified as self-generating or power-operated, and contacting or non-contacting. It then examines the dynamic response of zero order, first order, and second order instruments. For each order of instrument, an example is provided to illustrate the dynamic response. The document provides mathematical models to understand the fundamental concepts of dynamic response for measuring instruments.

1. PHY 504(B): Instrumentation-II
Dr. Mrs. Pritee M. Raotole
KBC, North Maharashtra University, Jalgaon
MGSM’s ASC, College, Chopda
Department of Physics

2. Classification of instruments
–Self-generating and
–power-operated types,
–Contacting and
–Non-contacting types.
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda

3. Self-generating Type instruments
In this Type of instrument the energy requirement of instrument
get entirely from input signal.
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda

4. Power Operated type Instrument
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda

5. Contacting and Non contacting type
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda

6. Contacting and Non contacting type
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda

7. Dynamic Characteristics of Instruments:
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda
Dynamic response of
• zero order,
• First order, &
• Second order instrument.

8. Dynamic Characteristics of Instruments:
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda
• When the measured quantity changes rapidly, it is important to consider
the dynamic response of measuring instruments.
• This handout addresses the response of instruments under such
operating conditions.
• In general, the response of measurement instruments under dynamic
conditions can be complex.
• The fundamental concepts of dynamic response, however, can be
understood by studying relatively simple mathematical models.
• We will consider three mathematical models for dynamic system
response: zeroth, first and second order systems.

9. Dynamic Characteristics of Instruments:
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda

10. Dynamic Characteristics of Instruments:

11. Zero order Instrument
• A potentiometer, which measures motion, is a good example of such an instrument, where the
output voltage changes instantaneously as the slider is displaced along the potentiometer track.

12. First order Dynamic Response
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda
• Divide this equation by a0 on both sides
𝒂 𝟏
𝒂 𝟎
𝒅𝒚 𝒕
𝒅𝒕
+
𝒂 𝟎
𝒂 𝟎
𝐲(𝐭)=
𝒃 𝟎
𝒂 𝟎
𝐱(𝐭)
𝝉
𝒅𝒚 𝒕
𝒅𝒕
+ 𝐲(𝐭)= 𝑲𝐱(𝐭)
𝒚(𝝉𝑫 + 𝟏) = 𝑲𝐱 𝑫 =
𝒅
𝒅𝒕
𝑲
(𝝉𝑫 + 𝟏)
=
𝒚
𝒙

13. First order Dynamic Response
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda
• Type equation here.+
1
𝑍
=
1
𝑅
+ DC
𝑒2
𝑒1
=
1
1 +
𝑅𝑖
𝑍
𝑒2
𝑒1
=
1
1 +
𝑅𝑖
𝑅
+ 𝑅𝑖𝐶𝐷
But
𝑅𝑖
𝑅
is neglected as compared to 1 and RiC= 𝜏
This is 1st order equation
𝑒2
𝑒1
=
1
1 + 𝜏𝐷

14. 𝑎2
𝑎0
𝐷2 +
𝑎1
𝑎0
𝐷 +
𝑎0
𝑎0
𝑦 𝑡 =
𝑏0
𝑎0
x(t)

15. Second order Dynamic Response U-tube Manometer
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda

16. Second order Dynamic Response
Dr. Mrs. Pritee M. Raotole, MGSM’s Arts Science and Commerce, College, Chopda
(𝜋𝐷2/4)