Experiment Report



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Experiment Report:

Characterizing Resonant Series RLC circuits using LabView


Submitted by:

Yulia Preezant (ID 322071986)

Submission date:

December 29, 2002

Table of contents:



Introduction 3

Theoretical background 3

Resonant RLC circuit 3

Program architecture and VIs hierarchy 6

SubVIs 7

Prediction SubVI 7

Single Measurement SubVI 8

Analysis SubVI 9

Main VI 11

Experimental data 13

Conclusions 15



Introduction

LabView is a power and flexible instrumentation and analysis software system. It is graphical programming language G that uses icons instead of lines of text to create applications (programs called virtual instruments)1. LabView is integrated for communication with hardware such as GRIB. In this project we had to analyze the properties of RLC circuit using LabView software of National Instruments for data Acquisition via the GRIB Bus from Hewlett Packard instruments.

As it was introductory project, the main purposes were:


  • Familiarization with basic components complex programming environment of LabView

  • To develop instruments for data acquisition, signal analysis, and instrument control

  • To measure resonant series RLC circuits using LabView software

Theoretical background

LabView programs are called virtual instruments (VIs). VIs contains three main components: the front panel, the block diagram, and icon of connector pane. The user interacts with program through the front panel and we build the front panel with controls and indicators, which are the interactive input and output terminals of VI2. Graphical source code called a block diagram. The connector pane defines the inputs and outputs you can wire to the VI so you can use it as a SubVI.


Resonant RLC circuit3

We have a series RLC circuit composed of an inductor L, a capacitor C, and a small resistor R. The Inductor has its own resistance RL from the coil winding.



A series RLC circuit exhibit a peak of the current when the driving frequency is equal to the resonance frequency of circuit.

The magnitude of the total impedance of the RLC circuit:

At very low frequencies, the capacitor acts like an open circuit; thus the total impedance Z goes to infinity and there is no current flowing through the circuit and hence no voltage across the series resistor, Rs. In the opposite limit of very high frequencies, the inductor acts like an open circuit. Again there is no current in the circuit, and hence no voltage across the series resistor, Rs. At the resonance frequency, the reactance of the capacitor Xc cancels the reactance of the inductor XL leaving only the small resistance of Rs and the resistance of the coil windings, RL. Now a large current flows through the circuit of magnitude and a large maximum voltage Umax now appears across the series resistor Rs, namely . And the resonance frequency f0 is found by setting XC = XL, yielding .

When we had measured the peak voltage Umax at the resonance frequency f0. We can also measure the two frequencies where the voltage across our series resistor Rs is only 70.7 % of Umax. One frequency will be somewhat lower than the resonance frequency, which we will denote as fLow. The second frequency will be somewhat higher than the resonance frequency, which we will denote as fHi.

The “Q” of the RLC circuit is defined as.

Formulas for programming:







,

Program architecture and VIs hierarchy

The art of successful programming in G is an exercise in modular programming. After dividing a given task into a series of simpler subtasks, you then construct a virtual instrument to accomplish each subtask. Modularity means that we can execute each SubVI independently, thus making debugging and verification easier4. Furthermore, our SubVIs we can use in other programs.

We dived our task on 3 parts:


  • Prediction (for scouring frequency only in required range)

  • Measurement

  • Analysis

Each of parts we divided according to comfortable and clear programming.

SubVIs




Prediction SubVI



This SubVI executes 2 independent procedures:

Input Cluster

We united all required input data (resistance, inductance, capacity and etc.) to the cluster for simplifying internal structure of block diagram

Output Cluster

We united all output data

Frequency

Given frequency in the given range

Voltage

Corresponding voltage

Front panel




We have to note that we set up voltage on HP arbitrary waveform generator in regime Vpp (Peak-to-Peak). But the data that we need we acquire from HP multimeter in Vrms (Root Mean Square) regime. For matching data we have to divide theoretical voltage by .

Block diagram




Single Measurement SubVI



This SubVI is a main measurement unit. It consists of 2 SubVIs:

  • Write_SubVI. It prepares an instrument (HP arbitrary waveform generator) to establish required signal

  • Read_SubVI. It accommodates another instrument (HP multimeter) to data accepting.

A final output of SubVI – voltage in numeric and string formats.

Signal Frequency

Required characteristics of signal

Signal Amplitude

Timeout Value

Delays between measurements

In Error

Input Error report

Measured Voltage Numeric

Voltage in different formats

Measured Voltage String

Out error Message String

Output Error report

Out Error

Front panel



Block diagram




Block diagrams of internal SubVI












We have to note that it was useful to insert timeout delay between measurements. The instruments have definite time for accepting and realizing a command. This time interval limits celerity but it necessary for normal execution5.


Analysis SubVI



In this SubVI we used a Sequence with 2 steps for serial operations of searching maximal value of voltage in file that formatted into 2 columns and searching frequencies corresponding to the 70,7% of maximal voltage (that found in the first operation).
Front panel


Block diagram


Searching for maximal voltage in the data file


Searching 2 frequencies with voltage equal to 70.7% of maximal value
Maybe this SubVI can be made easier if we have Mathlab Programming Environment on computer using Mathlab Script.

Main VI



This VI concatenates all of SubVIs and exhibits complete task. At start point of program SubVI creates a new/replace old file for data that will be measured, and during process of measurement SubVI writes data in string format into the file. FOR_loop that has N steps performs the process of multimeasurement. We can alter N in accordance with required precision. Data from theoretical prediction and from measurements are performed in 2 formats:

  • Graph

  • 2 clusters of values, which summarize theoretical and measured characteristics

Front panel




Block diagram

Experimental data

1. We measured directly some input parameters of RLC circuit (resistance of resistor Rs, resistance of inductor RL) using HP34401A Multimeter, which has accuracy6:






Accuracy

+Temperature variation to each 1°C

Resistance

0.003%

0.003%

Voltage (AC: 1750V) 10Hz20kHz

20Hz50kHz

50Hz100kHz

0.04%


0.1%

0.55%

0.02%

0.04%


0.08%

2. Values of C and L were written on plastic basis of RLC circuit. Seeing them as an ideal without deviation from denoted values.

3. Additional resistance includes output resistance of HP 33120A Function arbitrary waveform generator (50 Ohm) and does not include resistance of wires. HP 33120A Function arbitrary waveform generator creates voltage waveform signal with accuracy of the amplitude - 1%7.

We studied 2 RLC circuits.

Experiment 1:




Experiment 2:


Form the experimental data we can see that:

  • Measured peak of voltage (resonant peak) is shifted from theoretical peak site. It can be explained by inexact values of L and C (that we used without verification)

  • Measured resonant peak of voltage lower that theoretical

  • Theoretical Q and experimental Q differ. It can be explained by additional resistance that we did not take to consideration.

  • For precise results estimation we have to know all sources of error. Seeing on graph we can say only that curves look tenable.



Conclusions

We developed first virtual instrument

We can manage and control measurements in RLC circuits by our own driver

We can immediately compare theoretical and measured data

We can use our SubVIs in another different projects

We notified some nice properties of LabView:



  • Intuitively clear block diagram provides easy scheme understanding

  • Excellent debugging modes (“step by step”, “probe”)

  • Colors

  • Compatibility with MathLab

  • Great collection of examples

Also we descried some not good properties of LabView:




1 Robert Bishop, Learning with LabView 6i, 2001

2 Introductory course booklet (tutorials) from National Instruments

3 http://www.tau.ac.il/~electro/doc_files/micro/Resonant_LCR%20using_Function_Generator.doc

4 Robert Bishop, Learning with LabView 6i, 2001

5 About this property of program execution we was informed by instructor Oren Zarcin

6 HP34401A Multimeter User’s guide

7 HP33120A Function/arbitrary Waveform Generator User’s Guide



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